Steel–Concrete–Steel Sandwich Immersed Tunnels For Large Spans August 2016 Thesis Kubilay Bekarlar HASKONINGDHV NEDERLAND B.V. INFRASTRUCTURE George Hintzenweg 85 Postbus 8520 3009 AM Rotterdam +31 10 443 36 66 Telefoon Fax info@rotterdam.royalhaskoning.com www.royalhaskoningdhv.com Amersfoort 56515154 Document title Status Date Project name Reference Author E-mail Internet KvK Steel-Concrete-Steel Sandwich Immersed Tunnels For Large Spans Final Thesis August 2016 Master Thesis Kubilay Bekarlar Kubilay Bekarlar Collegiale toets Datum/paraaf …………………. …………………. …………………. …………………. Vrijgegeven door Datum/paraaf A company of Royal HaskoningDHV Preface This thesis is written to complete the master Hydraulic Engineering – Hydraulic Structures, at the technical university of Delft in the Netherlands. This research has been performed in collaboration with Royal HaskoningDHV. I would like to thank my graduation committee, consisting of Prof. Dr. Ir. S.N. Jonkman, Dr. Ir. K.J. Bakker, Dr. Ir. drs. C.R. Braam, Ir. C.M.P ‘t Hart, for all their assistance during this research project. I also would like to thank Dr. Ir. M.A.N. (Max) Hendriks, Ir. E. van Putten, A. Doorduyn and H. Meinderts for their contribution for this thesis. This research has been performed at the office of Royal HaskoningDHV in Rotterdam. I would like to thank Royal HaskoningDHV for providing me the required facilities and assistance. I have had a good time with my colleagues of the infrastructure department and I am grateful for their warm welcome and their help during my stay. Kubilay Bekarlar Delft, August 2016 Kubilay Bekarlar – Master Thesis ii August – 2016 Abstract The steel-concrete-steel (SCS) sandwich immersed tunnel is a type of tunnel which has been constructed in Japan the last two decades. Recent developments in immersed tunnel engineering show the trend that also other countries started applying SCS sandwich tunnels more often. The SCS sandwich tunnel has several advantages compared with the traditional reinforced concrete immersed tunnel among others, to be applied in shallow waters, able to resist higher loads on the structure. Traditional reinforced concrete tunnels show limits regarding large spans (for roof and floor element) in the cross direction. There was a lack of knowledge whether the SCS sandwich tunnel can be a solution for tunnels with extreme large spans. Also research was needed to understand the structural response of a large span SCS tunnel to the load applied. For the detailed analysis of the distribution of internal forces a finite element program was used. In order to compare a SCS sandwich tunnel for a large span with a reinforced tunnel, two base case tunnels were designed. From this comparison the critical span for each type was determined. It was seen that the reinforced tunnel critical span is 18 / 19 m, whereas the SCS tunnel could be designed for a span of 27 m (boundary condition reference project). In this thesis two 2-D models have been analysed in DIANA: one simplified model and a detailed model. Both models use linear-elastic material behaviour. The results of the hand calculations are first compared with that from the simplified model, to verify the simplified model. The results of both FEM models are compared and the differences are investigated. From the stress / strain analysis of the SCS tunnel cross section for a large span, it was seen that the tensile strength of the concrete was reached. This would result in the formation of tensile cracks. The allowable compressive stresses / strains were only locally exceeded. Concrete cracking and plasticity however may have impact on the degree of connection between the steel and concrete. Due to the cracks the shear stiffness of the steel and concrete connection can decrease. This may have impact on the overall stiffness of the structure. From the durability point of view these cracks have no impact on the durability of the structure since the concrete is situated in a confined space. Although the other side the exceedance of the stress is only locally, it might result in a redistribution of forces. By using a detailed FEM analysis, detailed insight was obtained in the distribution of internal design forces. This resulted in a significant reduction of the amount of steel applied. Namely 21 %. In absolute values, this is a reduction of 2,51 m3 of steel per meter in the axial direction. Since the reinforced concrete tunnel was not able to have a span up to 27 m, it was investigated, whether prestressing (post tensioning) the tunnel could be a solution. From the new design it was concluded that a span of 27 m is not a feasible solution when using prestressing. This is due to the large size of the prestress tendon anchors and the large axial forces which the concrete cross section could not resist. Further there was observed that a steel shell tunnel is a feasible solution for tunnels with large spans up to 28 m. From the costs analysis it was seen that steel shell tunnel variant 1 (regular steel shell) would cost 315 000 euros per meter length. Steel shell tunnel variant 2 (with steel cover plates on the inner side) is slightly more expensive than variant 1. The costs for this tunnel per meter length is 351 000 euros. The same analysis was performed for the SCS tunnel. This variant is with 421 000 euros per meter length, more expensive than the other two steel shell tunnel variants. Kubilay Bekarlar – Master Thesis iii August – 2016 It can be stated that in terms of costs, a reinforced concrete tunnel is the preferred solution for tunnels with a span up to 18 / 19 m. This is also the limiting span for a reinforced concrete tunnel. For a span from 19 till 28 m, the steel shell is a more cost efficient solution than the SCS tunnel. However, applying the SCS for spans shorter than 29 m, has some advantages as well, since the shear force and bending moment capacity of a SCS tunnel are larger than in case of a steel shell tunnel. This advantage can be important for changing boundary conditions or accidental loading on the tunnel structure, e.g. an earthquake loading, explosion, sunken ship on top of the tunnel, extra loading due to sedimentation on top of the tunnel, erosion below the tunnel floor or more ductile behaviour. When the construction area is in a region where the risks for earthquakes are significant, the SCS sandwich is the preferred solution for a span between 19-28 m. This is the case for the reference project Sharq Crossing (Qatar). Finally it can be stated that the SCS sandwich tunnel is the only solution available for spans larger than 28 m. Kubilay Bekarlar – Master Thesis iv August – 2016 Graduation committee members: Chairman: Prof. Dr. Ir. S.N. Jonkman TU Delft - Section Hydraulic Engineering Supervisor TU Delft: Dr. Ir. K.J. Bakker - Bored and immersed tunnels Supervisor TU Delft: Dr. Ir. drs. C.R. Braam - Concrete structures Supervisor Royal Haskoning DHV: Ir. C.M.P ‘t Hart – Senior Engineer Royal Haskoning DHV – TEC Author: K.Z. Bekarlar Student ID: 1239724 Kubilay Bekarlar – Master Thesis v August – 2016 TABLE OF CONTENTS RESEARCH APPROACH PLAN 2 1 INTRODUCTION 1.1 SCS sandwich tunnel 1.2 SCS sandwich tunnel projects 1.3 Earlier Studies 2 2 3 4 2 PROBLEM DESCRIPTION 2.1 Research objectives 2.2 Research questions 4 5 5 BASE CASE 3 BASE CASE 3.1 Purpose of the base case calculation 7 7 4 REINFORCED CONCRETE TUNNEL 4.1 Dimensions reinforced concrete tunnel 4.2 Loading on the reinforced concrete tunnel 4.3 Design moment calculation 4.3.1 Capacity reinforced concrete tunnel 4.3.2 Roof element 4.3.3 Floor element 4.3.4 Determination of the dimensions of the outer walls 4.4 Uplift and immersion calculations 4.5 Drawing of the reinforce concrete base case design 8 8 8 11 12 13 21 24 25 28 5 SCS SANDWICH TUNNEL 5.1 Loading on SCS sandwich tunnel 5.2 Design moment calculation 5.3 Capacity SCS tunnel 5.3.1 Shear capacity SCS tunnel (ULS) 5.3.2 Moment capacity SCS tunnel (ULS) 5.3.3 Design of stud connectors and stiffeners 5.4 Uplift and immersion calculations 5.5 Drawing of the SCS base case design 29 29 31 31 33 35 38 43 46 6 BASE CASE SUMMARY 47 FEA MODEL ANALYSIS 7 FEA MODEL 7.1 7.2 7.3 7.3.1 7.3.2 7.4 Introduction 2-D or 3-D Analysis Material model Material model - concrete linear elastic Material model - steel linear elastic Schematization of the SCS sandwich tunnel element Kubilay Bekarlar – Master Thesis vi 50 50 50 50 50 51 51 August – 2016 7.4.1 7.4.2 7.4.3 Constraints Type of elements Dimensions of the roof, floor and wall 51 52 53 8 LINEAR ELASTIC ANALYSIS SIMPLIFIED MODEL 8.1 Material properties sandwich elements 8.2 Determination of the passion ratio of composite material 8.3 Determination of the bedding constant 8.4 Main Dimensions being modeled 53 53 55 56 56 9 MODELLING SIMPLIFIED MODEL IN IDIANA - LINEAR ELASTIC ANALYSIS 9.1 Geometry definition 9.2 Boundary conditions 9.3 Meshing 9.4 Loads 9.5 Material and physical properties 57 57 57 57 57 58 10 RESULTS OF THE SIMPLIFIED LINEAR ELASTIC ANALYSIS 10.1 Moment distribution and deflection 10.1.1 Lc1 – Load case 1 10.1.2 Lc2 - Load case 2 10.1.3 Lc3 - Load case 3 10.1.4 Lc4 - Load case 4 10.1.5 Lc5 - Load case 5 10.1.6 Lcc - Load case total 10.1.7 Displacement Lcc – Load case total 58 58 58 58 59 59 60 60 61 11 VALIDATION OF THE MODEL 61 11.1 Validation of moment distribution - deflections per load case 61 11.1.1 Load case 1 – self weight of the structure 61 11.1.2 Load case 2 – vertical loading on top of the structure 63 11.1.3 Load case 3 – Vertical hydraulic loading on the bottom of the structure64 11.1.4 Load case 4 – Loading on the left side of the tunnel element 65 11.1.5 Load case 5 – Loading on the right side of the tunnel element 66 12 ANALYSIS RESULTS FROM THE SIMPLIFIED LINEAR ELASTIC ANALYSIS 12.1 Axial force distribution - All load cases (Lcc) 12.2 Shear force distribution - Lcc 12.3 Moment distribution Lcc 12.4 Primary stress distribution Lcc 12.5 Principal stress distribution 12.6 Analysis of moment and shear capacity (fully connected composite) 69 69 70 71 72 73 73 13 LINEAR ELASTIC ANALYSIS DETAILED MODEL 13.1 Schematization of detailed SCS sandwich tunnel model 13.2 Input IDIANA – Detailed linear elastic analysis 13.2.1 Geometry 13.2.2 Boundary constraints 13.2.3 Meshing 13.2.4 Loads 13.2.5 Variable loading 75 75 77 77 78 78 79 79 Kubilay Bekarlar – Master Thesis vii August – 2016 13.2.6 13.3 13.4 14 Accidental loading Material and physical properties Composed elements 80 81 82 LINEAR ELASTIC ANALYSIS OF DETAILED MODEL 82 14.1 Comparison of the simplified and detailed model (fully connected SCS)82 14.1.1 Load case 1 – self weight of the structure 82 14.1.2 Load case 2 – vertical loading on top of the structure 83 14.1.3 Load case 3 – Vertical hydraulic loading on the bottom of the structure84 14.1.4 Load case 4 – Loading on the left side of the tunnel element 85 14.1.5 Load case 5 – Loading on the right side of the tunnel element 86 14.2 Axial, moment, shear force distribution and deflection 87 14.2.1 Axial force distribution – All load cases (Lcc) 87 14.2.2 Moment distribution Lcc 88 14.2.3 Shear force distribution Lcc 90 14.2.4 Deflection as a result of all load cases 91 14.3 Analysis of the stress distribution 92 14.3.1 Analysis of stress in concrete core 92 14.3.2 Analysis of stress in steel 93 14.3.3 Analysis of moment and shear capacity of a detailed fully connected composite element 93 OPTIMIZATION 15 PARTIALLY CONNECTED SCS SANDWICH MODEL 15.1 Determination of the linear and tangential stiffness of the interfaces 15.1.1 Approach 1 - Gelfi and Giuriani (1987) 15.1.2 Approach 2 - D.J. Oehlers, M.A. Bradford (1995) 15.2 Detailed analysis of the stress distribution in concrete core 15.2.1 Stress and strain distribution in the roof 15.2.2 Stress distribution in the floor 15.2.3 Stress distribution in the walls 15.2.4 Stress distribution in steel parts 15.3 Principal vector stress analysis of concrete core 15.4 Conclusions of the stress analysis 95 95 96 98 98 99 101 103 104 104 107 16 ULTIMATE MOMENT CAPACITY INTERACTION AXIAL FORCE – MOMENT 16.1 Interaction axial force and bending moment 16.1.1 Roof element – Outside part (inclination) 16.1.2 Roof element – Mid span 16.1.3 Floor element – Outside part (inclination) 16.1.4 Floor element – Mid span 16.1.5 Wall element - Outside part (inclination) 16.1.6 Wall element – Mid span 107 107 107 109 110 110 111 112 17 OPTIMIZATION OF THE DESIGN USING DETAILED LINEAR STRUCTURAL ANALYSIS 17.1 Optimization due to detailed analysis of the internal forces 112 112 Kubilay Bekarlar – Master Thesis viii August – 2016 DESIGN AND COST COMPARISON OF TUNNEL VARIANTS 18 TRANSVERSE PRESTRESSED (POST TENSIONED) REINFORCED CONCRETE TUNNEL 118 18.1 Roof element 118 18.2 Floor element 123 19 STEEL SHELL TUNNEL 19.1 Variant 1 19.1.1 Floor element 19.1.2 Roof element 19.1.3 Amount of materials applied variant 1 19.2 Variant 2 19.2.1 Roof element 19.2.2 Floor element 19.2.3 Amount of materials applied variant 2 19.3 Critical span steel shell tunnel 127 127 127 132 135 138 138 140 142 144 20 SCS SANDWICH 145 21 COMPARE THE COSTS OF VARIANTS 21.1 Comparing the material quantities 21.2 Comparing the costs 146 146 147 CONCLUSION AND RECOMMENDATIONS 22 CONCLUSION AND RECOMMENDATIONS 22.1 Conclusions 22.2 Recommendations 151 151 155 APPENDIX 23 LITERATURE 157 24 APPENDIX A 158 25 APPENDIX B 164 26 APPENDIX C 168 27 APPENDIX D 174 28 APPENDIX E 175 29 APPENDIX F 188 30 APPENDIX G 197 Kubilay Bekarlar – Master Thesis ix August – 2016 NOMENCLATURE Symbol Description Unit γ Specific weight of material [kN/m ] Φ soil Angle of internal friction [Degrees] K0 Coefficient of lateral earth pressure [-] fy Steel characteristic yield strength [N/mm ] γs Material factor steel [-] fy,d Steel design yield strength [N/mm ] fc,d Concrete design strength [N/mm ] γc Material factor concrete [-] fc,d Concrete design strength [N/mm ] fc,t,k 0,05 Concrete characteristic tensile strength [N/mm ] fc,t,d Concrete characteristicdesign strength [N/mm ] Esteel Elastic modulus of steel [N/mm ] Econcrete Elastic modulus of concrete [N/mm ] Ic Mass moment of inertia [m ] Wc Second moment area [m ] Sz First moment inertia [m ] Ac Surface of concrete [m ] Ø Diameter reinforcement bar [mm] d Distance reinforcement bar from a reference point [mm] σ Stress [N/mm ] ε Strain [-] ρ Reinforcement ratio [-] θ Angle between struts and the beam axis [Degrees] α Angle between the shear reinforcement and the beam axis [Degrees] t Thickness steel plate [mm] ts,c Thickness compressive steel plate [mm] ts,t Thickness tensile steel plate [mm] tweb Thickness of diaphragm [mm] τrd,c Design shear strength concrete [N/mm ] k Bedding constant [kN/m ] xu Height of the compression zone in concrete [mm] hc Height of the concrete part of an element [mm] q Distributed load [kN/m] f Drape of the prestress tendon [mm] R Radius of the prestress tendon [m] Kubilay Bekarlar – Master Thesis 3 2 2 2 2 2 2 2 2 4 3 3 2 2 2 3 x August – 2016 Pm0 Initial prestressing load [kN] fp,k Characteristic tensile strength of prestress cable [N/mm ] Ep Elastic modulus of the prestress tendon [N/mm ] σpm0 Initial tensile stress in prestress steel [N/mm ] Ap Surface of the prestress tendon [mm ] Sr,max maximum crack spacing [mm] εsm mean strain in the reinforcement [-] εcm mean strain in concrete between cracks [-] ρeff effective reinforcement ratio [-] kt factor dependent on the duration of the load [-] Kubilay Bekarlar – Master Thesis 2 2 2 2 xi August – 2016 RESEARCH APPROACH PLAN 1 INTRODUCTION An immersed tunnel is one of the options to cross a waterway. At the moment there are about 180 immersed tunnels built worldwide ever since 1893. Compared with other types of tunnels built this is a rather low number. This also means that this technique is still in its infancy. Initially it may seem that immersed tunnelling is a narrow field. But the opposite is the case, since there are a number of disciplines required for an immersed tunnel project such as: structural engineering, hydraulic engineering, geotechnical engineering etc. The countries where the immersed tunnels are constructed more often are the US, the Netherlands and Japan. There is a significant difference between the immersed tunnels constructed in these countries. In the US the immersed tunnels are constructed more often with a single or double steel shell. As for the Netherlands the traditional tunnel is built out of reinforced concrete segments. In Japan reinforced concrete, steel plate or steel concrete steel composite (sandwich) tunnels are constructed more often. Also in Japan, till around 1990 immersed tunnels were constructed as either reinforced concrete with or without a steel plate structure. However more recent tunnels are made out of steel concrete composite structures. Steel concrete steel (SCS) composite tunnels can be divided into full sandwich structures and open sandwich structures. Full sandwich structures are structures in which concrete is sandwiched between two steel plates. The open sandwich tunnel however is a composite structure where the one surface is covered with a steel plate and where the reinforced concrete side is exposed to the atmosphere. On locations where two tunnel parts have to fuse to one tunnel, large spans are inevitable. However this is not easy to realize since there are some restrictions to it. From earlier preliminary studies there was seen that there possibly are some limitations regarding the span for reinforced concrete tunnel. With this research there is aimed to know what the restrictions are for different types of immersed tunnels and which tunnel variant is the best solution for an immersed tunnel with a large span. 1.1 SCS sandwich tunnel Recent developments in the immersed tunnel engineering show a trend that also European countries apply SCS sandwich tunnels more often. This has several advantages regarding the traditional reinforced concrete immersed tunnel, as being able to immerse a tunnel in shallow waters, able to have larger span width in the tunnel cross section as well as being able to resist higher loads on the structure and several more. The SCS sandwich tunnel consists of a concrete layer which is sandwiched between two steel shells. Both the inner as well as the outer shells are load carrying and both act compositely with the inner concrete layer (detailed description in Appendix B). The concrete inner core is made out of low shrinkage self-compacting concrete and is unreinforced. For detailed information about selfcompacting concrete see Appendix C. Stiffness is added to the steel plates by welding L-shaped ribs on its inner sides. These L-shaped ribs also create bond between the steel plates and the concrete inner core. The stiffeners are sometimes combined with steel studs that are also welded on the steel plates. Studs are steel pins with a flat head creating extra bond between the concrete and steel. They also transfer shear forces. Once the concrete is cured it accounts for the compression forces and also gives stiffness to the steel shells. The steel shell carries the tensile Kubilay Bekarlar – Master Thesis 2 August – 2016 forces acting on the tunnel segment. In figure 1 below there is a concept of a SCS sandwich element given. Figure 1: Concept of a SCS sandwich element 1.2 SCS sandwich tunnel projects The Osaka Port Sakishima Tunnel is an application of the sandwich tunnel structure. This tunnel was finished in December 1977. It is an open sandwich tunnel structure where the floor and walls were constructed as an open sandwich structure and the roof slab as a reinforced concrete structure. The Osaka Yumeshima Tunnel is a rail-road tunnel finished in 2009. This tunnel is a partly full sandwich and partly open sandwich structure. As for the roof and walls, these are made as full sandwich structures. However the floor slab is an open sandwich structure . In Okinawa Naha a full sandwich tunnel structure was applied for all members including the floor slabs. This structure was opened for use in 2010, see figure 2. Figure 2: Longitudinal profile and cross section of the Okinawa Naha Immersed Tunnel Tunnel Engineering Consultants (TEC) is designing 5 tunnels for the Sharq Crossing in Doha Qatar, whereof three are made by cut-cover technique and two by immersed tunnel technique. One of the two immersed tunnels will be executed as a sandwich tunnel structure. This will be the first sandwich tunnel structure in this part of the world, see figure 3. From the hydrodynamic point of view, it will not be the biggest challenge which was encountered for the execution of the immersed tunnel, since the Persian / Arabian Gulf is a relative calm sea. But one can think that casting good quality concrete under high temperatures will be a challenge, due to cracking that might occur. Figure 3: SCS sandwich immersed tunnel, Doha - Qatar Kubilay Bekarlar – Master Thesis 3 August – 2016 1.3 Earlier Studies Report: Centrum Ondergronds Bouwen, 2000: “Stalen en composiet staalbeton tunnelconstructies – Staalbeton sandwichelementen, Deel 2: Modelvorming en rekenregels” in English: “Steel and composite steel concrete tunnel structures – Steel concrete sandwich elements”. This report of COB focusses on the numerical and analytical modelling of sandwich elements. It also compares the results gathered by both methods. Paper: N. Foundoukos, J.C. Chapman, 2007: “Finite element analysis of steel concrete steel sandwich beams”. This study focused on the static behaviour of SCS sandwich beams where the beam was simulated by using a FEM program. The results from the model were compared with test results, which showed good agreement. Report: European Commission Technical Steel Research, 1997: “Double skin composite construction for submerged tube tunnels”. In this report there are two main focusses, one is the focus on the test results carried out at the University of Wales Cardiff. The other focus is on the design rules to give dimensions to the elements under a certain loading. These studies and more are described in more detail in the literature study part. 2 PROBLEM DESCRIPTION As stated before the steel concrete steel (SCS) sandwich tunnel is designed and constructed the last few decades, predominantly in Japan. These SCS tunnels have an ideal configuration of tensile and compressive elements compared with a reinforced concrete tunnel for example because the outer steel plates account for tensile stress and the inner concrete core for compressive stress. This results in the structure being designed as a more slender structure. For tunnels with a short span in the cross section, both the SCS and the reinforced concrete tunnel are applicable. The most suitable solution for that particular situation will be chosen, taking into consideration the financial and executional characteristics. However no thoroughgoing research has been performed for SCS and reinforced concrete tunnels for a large span in the cross section. First of all it is unknown what the maximum span is for a SCS tunnel element. The same holds for the conventional reinforced concrete tunnel. In other words, first the maximum span for both types of tunnel need to be investigated and the cause of the limitations will be understood. Because of the lack of knowledge on this topic, it’s impossible to say which type of tunnel is the most feasible solution for a tunnel with a large span. For the feasibility the financial and executional aspects should be studied. As stated before, the SCS sandwich tunnel is a tunnel which can be designed as a slender structure. This will reduce the amount of materials applied, hereby also the costs. On the other hand high loads on a slender structure may lead to local high stress / strain concentration points, which might exceed the design stress / strain. It is not known how high the stresses will be for a SCS tunnel element with a large span. There should be investigated whether the design stresses / strains are exceeded or not. Also in case there is local exceedance of design stresses / strains, then there should be examined what the consequence might be for the durability of the structure. Since there is a complicated steel, concrete and stud interaction, hereby stress concentration points cannot be determined by hand calculations. A finite element method (FEM) program should be Kubilay Bekarlar – Master Thesis 4 August – 2016 used. With the insight gathered from the FEM model, some conclusions can be drawn how the structure will respond to loading on a SCS tunnel with a large span. 2.1 Research objectives One of the objectives of this research is to learn what the maximum span in the cross section is for a SCS and a reinforced concrete tunnel. While determining the maximum span for both types of tunnel there will be understood what the causes are for the limit in the span. Another aim of this research is to know how high the maximum stresses will be for a SCS tunnel element for large spans. There should be investigated whether the design stresses / strains are exceeded or not. From the scale of the stress / strain exceedance, some conclusions will be drawn about the response of the structure to the stress / strain exceedance. Due to the complexity of the structure a FEM program will be used and this will also give detailed insight on the location of the potential stress / strain exceedance. Because of the lack of knowledge on this topic, it’s impossible to say which type of tunnel is the most ideal solution for a tunnel with a large span. With all previous research objectives achieved, there is enough knowledge to conclude which type of tunnel is the most ideal solution for a tunnel with a large span in the cross direction. 2.2 Research questions Main research question: Is a SCS sandwich immersed tunnel the most ideal solution for tunnels with large span in the cross direction? Sub questions: How to design a Steel – Concrete - Steel sandwich immersed tunnel? What is the critical span of a Reinforced concrete tunnel and a SCS immersed tunnel? How to schematize and model SCS sandwich elements in a FEM program? How are internal forces (stresses) distributed over a SCS sandwich tunnel element for a large span? How to optimize a design of a SCS sandwich immersed tunnel with a detailed FEM analysis? Is a prestressed reinforced concrete tunnel and a steel shell tunnel a feasible solution for tunnels with a large span in the cross direction? How does a SCS immersed tunnel relate to other types of tunnels for large spans in terms of materials and cost? Kubilay Bekarlar – Master Thesis 5 August – 2016 Base case calculation of reinforced concrete tunnel and SCS sandwich tunnel Kubilay Bekarlar – Master Thesis 6 August – 2016 3 BASE CASE 3.1 Purpose of the base case calculation TEC (Tunnel Engineering Consultants) prepared the validated concept design of two immersed tunnels and three cut and cover tunnels for the Sharq crossing in Doha – Qatar (for more see Appendix D). The northern immersed tunnel is 2,8 km long and the southern is 3,1 km long. These two immersed tunnels connect the north side of the Sharq bay with the middle and south side and vice versa. Whereas the cut and cover tunnels connect the land with the bridges in the bay by crossing under the shoreline, see figure 4. Figure 4: Overview Sharq bay with the Sharq crossing drawn as a line The northern immersed tunnel connection and the middle bay connection come together and both continue in the southern immersed tunnel, see intersection of the line in figure 5. Both the northern and the middle connection are 2x2 lane road connections with safety lanes on both sides. Consequently at the connection of both roads a 2x4 lane with safety lanes on each side is necessary. This is also the position where the southern immersed tunnel will start. The 2x4 plus safety lane connection is gradually reduced to a 2x3 and safety lanes tunnel connection. This will continue all the way to the southern side of the bay. Special attention needs to be paid to the immersed tunnel part with a 2x4 lane formation and the transition of this part to a 2x3 formation. For a 2x4 lane with safety lanes on both sides a tunnel the span of each cross sectional tube is about 27 meters. With a gallery width of 3,25 m the total width of the immersed tunnel would be around 60 meters. The 2x2 lane and 2x3 lane immersed tunnel will be constructed as conventional reinforced concrete tunnel. Applying the conventional reinforced concrete immersed tunnel for this 2x4 lane cross section is a challenge, if not impossible. Figure 5: Top view transition zone In short, the aim of the base case study is to investigate whether or not the transition zone of a 2x4 lane to a 2x3 lane immersed tunnel can be executed as a reinforced concrete tunnel part and what are its limits regarding the cross sectional span. Another aim of the base case design is that there will be checked whether or not a SCS sandwich tunnel element can realize a 2x4 lane with Kubilay Bekarlar – Master Thesis 7 August – 2016 safety lanes on both sides. Consequently by making these calculations, insight will be generated in the design rules and parameters to design a reinforced concrete / SCS sandwich tunnel. The designed base case for the SCS sandwich tunnel element will be analysed in more detail during this research project. 4 REINFORCED CONCRETE TUNNEL 4.1 Dimensions reinforced concrete tunnel First the dimensions of the tunnel elements will be determined. This can be done either by rules of thumb or from experience. Later on these dimensions will be checked on moment, shear and normal force resistance and if needed the dimensions can be adjusted. The dimensions are listed in table 1 and figure 6 below. Table 1: Dimensions Dimensions Width of gallery 3250 [mm] Thickness floor 1900 [mm] Thickness roof 1600 [mm] Thickness outer wall 1500 [mm] Thickness inner wall 1300 [mm] Inner height tunnel 7900 [mm] Figure 6: Tunnel cross section Now the total height can be calculated, see table 2, which is the sum of the inner height, thickness of floor and roof. Table 2: Total height Total height tunnel 4.2 11400 [mm] 11,4 [m] Loading on the reinforced concrete tunnel To determine the loading on the tunnel first the material properties, dimensions of the elements, thickness of the materials applied as well as the depth below the water surface need to be specified. These are listed in table table 3 below, in the first column the specific weight of the materials applied are listed, in the second column the dimensions of the tunnel and in the last column the water and ground levels. Kubilay Bekarlar – Master Thesis 8 August – 2016 Table 3: Material properties, dimensions and levels Material properties Dimensions 3 γsediment [kN/m ] 17,5 [m] Reference levels Protection layer 1,0 Design HWL 3,0 20 Roof thickness 1,6 Ground level -8,46 γrock [kN/m ] 22 Asphalt thickness 0,12 Road level -17,64 3 10,35 Ballast concrete 1,1 Bottom level -20,66 3 γbackfill [kN/m ] 3 γwater [kN/m ] φ soil [deg] 30 Floor thickness 1,9 K0 0,5 Inner height 7,9 First the hydraulic loading on the tunnel element will be determined. For this the hydraulic stresses over the height of the tunnel cross section will be determined. Hereafter the total vertical stress will be determined. Subtracting the hydraulic stress from the total vertical stress will give the effective vertical stress. With the angle of internal friction of 30⁰ the coefficient of lateral earth pressure at ( ) rest becomes . This way the effective horizontal stress can be calculated, by multiplying the effective vertical stress with the coefficient of lateral earth pressure. Now the total horizontal stress on the tunnel can be determined by adding the hydraulic stress with the effective horizontal stress. These calculations can be seen in table 4 below. Table 4: Hydraulic stress distribution over a tunnel Levels [m] 3 σhydraulic [kN/m ] 3 3 3 σsoil [kN/m ] σeff [kN/m ] σkh [kN/m ] 3 σh [kN/m ] Water level 3 0,00 0,00 0,00 0,00 0,00 Ground level -8,46 118,61 118,61 0,00 0,00 118,61 Top side roof -9,46 128,96 140,61 11,65 5,82 134,79 Bottom side roof -11,06 145,52 172,61 27,09 13,55 159,07 Top side floor -18,96 227,29 330,61 103,33 51,66 278,95 Bottom side floor -20,86 246,95 368,61 121,66 60,83 307,78 The next step is determining the other loads on the structure. These are compacting -weight, earth load (back fill), rock protection, ballast concrete and traffic load. For these load types the following load factors are applied, table 5. Table 5: Load types and load factors Load types SLS ULS ULS - favorable Self-Weight Permanent 1,00 1,25 0,95 Hydrostatic load MWL Permanent 1,00 1,15 0,95 Earth Load Permanent 1,00 1,15 0,95 Rock protection Permanent 1,00 2,00 0,95 Ballast concrete Permanent 1,00 1,25 0,95 Traffic load Variable 1,00 1,50 0,00 With these load factors the total loading on the tunnel in SLS and ULS will be determined. However, still the self-weight of the elements need to be determined. For this the concrete and steel area is multiplied with its specific mass. The steel area can be estimated by applying the Kubilay Bekarlar – Master Thesis 9 August – 2016 maximum reinforcement ratio of about 2%. Consequently the total self-weight of the roof and floor slabs is determined as follows, table 6 and table 7. Table 6: Material properties Material properties 3 Density [kN/m ] Water 10,35 Concrete 23,2 Steel 77 Ballast concrete 23,2 Table 7: Surface area of steel / concrete and the self-weight of the roof / floor. Self-weights Self-weight roof Ac-roof As-roof q 83360000 1563200 2 83,36 2 1,5632 [mm ] [mm ] [m2] 39,59 [kN/m] [m2] 2,46 [kN/m] Total 42,05 [kN/m] Self-weight floor 2 92,815 [m2] 44,08 [kN/m] 2 1,8563 [m2] 2,93 [kN/m] Total 47,01 [kN/m] Ac-floor 92815000 [mm ] As-roof 1856300 [mm ] Finally the total loading on the tunnel can be determined. In order to do so the self-weight of the element, hydrostatic load, load due to ballast concrete, rock load and soil load will be summed up. The total loading on the roof, floor and outer wall is displayed in SLS and ULS in table 8 below. Table 8: The q-load on the elements in SLS and ULS Elements Roof SLS [kN/m] ULS [kN/m] Floor SLS [kN/m] ULS [kN/m] Self-Weight 42,05 52,56 Hydrostatic load MWL -246,95 -283,99 Hydrostatic load MWL 128,96 148,30 Self-Weight 47,01 44,66 Rock protection 11,65 23,30 Ballast concrete 11,9505 11,35 Traffic load UDL 10,00 0,00 Total 182,66 224,17 Total -177,9895 -227,98 Walls – Top SLS [kN/m] ULS [kN/m] Wall - Bottom SLS [kN/m] ULS [kN/m] Hydrostatic load MWL 134,79 155,0085 Hydrostatic load MWL 307,78 353,947 Back fill 5,83 6,7045 Back fill 60,31 69,3565 Total 140,62 161,713 Total 368,09 423,3035 Kubilay Bekarlar – Master Thesis 10 August – 2016 4.3 Design moment calculation The occurring moment MEd changes for different spans in the cross section of the tunnel. Initially the MEd was calculated by using a rule of thumb which is: . Later this value is checked by using a framework program Matrixframe. The design moment MEd is determined by hand calculation for different spans of the tunnel structure. These moments will be compared with the moment resistance of the cross sectional elements. At a certain span the design moment or crack width will be bigger than the moment resistance or maximum allowable crack of an element, with the maximum reinforcement ratio already applied. In that case there can be concluded that the limit of a reinforced concrete tunnel is achieved. Besides moment capacity check and crack width control, the same steps will be repeated for the normal stress check, shear capacity check. The check which results in the smallest span is the limiting factor and will determine the limit for the span. The hand calculation of the design forces has been performed. The results are only shown for a span of 27 m see table 9, the results for the other spans can be found in Appendix (28.1). Table 9: Hand calculation of the design forces for different spans Design forces 27 Span Internal Forces - approximation – ULS Internal Forces - approximation – SLS Med - roof 16341,99 kNm Med - roof 13315,91 kNm Med - floor -16619,7 kNm Med - floor -12975,5 kNm V-roof 3026,295 kN V-roof 2465,91 kN V-floor -3077,73 kN V-floor -2402,87 kN N-roof 1294,513 kN N-roof 1125,679 kN N-floor 2040,044 kN N-floor 1773,968 kN Structural calculation software Matrixframe is used to check the hand calculations for the ULS case. The bedding is assumed to be uniform. This analysis is done for spans of 15m, 20m, 25m, and 27m. The result is only shown for 27 m in figure 9 below, where the results for the other spans can be found in Appendix (28.1). Internal forces - Span 27 m Kubilay Bekarlar – Master Thesis 11 August – 2016 Figure 7: Internal forces (ULS) for different spans from Matrixframe. There can be concluded from the results that the hand calculation is in accordance with the results from the software program Matrixframe. The differences that are present between the hand calculation and the model can be explained by the assumptions made for the bedding boundaries. For all other normal, moment and shear force distributions both methods coincide. 4.3.1 Capacity reinforced concrete tunnel Since the dimensions of the elements and the loading on the reinforced concrete tunnel have been determined, now the capacity of the tunnel can be calculated. To do so first the material properties classes are specified. Reinforcing steel B500 and concrete class C35 is applied. The yielding stresses of these materials will be divided by material factors to get the design yield stresses. For concrete this is done for the compressive as well as the tensile stresses. In table 10 on the right side the Young’s modulus for steel and concrete have been given. Table 10: Material characteristics for steel and concrete Material properties 2 Elasticity modulus 2 2] Steel [N/mm ] Concrete [N/mm ] E - steel 200000 [N/mm fy 500 fck 35,0 E - concrete 34000 [N/mm2] γs 1,15 γc 1,5 fyd 434,8 fcd 23,3 fctk, 0,05 2,0 fctd 1,33 The dimensions of the elements and the loadings that will be used for the calculations, as determined earlier, are summarized in table 11 below. Kubilay Bekarlar – Master Thesis 12 August – 2016 Table 11: Dimensions of the elements and summary of the loading Dimensions 4.3.2 Loads ULS SLS Width of gallery 3,25 [m] q roof 224,2 [kN/m] 182,7 [kN/m] Thickness floor 1,9 [m] q floor -227,9 [kN/m] -177,9 [kN/m] Thickness roof 1,6 [m] q side wall - top 161,7 [kN/m] 140,6 [kN/m] Thickness outer wall 1,5 [m] q side wall - bottom 423,3 [kN/m] 368,1 [kN/m] Thickness inner wall 1,3 [m] Inner height tunnel 7,9 [m] Roof element Since the cross sectional dimensions, the loadings, the material properties and safety factors have been determined, now the capacity of the concrete tunnel element can be calculated. First the moment resistance capacity of the roof will be determined. To do so the position of the reinforcement and its area needs to be determined. In table 12 below the cross sectional parameters are summarized and in figure 8 the layout of the reinforcement is drawn. Table 12: Parameters Parameters Ic Wc,top Wc,bottom 0,341 0,427 4 Ø -stirrup 16 [mm] 3 Ø -tensile/compression 28 [mm] 3 [m ] [m ] 0,427 [m ] Ø -tensile/compression 40 [mm] 1 [m] Spacing reinforcement – 1 50 [mm] 1,6 [m] Spacing reinforcement – 2 50 [mm] Ac, eff 1,6 2 [m ] Spacing reinforcement – 3 95 [mm] Cover 91 [mm] Width roof /m Height roof Figure 8: Layout reinforcement (tensile: 8-40ɸ; 8-32 ɸ; 8-32 ɸ Compressive 8-28 ɸ; 8-28 ɸ) 4.3.2.1 Moment capacity – span 22 m (ULS) These calculations are initially made for a span of 22m, this in order to do the unity check for each capacity. Later on several other spans will be checked as well. After the parameters for the cross section of the roof have been chosen, the amount of tensile, compressive reinforcement and the stirrups can be determined. Specifying their position is of importance, because it will result in an internal level arm, which will lead to the design moment resistance of the cross section. First the strains in the roof element need to be calculated. With the cross sectional area and the ULS strain Kubilay Bekarlar – Master Thesis 13 August – 2016 in the concrete there is only one parameter missing to calculate the strain in each element of the cross section. This parameter is the compression zone height Xu. Since the compression zone height can be determined by an iterative calculation a spreadsheet program has been used. From the calculations carried out the compression zone height is 345,5mm. Now the strains can be calculated as shown in Table 13 below. Table 13: Reinforcement area, layout and the strains Distances 1st layer ds 1486 Tensile reinforcement [mm] 1st layer 4926 Compressive reinforcement 2 1st layer 4926 [mm ] 2 2nd layer 4926 [mm ] 804,2 [mm ] Asw 8,47 [mm /mm] [mm ] 2nd layer 1422 [mm] 2nd layer 4926 [mm ] 3th layer 1313 [mm] 3th layer 10053 [mm ] 2 2 2 Stirrups 1st layer d eff 1382,79 [mm] Total 2 2 19905 [mm ] Stirrups Effective depths Strains ε'cu,3 -3,50% ds1 1486 [mm] ε s1 5,26% ρtensile 1,25 % ds2 1422 [mm] ε s2 4,88% ρcompressive 0,62 % ds3 1313 [mm] ε s3 4,24% ds4 91 [mm] ε s4 -2,96% ds5 155 [mm] ε s5 -2,59% 2 After the strains have been determined, now the forces in the reinforcement and the concrete compression zone can be calculated. From the horizontal force equilibrium the sum of the forces should be equal to the axial loading on the element. Then the design moment resistance M,rd of the roof element can be calculated by multiplying the forces with their eccentricities. This moment of resistance will be compared with the occurring moment due to loading MEd. In case the moment resistance of the cross section is larger than the occurring moment due to loading, then the cross section will fulfill the moment capacity check. These steps are summarized in the spreadsheet below for a roof element, table 14. Table 14: Forces and moment resistance Steel, concrete forces N'cd;1 Moment resistance -6046,25 [kN] MN'cd;1 -812,61 [kNm] Ns1 2141,91 [kN] MNs1 3167,89 [kNm] Ns2 2141,91 [kN] MNs2 3000,82 [kNm] Ns3 4371,23 [kN] MNs3 5586,43 [kNm] Ns4 -2141,91 [kN] MNs4 -194,91 [kNm] Ns5 -1761,53 [kN] MNs5 -297,70 [kNm] Nd 1294,51 [kN] MNd 1035,61 [kNm] ΣMRd 11485,53 [kNm] Eccentricity e0 Kubilay Bekarlar – Master Thesis 14 0,05 [m] August – 2016 Med 10918,87 [kNm] U-check 0,95 4.3.2.2 Normal stress capacity – span 22 m check (ULS) The second check that will be made is the compressive stress check in the roof element as the result of the normal force and the moment. This can be calculated as follows: ( ) In which: N is the normal force in the floor element Ac,eff is the effective cross sectional area of the floor M is the design moment W is the sectional modulus Table 15: Normal stresses Normal stresses 2 fcd -23,33 [N/mm ] σc,top -26,24 [N/mm ] 2 U-check 1,124501 2.4.1.3 - Shear force capacity – span 22 m check (ULS) The structure is also checked for the shear capacity. This is first done for the case without shear reinforcement (stirrups). The following formula is applied to calculate the shear resistance for concrete. [ ( ) ] In which: √ d = effective depth in [mm] ρ = reinforcement ratio As = reinforcement area b = width of the cross section in tensile area σcp = stress due to axial loading Ned = axial force in the cross section due to loading (in case of compression) Ac = area of concrete cross section fcd = design concrete compressive stress Kubilay Bekarlar – Master Thesis 15 August – 2016 These calculations are made for all the spans that are investigated. The results for a span of 22 m are listed in table 15 below. As can be seen the cross section is not able to bear the shear force in case no shear reinforcement is applied. This means that shear reinforcement has to be applied and the shear capacity check has to be done again, now for the shear reinforced cross section. The formula that is applied for the calculation of the shear reinforcement is: ( ) In which: Asw = cross sectional area of shear reinforcement S = spacing of stirrups z = 0,9 d = effective depth of the cross section fyd = design yield strength of shear reinforcement θ = angle of inclined strut α = coefficient for the compression chord b = width of the cross section v1 = strength reduction factor for concrete in shear The minimum value of the two calculated shear force resistances will be used to calculate the unity check. ( ) The unity check for the shear capacity of the cross section with 8,47 mm 2/mm of shear reinforcement, shows that for a span of 22m the working shear force can be carried, table 16. Table 16: Shear force resistance Shear resistance Ved 2465,87 [kN] Nd 1294,5128 [kN] Bearing capacity without stirrups Bearing capacity with stirrups Crd,c 0,12 [-] θ 45 ⁰ αcw K 1,38 [-] α 90 ⁰ V1 k1 0,15 [-] cot θ ρ1 0,0146556 [-] 1 Asw 8,47 tan θ 1 2 [mm /mm] 2 σcp 0,81 [N/mm ] Vrd,c 1002,8 [kN] Vrs,d 4501,9 [kN] Ved 2465,9 [kN] Vrd,max 8556,5 [kN] Ved 2465,9 [kN] U-check 1 0,6 2,46 U-check 0,55 There can be seen that the shear force capacity is fulfilled. However the angle of compression Θ can vary from 21,8˚ to 45˚. This would mean that the value of Vrs,d and Vrd,max can change. By Kubilay Bekarlar – Master Thesis 16 August – 2016 reducing the value of Θ the value of Vrd,max will reduce and Vrs,d will increase, doing so a larger unity check will appear. That would mean that the rest shear capacity would increase, which means that there is room for further optimization of the stirrups. Table 17: Applied stirrups Ø 16 mm - 200 mm 2 pcs Asw 2 2,01 [mm /mm] Table 18: Unity check for the optimized stirrup layout Asw, new Θ α 2,01 mm²/mm 25 ° 90 ° Vrs,d 2831 [kN] Vrd,max 6964 [kN] 2465,9 [kN] Ved cot θ 2,14 - U-check 0,87 Now the new unity check is performed for the optimized stirrup layout. The results can be seen in table 18 above. The newly applied stirrup Asw is 2,01 mm2/mm and an angle of compression diagonal of 25˚ results in a new unity check of 0,87. This is indeed more optimal solution shear force reinforcement. 4.3.2.3 Crack width control reinforced concrete tunnel (SLS) The next check will be the crack width control check. This is a serviceability limit state (SLS) check, which means that the moments and normal forces in SLS will be used. In order to calculate the crack width, first the concrete compression zone is determined. For this a spreadsheet model is used, since this is an iterative process. With the moment and force balance ΣM = 0 and Σ N = 0 the unknown strain in concrete εc and the compression zone x in SLS can be determined. Consequently the stress distribution over the height can be determined. This will result in the force distribution over the cross section. From the balance of forces principle the sum of the forces should be zero. With the force in the reinforcing steel the stress in the reinforcing steel will be calculated. These calculations are listed in table 19 below. Table 19: Strain, forces, moments and steel stress Strain, force, stress, moment SLS Nrep 1125,7 [kN] Eccentricities Mrep,sls - 8840,74 Strains ec 619 [mm] ε'c -1,14 ‰ es1 679 [mm] ε s1 1,97 ‰ es2 601 [mm] ε s2 1,80 ‰ es3 478 [mm] ε s3 1,55 ‰ es4 709 [mm] ε s4 -0,95 ‰ Kubilay Bekarlar – Master Thesis 17 x 543,4 e'c3 0,00175 August – 2016 es5 631 [mm] ε s5 Forces -0,79 ‰ Moments N'c -6213,0 kN MN'c 3845,0 [kNm] Ns1 1939,4 kN MNs1 1316,9 [kNm] Ns2 1777,8 kN MNs2 1068,4 [kNm] Ns3 3107,7 kN MNs3 1485,5 [kNm] Ns4 -937,8 kN MNs4 664,9 [kNm] Ns5 -776,1 kN MNs5 489,7 [kNm] Nrep 1125,7 kN Mrep 8840,7 [kNm] σs 393,715 Since the stress in the reinforcing steel has been determined, the crack width that will occur can be calculated. In order to do so the following formula is used: ( ) In which: Sr,max = maximum crack spacing εsm = mean strain in the reinforcement εcm = mean strain in concrete between cracks ( ) σs = stress in the reinforcement fct, eff = concrete tensile stress α = ratio Es / Ecm ρeff = effective reinforcement ratio Es = Elasticity modulus steel kt = factor dependent on the duration of the load As = reinforcement steel area Ac,eff = effective concrete area These calculation steps have been carried out by making use of a spreadsheet program and the results are given in table 20 below. Table 20: Crack width check Crack width εsm - εcr 1,74 αe 5,88 ρp,eff 0,033 heff 604,54 Ac,eff fct,eff 604544,84 3,21 ‰ s1 125 [mm] wk 0,788 [mm] s1,max 525 [mm] wmax 0,3 [mm] [-] sr,max 453 [mm] [mm] k1 0,8 [-] U-check 2,63 k2 0,5 [-] k3 3,4 [-] 2 [mm ] 2 [N/mm ] Kubilay Bekarlar – Master Thesis 18 August – 2016 ξ1 1 [-] k4 0,425 [-] kt 0,4 [-] φeq 28 [mm] kx 1 [-] As can be seen from the unity check in table 18 above, the occurring crack width exceeds the maximum allowed crack width. This is valid for a span of 22 m and current reinforcement ratio of ρtensile :1,25 % ρcompression :0,62%. It means that additional measures have to be taken, such as applying more reinforcement or more reinforcement with a smaller diameter or concrete with better tensile stress properties. 4.3.2.4 Determination of the critical span of the reinforced concrete roof element The calculations above were given for a span of 22 m. In the tables below the unity checks are summarized for different spans in order to determine the critical span each check. Table 21: Moment capacity check Roof - Moment capacity check Span 15 m [kNm] Span 20 m [kNm] Span 25 m [kNm] Span 27 m [kNm] Mrd 11485,53 Mrd 11485,53 Mrd 11485,53 Mrd 11485,53 Med 5043,83 Med 8966,8 Med 14010,63 Med 16341,99 Unity check 0,439147 Unity check 0,78 Unity check 1,22 Unity check 1,42 Span 22 m [kNm] Span 23 m [kNm] Mrd 11485,53 Mrd 11485,53 Med 10849,83 Med 11858,59 Unity check 0,94 Unity check 1,03 Interpolation In table 21, the critical span for the moment capacity is determined by interpolation. There can be stated that for the applied reinforcement ratio of ρtensile :1,25 % ρcompression :0,62%, the maximum span for a reinforced concrete tunnel will be about 22 m for the roof element. Table 22: Normal stress check Roof - Normal stress check 2 2 2 2 Span 15 m [N/mm ] Span 20 m [N/mm ] Span 25 m [N/mm ] Span 27 m [N/mm ] fcd -23,33 fcd -23,33 fcd -23,33 fcd -23,33 σc,top -12,63 σc,top -21,83 σc,top -33,65 σc,top -39,11 Unity check 0,54 Unity check 0,94 Unity check 1,44 Unity check 1,68 Span 21m [N/mm ] fcd -23,33 σc,top -23,98 Unity check 1,028 Interpolation 2 In the table 22 above the normal stresses for different spans are summed up. There can be seen that for a span larger than 20 m the normal stress capacity will be exceeded, which means that the limiting span is about 20 m. Kubilay Bekarlar – Master Thesis 19 August – 2016 Table 23: Shear force capacity check without shear reinforcement Roof - Shear force capacity - concrete without shear reinforcement Span 15 m [kN] Span 20 m [kN] Span 25 m [kN] Span 27 m [kN] Vrd,c 1002,78 Vrd,c 1002,78 Vrd,c 1002,78 Vrd,c 1002,78 Ved 1681,28 Ved 2241,70 Ved 2802,13 Ved 3026,30 Unity check 1,68 Unity check 2,24 Unity check 2,79 Unity check 3,02 Span 8 m [kN] Span 9 m [kN] Vrd,c 1002,78 Vrd,c 1002,78 Ved 896,68 Ved 1008,77 Unity check 0,89 Unity check 1,01 Interpolation First the shear force capacity has to be checked in case no shear force reinforcement (stirrups) is applied. In table 23 there can be seen that in case no shear reinforcement is applied the maximum span that is possible is about 8 m. This is too short, which means that shear reinforcement has to be applied. The results are given in table 24 below. Table 24: Shear force capacity check with shear reinforcement Roof - Shear force capacity - concrete with shear reinforcement Span 15 m [kN] Span 20 m [kN] Span 25 m [kN] Span 27 m [kN] Vrs,d 4501,86 Vrs,d 4501,86 Vrs,d 4501,86 Vrs,d 4501,86 Vrd,max 8556,55 Vrd,max 8556,55 Vrd,max 8556,55 Vrd,max 8556,55 Ved 1681,28 Ved 2241,7 Ved 2802,13 Ved 3026,30 Unity check 0,37 Unity check 0,49 Unity check 0,62 Unity check 0,67 The applied shear reinforcement is 8,47 mm2/mm. This results in a span which is more than the previous case without shear reinforcement. In this case the shear force capacity is not governing the span of the cross section. Since the span is more than the maximum investigated span of 27 m. 4.3.2.5 Crack width – Roof element From the calculations there was seen that the crack width boundary condition is the limiting condition. With the current reinforcement ratio of ρtensile :1,25 % ρcompression :0,62% and its span of approximately 16 m can be made. By increasing the reinforcement ratio to the maximum of ρ tensile :1,82 % ρcompression :0,31%, the limit of span for a reinforced concrete tunnel can be determined. This because the crack width control check is the governing check. For this reinforcement ratio for all other checks were fulfilled. Table 25: Crack width Crack width Span 15 m wk wmax U-check Span 17m 0,264919 [mm] wk 0,3 [mm] wmax 0,883062 Kubilay Bekarlar – Master Thesis U-check 0,389518 [mm] 0,3 [mm] 1,298393 20 August – 2016 So after the reinforcement ratio is increased to its maximum of 2%, the maximum span is determined again. This span will be the limit for the span since the crack width condition is governing. The results are summarized in table 26. Figure 9: New reinforcement layout (tensile: 10-40ɸ; 8-40 ɸ; 8-32 ɸ Compressive 8-28 ɸ) Table 26: Unity check crack width Span 15 Span 18 Crack width Crack width wk 0,16 [mm] Wk 0,27 [mm] wmax 0,3 [mm] wmax 0,3 [mm] U-check 0,541 U-check 0,91 Span 19 Span 20 Crack width Crack width wk 0,316182 [mm] wk 0,35982 [mm] wmax 0,3 [mm] wmax 0,3 [mm] U-check 1,04 U-check 1,199 From the table 24 above there can be seen that the maximum span for the roof with a reinforcement ratio of ρtensile :1,82 % ρcompression :0,31%, is now about 18 -19 m. 4.3.3 Floor element The cross sectional dimensions, the loadings, material properties and safety factors have been determined, so the capacity of the concrete tunnel element can be calculated. First the moment resistance capacity of the floor will be determined. The position of the reinforcement and its area needs to be specified first. In table 27 below the cross sectional parameters are summarized. Table 27: Parameters Parameters Ic 0,341 [m4] Wc,top 0,427 [m ] Wc,bottom 0,427 cover 91 [mm] 3 Ø -stirrup 16 [mm] 3 Ø -tensile/compression 28 [mm] [m ] Kubilay Bekarlar – Master Thesis 21 August – 2016 Width floor /m 1 [m] Ø -tensile/compression 40 [mm] Height floor 1,9 [m] Spacing reinforcement - 1 Ac, eff 1,9 2 [m ] Spacing reinforcement - 2 50 [mm] cover 91 [mm] Spacing reinforcement - 3 50 [mm] Ø -stirrup 16 [mm] [mm] Figure 10: Layout reinforcement (tensile: 8-40ɸ; 8-40 ɸ; 8-40 ɸ Compressive 8-28 ɸ) 4.3.3.1 Capacity unity checks for a span of 20 m The intermediate steps for the moment-, normal- , shear force capacity and the crack width will not be listed here. Those numbers can be found in Appendix (28.2). The final results of the calculation will only presented, see table 28. Table 28: Unity checks for a span of 20 m Unity checks Moment resistance Shear resistance MRd 20048,90 [kNm] Vrs,d 5578,5 [kN] Med 9248,40 [kNm] Vrd,max 10602,9 [kN] U-check 0,46 Ved 2279,8 [kN] U-check 0,41 Normal stresses fcd -23,33 σc,top -16,23 U-check 0,695 2 Crack width check 2 wk 0,2485 [mm] wmax 0,3 [mm] U-check 0,83 [N/mm ] [N/mm ] There can be concluded that for a span of 20 m, that all unity checks are smaller than 1. This means that the moment-, normal-, shear capacity as well as the crack width fulfill their conditions. However what is again interesting is to find out what the limiting span is for the floor element. This will be further elaborated in the chapter below. 4.3.3.5 - Determination of the critical span of the reinforced concrete floor element The calculations above were given for a span of 20 m. In the tables below the unity checks are summarized for different spans in order to determine the critical span. Kubilay Bekarlar – Master Thesis 22 August – 2016 Table 29: Moment capacity check Floor - moment capacity check Span 15 m [kNm] Span 20 m [kNm] Span 25 m [kNm] Span 27 m [kNm] MRd 20048,9 MRd 20048,9 MRd 20048,9 MRd 20048,9 Med 5258,8 Med 9248,4 Med 14377,9 Med 16748,9 Unity-check 0,26 Unity-check 0,46 Unity-check 0,71 Unity-check 0,84 In table 29, the critical span for the moment capacity is determined by interpolation. There can be stated that for the applied reinforcement ratio of ρtensile :1,59 % ρcompression :0,26%, the maximum span for a reinforced concrete tunnel will more than 27 m. From experience of the previous calculations there can be concluded that the moment capacity will not be the governing for the critical span. Table 30: Normal stress check Roof - Normal stress check 2 2 2 2 Span 15 m [N/mm ] Span 20 m [N/mm ] Span 25 m [N/mm ] Span 27 m [N/mm ] fcd -23,33 fcd -23,33 fcd -23,33 fcd -23,33 σc,top -9,60 σc,top -16,23 σc,top -24,8 σc,top -28,70 Unity check 0,41 Unity check 0,70 Unity check 1,06 Unity check 1,23 In the table 30 above the normal stresses for different spans are summed up. There can be seen that for a span larger than about 24 m the normal stress capacity will be exceeded, which means that the limiting span is about 24 m. Table 31: Shear force capacity check without shear reinforcement Roof - Shear force capacity - concrete without shear reinforcement Span 15 m [kN] Span 20 m [kN] Span 25 m [kN] Span 27 m [kN] Vrd,c 1350,1 Vrd,c 1350,1 Vrd,c 1350,1 Vrd,c 1350,1 Ved 1709,9 Ved 2279,8 Ved 2849,8 Ved 3026,30 Unity check 1,27 Unity check 1,69 Unity check 2,11 Unity check 2,28 The shear force capacity will first be checked in case no shear force reinforcement (stirrups) is applied. In table 31 there can be seen that in case no shear reinforcement is applied the maximum span that is possible is well below 15 m. This is too short, which means that shear reinforcement has to be applied. The results for concrete with shear reinforcement are given in table 32 below. Table 32: Shear force capacity check with shear reinforcement Roof - Shear force capacity - concrete with shear reinforcement Span 15 m [kN] Span 20 m [kN] Vrs,d 5578,5 Vrs,d 5578,5 Vrs,d Vrd,max 10602,9 Vrd,max 10602,9 Vrd,max Ved 1709,9 Ved Unity check 0,31 Unity check 2279,8 0,41 Ved Kubilay Bekarlar – Master Thesis Span 25 m Unity check 23 [kN] Span 27 m [kN] 5578,5 Vrs,d 5578,5 10602,9 Vrd,max 10602,9 2849,8 0,51 Ved 3077,7 0,55 Unity check August – 2016 The applied shear reinforcement is 8,47 mm2/mm. This results in a span which is more than the span in the previous case without shear reinforcement. In this case the shear capacity is not governing the limit span. Since the span is more than the maximum investigated span of 27 m. 4.3.3.6 - Crack width – Floor element For the floor element the crack width boundary condition is the limiting condition. With the current reinforcement ratio of ρtensile :1,59 % ρcompression :0,26% the critical span will be determined with the results in table 33. Table 33: Crack width control Span 15 Span 20 Crack width Crack width wk 0,09 [mm] wk 0,274 [mm] wmax 0,3 [mm] wmax 0,3 [mm] U-check 0,30 U-check 0,914646 Span 25 Span 27 Crack width Crack width wk 0,45 [mm] wk 0,54 [mm] wmax 0,3 [mm] wmax 0,3 [mm] U-check 1,48 U-check 1,79 The crack width check is interpolated in table 34 below. Table 34: Crack width control Span 22 m Crack width wk 0,319 [mm] wmax 0,3 [mm] U-check 1,06 From this unity check for the crack width there can be concluded that the critical span that can be made is 21 m. 4.3.4 Determination of the dimensions of the outer walls The steps above for the roof and floor are repeated for the outer wall and the results are shown below. First the moment resistance capacity of the floor will be determined. Therefor the position of the reinforcement and its area needs to be specified. In table 38 below the cross sectional parameters are summarized. Table 35: Parameters Parameters Ic Wc,top Wc,bottom 0,341 0,427 0,427 4 Ø -stirrup 16 [mm] 3 Ø -tensile/compression 28 [mm] 3 Ø -tensile/compression 40 [mm] [m ] [m ] [m ] Kubilay Bekarlar – Master Thesis 24 August – 2016 Width floor /m 1 [m] Spacing reinforcement - 1 [mm] Thickness outer wall 1,5 [m] Spacing reinforcement - 2 50 [mm] Ac, eff 1,5 2 [m ] Spacing reinforcement - 3 50 [mm] Cover 91 [mm] Ø -stirrup 16 [mm] Figure 11: Layout reinforcement (tensile: 8-40ɸ; 8-40 ɸ; 8-40 ɸ Compressive 8-28 ɸ) The capacity checks will be performed for a span of the roof and floor of 20 m. This has to do with the fact that the limiting span for the roof is about 19 m and for the floor it is about 21 m. Since the smallest span is the governing span, 19 m should be taken. In order to have a small safety margin 20 m span is taken as the loading on the structure, respectively on the outer wall. 4.3.3.1 Capacity unity checks for a span of 20 m The intermediate steps for the moment-, normal- , shear force capacity and the crack width will not be presented here. Those numbers can be found in Appendix (28.3). The final results of the calculation will only presented, see Table 36. Table 36: Unity checks for a span of 20 m Unity checks Moment resistance Shear resistance MRd 11343,53 [kNm] Vrs,d 4401,8 [kN] Med 5504,25 [kNm] Vrd,max 8366,4 [kN] U-check 0,485 Ved 1684,3 [kN] U-check 0,38 Normal stresses fcd -23,33 σc,top -15,85 U-check 0,68 2 Crack width check 2 wk 0,254 [mm] wmax 0,3 [mm] U-check 0,85 [N/mm ] [N/mm ] There can be concluded that for a span of 20 m, that all unity checks are smaller than 1. This means that the moment-, normal-, shear capacity as well as the crack width fulfill its condition. There can be concluded that the outer wall with these dimensions is feasible for a span of 20 m. 4.4 Uplift and immersion calculations After the construction of a tunnel element is completed, both ends of the tunnel element are sealed with bulkheads. Before the tunnel element is floated up, some ballast tanks are installed to have a Kubilay Bekarlar – Master Thesis 25 August – 2016 controlled floating up as well as immersion. The tunnel elements should be designed such that they can float up and be immersed. So, buoyancy balance equations should be used to check whether the floating and immersing conditions hold. If this tunnel cross section does not hold the balance conditions, then changes to the cross section should be made. The dimension for the span of the element is taken as maximum, which is 18 m. In the previous section the dimensions of the elements in a reinforced concrete tunnel have been determined, now the uplift and immersion calculations can be made. For this the weight of the tunnel element has to be determined first. In order to do so the concrete and steel area applied has to be determined. These calculations are made in table 37 and table 38 below. Table 37: Determination of the concrete area Dimension concrete b [mm] h [mm] 2 A [mm ] Dimension concrete Floor 2 b [mm] h [mm] A [mm ] Roof Outer wall 1 1500 1900 2850000 Outer wall 1 1500 1600 2400000 Floor 2 18000 1900 34200000 Roof 2 18000 1600 28800000 Inner wall 2 1300 1900 2470000 Inner wall 2 1300 1600 2080000 Gallery floor 4 3250 1900 6175000 Gallery roof 4 3250 1600 5200000 Inner wall 3 1300 1900 2470000 Inner wall 3 1300 1600 2080000 Floor 6 18000 1900 34200000 Roof 6 18000 1600 28800000 Outer wall 4 1500 1900 2850000 Outer wall 4 1500 1600 2400000 Gallery floor 1 3250 1600 5200000 Walls Outer wall 1 1500 7900 11850000 Inner wall 2 1300 7900 10270000 Inner wall 3 1300 7900 10270000 Outer wall 4 1500 7900 11850000 2 Total concrete area 206415000 [mm ] Total concrete area 206,415 [m ] 2 Table 38: Determination of the steel area (ρ approximated) Mass reinforcing steel 2 2 ρ l [mm] Ac [mm ] As [m ] Reinforcement floor 2% 44850 85215000 1704300 Reinforcement roof 2% 44850 71760000 1435200 Reinforcement outer wall 2% 22800 34200000 684000 Reinforcement inner wall 2% 22800 29640000 592800 0,02 2 Total steel area [mm ] Total steel area 2 [m ] 4416300 4,4163 With the calculated surfaces, the weight of the element can be determined by multiplying the area with the specific weight. Consequently the total weight of the structure will be calculated. Only the Kubilay Bekarlar – Master Thesis 26 August – 2016 amount of ballast concrete to be applied after immersion needs to be calculated. Since the total height of the structure is already determined, the space for ballast concrete can be calculated as follows: In which: hballast is the height of the ballast concrete htotal is the total inner height of the structure hfree traffic is the free height which is needed for the traffic hequipment is the height needed for the installations hasphalt is the height of the asphalt which will be executed at a slope of 2% The dimensions of the elements which are needed in order to make a buoyancy balance calculation are now known. For the floating up conditions the upward hydrostatic load, should be about 1% larger than the weight of the tunnel element. For the immersing condition, in order to have a safety margin against floating up the weight of the element need to be increased further by applying ballast (first water later replaced with ballast concrete). This safety margin is about 7,5%. The results of these calculations are listed in the table 39 and table 40 below. ( ) Table 39: Floating calculation Floating calculation 3 3 Total areas [m ] [kN/m ] [kN] [factor] Concrete 206,42 23,50 4850,75 1,00 Steel 4,42 53,50 236,27 1,00 Ballast 0,00 23,50 0,00 1,00 Hydrostatic load 511,29 10,00 5112,90 1,00 Check 0,99 <1 height 0,72 1,08 >1 Table 40: Immersion calculation Immersion calculation 3 3 Total areas [m ] [kN/m ] [kN] [factor] Concrete 206,42 23,20 4788,83 1,00 Steel 4,42 77,00 340,06 1,00 Ballast 25,92 23,20 601,34 1,00 Earth 0,00 7,50 0,00 1,00 Hydrostatic load 511,29 10,35 5291,85 1,00 Check From the calculations above there can be concluded that the designed reinforced concrete tunnel element fulfils the floating and immersion conditions. For the immersing conditions a lower concrete specific weight is assumed. This is done to account for the uncertainties regarding the concrete density and inaccurate concrete thickness (casting inaccuracy). Kubilay Bekarlar – Master Thesis 27 August – 2016 4.5 Drawing of the reinforce concrete base case design Figure 12: Cross section of the reinforced concrete tunnel Kubilay Bekarlar – Master Thesis 28 August – 2016 5 SCS SANDWICH TUNNEL The first step is determining the dimensions of the tunnel element. Later on these dimensions will be checked on moment, shear resistance and if needed these dimensions can be adjusted. The dimensions are listed in table 41 below. Table 41: Dimensions SCS sandwich elements Roof 5.1 Floor Walls Dimensions outside inside outside inside outside inside h [mm] 1600 1600 1900 1900 1600 1600 b [mm] 1500 1500 1500 1500 1500 1500 tsc [mm] 25 35 20 35 20 25 tst [mm] 35 25 35 20 25 20 hc [mm] 1540 1540 1845 1845 1455 1455 tweb [mm] 20 20 20 20 10 10 ctc web [mm] 1500 1500 1500 1500 1500 1500 Loading on SCS sandwich tunnel In order to determine the loading on the tunnel the material properties, dimensions of the elements, thickness of the materials applied as well as the depth below the water surface need to be specified. These parameters are listed in the table 42 below, in the first column the specific weight of the materials applied are listed, in the second column the dimensions of the tunnel and in the last column the water and ground levels. Table 42: Material properties, dimensions and levels Material properties γsediment γbackfill γrock 17,5 20 22 Dimensions General levels 3 Protection layer 1,0 [m] Design HWL 2,68 [m] 3 Roof thickness 1,6 [m] Ground level -8,46 [m] 3 Asphalt thickness 0,12 [m] Road level -17,64 [m] 3 Bottom level -20,66 [m] [kN/m ] [kN/m ] [kN/m ] γwat 10,35 [kN/m ] Ballast concrete 1,1 [m] φ 30 [deg] Floor thickness 1,9 [m] K0 0,5 [-] Inner height 7,9 [m] Now the hydraulic loading on the tunnel element will be determined. To do so first the hydraulic stress distribution over the tunnel element needs to be determined. By subtracting the hydraulic stress from the total vertical stress, the effective vertical stress is determined. With the angle of ( ) internal friction of 30⁰ the coefficient of lateral earth pressure at rest becomes . By multiplying this parameter with the effective vertical stress, the horizontal stress on the tunnel element can be determined. By summing the hydraulic stress with the effective horizontal stress, the total horizontal stress is calculated. These steps are summarized in table 43. Table 43: Hydraulic stress distribution 3 3 3 3 3 Levels [m] σhydraulic [kN/m ] σsoil [kN/m ] σeff [kN/m ] σkh [kN/m ] σh [kN/m ] Water level 3 0,00 0,00 0,00 0,00 0,00 Kubilay Bekarlar – Master Thesis 29 August – 2016 Ground level -8,46 118,61 118,61 0,00 0,00 118,61 Top side roof -9,46 128,96 140,61 11,65 5,82 134,79 Bottom side roof -11,06 145,52 172,61 27,09 13,55 159,07 Top side floor -18,96 227,29 330,61 103,33 51,66 278,95 Bottom side floor -20,76 245,92 366,61 120,70 60,35 306,26 The following loads on the structure can be distinguished, from self-weight, earth load (back fill), rock protection, ballast concrete and traffic load. Table 44: Load types and load factors Load types SLS ULS ULS - favourable Self-Weight Permanent 1,00 1,25 0,95 Hydrostatic load MWL Permanent 1,00 1,15 0,95 Earth Load Permanent 1,00 1,15 0,95 Rock protection Permanent 1,00 2,00 0,95 Ballast concrete Permanent 1,00 1,25 0,95 Traffic load Variable 1,00 1,50 0,00 With these load factors the total loading on the tunnel in SLS and ULS will be calculated. Now the self-weight of the elements need to be determined, table 46. For this the concrete and steel area is multiplied with its specific mass, table 45. Table 45: Material properties Material properties 3 Density [kN/m ] Water 10,35 Concrete 23,2 Steel 77 Ballast concrete 23,2 Table 46: Steel / concrete area and the q-load Self-weight Self-weight roof Ac-Roof As-Roof q 1535000 65000 2 [mm ] 2 [mm ] 1,535 0,065 2 35,612 [kN/m] 2 [m ] 5,005 [kN/m] Total 40,617 [kN/m] [m ] Self- weight floor Ac-Floor As-Floor q 1840000 60000 2 [mm ] 2 [mm ] Kubilay Bekarlar – Master Thesis 1,84 0,06 2 42,688 [kN/m] 2 [m ] 4,62 [kN/m] Total 47,308 [kN/m] [m ] 30 August – 2016 The next step is the determination of the total loading on the tunnel roof / floor by summing the self-weight of the structure, the ballast concrete, hydraulic pressure, rock protection and backfill. This is done in table 47 below. Table 47: Total loading on the elements Element Roof SLS [kN/m] ULS [kN/m] Floor SLS [kN/m] ULS [kN/m] Self-Weight 40,62 50,77 -245,92 -282,81 Hydrostatic load MWL Rock protection 128,96 148,30 Hydrostatic load MWL Self-Weight 47,308 44,94 11,65 23,30 Ballast concrete 11,9505 11,35 Traffic load UDL 10,00 0,00 Total 181,23 222,38 Total -176,6615 -226,51 Walls - Top SLS [kN/m] ULS [kN/m] Wall - Bottom SLS [kN/m] ULS [kN/m] Hydrostatic load MWL Back fill 134,79 155,01 306,26 352,20 5,83 6,7045 Hydrostatic load MWL Back fill 60,35 69,40 Total 140,62 161,71 Total 366,61 421,60 Element 5.2 Design moment calculation The design moment Med is determined for different spans of the tunnel cross section. This is done by making use of an approximation (rule of thumb), . These values were verified by making use for a framework program Matrixframe, for the reinforced concrete tunnel. This showed that the values of the hand calculation and the computer program do coincide. The calculated design moment MEd will be compared with the moment resistance of the cross section. When the design moment of a certain span exceeds the moment capacity of the cross section, than the maximum span of that particular cross section is exceeded. The same holds for the shear capacity. The span which results in a shear force which exceeds the shear force capacity is also the limit span for the SCS tunnel cross section. The smallest span of these two checks is the governing or limiting span. The calculated internal design forces for different spans can be found in Appendix (28.1). 5.3 Capacity SCS tunnel Provided the dimensions and the loading on the SCS tunnel elements are known, now the capacity can be calculated. In order to do so first the materials that are applied need to be specified. Concrete class C30 and steel class S355 is applied. The properties of these materials are listed in table 48 below. Kubilay Bekarlar – Master Thesis 31 August – 2016 Table 48: Material properties steel and concrete Material properties Steel S355 Elasticity modulus 2 [N/mm ] Concrete 2 [N/mm ] fy 355 fck 30,0 γs 1,1 γc 1,5 fyd 322,73 fcd 20,0 fctk, 0,05 E - steel E - concrete 2 200000 [N/mm ] 34000 [N/mm ] 2 2,0 fctd 1,35 The preliminary dimensions of the cross section are summarized in table 57. In this table there is calculated with a changing thickness of the outer steel and the inner steel over the length roof, floor and wall. This has to do with the fact that the flexural moment causes different tensile and compressive stresses on the inner and outer side of the over the length of the element. This variation of the flexural moment over the length of the element causes different internal forces. That is why the calculation will be done for the outer side and inner side of each element, figure 13 . In order to account for this difference, the calculations are performed for changing steel layout. This will be explained in more detail in the moment capacity calculation. Figure 13: Explanation of the outside and inside section of the roof (red) and floor (blue) elements In the table 49, h is the total height of the element, b is the chosen width unit, t sc the thickness of the steel plate compression zone, tst the thickness of the steel plate in the tensile zone, hc is the height of the concrete only, tweb is the thickness of the diaphragm (web) and ctc web is the centre to centre distance of the diaphragm. Table 49: Dimensions of the elements Dimensions Roof Floor Walls outside inside outside inside outside Inside h [mm] 1600 1600 1900 1900 1500 1500 b [mm] 1500 1500 1500 1500 1500 1500 tsc [mm] 25 35 20 35 20 25 tst [mm] 35 25 35 20 25 20 hc [mm] 1540 1540 1845 1845 1455 1455 tweb [mm] 20 20 20 20 10 10 ctc web [mm] 1500 1500 1500 1500 1500 1500 Kubilay Bekarlar – Master Thesis 32 August – 2016 5.3.1 Shear capacity SCS tunnel (ULS) After the dimensions of the cross section are determined, the capacity checks can be made. In first place the shear force capacity will be calculated. The shear force capacity has two components. One is the concrete shear force capacity and the other the steel shear force capacity. First the shear force capacity of the concrete part will be determined. The following steps will be performed, consecutively the height of the concrete zone will be determined and hereafter the total concrete area is calculated. With the ultimate allowable shear stress in concrete determined, the shear force resistance of the concrete part will be calculated. These steps are shown in the formulas below. ( ) In which: h is the total height of the cross section tsc is the thickness of the steel plate in the compression zone tst is the thickness of the steel plate in the tensile zone hc the height of the concrete Ac is the concrete area τrd,c,min is the allowable shear stress in concrete fctd is the concrete tensile design stress fctk is the concrete tensile characteristic stress fcd is the compressive design stress of concrete Ac is the concrete area Vrd,c is the shear force resistance of the concrete part Now the shear force resistance for the steel will be calculated. First the height of the diaphragm (web) will be determined. This is used to calculate the total steel area that contributes to the shear force resistance of the cross section. With this area and the design yield stress of the steel known, the steel shear force resistance can be calculated. These steps are summarized below: In which: hs,web is the height of the web Av,s is the steel area that contributes to the shear force resistance Vrd,s is the shear force resistance by steel Vrd,c+s is the total shear force resistance contributed by concrete and steel Kubilay Bekarlar – Master Thesis 33 August – 2016 Table 50: Shear force capacity Shear capacity Roof Floor Walls outside inside outside inside outside inside τrd,c,min [N/mm ] 0,54 0,54 0,54 0,54 0,54 0,54 Vrd,c [kN] 1249 1249 1496 1496 1180 1180 hs,web [mm] 2 1540 1540 1845 1845 1455 1455 Av,s [mm ] 30800 30800 36900 36900 14550 14550 Vrd,s [kN] 5739 5739 6875 6875 2711 2711 Vrd,c+s [kN] 6988 6988 8372 8372 3891 3891 Vrd [kN/m1] 4659 4659 5581 5581 2594 2594 2 This calculated shear force resistance of the cross section will be compared with the design shear force Ved due to external loading and self-weight. The span, for which the acting shear force is larger than the shear force resistance, is the limiting span for the shear force check. In table 51 below the design shear forces for different spans of the tunnel cross section is given. Table 51: Design shear force for different spans Ved (ULS) Span 15 m [kN] Span 20 m [kN] Span 25 m [kN] Span 27m [kN] Ved – Roof 1667,81 Ved - Roof 2223,75 Ved - Roof 2779,69 Ved - Roof 3002,1 Ved - Floor -1698,84 Ved Floor -2265,12 Ved Floor -2831,41 Ved Floor -3057,9 Ved-Wall top 986,74 Ved-Wall top 986,74 Ved-Wall top 986,74 986,74 Ved-Wall bottom 2032,79 Ved-Wall bottom 2032,79 Ved-Wall bottom 2032,79 Ved-Wall top Ved-Wall bottom 2032,79 Because both, the shear force resistance and the design shear forces have been determined, the unity checks for different span can be calculated. These values are summarized in table 52. Table 52: Shear force capacity check of the roof floor and wall Unity check Roof Span 15 m [kN] Span 20 m [kN] Span 25 m [kN] Span 27 m [kN] Ved - Roof 1667,8 Ved - Roof 2223,8 Ved - Roof 2779,7 Ved - Roof 3002,1 Vrd - Roof 4659,0 Vrd - Roof 4659,0 Vrd - Roof 4659,0 Vrd - Roof 4659,0 Unity check 0,36 Unity check 0,48 Unity check 0,60 Unity check 0,64 Unity check Floor Span 15 m [kN] Span 20 m [kN] Span 25 m [kN] Span 27 m [kN] Ved - Floor 1698,8 Ved - Floor 2265,1 Ved - Floor 2831,4 Ved - Floor 3057,9 Vrd - Floor 5581,0 Vrd - Floor 5581,0 Vrd - Floor 5581,0 Vrd - Floor 5581,0 Unity check 0,30 Unity check 0,41 Unity check 0,51 Unity check 0,55 Kubilay Bekarlar – Master Thesis 34 August – 2016 Unity check Wall top [KN] Unity check Wall bottom [KN] Ved - Wall 986,74 Ved - Wall 2032,8 Vrd - Wall 2594,0 Vrd - Wall 2594,0 Unity check 0,38 Unity check 0,78 As there can be seen in table 52 the SCS sandwich tunnel roof can resist the shear load for all calculated spans. There can also be stated that it can resist the loads of even larger spans. The same holds also for the floor, also here the loads of the largest span of 27 m can be carried. The shear force resistance of the outer wall is not depending on the span of the cross section. Also this element can resist the occurring design load on the top of the wall as well as on the bottom side. There can be seen that the tunnel element has the biggest unity check value at the bottom side of the outer wall. 5.3.2 Moment capacity SCS tunnel (ULS) After the shear force resistance calculations, the moment capacity for the SCS tunnel element will be checked. This will be done for the roof, floor and wall element of the SCS tunnel. These calculations will be performed for each element in the changing tensile and compression zone. Doing so, for each element two moment resistance calculations will be performed for the two different steel plate configuration. The dimensions of the steel plates and concrete layer are determined such that the moment resistance Mrd of the cross section is larger than the design moment Med. In order to determine the moment resistance of the cross section the following calculation steps are carried out. In which: B is the width tsc is the thickness of the steel plate in the compression zone tst is the thickness of the steel plate in the tension zone fyd is the design yield strength of the steel Nsc is the normal force in the steel plate in the compression zone Nst is the normal force in the steel plate in the tensile zone Ncu is the concrete compression force fcd is the design compression strength of the concrete hc is the height of the concrete xu is the height of the compression zone in the ultimate limit state The first step is the calculation of the compressive and tensile forces in the steel plates. This is done by multiplying the steel area with the design yield strength of steel. This way the concrete compressive force Ncu in the ultimate limit state can also be calculated. The force distribution and the level arms over the cross section are illustrated in figure 14. These forces with their internal level arms create a moment which is known as the moment resistance. Kubilay Bekarlar – Master Thesis 35 August – 2016 Figure 14: Cross sectional forces in a scs tunnel element. The moment resistance is calculated in two steps. First the moment due to the compressive forces will be calculated, denoted as Mrd,c. This has two components the normal force in the steel component and the concrete compressive force. By taking the centre of the bottom steel plate as the reference line, the normal force in this element is left out of the moment equilibrium. This way the moment resistance due to the compressive forces is determined. This is shown in figure 15. Figure 15: Compressive forces, level arms and design moment resistance SCS sandwich element The same is done for the moment as a result of the tensile force in the bottom steel plate, which is denoted as Mrd,t. The internal level arm is chosen such that the force in the steel plate is left out of the moment equilibrium calculation. This is illustrated in figure 16 below. Figure 16: Tensile force, level arm and design moment resistance SCS sandwich element The smallest moment out of these two determined moments will be taken as governing moment which is used for the design. To get the moment per meter this value will also be divided by the width. These steps were carried out in a spreadsheet program and the results are summarized in table 53 below. Kubilay Bekarlar – Master Thesis 36 August – 2016 Table 53: bending moment capacity Bending capacity Roof Floor Walls outside inside outside inside outside inside Nsc, rd [kN] 12102 16943 9682 16943 9682 12102 Nst, rd [kN] 16943 12102 16943 9682 12102 9682 Ncu,rd [kN] 4841 -4841 7261 -7261 2420 -2420 N axial 1295 1295 2040 2040 2308 2308 x [mm] 308 308 369 369 291 291 Mpl,rd,c [kNm] 27612 21642 33737 23004 20556 17733 Mpl,rd, t [kNm] 27637 20037 33357 19761 19728 16151 Mpl,rd [kNm] 27612 20037 33357 19761 19728 16151 Mpl,rd/m [kNm/m] 18408 13358 22239 13174 13152 10768 As there can be seen in table 53, the steel plates are exerted to compressive and tensile stresses over the length of the roof / floor. This has to do with the moment distribution that varies over the element. For example the roof element is exposed to tensile forces on the outer side and compressive forces on the inner side. This is only valid for the parts close to the connection with the walls. The opposite is valid for the middle of the span, in which tensile forces on the bottom and compressive on top. This results in a different moment capacity for the SCS roof element for its mid-span and the sides. This difference is denoted in the table as inside and outside. Now the design moment will be compared with the moment resistance. In the previous case the biggest moment was used as the governing moment and the structure was designed on that. Also a hand calculation was used to calculate the internal forces. However in this case the changing moment distribution will be taken into account. The design moments will be the moment in the mid span and the moment at the connection of the roof/floor-wall. This is the reason why the Matrixframe output will be used, since it gives a detailed output of the moment distribution. As for the floor element the moment distribution differs from the hand calculation, this has to do with the uniform elastic soil bedding. While in reality the structure is not supported uniformly and there might be gaps underneath the structure. If these moments were used than the structure capacity would be overestimated. So since the loading on the floor element is only slightly bigger, the moment distribution of the roof element can be used with a small safety margin. In figure 17 the moment distribution for a span of 27 m is given. The dimensions of the steel plates and concrete were chosen such that these moments plus safety margin won’t be bigger than the moment resistance of the element. Figure 17: Design moment distribution for a span of 27 m Kubilay Bekarlar – Master Thesis 37 August – 2016 In table 54 below the design moments and the moment resistances are given. The added margin on the floor design moment is 1000 kNm on top of the design moment of the roof. Also the unity checks are given, which show that with the current dimensions the cross sectional moment capacity is larger than the design moment. Table 54: Unity check moment capacity Bending capacity 5.3.3 Roof Floor Walls outside inside outside inside outside inside Mpl,rd/m [kNm/m] 18408 13358 22239 13174 13152 10768 Med [kNm/m] 15247,4 10607,5 16247,4 11607,5 8029,1 0 Unity Check 0,829 0,794 0,73 0,881 0,611 0 Design of stud connectors and stiffeners In order to have a good connection between the steel plate and the concrete stiffeners and /or studs are applied. As the name states, the stiffeners also give the steel plate enough stiffness which prevents it from deforming during concrete pouring. These elements are welded on both sides of the steel plates. They transfer the forces in the steel plates to the concrete. In figure 18 the studs and stiffeners are illustrated for the upper steel plate of a sandwich element. Figure 18: Illustration of stiffeners (L- shaped) and shear studs (straight) First the design longitudinal shear force will be determined. For this a part of the cross section is assumed to be shearing, see figure 19. Figure 19: Longitudinal shear of a steel concrete connection In the next stage the centre of gravity of the cross section will be determined. Here after the moment of inertia Fizz, first moment of area Spa and the shear force per unit length Sax will be determined. The calculations for the roof element will be presented below: Kubilay Bekarlar – Master Thesis 38 August – 2016 Figure 20: Dimensions used for a longitudinal shear calculation ( ) Figure 21: Development of the longitudinal shear force in the SCS roof element Since the longitudinal shear force per unit length is known the total longitudinal shear force can be calculated as follows: Another way to compute the longitudinal shear force can be done by using the moment: Now the capacity of the stiffener is determined. This element will yield if the maximum stress of the connection between the stiffener and the steel plate is reached. So the maximum moment the stiffener can bear can be calculated as follows: In which: M is the moment σ is the yielding stress fyd w is the section modulus t stiffener is the thickness of the stiffener The resisting bending moment of the stiffener should be in balance with the bending moment caused by the interaction of the stiffener and the concrete, figure 22. This is determined as follows: Kubilay Bekarlar – Master Thesis 39 August – 2016 Figure 22: Forces acting on a stiffener In which: b is the width of the stiffener fcd is the design compressive stress of concrete So the force in the stiffener can be written as: The only unknown is the “a” which can be acquired by solving the equation of the moments. This results in: √ The capacity of a stud is calculated with the following formula: Figure 23: Variable dimensions of a steel stud element The minimum length of a stud should be 4 times the stud diameter, where the diameter should be in the range of 16 mm ≥ Ø ≤ 25 mm. There are two possible failure mechanisms for steel studs one which is the shearing of the steel stud, see figure 24 and the other being the crushing of the concrete, figure 25. The capacity of the steel stud will be calculated for both cases. For determining the number of studs required the lowest stud capacity will be used, since the lowest capacity is governing. Figure 24: Shearing of a steel stud The shear force capacity of the stud for shearing can be calculated as follows: Kubilay Bekarlar – Master Thesis 40 August – 2016 In which: fyd is the design yield stress of steel d is the diameter of the steel stud Figure 25: Crushing of concrete The shear force capacity of the stud for concrete crushing can calculated with: √ In which: feck is the characteristic compressive strength of concrete Ecm is the modulus of elasticity of concrete If both the capacity of the stiffener and stud is combined both contributions are summed: The results of these calculations are shown in table 55 below. Table 55: Calculation of shear force capacity of stiffener and stud in respectively kN/m and kN Roof Floor Nc [mm] Izz 4 [mm ] 6,4 x 10 a [mm ] 3 12,05 x 10 a [N/mm] 570 668 392 a [kN] 3847,5 4510 1117 Sz Sx Rs 372 Walls 417 10 351 9,11 x 10 6 20 x 10 10 6 10 6 12,5 x 10 Roof Floor Walls outside inside outside inside outside inside 2 322,72 322,72 322,72 322,72 322,72 322,72 2 20,0 20,0 20,0 20,0 20,0 20,0 2 30,0 30,0 30,0 30,0 30,0 30,0 2 fyd [N/mm ] fcd [N/mm ] fck 5,3 x 10 [N/mm ] Ecm [N/mm ] 35000 35000 35000 35000 35000 35000 d,stiff [mm] 15 15 15 15 15 15 W [mm ] 56250 56250 56250 56250 56250 56250 a [mm] 42,6 42,6 42,6 42,6 42,6 42,6 F,stiff [kN] 852,1 852,1 852,1 852,1 852,1 852,1 d,stud [mm] 25 25 25 25 25 25 α - 1,0 1,0 1,0 1,0 1,0 1,0 γ - 1,25 1,25 1,25 1,25 1,25 1,25 3 Kubilay Bekarlar – Master Thesis 41 August – 2016 F stud shear [kN] 127 127 127 127 127 127 F stud crushing [kN] 149 149 149 149 149 149 Now the layout of the stiffeners (150x150x15 mm3) and the studs (35 ɸ - h 100 mm) will be determined. As stated before the studs and stiffeners should be able to bring over the force of the steel plates to the concrete. Despite the forces in the steel plates changes over the length of the element (roof, floor and wall), one layout will be applied for one element. In practice, changing layouts over an element is not feasible. That is why the governing steel force (max) will be used in the calculation, denoted in bold table 55. The layout for the studs and stiffeners will be calculated as follows: In which: n is the number of studs welded to the plate L is the stiffener unit length The following layout is determined, see Figure 26 and Figure 27. Figure 26: 3-D illustration of stiffener and stud layout Figure 27: 3-D illustration of stiffener layout Kubilay Bekarlar – Master Thesis 42 August – 2016 The unit length which is needed in order to transfer the load from the steel into the concrete is 3,5 m. However there is a boundary condition, which is related to the maximum amount of concrete that can be poured in one unit. This amount is 10 m3 in one pour. From the calculation above there can be seen that also the unit volume does not exceed the 10 m 3. This is calculated for the governing height of the floor slap, which is 1,9 m. 5.4 Uplift and immersion calculations The floating and immersing processes are essential aspects of immersed tunnels. This means that the tunnel elements should be designed such that they can float up and be immersed. For this reason balance equations are used to check whether the floating and immersing conditions hold. If this tunnel cross section does not hold the balance conditions, then changes of cross section are inevitable. The dimension of the span of the element is taken as maximum, which is 27 m. This is the span which is needed for the reference project in order to cover the transition zone in two spans of 27 m. In the previous section the dimensions of the elements in a scs sandwich tunnel have been determined, now the uplift and immersion calculations can be made. For this the weight of the tunnel element has to be determined first. In order to do so the concrete and steel area applied has to be determined. These calculations are made in table 56 and table 57 below. Table 56: Determination of concrete area Concrete Area Element b [mm] h [mm] 2 A [mm ] Element Roof Outer wall 1 b [mm] h [mm] 2 A [mm ] Floor 1600 1900 3040000 Outer wall 1 1600 1600 2560000 27000 1900 51300000 Roof 2 27000 1600 43200000 Inner wall 2 1000 1900 1900000 Inner wall 2 1000 1600 1600000 Gallery floor 4 3250 1900 6175000 Gallery roof 4 3250 1600 5200000 Inner wall 3 1000 1900 1900000 Inner wall 3 1000 1600 1600000 27000 1900 51300000 Roof 6 27000 1600 43200000 1600 1900 3040000 Outer wall 4 1600 1600 2560000 Gallery floor 1 3250 200 650000 Floor 2 Floor 6 Outer wall 4 Walls Outer wall 1 1600 7900 12640000 Inner wall 2 1000 7900 7900000 Inner wall 3 1000 7900 7900000 Outer wall 4 1600 7900 12640000 Total concrete area Total concrete area Kubilay Bekarlar – Master Thesis 159735000 159,735 2 mm /m 2 m /m 43 August – 2016 Table 57: Determination of steel area Steel Area 2 Element t [mm] l [mm] A[mm ] Outer side floor 35 62450 2185750 Inner side floor 25 57250 1431250 Outer side roof 40 62450 2498000 Inner side roof 25 57250 1431250 Outer side wall outside 30 11400 684000 Inner side wall inside 20 7900 316000 Web plate - ctc 1500 20 3356733 1500 2 Total steel area 11902983 [mm /m] Total steel area 11,902 [m /m] 2 Because the surfaces have been calculated, the weight can be determined by multiplying the area with the specific weight. Consequently the total weight of the structure will be calculated. Only the amount of ballast concrete to be applied after immersion needs to be calculated. Since the total height of the structure is already determined, the space for ballast concrete can be calculated as follows: In which: hballast is the height of the ballast concrete htotal is the total inner height of the structure hfree traffic is the free height which is needed for the traffic hequipment is the height needed for the installations hasphalt is the height of the asphalt which will be executed at a slope of 2% All elements are known in order to make a buoyancy balance calculation. For the floating up conditions the upward hydrostatic load, should be about 1% larger than the weight of the tunnel element. For the immersing condition, in order to have a safety margin against floating up the weight of the element need to be increased further by applying ballast (with water during immersing later replaced with ballast concrete). This safety margin is about 7,5%. The results of these calculations are listed in the table 58 and table 59 below. ( ) Table 58: Floating calculation of SCS sandwich tunnel element Floating calculation 3 3 [m ] [kN/m ] [kN] [factor] Concrete 260,31 23,50 6117,17 1,00 Steel 11,90 77,00 916,53 1,00 Ballast 0,00 23,50 0,00 1,00 Kubilay Bekarlar – Master Thesis 44 August – 2016 Hydrostatic load 711,93 10,00 7119,30 1,00 Check 0,99 <1 Table 59: Immersion calculation of SCS sandwich tunnel element Immersion calculation 3 3 [m ] [kN/m ] [kN] [factor] Concrete 260,31 23,20 6039,08 1,00 Steel 11,90 77,00 640,38 1,00 Ballast 50,22 23,20 1165,10 1,00 Earth 0,00 7,50 0,00 1,00 Hydrostatic load 711,93 10,35 7368,48 1,00 Check height 0,93 1,06 >1 From the calculations above there can be concluded that the designed SCS sandwich tunnel element fulfils the floating and immersion conditions. Also in this case there should be pointed out that for the immersing conditions a lower concrete specific weight is assumed. This is done to account for the uncertainties regarding the concrete density and inaccurate concrete thickness (inaccuracy during filling of the concrete / void forming). Kubilay Bekarlar – Master Thesis 45 August – 2016 5.5 Drawing of the SCS base case design Figure 28: Cross section of the SCS sandwich tunnel element Kubilay Bekarlar – Master Thesis 46 August – 2016 6 BASE CASE SUMMARY As has been noted, this base case design has several purposes. One purpose is to investigate whether or not the transition zone of a 2x4 lane to a 2x3 lane immersed tunnel can be executed as reinforced concrete tunnel part and what are its limits regarding the cross sectional span (in case the max. reinforcement ratio applied). Another aim of the base case design is that it will be checked whether or not the SCS sandwich tunnel element can realize a 2x4 lane with safety lanes on both sides. In other words to check whether or a SCS sandwich tunnel can make a span of 27m. This way insight will be gathered in the design rules and parameters for the design of a SCS sandwich and reinforced tunnel. The designed SCS sandwich tunnel will be used for further detailed analysis in the remainder of this research. First the base case for a reinforced concrete tunnel was worked out. Initially the loading on the tunnel was worked out, which resulted in the determination of the design loads. These design loads were used to determine the design forces, such as the moment, shear force and normal force. First hand calculation was used, which was checked with a framework software program Matrixframe. There was concluded that the overall results of the hand calculations and the framework software program calculation were in accordance with each other. The only difference that was present had to do with the assumptions that was made for the bedding boundaries. In which the bedding was assumed to be uniform over the entire length of the floor. However in reality this might not be the case. This has to do with the fact that scour may occur below the floor element, which will result in higher loads than assumed with a uniform bedding. In order not to underestimate the design load on the structure, a hand calculation is used for further design. Since both calculations correspond well, this is allowed. Here after the capacity of the reinforced tunnel is determined for the roof, floor and wall element. First the cross sectional dimensions were determined. Here after the moment capacity check, normal stress capacity check, shear force capacity check and crack width control was performed for the roof. For which a reinforcement ratio of 1,2 % in tensile zone and 0,6% in compressive zone has been applied with a span of 22 m. For this reinforcement ratio and span, the moment capacity was not exceeded. The normal stress in the cross section was slightly higher than what is allowed. Shear force capacity with stirrups was not exceeded, however the crack width was larger than the maximum crack width. For the roof element these checks were repeated for different spans. From these calculations there was seen that the crack width was the limiting factor for the span. By changing the reinforcement ratio (1,8% in tensile zone and 0,3% in compression zone) and its layout the critical span for the crack width was calculated again, since this is the governing span. This way the critical span for the roof element became 18 to 19 m. The same steps for the roof element are repeated for the floor element. This time the reinforcement ratio is 1,59% in tensile zone and 0,26% in the compressive zone. The moment capacity check, normal stress check, shear force check and the crack width control were performed for different spans of the element. From these calculations there was again concluded that the crack width control was the critical factor, since it resulted in the smallest span. This span is 21 m for the floor element. Now the outer wall will be checked as well. Here the capacity checks were performed for a span of the roof and floor of 20 m. This has to do with the fact that the limiting span for the roof is about 19 m and for the floor it is about 21 m. Since the smallest span is the governing span, 19 m should be taken. In order to have a small safety margin 20 m span is taken as the loading on the structure, respectively the outer wall. Kubilay Bekarlar - Master Thesis - 47 - August – 2016 After the dimensions of the reinforced concrete tunnel are determined the uplift and immersion checks were done. The designed tunnel cross section should hold for the buoyancy balance equations, if not adjustments should be made. From the calculations there was concluded that the reinforced concrete tunnel is in accordance with the immersion and floating boundary condition. Just like the reinforced concrete tunnel, also for the SCS sandwich tunnel first the external load per meter width was determined. With the design loads due to external loading, self-weight etc. the total design forces acting on the structure will be determined (M, V and N forces). Because the loading is known, next the dimensions are estimated. These dimensions determined by earlier experience will be checked later on and adjusted if they don’t fulfill the boundary conditions. The estimated dimensions for the cross section are the thicknesses of the steel plates, thickness of the concrete, c.t.c. distance of the diaphragms and the thickness of the diaphragm. Since the dimensions are determined, the checks can be performed. First the shear capacity check is performed for different spans of the elements. This is an iterative process and if the design shear force exceeded the shear force resistance the cross sectional dimensions were adjusted. From the calculations there was concluded that the shear force capacity, for all spans investigated 15 -27 m, did not exceed the shear force capacity. The second check is the moment capacity check. For this step the moment distribution for the maximum span of 27 m is used. Because the changing moment distribution is of importance for this analysis, the Matrixframe output will be used rather than the hand calculation. For the chosen dimensions of the elements and the maximum span of 27 m, there was concluded that each element fulfilled the capacity condition. Everything is known to determine the stud connectors and the stiffeners. The dimensions of the stiffeners and studs applied is respectively 150x150x15 and 35 ɸ - h is 100 mm, with a ctc distance of 500 mmm. With these dimensions the length of a steel unit is 3,5m. This length is needed to transfer the forces in the steel shell to the concrete. There is also checked whether the unit volume meets the executional boundary condition, which states that the volume should be less than 10 m 3. The last step is again checking whether the floating and immersing conditions are met, if not the ballast or the structural dimensions needs to be adjusted. From the calculations there can be seen that the floating and immersion conditions are met (this was also an iterative process). All things considered, from the results above there can be concluded that even with the maximum reinforcement ratio applied for a reinforced concrete tunnel, a span of 27 m is not feasible. The normative check that determines the critical span is the crack width control. In the calculations this condition was exceeded first. Whereas for the SCS sandwich tunnel no crack width check is needed. Nor is there a limit for the steel applied, against brittle failure. From the calculations performed, there is concluded that a span of 27 m with a SCS sandwich element is feasible. The designed SCS sandwich base case will be used for further analysis. Kubilay Bekarlar - Master Thesis - 48 - August – 2016 FEM Analysis SCS Immersed Tunnel & Design Optimization Kubilay Bekarlar - Master Thesis - 49 - August – 2016 7 FEA MODEL 7.1 Introduction In the previous chapters a “Base Case” design was made, for a SCS tunnel. In order to get a good understanding of the structural response to the loadings a finite element model (FEM) needs to be used. The finite element analysis (FEA) program that will be used is DIANA. Dimensions of the earlier designed “Base Case” of the SCS sandwich tunnel will be used for this model. This program can perform a linear as well as nonlinear structural analysis. Before the actual modelling in DIANA, the essence of FEM analysis, linear analysis and non-linear analysis was studied in detail. The nonlinear analysis can also be separated in material (physical) nonlinear analysis, geometrical nonlinear analysis and boundary (contact) nonlinear analysis. These types of analysis are discussed in detail in Appendix F. 7.2 2-D or 3-D Analysis In this section there will be explained why there will be chosen for a 2-D or 3-D analysis for the SCS sandwich tunnel element. Whether 2-D or 3-D analysis will be performed depends on type of foundation that will be assumed to be present in the model. In case the foundation is assumed to be well behaving, than 2-D analysis will suffice. Well behaving foundations are foundations that deliver permanent uniform support to the structure resting on top of it. However if the support is assumed to be non-uniform due uneven settlement, then local concentrated loads are introduced. These concentrated loads result in a complex redistribution of the internal forces. In that case a 3-D analysis should be preferred in order to see how the forces are redistributed (which is not possible in 2-D). In contradictory to reinforced concrete immersed tunnels, SCS immersed tunnels don’t consist of segments that form one element. SCS immersed tunnels are manufactured as an element of around 100 m. This means that uneven settlement of the subsoil can indeed lead to large force in the axial direction of the tunnel. These forces should also be investigated by looking in the axial direction. However, this can also be done by a FEM analysis or a hand calculation analysis. This is why for the cross sectional analysis of a SCS element a 2-D structural analysis is sufficient. 7.3 Material model Finite element programs have different material models in their database that can simulate the behaviour of the materials applied for a certain loading. In this chapter the chosen material models are named and the reasons why they are chosen will be explained. 7.3.1 Material model - concrete linear elastic Concrete: stress strain diagram (one with tension softening), Ec For the self-compacting concrete class which will be applied to the SCS sandwich element is class C30. Concrete behaves differently in the elastic and plastic state. In figure 29 below, an idealized stress strain diagram is given for concrete in the elastic state. The elasticity modulus of concrete applied for the SCS sandwich element is Ecm 34 000 N/mm2. For the Poisson’s ratio a value ⱱ = 0,3 is applied. Kubilay Bekarlar - Master Thesis - 50 - August – 2016 Figure 29: Idealized elastic behaviour of concrete 7.3.2 Material model - steel linear elastic Steel class S355 will be used for the model of the SCS sandwich plates, stiffeners and studs. The steel will also behave differently in its linear and plastic domain. For the linear elastic domain of the steel, the material behaviour is idealized as shown in figure 30. The elasticity modulus applied for the linear domain of steel is Es 210 000 N/mm2. Poisson’s ratio ⱱ = 0,2 will be applied. Figure 30: Idealized elastic behaviour of steel 7.4 Schematization of the SCS sandwich tunnel element In this section the schematization of the SCS sandwich tunnel will be discussed in detail. One of the aspects that will be covered first is the idealization of the tunnel structure. This has to do with the fact that the SCS sandwich element will be simplified in order to reduce the computation time. The degree of detail of the structure should be justified by the degree of detail that is needed as output. Another issue is whether or not making use of the symmetry of the structure. To understand the behaviour of the structure and to get insight in the distribution of the forces, modelling only a part of the tunnel can suffice. This on the precondition that symmetry axis are available. 7.4.1 Constraints Since the model will perform a linear elastic analysis the computation time is limited. Also the modelling time can be limited by using the mirror function which mirrors the model around the symmetry axis. That is why the entire cross section will be modelled. Further the normal displacements should be constrained as well. The bedding has to be constrained in all directions. In figure 31 below the symmetry axis for the 2D cross section is given. This bedding element will be constraint in two directions, X and Y. Kubilay Bekarlar - Master Thesis - 51 - August – 2016 Figure 31: Symmetry axis of the SCS sandwich tunnel, base case design 7.4.2 Type of elements There are several elements which can be used to model the SCS sandwich tunnel element. In this section the elements that will be applied are discussed and the reason why they are chosen will be motivated. SCS elements For the SCS element a plain strain element will be used. The element that will be applied is the three node plain strain element– CL9PE. Plain strain elements are preferred because these elements give good insight in the stress and strain distribution, from which the correct internal forces will be calculated when intagrated over the height of an element. Another important aspect of the plain strain element is that they are infinitely long in the axial direction. In figure 32 below the schematization of a CL9PE element can be observed. Figure 32: Plain strain element CL9PE Bedding The subsoil will be schematized with an interface element. These elements don’t have material nor physical properties. Only linear and tangential stiffnesses of these elements have to be specified. Interface element – CL12I is chosen which is a six node interface element. As there can be seen the position of the nodes correspond with the position of the nodes of the plain strain element, see figure 33. Kubilay Bekarlar - Master Thesis - 52 - August – 2016 Figure 33: Interface element CL12I 7.4.3 Dimensions of the roof, floor and wall The global dimensions of the structure that will be modeled in Diana are given in table 60 and table 61 below. Table 60: Dimenions of the roof, floor and wall element Roof Floor Wall h [mm] – Total height of the element 1600 1900 1500 b [mm] – Unit width of the element 1500 1500 1500 to [mm] – Thickness steel plate outside 35 35 25 ti [mm] – Thickness steel plate inside 25 20 20 hc [mm] – Height of concrete 1540 1845 1455 tweb [mm] – Thickness of the diaphragm (web) 20 20 10 ctc web [mm] – Centre to centre distance of diaphragm (web) 1500 1500 1500 Table 61: Global dimensions Dimensions Width of one tunnel tube 27000 [mm] Total width of the tunnel 63100 [mm] Total height of the tunnel 11400 [mm] Inner height of the tunnel 7900 [mm] Now the tunnel elements will be schematized. This means that the elements which will be used will be named and explained why they are chosen. The boundary conditions will be chosen as well as the loading. 8 LINEAR ELASTIC ANALYSIS SIMPLIFIED MODEL 8.1 Material properties sandwich elements Composite materials have different modulus of elasticity than the steel and concrete which it consists of. The elastic modulus is an input value for the simple Diana model which will describe the linear elastic behaviour of the model in a linear analysis. Since the modulus of elasticity and the dimensions of the steel and concrete are known the elastic modulus of the SCS elements can be derived, see figure 34 for a composed cross section. Kubilay Bekarlar - Master Thesis - 53 - August – 2016 Figure 34: Composed cross section of steel and concrete First of all there has to be stated that a SCS composite material is inhomogeneous. This means that the composite material has different material properties in each of its axis. For a 2-D analysis the material properties of the composite material will be determined in the XX direction and the YY direction. That is why the elasticity modulus for the XX and YY direction will be determined. The first calculation is the determination of the Exx Ixx and the Eyy Iyy of the overall cross section. [N mm2] ( ) ( ) ( ) [N mm2] [N] In which: Es is the Young’s modulus of steel 2,1 x 105 [N/mm2] Ec is the Young’s modulus of concrete 3,4 x 104 [N/mm2] hc is the height of the concrete in the floor 1845 [mm] hs is the total height of both steel plates of the floor 55 [mm] b is the unit width 1000 [mm] A is the surface area z is the eccentricity of the steel plates towards the centre of gravity of the cross section approximated by htot/2 Exx Ixx is the overall bending stiffness in the XX direction of the element Eyy Iyy is the overall bending stiffness in the YY direction of the element Eyy Ayy is the Young’s modulus times the area of each element There can be seen that only for one direction the Eyy Ayy is determined, this weak axis will be neglected. Now the Young’s modulus of the composed element has to be determined for its XX and YY direction as well as the height. These values are denoted with an asterisk: E*xx , E*yy and h*. There are three equations available and there are three unknowns, which means that these values can be solved: [N/mm2] [N/mm2] [N] Kubilay Bekarlar - Master Thesis - 54 - August – 2016 From these calculations the representative values of the Young’s moduli E*xx , E*yy and the height h* can be determined. These steps are done for the floor, roof and wall element of the SCS tunnel. The results for each element can be seen in the table 62 and table 63 below. Table 62: Calculation of the composed modulus of elasticity and height of the floor element Floor Inner steel plate Concrete core t [mm] 20 b [mm] 1000 2 E [N/mm ] z [mm] Outer steel plate Composed 1845 35 1900 1000 1000 1000 210000 34000 210000 10 922,5 17,5 950 2 A [mm ] 20000 1845000 35000 1900000 4 1,67E+09 1,5375E+11 2,92E+09 1,58E+11 4 1,74E+10 5,23E+11 3,09E+10 5,72E+11 Ixx [mm ] Iyy [mm ] EA [N] 4,20E+09 6,27E+10 7,35E+09 7,43E+10 2 3,50E+14 5,23E+15 6,13E+14 6,19E+15 2 3,65E+15 1,78E+16 6,50E+15 2,79E+16 EIxx [N mm ] EIyy [N mm ] h* 2124,63 [mm] Exx* 34961,36 [N/mm ] Eyy* 34961,36 [N/mm ] 2 2 Only the results of the calculations for the roof and wall element are presented in Table 63. The detailed overview is presented in Appendix (28.4). Table 63: Calculation of the composed modulus of elasticity and height of the roof element Roof h* Wall 1829,65 [mm] h* 1681,77 [mm] 2 Exx* 35034,57 [N/mm ] 2 Eyy* 35034,57 [N/mm ] Exx* 35503,98 [N/mm ] Eyy* 35503,98 [N/mm ] 2 2 These values will be used for the definition of the material properties and physical properties of the SCS sandwich cross section in Diana. 8.2 Determination of the passion ratio of composite material A composite material has a different passion ratio than the materials which it consists of. This value can be calculated from the volume fractions of each material relative to the total volume. So the passion ratio of the SCS element is calculated as follows: VSCS = VConcrete * Volume fraction concrete + VSteel * Volume fraction steel For the calculation a spreadsheet program was used. The results can be seen in table 6 below. Table 64: Calculation of the passion ratio for each composed element Dimensions Roof Floor Walls h [mm] 1600 1900 1500 [mm] b [mm] 1000 1000 1000 [mm] Kubilay Bekarlar - Master Thesis - 55 - August – 2016 8.3 tsc [mm] 25 20 20 [mm] tst [mm] 35 35 25 [mm] hc [mm] 1540 1845 1455 [mm] tweb [mm] 20 20 10 [mm] Total stiffener Surface - 150x150x15 9000 9000 9000 [mm ] Total stud surface - 35 Ø - 100 7000 7000 7000 [mm ] Volume Fraction Steel 0,07 0,06 0,05 Volume Fraction Concrete 0,93 0,94 0,95 Passion ratio Steel 0,30 0,30 0,30 Passion ratio Concrete 0,20 0,20 0,20 Passion ratio SCS 0,21 0,21 0,21 2 2 Determination of the bedding constant Also the bedding conditions need to be determined. The soil at the location of the reference project is predominantly sandy. Rules of thumb are used in order to determine the design value of the bedding constant. The characteristic value for the beddings constant of sand is 50 000 kN/m 3. Design beddings constant should be in the range of characteristic value multiplied by √2 and divided by √2. √ √ Any value within this range can be chosen with regard to the local conditions. For the Diana model a beddings constant of 60 000 kN/m3 is taken. The tangential stiffness: 8.4 Main Dimensions being modelled The dimensions of the tunnel that will be put in Diana are the centre to centre (c.t.c.) distance between the elements. These main dimensions are visualized in figure 35 below. Figure 35: Centre line dimensions of the tunnel cross section Kubilay Bekarlar - Master Thesis - 56 - August – 2016 9 MODELLING SIMPLIFIED MODEL IN IDIANA - LINEAR ELASTIC ANALYSIS In this chapter the modelling of the simplified model will be explained. A detailed explanation of the simplified model can be found in Appendix 9. 9.1 Geometry definition First the geometry will be defined of the concrete tunnel structure as well as the subsoil. The concrete elements will be schematized with dots and lines. While the subsoil is schematized with an interface surface element. 9.2 Boundary conditions After the geometry is defined the boundary conditions also need to be defined. A part of the interface element is constraint in the Y direction and the lower left corner is constraint in the X, Y and Z direction, see figure 36. Figure 36: Cross sectional boundaries 9.3 Meshing Now the mesh division of each element will be realized. The mesh division of the elements should be chosen in accordance with the mesh of other elements, figure 37. Figure 37: Schematization of the geometry division 9.4 Loads In this stage the loads on the structure are applied including the self-weight, see figure 38. Kubilay Bekarlar - Master Thesis - 57 - August – 2016 Figure 38: Loading on the tunnel cross section 9.5 Material and physical properties In the final stage the material and physical properties are attached to the structure. 10 RESULTS OF THE SIMPLIFIED LINEAR ELASTIC ANALYSIS 10.1 Moment distribution and deflection 10.1.1 Lc1 – Load case 1 Figure 39: Bending moment due to gravity loading, Max. 0.324E7 Min. – 0.223E7 10.1.2 Lc2 - Load case 2 Figure 40: Load on the structure Figure 41: Bending moment due to loading on top of the tunnel, Max. 0.121E8 Min. 0.776E7 Kubilay Bekarlar - Master Thesis - 58 - August – 2016 10.1.3 Lc3 - Load case 3 Figure 42: Load on the structure Figure 43: Bending moment due to hydraulic pressure below the floor element, Max. 0.523E-5 Min. -0.65E-5 10.1.4 Lc4 - Load case 4 Figure 44: Load on the structure Figure 45: Bending moment as a result of loading on the left outer wall, Max. 0.274E7 Min. -0.276E7 Kubilay Bekarlar - Master Thesis - 59 - August – 2016 10.1.5 Lc5 - Load case 5 Figure 46: Load on the structure Figure 47: Bending moment as a result of loading on the right outer wall, Max. 0.218E7 Min. -0.249E7 10.1.6 Lcc - Load case total Figure 48: Load on the structure Figure 49: Bending moment as a result of all loads on the tunnel cross section, with interface bedding Kubilay Bekarlar - Master Thesis - 60 - August – 2016 Figure 50: Bending moment as a result of all loads on the tunnel cross section, without interface element 10.1.7 Displacement Lcc – Load case total Figure 51: Displacement of the structure as a result of total load (extreme scale) Max. 0.409E-2 Min. -0.392E-1 11 VALIDATION OF THE MODEL 11.1 Validation of moment distribution - deflections per load case In this part the results from the simplified Diana model will be validated by the results of the hand calculation. This will be performed for the moment and deflection of each load case acting on the structure. 11.1.1 Load case 1 – self weight of the structure The results obtained from Diana for the moment and the deflection of the roof element for load case 1 are given in figure 52 below. Figure 52 Left: Moment distribution in the roof element Right: Deflection of the roof element due to load case 1 These results will be checked by making use of rules of thumb from mechanics, figure 53. Kubilay Bekarlar - Master Thesis - 61 - August – 2016 Figure 53: Rule of thumb from mechanics The roof element can be schematized by a beam element which is fully inclined on both sides. The load on top of it is a distributed load. In order to calculate the moments in the inclination and the deflection of the mid span the following rules of thumb can be used: A spreadsheet program has been used to calculate the deflection and moments. The results for load case 1 are given in table 65 below. Table 65: Deflection hand calculation LC1 Deflection hand calculation LC1 q 45,75 L 28,4 E 35503000 h* b I kN/m m kN/m 1,83 m 1 m 0,511 m 2 Hand calculation Deflection Diana model 0,00427 4 4,27 m Deflection 0,00675 mm 6,75 m mm Table 66: Moment hand calculation and Diana model Moment hand calculation and Diana model Hand calculation Diana model M1 3075 kNm M1 1800 kNm M2 3075 kNm M2 3200 kNm Moment Middle -1538 kNm Moment Middle -2000 kNm Moment Total 4613 kNm Moment Total 4500 kNm Now the results from the hand calculation and the Diana model will be compared for the structure loaded by its self-weight. There can be seen from the results that the deflection from the model is larger than the deflection calculated by hand calculation, see figure 52 and table 65. This difference can be explained by the difference in schematization. The hand calculation formula will give good results is both sides of the beam is fully inclined. However in the model this is not the case. This results in a slightly different value. Kubilay Bekarlar - Master Thesis - 62 - August – 2016 The moments of the hand calculation and the Diana model also show some differences, this can be explained by the fact that the roof element acts as a continuous beam. Since the formula is an inclined beam on both sides, this gives different values for the hand calculation. However the total moment should be the same. This is indeed the case, see figure 52 and table 66 above. 11.1.2 Load case 2 – vertical loading on top of the structure The results from the model for the moment and the deflection of the roof element for load case 2 are given in figure 54 below. Figure 54: Left Moment distribution in the roof element, Right: Deflection of the roof element due to load case 2 Table 67: Calculation of the deflection LC2 Calculation of the deflection LC2 q 172 kN/m L 28,4 m E 35503000 h* b I kN/m 1,83 m 1 m 0,511 m 2 Hand calculation Deflection Diana model 0,016071 4 16,07 m Deflection 0,0255 mm 25,5 m mm Table 68: Moment hand calculation and Diana model Moment hand calculation and Diana model Hand calculation Diana model M1 11561 kNm M1 8000 kNm M2 11561 kNm M2 12000 kNm Moment Middle -5780 kNm Mmiddle -7500 kNm Moment Total 17341 kNm Mtot 17500 kNm For the load case where the structure is loaded by an external force on top, there can be seen that the results of the hand calculation and the Diana model show differences, see figure 54 and table 67. Just like explained in load case 1, this is due to the assumption of the hand calculation rule which assumed that both sides are fully inclined. However in the model this is not the case. The differences in the moments see figure 54 and table 68, can be explained by the fact that the roof element should be schematized as a continuous beam. The rule of thumb however schematizes the element as beam which is fully inclined on both sides. The total moment should be in the same order of magnitude. Kubilay Bekarlar - Master Thesis - 63 - August – 2016 11.1.3 Load case 3 – Vertical hydraulic loading on the bottom of the structure Figure 55: Moment distribution obtained from Diana for loadcase 3 The moment distribution and deflection of the floor element due to the hydraulic loading obtained from Diana is given in figure 55. There can be observed from the graphs that the moments and deflections are very small, which indicates an error value. This can be explained by the fact that the loading on an element connected with an interface element will result in an error value since it assumes that the loading is diverged directly into the bedding. The loading on an element connected with an interface element is schematized in figure 56 below. Figure 56: Hydraulic loading on an element connected to an interface element This meant that the model had to be adjusted in order to take the loading on the floor element into consideration. The interface element on the bottom was removed and 4 supports were installed instead. Doing so realistic moments and deflections were gathered from the model. Figure 57 Left: Moment distribution in the floor element Right Deflection of the floor element due to load case 3 Table 69: Calculation of the deflection LC3 Calculation of the deflection LC3 q 273 kN/m L 28,4 M E 34961000 h* 2,124 kN/m 2 M Kubilay Bekarlar - Master Thesis Hand calculation - 64 - Diana model August – 2016 b I 1 0,799 M m Deflection 0,0166 4 16,6 m Deflection mm 0,027 27,0 m mm Table 70: Moment hand calculation and Diana model Moment hand calculation and Diana model Hand calculation 11.1.4 Diana model M1 18349 kNm M1 -10000 kNm M2 18349 kNm M2 -18000 kNm Moment Middle -9175 kNm Mmiddle 13000 kNm Moment Total 27524 kNm Mtot 27000 kNm Load case 4 – Loading on the left side of the tunnel element In figure 59 below the moment distribution and the deflection of the wall element due to the external loading is given. The distributed load varying over the height of the tunnel can be analyzed in two steps. It can be seen as the sum of a constant distributed load and a varying triangular load over the height, see figure 58. Figure 58: Rule of thumb from mechanics Figure 59 Left: Moment distribution in the wall element, Right: Deflection of the wall element due to load case 4 For the displacement of the wall element there can be seen that this is very small, nearly zero see figure 36. The structure acts like a rigid body for the forces acting on the outer wall. For the hand Kubilay Bekarlar - Master Thesis - 65 - August – 2016 calculation the average distributed load will be taken, to check whether this small deflection can confirm the results of the model. The initially used average distributed load is: ( ) Table 71: Calculation of the deflection LC4 Calculation of the deflection LC4 q 293 kN/m L 9,65 M E 35035000 h* b I kN/m 2 1,682 M Hand calculation 1 M Deflection 0,396549 m Diana 0,000476 4 0,476 m Deflection mm << m << mm There can be seen that also the deflection of the hand calculation is very small, not even a half of a millimetre, see table 71. There can be concluded that both approaches do coincide. For the moment line however there are some differences. The moment at the bottom is much larger than the moment at the top of the structure. This can be explained as follows. First there is an increasing loading towards the bottom. This results in a larger moment at the bottom of the wall. Secondly the larger floor element and a stiffer connection results in a larger moment at the bottom side as well. Table 72: Moment hand calculation and Diana model Moment hand calculation and Diana model Hand calculation 11.1.5 Diana model M1 2274 kNm M1 2750 kNm M2 2274 kNm M2 -200 kNm Moment Middle -1137 kNm Mmiddle -2100 kNm Moment Total 3411 kNm Mtot 3375 kNm Load case 5 – Loading on the right side of the tunnel element The same loading is applied again, but this time on the outer wall on the right side. This means that the results are identical with an opposite sign. The same argumentation of the results as for load case 4 is also applicable here. The results are given in figure 60 below. Figure 60 Left: Moment distribution in the wall element, Right: Deflection of the wall element due to load case 4 Kubilay Bekarlar - Master Thesis - 66 - August – 2016 Table 73: Calculation of the deflection LC5 Calculation of the deflection LC5 q 293 kN/m L 9,65 m E 35035000 h* b I kN/m 1,682 m 1 m 0,396549 m 2 Hand calculation Deflection Diana 0,000476 4 0,476 m Deflection mm << m << mm Table 74: Moment hand calculation and Diana model Moment hand calculation and Diana model Hand calculation Diana model M1 2274 kNm M1 2750 kNm M2 2274 kNm M2 -200 kNm Moment Middle -1137 kNm Mmiddle -2100 kNm Moment Total 3411 kNm Mtot 3375 kNm 10.1.6 - Reaction forces validation In this section there will be checked whether the loading on the structure coincides with the reaction forces exerted by the interface on the structure. In figure 61 and figure 62 the reaction forces of the bedding is give. The response of the bedding for each load case is given in table 75. In which the total of these forces in the Y-direction should be equal to the total loading in the Ydirection, given in table 76. Figure 61: Reaction forces of the subsoil, Max. 0.969E5 Min. 0.206E6 As there can be seen in the figure above, also tensile forces are present in the subsoil. This is not possible, since the sobsoil cannot bear tensile forces. This figure was only obtained to check the vertical forces balance, whether the forces on the structure are equal to the forces of the subsoil on the structure. The interface was replaced by 4 supports below the floor element (also see 11.1.3). So also normal design loads values were present for the floor element. Kubilay Bekarlar - Master Thesis - 67 - August – 2016 Figure 62: Magnitude of the reaction forces over the width of the subsoil Table 75: Response of the bedding for each load case Loadset Total response in X - direction Total response in Y - direction LC 1 0 -0.7543E+07 N LC 2 0 -0.1055E+08 N LC 3 0 0.1675E+08 N LC 4 0.2827E+07 N 0 LC 5 -0.2827E+07 N 0 Resultant 0 -0.1343+07 N The resultant of the reaction force exerted by the bedding on the structure should be equal to the resultant of the loading on the bedding. This will be checked by summing up the loadings in the Y direction. Table 76: Hand calculation of the resultant force in the Y - direction Loadset Loading Y-direction Width loading Total loading in Y - direction LC 1 -7,543E+06 N - -0,7543E+07 N LC 2 -172000 N 61,35 m -0,106E+08 N LC 3 273000 N 61,36 m 0,168E+08 N LC 4 0 0 LC 5 0 0 Resultant -0,1344E+07 N As there can be seen in table 75 and table 76, the total of reaction forces equals the total of loading on the structure. Kubilay Bekarlar - Master Thesis - 68 - August – 2016 12 ANALYSIS RESULTS FROM THE SIMPLIFIED LINEAR ELASTIC ANALYSIS 12.1 Axial force distribution - All load cases (Lcc) In the next stage the axial forces in the elements are determined. This is the axial force as a result of all load cases (Lcc). There can be observed from figure 63 below that the axial force for the roof element is -1,35E6 N. Figure 63: Normal force distribution of the roof element For the floor element the axial force is determined as well. The value of this the axial force is 1,45E6 N, see figure 64. As there can be seen, this value is larger than the axial force in the roof element. This is due to the varying distributed load over the depth of the tunnel. Figure 64: Normal force distribution of the floor element Now there will be checked whether the total axial forces in the roof and floor element equals the force acting on the outer wall. ( ) Kubilay Bekarlar - Master Thesis - 69 - August – 2016 There can be seen that the results from Diana coincides with hand calculation. The axial force for the wall element is about -2,7E6 N, see figure 65 below. Figure 65: Normal force distribution of the wall element 12.2 Shear force distribution - Lcc First the shear forces gathered from the FEA model are checked whether the shear force capacity is exceeded or not. This is done for the roof, floor and wall elements. The shear force distribution over the roof element is given in figure 66 below. During the base case design stage the shear force capacity of 4659 kN/m1 was determined. From the results of the FEA model there can be concluded that the shear force capacity is not exceeded. Figure 66: Shear force roof element Kubilay Bekarlar - Master Thesis - 70 - August – 2016 The same steps are also performed for the floor element. In figure 67 below the shear force distribution for the floor element is presented. The shear force capacity calculated for the floor element is 5581 kN/m1. There can be seen that also the shear force in the floor element does not exceed the shear capacity. Figure 67: Shear force in the floor element In figure 68 below the shear force acting on the outer wall is given. The shear force capacity determined for the outer wall is 2594 kN/m1. From this figure there can be seen that the capacity is not exceeded. Figure 68: Shear force in the wall element 12.3 Moment distribution Lcc Also the moment distribution over the tunnel elements are also checked whether the moment determined with the FEA model does not exceed the moment capacity. First the moment development in the roof element is determined, see figure 69. The value of the moment in the roof element is compared with the moment capacity of the roof element. As determined in the base case design stage the moment capacity in the inclination and mid span, these values are respectively 17197 kNm/m1 and 12667 kNm/m1. There can be concluded that the moment capacity is not exceeded. Kubilay Bekarlar - Master Thesis - 71 - August – 2016 Figure 69: Moment distribution of the roof element The same check is done for the floor element. In figure 70 below the moment distribution for the floor element is given. Previously determined value for the moment capacity of the floor element is 20209 kNm/m1 and 12086 kNm/m1 respectively for the inclination and mid span. With these results there can again be concluded that the moment capacity is not exceeded. Figure 70: Moment distribution of the floor element The moment development is the outer walls is given in figure 71. The value for the moment capacity of the outer wall is 9537 kNm/m1 and 11670 kNm/m1, respectively for the inclination and mid span. Figure 71: Moment distribution of the wall element 12.4 Primary stress distribution Lcc In figure 72 below the primary stress distribution is given for the model with an interface element which represents the bedding. There can be seen that the stresses in the floor element are low compared with the roof element. This again has to do with the fact that the loads on the floor are directly diverted to the supports. Since the floor elements are connected with interface elements. Kubilay Bekarlar - Master Thesis - 72 - August – 2016 Figure 72: primary stress distribution in the global x – direction over the structure as a result of the total loading In order to solve this problem the tunnel is schematized without using an interface element, but rather straight forward with three supports constrained in Y – direction and one in X- and Ydirection. The resulting stress distribution is illustrated in figure 73 below. There can be seen that the largest positive stresses are there where the roof elements and the walls meet. The largest negative stresses on the other side are at the mid span of the roof element. For the floor element there can be seen that the largest positive stresses are at the center of the floor element. The largest negative stresses on the other hand are at the parts of the floor close to the connection with the walls. Figure 73: Primary stress distribution in the global x – direction over the structure as a result of Lcc constraint on top (without an interface element) 12.5 Principal stress distribution The principal stress is the maximum and minimum value of the normal stress at a specific point on a structural element. At the orientation in which the principal stresses occur the shear stresses are zero. The principal stresses are used because it gives a more realistic display of the stress distribution and direction. This is why Diana is asked to calculate the principal stresses from the primary stresses. In figure 74, the principal stresses for the tunnel cross section is given. Figure 74: Principal stress distribution in the global x – direction over the structure as a result of Lcc constraint on top (without an interface element) 12.6 Analysis of moment and shear capacity (fully connected composite) For the analysis of the SCS sandwich element there can be assumed that the steel plates and concrete either act independent, fully connected or partially connected. For this analysis the steel and concrete parts are assumed to be fully connected. In other words the connection will be infinitely stiff. This means that these elements will not slip relative to each other. As a result the Kubilay Bekarlar - Master Thesis - 73 - August – 2016 strain diagram over the cross section of the element will be linear. The stress distribution over the cross section of a composite material is not linear. Since the modulus of elasticity of steel and concrete are different. This explains the big jumps in the stress distribution over the cross section. A part of the stress distribution curve is zero, this is concrete tensile region. The stress is zero because the concrete is assumed to be cracked and does not contribute to the tensile strength of the structure. The strain and stress distribution diagram over the cross section is given in figure 75 below. Figure 75: Strain and stress distribution over the cross section of the SCS sandwich element In the next step the moment capacity of each element will be compared with the new design moments. The new unity check will be compared with the unity check of the base case design. The moment capacity and the unity check are given in table 77 and table 78. Table 77: Earlier determined moment capacity Bending capacity Roof Floor Walls outside inside outside inside outside inside Nsc, rd [kN] 12102 16943 9682 16943 9682 12102 Nst, rd [kN] 16943 12102 16943 9682 12102 9682 Ncu,rd[kN] 4841 -4841 7261 -7261 2420 -2420 x [mm] 308 308 369 369 291 291 Mpl,rd/m [kNm/m] 17197 12667 20209 12086 11670 9537 Table 78: Moment capacity of the base case Bending capacity Roof Floor Walls outside inside outside inside outside inside Med [kNm/m] 15247,4 10607,5 16247,4 11607,5 8029,1 0 Mpl,rd/m [kNm/m] 17197 12667 20209 12086 11670 9537 Unity Check 0,887 0,837 0,804 0,961 0,688 0 If the results in table 78 above are compared with the earlier calculated unity checks in table 79, there can be seen that the unity check decreases. Table 79: Moment capacity due to simplified linear elastic analysis Roof Floor Wall Out In Out In Out In M design [kNm] 14000 10000 15000 11000 9800 0 M capacity [kNm] 17197 12667 20209 12086 11670 9537 Kubilay Bekarlar - Master Thesis - 74 - August – 2016 Unity check 0,81 0,79 0,74 0,91 0,84 0 There can be concluded that the design moments of each element and for each section of the element, is smaller than the moment capacity of the element. In table 80 below the same steps are taken for the shear force capacity. Table 80: Shear capacity check Roof Floor Wall V design [kN] 3300 3400 1500 V capacity [kN] 4659 5581 2594 Unity check 0,71 0,61 0,58 From these results there can be concluded that also the shear capacity of the elements are not exceeded. 13 LINEAR ELASTIC ANALYSIS DETAILED MODEL 13.1 Schematization of detailed SCS sandwich tunnel model In this part there will be explained how the detailed model will be schematized. For the simple model the SCS sandwich element was schematized as a line element with a representative modulus of elasticity and a height of the element. In that case the cross section acts as one material instead of three layers of two different materials. However with this detailed model the SCS sandwich tunnel element will be modelled as it is designed in reality. This means that the steel parts for the inner side and outer side of the roof, floor and wall element have a specified thickness. The same holds for the diaphragms that connect the inner and outer steel plates. In figure 76, below the different elements of the tunnel are given. Figure 76: Tunnel cross section with different elements, with each their distinct dimensions (thicknesses). Next the Diana elements used and their configuration will be discussed in detail. The steel inner, outer and the diaphragm parts will be modelled by using the plain strain element CL9PE. This is a three node plain strain element. This shell element is chosen for the steel since it has a small height compared with its length, just like the steel plates applied. Another point is that the plain strain elements plain strain elements also have an infinite length in the axial direction. These elements give a good stress and strain distribution from where the internal forces can be calculated by integrating over the height. The three node pain strain element is illustrated in figure 77 below. Kubilay Bekarlar - Master Thesis - 75 - August – 2016 Figure 77: Three node plain strain element CL9PE The concrete inner core of a SCS sandwich cell is modelled with the CQ16E element, which is an eight node plain strain element. This element is square shaped and can be applied for all kind of analysis including linear, nonlinear and cracking. Also this element has a length which is infinitely long in its axial direction. This element is illustrated in figure 78. Figure 78: Eight node plain strain element CQ16E The stiffeners and studs which connect the steel and concrete should also be modelled. However they won’t be modelled physically, rather by making use of interface elements. For these interface elements a certain stiffness will be entered. The stiffness resembles the degree of connection between these two elements. In this case a high k value will be entered for the connection of the steel and concrete, because steel and concrete are initially assumed to be fully connected. In figure 79 below the applied interface element CL12I is schematized. Figure 79: Interface element CL12I As illustrated in figure 80 below, the steel plates are on all four sides of the concrete element CQ16E. Since the steel and concrete elements cannot be connected directly, four interface elements are applied on each side of the concrete square. This is the layout as it will be modelled in Diana. The dots in figure 80 are not the modelled points but the nodes of each element. These cell elements are repeated with different dimensions for the roof, floor and wall elements. Kubilay Bekarlar - Master Thesis - 76 - August – 2016 Figure 80: Layout of two SCS sandwich cells 13.2 Input IDIANA – Detailed linear elastic analysis 13.2.1 Geometry In this section there will be explained how the detailed model is constructed. First there will be started by entering the geometry of the tunnel cross section. Below in table 81 and table 82 the geometry entered in the model is tabulated. Table 81: Dimensions tunnel to be modelled Dimensions Width of one tunnel tube 27000 [mm] Total width of the tunnel 63100 [mm] Total height of the tunnel 11400 [mm] Inner height of the tunnel 7900 [mm] Table 82: Dimensions tunnel to be modelled Roof Floor Wall h [mm] – Total height of the element 1600 1900 1500 b [mm] – Unit width of the element 1500 1500 1500 ctc web [mm] – Center to center distance of diaphragm (web) 1500 1500 1500 The tunnel geometry as it is modelled is given in figure 81. As there can be seen the entire cross section is modelled in detail, where all connections are physically modelled except for the stiffeners and studs, as stated before for this interface is used. Kubilay Bekarlar - Master Thesis - 77 - August – 2016 Figure 81: Tunnel geometry 13.2.2 Boundary constraints The tunnel cross section is supported at four points below the floor element at places where the walls are connected with the floor. In the simplified model first interface elements where used, however there was seen that for the floor element the interface resulted in a reduced moment. It would mean that the floor element would be under dimensioned. That is why there is chosen for a point supports. The location of the supports is given in figure 82. Figure 82: Boundary constraints detailed model 13.2.3 Meshing Picking a proper mesh is important for the model. Proper in the sense that the mesh division is large enough to give an accurate result and that the mesh division is not too large to increase the calculation time without much contribution to improve the results. Taking this into consideration, the steel plates and concrete core are subdivided into 10. This also means that the interfaces between these elements have to be divided into 10. As for the vertical division of the interface element Diana provides a default value of 1 division. In figure 83 the divisions of a single SCS sandwich cell is illustrated. Figure 83: Meshing division of the lines After the geometry is divided the meshing is generated for the cross section, figure 84 below. Kubilay Bekarlar - Master Thesis - 78 - August – 2016 Figure 84: Mesh of the SCS cross section 13.2.4 Loads Permanent loads The loading on the tunnel cross section is the same as for the simplified model. Here also selfweight, soil and hydraulic loading has been taken into consideration. In figure 85 the loads on the tunnel are illustrated. Figure 85: Loading on the tunnel cross section 13.2.5 Variable loading Sea level rise The sea level rise acts as a variable loading on the tunnel structure. For the Arabian Gulf which is the region that was chosen for the base case design the sea level rise in the Arabian Gulf is 2,27 mm/year (A. Alothman and M. E. Ayhan 1). A service life time for the tunnel of 100 – 120 years, this corresponds with 27 cm. This is a rather low value, which will not have a significant impact on the overall distribution of internal forces. In other words the variable lading due to the sea level rise will be neglected. Traffic load The Load due to road traffic is determined according to Eurocode 1NEN-En 1991. In figure 86 below the layout of the traffic load on the structure is given. There will be investigated whether the design moment due to traffic loading is still smaller than the moment capacity. From the configuration of the variable traffic load is that this loading will reduce the value of the design load, because it works in the opposite direction of the governing permanent loading. That is why this 1 Sea level rise within the west of Arabian Gulf using tide gauge and continuous GPS measurements: A. Kubilay Bekarlar - Master Thesis - 79 - August – 2016 load will not be governing for the design, as well as for the optimization of the tunnel. Figure 86: Design load due to traffic according to Eurocode 1 This loading from the Eurocode is schematized in Diana as illustrated in figure 87 below. Figure 87: Distributed traffic load (upper), point loads due to traffic (lower) For the moment distribution obtained due to traffic loading, a reduction of the bending moment distribution can be observed. This because the loading on the tunnel cross section works favourable, that is why this loading is not taken into consideration for further design. 13.2.6 Accidental loading Sunken ship load In a very extreme case a ship can sink upon a tunnel element. This will result in an additional loading on the structure. The optimized structure should still be able to resist this loading upon the already present permanent loading. However the situation of the base case, no big ships enter the bay, only small private yachts which has a limited impact on the overall moment and shear force distribution. Kubilay Bekarlar - Master Thesis - 80 - August – 2016 Explosion and fire in one tunnel section Another accidental loading is the explosion of an object with one of the tunnel sections. This very short loading should be resisted by the structure as well. The loading due to an explosion is approximated by a distributed load of 100 kN/m2. In figure 88 the schematization of the load due to explosion is given. The permanent load acts in the opposite direction compared with the load due to explosion, this will only reduce the governing design moment. That is why this accidental load will not taken into account for the design optimization. With an explosion, it will also be likely that a fire will break out. To prevent the fire from reaching the steel plate of a SCS tunnel a fire protective layer is placed on the steel plate. However loading due to an explosion and/or fire inside a SCS tunnel should be research thoroughly (see recommendations 22.2). Figure 88: Distributed load due to explosion in one part of the tunnel cross section 13.3 Material and physical properties As stated before the connection between the steel and the concrete is achieved by interface elements. The degree of connection is determined by the stiffness constants entered in Diana. There is assumed that the stiffness of the connection is very large, this because the steel and concrete elements are initially assumed to be fully connected. That is why a very large stiffness value is entered into Diana. A value of 3e+13 N/m3 is entered for the linear and tangential stiffness of the interfaces, see table 83 for the material properties. Table 83: Material properties Elasticity / Linear stiffness Concrete 3,4e+10 [N/m ] Steel 2,1e+11[N/m ] Interface Passion ratio 2 Tangential stiffness 0,2 2 0,3 3 3 3,0e+13 [N/m ] 3,0e+13 [N/m ] The physical properties are also defined in this section, where the values below table 84 are entered in Diana. Table 84: Thickness steel plates applied Roof Floor Wall to [mm] – Thickness steel plate outside 35 35 25 ti [mm] – Thickness steel plate inside 25 20 20 hc [mm] – Height of concrete 1540 1845 1455 tweb [mm] – Thickness of the diaphragm (web) 20 20 10 Kubilay Bekarlar - Master Thesis - 81 - August – 2016 13.4 Composed elements As stated before the cross section consists of three layers. If the analysis of the model would be run now, the moments and force distribution of each element would be calculated individually. In order to get the forces and moments over the total structure, the stresses of the individual elements need to be integrated. There is a tool in Diana that composes the three layers as one and calculates the total moment over the cross section. This is the composed element CL3CM, figure 89. There are a few things that need to be adjusted to the geometry. A line in the center of the roof, floor and wall element should be made. The composed element CL3CM properties will be assigned to this line. Here after a thickness will be assigned to this line such that all three layers of the roof, floor and wall fall within this range. Composed element in the tunnel cross section is given in figure 90. Figure 89: Composed element CL3CM Figure 90: Position of the composed element (blue) in the cross section 14 LINEAR ELASTIC ANALYSIS OF DETAILED MODEL 14.1 Comparison of the simplified and detailed model (fully connected SCS) In this section the results of the detailed Diana model will be compared with the results obtained with the hand calculation and simplified Diana model. This is done to verify the model. In case there is difference in value, there will be explained why that is the case. As there can be seen in the title, the detailed SCS sandwich model is schematized as fully connected elements. This is done by increasing the linear and tangential stiffness of the connection between the steel and concrete to a high value. By doing so, the simplified and the detailed model can be compared better since the simplified model was also constructed with the assumption of fully connected elements. 14.1.1 Load case 1 – self weight of the structure The results obtained from Diana for the moment and the deflection of the roof element for load case 1 are given in figure 91 below. There can be seen that there is a kink in the left part of the moment line. This is the part within the wall and the nicely curved part is the moment development in the span of the cross section. Kubilay Bekarlar - Master Thesis - 82 - August – 2016 Figure 91: Left Moment distribution in the roof element, Right: Deflection of the roof element due to load case 1 Next step will be the comparison of the results obtained with the detailed Diana model with the hand calculation and the simplified model. In table 85 below the deflections are tabulated for the three cases mentioned. There can be seen from the results of the detailed model that the deflection for load case 1, is close to values obtained by hand calculation and the simplified model. Table 85: Deflection roof LC1 Deflection roof LC1 Hand calculation Deflection Diana simplified model 0,00427 4,27 m Deflection Diana detailed model 0,00675 mm 6,75 m Deflection 0,0053 mm 5,30 m mm The results for moment distribution of the roof element for load case 1 are given in table 86 below. There can be seen that the moment distribution for the hand calculation, simplified model and the detailed model differ. The difference between the simplified and detailed model can be explained by the fact that the simplified model takes the center to center (c.t.c) distance of the cross section, where the detailed model takes the actual dimensions. The c.t.c. span of the simplified model is 28,4 m whereas the real span is 27,0 m. Since this value is squared for the calculation of the moment, it has a noticeable impact on the overall moment distribution. The difference should be in the range of , which is around 11%. If the results are compared by taking this into account the difference can be justified. Table 86: Moment hand calculation and Diana model Moment hand calculation and Diana model Hand calculation 14.1.2 Diana simplified model Diana detailed model M1 3075 kNm M1 1800 kNm M1 1500 kNm M2 3075 kNm M2 3200 kNm M2 2300 kNm Moment mid -1538 kNm Moment mid -2000 kNm Moment mid -1700 kNm Moment tot 4613 kNm Moment tot 4500 kNm Moment tot 3600 kNm Load case 2 – vertical loading on top of the structure For load case 2 the same steps are repeated for the roof elements. The results for the deflection and the moment distribution can be seen in figure 92. Again the kink is due to the connection of the roof and wall. Kubilay Bekarlar - Master Thesis - 83 - August – 2016 Figure 92: Left Moment distribution in the roof element Right: Deflection of the roof element due to load case 2 First the deflection of the hand calculation, simplified model and the detailed model are compared. From the results presented in table 87 there can be concluded that the deflection obtained by the detailed model is close to the deflection of the simplified model, as well as the hand calculation. Table 87: Deflection roof LC2 Deflection roof LC2 Hand calculation Deflection Diana simplified model 0,0161 16,1 m Deflection Diana detailed model 0,0255 mm 25,5 m Deflection 0,0250 mm 25,0 m mm The moment distribution for all three methods is tabulated in table 88. There can be seen that the moments of the detailed model are little smaller than the moments gathered with the simplified model. Again this can be explained by the fact that the simplified model uses the c.t.c distance, while the detailed model uses the actual dimensions. The difference in approach accounts for a moment difference of 11%. Taking this into account there can be concluded that the results of the detailed model are correct. Table 88: Moment hand calculation and Diana model Moment hand calculation and Diana model Hand calculation 14.1.3 Diana simplified model Diana detailed model M1 11561 kNm M1 8000 kNm M1 5800 kNm M2 11561 kNm M2 12000 kNm M2 9800 kNm Moment mid -5780 kNm Moment mid -7500 kNm Moment mid -7500 kNm Moment tot 17341 kNm Moment tot 17500 kNm Moment tot 15300 kNm Load case 3 – Vertical hydraulic loading on the bottom of the structure The results of the deflection and moment distribution for the floor element are given in figure 93. Kubilay Bekarlar - Master Thesis - 84 - August – 2016 Figure 93 Left: Moment distribution in the floor element Right Deflection of the floor element due to load case 3 The results of the deflection in the floor element are given in table 89. There can be seen that the deflection of the detailed model is close to the deflection of the simplified model and the hand calculation. Table 89: Deflection floor LC3 Deflection floor LC3 Hand calculation Diana simplified model Deflection 0,0166 16,6 m Deflection Diana detailed model 0,027 mm 27,0 m Deflection 0,0245 mm 24,5 m mm Like in load case 1 and 2, the moment distribution of the detailed model for load case 3 is also smaller. This is also due to the c.t.c. approach of the simplified model. Table 90: Moment hand calculation and Diana model Moment hand calculation and Diana model Hand calculation 14.1.4 Diana simplified model Diana detailed model M1 18349 kNm M1 -10000 kNm M1 -5500 kNm M2 18349 kNm M2 -18000 kNm M2 -17300 kNm Moment mid -9175 kNm Moment mid 13000 kNm Moment mid 13200 kNm Moment tot 27524 kNm Moment tot 27000 kNm Moment tot 24600 kNm Load case 4 – Loading on the left side of the tunnel element In figure 94 below the moment distribution and deflection are shown for the left side wall for load case 4. Kubilay Bekarlar - Master Thesis - 85 - August – 2016 Figure 94: Left: Moment distribution in the wall element Right: Deflection of the wall element due to load case 4 From the results in table 91, there can be seen that the deflection of the side wall is 6,0 mm. This value is considerably larger than the deflection calculated with the hand calculation as well as the simplified model. Table 91: Deflection wall LC4 Deflection wall LC4 Hand calculation Deflection Diana simplified model 0,000476 0,476 m Diana detailed model Deflection mm << m << mm Deflection 0,006 6,0 m mm The moment distribution also has a different shape. The total moment that should be active over the height of the wall is there, but the moments at the intersection are different. Table 92: Moment hand calculation and Diana model Moment hand calculation and Diana model Hand calculation 14.1.5 Diana simplified model Diana detailed model M1 2274 kNm M1 2750 kNm M1 0 kNm M2 2274 kNm M2 -200 kNm M2 0 kNm Moment mid -1137 kNm Moment mid -2100 kNm Moment mid 2900 kNm Moment tot 3411 kNm Moment tot 3375 kNm Moment tot 2900 kNm Load case 5 – Loading on the right side of the tunnel element The results for load case 5 are presented in figure 95. Figure 95: Left: Moment distribution in the wall element Right: Deflection of the wall element due to load case 5 Kubilay Bekarlar - Master Thesis - 86 - August – 2016 Just as in load case 4, also here the deflection is larger than the deflection of the hand calculation and the simplified model. Results of the deflections for this load case are given in table 93. The moment distribution is given in table 94. The total moment is close to the hand calculation and the simplified model. Table 93: Deflection wall LC5 Deflection wall LC5 Hand calculation Diana simplified model Deflection 0,000476 0,476 m Deflection mm Diana detailed model << m << mm Deflection 0,004 m 4,0 mm Table 94: Moment hand calculation and Diana model Moment hand calculation and Diana model Hand calculation Diana simplified model Diana detailed model M1 2274 kNm M1 2750 kNm M1 1100 kNm M2 2274 kNm M2 -200 kNm M2 0 kNm Moment mid -1137 kNm Moment mid -2100 kNm Moment mid -2300 kNm Moment tot 3411 kNm Moment tot 3375 kNm Moment tot 2850 kNm 14.2 Axial, moment, shear force distribution and deflection 14.2.1 Axial force distribution – All load cases (Lcc) Now the axial force distribution in the roof, floor and wall elements are investigated as a result of all load cases, figure 96. Figure 96: Axial force distribution in the tunnel First the axial force in the roof element will be checked. The axial force in the roof has a value of 1600 kN, see figure 97. Kubilay Bekarlar - Master Thesis - 87 - August – 2016 Figure 97: Axial force in the roof element – Lcc The axial force in the floor element has a value of 1900 kN, see figure 98. Figure 98: Axial force in the floor element – Lcc The axial force in the wall element is around 3400 kN. This can be seen in figure 99. Figure 99: Axial force in the wall element – Lcc 14.2.2 Moment distribution Lcc For the next step the bending moment distribution is obtained as a result of all load cases. The shape of the total moment combination is presented in figure 100. Kubilay Bekarlar - Master Thesis - 88 - August – 2016 Figure 100: Bending moment distribution as a result of all load cases - Lcc The total bending moment distribution above is illustrated in more detail in the figures below. First the total bending moment in the roof element is discussed. There can be seen in figure 101 that the maximum bending moment in the roof element is at the intersection with the inner wall. The moment here has a value of 12 000 kNm. On the left hand side a kink is observed, this is the moment development at the intersection of the roof and the wall. Figure 101: Bending moment distribution roof - Lcc For the floor element the bending moment development is shown in figure 102. The governing moment is again at the intersection of the floor and the inner wall. At this spot the maximum moment has a value of 13 000 kNm. Figure 102: Bending moment distribution floor - Lcc The moment distribution in the wall is given in figure 103. There can be seen that the maximum bending moment in the wall is 10 000 kNm. Kubilay Bekarlar - Master Thesis - 89 - August – 2016 Figure 103: Bending moment distribution wall - Lcc 14.2.3 Shear force distribution Lcc In figure 104 below the total shear force distribution over the cross section of the tunnel is given. Figure 104: Shear force distribution due to all load cases - Lcc The shear force distribution in the roof element is given in figure 105. There can be seen that the maximum shear force occurring in the roof element is 3100 kN. Figure 105: Shear force distribution in the roof element - Lcc The shear force distribution the floor element is presented in figure 106, which has a maximum value of 3400 kN. Kubilay Bekarlar - Master Thesis - 90 - August – 2016 Figure 106: Shear force distribution in the floor element - Lcc In figure 107 below the shear force distribution in the wall element is presented. The shear force in the wall element has a maximum value of 1200 kN. Figure 107: Shear force distribution in the wall element - Lcc 14.2.4 Deflection as a result of all load cases The vertical deflection as a result of all load cases is illustrated in figure 108. As there can be seen the deflection is presented on a larger scale in order to make the deflection more visible. The maximum deflection of the roof element is about 32 mm, whereas the deflection of the floor element is 25 mm. Also the horizontal deflection of the wall elements is presented in figure 109, there can be seen that the maximum horizontal deflection is about 7 mm. Figure 108: Vertical deflection due to all load cases, Max 0,251E-1 Min -0,317E-1 (extreme scale) Kubilay Bekarlar - Master Thesis - 91 - August – 2016 Figure 109: Horizontal deflection due to all load cases, Max 0,2E-2 Min -0,693E-2 (extreme scale) 14.3 Analysis of the stress distribution 14.3.1 Analysis of stress in concrete core The stress distribution for the concrete inner core is given in figure 110 below. There has to be emphasized that this is the stress distribution for the case when the SCS sandwich elements are fully connected. In other words, the connection between steel and concrete has a high value for its stiffness. To account for the high stiffness a value of 3,0 e+13 N/m3 was entered in Diana. This resulted in the stress distribution over the cross section given below. First the concrete tensile stresses will be checked. In the previous calculations there was assumed that the concrete parts exposed to tensile forces were already cracked and no tensile force was acting in the concrete. There can be checked whether this approach is justified. In figure 110 the tensile forces in the concrete is given from orange all the way to red. The maximum tensile stress occurring in concrete is about 12 N/mm2. However the design value of the concrete tensile stress is 1,35 N/mm2. It means indeed that the concrete tensile part is cracked and will not be able to resist tensile forces anymore. For the concrete compressive stresses are given from the colour range of green till blue. The maximum compressive stress occurring in the cross section is nearly 22 N/mm 2. In the initial design the characteristic concrete compressive stress is 30 N/mm2. The design value of the concrete compressive force is 20 N/mm2. From the results presented in the figures below there can be concluded due to the governing loading cracks might occur in the concrete compression zone. Again there should be emphasized that this is true with the precondition that the steel and concrete are fully connected. Figure 110: Stress distribution in the concrete core, horizontal elements In figure 111, the stress distribution over the vertical elements is given. More or less the same can be said for the wall elements. The concrete parts in tensile will be cracked anyway, so they will not resist the tensile forces. As for the compressive stresses, some cracks might occur in the concrete compressive zone. A concrete with a higher compressive strength will resolve this problem. Kubilay Bekarlar - Master Thesis - 92 - August – 2016 Figure 111: Stress distribution in the concrete core, vertical elements 14.3.2 Analysis of stress in steel The stress distribution over the steel plates is given in figure 112 and figure 113 below. Again the tensile and compressive stresses are respectively given with orange/red and green/blue. There can be seen that the maximum tensile stress in steel is 124 N/mm2 and the maximum compressive stress is 143 N/mm2. Both stresses are smaller than the design yield stress of the steel applied, which is 323 N/mm2. There can be concluded that at no place of the cross section the yielding stress of the steel will be exceeded. Figure 112: Stress distribution in steel plates, horizontal elements Figure 113: Stress distribution in steel plates, vertical elements 14.3.3 Analysis of moment and shear capacity of a detailed fully connected composite element Also for the force distribution of the detailed model the moment and shear capacity will be checked. Since a large value for the stiffness of the connection is applied, this model can be assumed as fully connected. In other words the connection will be very stiff. This means that the slip between the concrete and steel plates will be small. As a result the strain diagram over the cross section of the element will be linear. The stress distribution over the cross section of a composite material is not linear, due to the difference in the E modulus. Concrete in tensile is assumed to be cracked and does not contribute to the tensile strength of the structure. The strain and stress distribution diagram over the cross section is given in figure 114 below. Kubilay Bekarlar - Master Thesis - 93 - August – 2016 Figure 114: Strain and stress distribution over the cross section of the SCS sandwich element Also for the detailed model the moment and shear capacity check will be done. The force distribution over the cross section is given in figure 115. Figure 115: Force distribution over the cross section of the SCS sandwich element Now the detailed design moments are compared with the moment capacity of each element. The results are presented in table 95. Table 95: Detailed model Roof Floor Wall Out In Out In Out In M design [kNm] 12000 9500 13000 11000 9800 0 M capacity [kNm] 17197 12667 20209 12086 11670 9537 Unity check 0,69 0,75 0,64 0,91 0,84 0 Table 96: Simplified model Roof Floor Wall Out In Out In Out In M design [kNm] 14000 10000 15000 11000 9800 0 M capacity [kNm] 17197 12667 20209 12086 11670 9537 Unity check 0,81 0,79 0,74 0,91 0,84 0 There can be concluded that the design moments of each element and for each section of the element, is smaller than the moment capacity of the element. In table 96 below the results of the moment capacity check are presented for the simplified model. There can be seen that with the detailed FEM model the unity check for the roof element is reduced from around 80% to around Kubilay Bekarlar - Master Thesis - 94 - August – 2016 72%. For the floor element the reduction of the unity check reduced from 83% to 77%. For the wall element the unity check has remained the same. The new unity check for the shear capacity, as a result of the detailed FEM analysis is given in table 97 below. Table 97: Detailed model Roof Floor Wall V design [kN] 3100 3400 1200 V capacity [kN] 4659 5581 2594 Unity check 0,67 0,61 0,46 Roof Floor Wall V design [kN] 3300 3400 1500 V capacity [kN] 4659 5581 2594 Unity check 0,71 0,61 0,58 Table 98: Simplified model From these results there can be concluded that also the shear capacity of the elements are not exceeded. Comparing the unity checks for the shear force capacity of the detailed model with the simplified model (see table 98), there can be seen that the unity check for the detailed model is slightly smaller for the detailed model. The unity check for the roof element has gone from 71% to 67%, for the floor element it remained the same, where for the wall element the unity check reduced from 58% to 46%. 15 PARTIALLY CONNECTED SCS SANDWICH MODEL In this section the model results will be analysed in case the stiffness between the elements is not infinitely large, but close to a value that is representative to a stud connection. Therefor first the linear and tangential stiffness of a stud connection has to be determined. 15.1 Determination of the linear and tangential stiffness of the interfaces As there was emphasized in the preliminary study of this research project, the ultimate strength of SCS composite sandwich elements depends on the strength and ductility of the shear connection. When the load-slip diagram of a stud is studied in more detail there can be noted that up to 0,5 Fmax, the stud behaves linear elastic. If the loading is increased further nonlinear slip will be observed. This is the horizontal plateau shape in the load-slip diagram given in figure 116 and eventually the stud fails at 95% of the ultimate force. In order to evaluate the performance of the composite elements, determining the true shear stiffness is important. Two different approaches have been used to determine the shear stiffness of the stud connection. One is the method used by Gelfi, Giuriani and the other by D.J. Oehlers, M.A. Bradford. Kubilay Bekarlar - Master Thesis - 95 - August – 2016 Figure 116: Force slip diagram, International Journal of Composite Materials (2012) 15.1.1 Approach 1 - Gelfi and Giuriani (1987) The analysis has been performed for designs with different stiffness values for the connection between the steel and concrete. There was observed that the stiffness value had impact on the overall force and moment distribution of the cross section. So in order to model a SCS sandwich connection as realistic as possible the stiffness of the connection need to be investigated in more detail. A stud embedded in concrete can be observed in figure 117. Figure 117: Stud connected to a steel plate embedded in concrete In order to determine the shear stiffness of a SCS connection, the behaviour of the studs needs to be studied in more detail. In the initial loading phase the stud resists the loading and retains its shape, see figure 118 on the left side. When the loading increases further the stud cannot retain its shape anymore and deforms, denoted with s of slip figure 118 right side. This slip value is needed in order to determine the shear stiffness of the connection. Figure 118: Deformation of a stud Kubilay Bekarlar - Master Thesis - 96 - August – 2016 The shear acts as a distributed load over the height of the stud. In order to determine the slip of the stud, the distributed shear force is schematized as a point load acting on the head of the stud. As the force acts on the stud, the concrete which surround the stud prevents the stud from bending to one side. In other words the concrete acts as a distributed spring that resists the bending of the stud, see figure 119. Figure 119: Schematization of a stud as a spring system The slip can be determined as follows. First the moment of inertia of the stud element needs to be determined. With the moment of inertia and modulus of elasticity of the stud and the stiffness of concrete, the value α can be determined. First the stiffness of concrete should be determined. Gelfi and Giuriani (1987) proposed a relationship between the modulus of elasticity of concrete and the stiffness. In which: β is a function of stud diameter and stud spacing, approximated with Next step is the determination of the moment of inertia of a stud. The diameter of the studs applied is 35 mm and the height is 100 mm. Now everything is known in order to determine √ α. This can be calculated as follows: √ In which the Es is the modulus of elasticity of the steel studs 2,1 * 10 5 N/mm2. Here after the angle of slip as a result of a concentrated load can be determined. With the angle of slip the total slip can be determined by multiplying the angle with the height of the studs. Kubilay Bekarlar - Master Thesis - 97 - August – 2016 In which h is the height of the stud, 100 mm. Finally the shear stiffness of the stud connection can be calculated. With the shear stiffness determined in more detail, a better understanding of the structural behaviour can be obtained. 15.1.2 Approach 2 - D.J. Oehlers, M.A. Bradford (1995) D.J. Oehlers, M.A. Bradford have drafted a formula with which the shear stiffness of the studs can be calculated. This formula is given below. ( ) In which: K is the shear stiffness of the stud connection Fmax is the ultimate load that a stud can bear d is the stud diameter mm α is a constant value that ranges from 0,08 – 0,16 – 0,24 fc is the compressive yield stress of concrete ( ) There can be seen that the shear stiffness of the studs differ a factor 3. The value that will be chosen for the stiffness of the connection should be within this range. 15.2 Detailed analysis of the stress distribution in concrete core Previously the distribution of the internal forces was obtained for the case where the SCS sandwich elements are fully connected. This way a better comparison could be made between the detailed and simplified model, since in both the elements were assumed to be fully connected. However for an even better approximation of the distribution of the internal forces, the shear stiffness of the studs should be applied. This value was determined in the previous section by two different approaches. With the newly determined stiffness the internal forces are determined again. In this section the stress distribution for the governing load cases will be analysed. The shear stiffness applied for a single cell of a SCS box is given in figure 120 below. Figure 120: Configuration of the applied stiffness for a single SCS cell Kubilay Bekarlar - Master Thesis - 98 - August – 2016 Stress distribution over the concrete core layer is given in figure 121 below. In this figure three critical spots can be identified for the roof and floor element. On the left hand side the connection with the outer wall, in the middle of the span and at the connection with the inner wall. These spots are critical since there are higher stresses at these locations than the rest of the cross section. In the section below these spots will be discussed in more detail. Figure 121: Stress distribution over concrete cross section 15.2.1 Stress and strain distribution in the roof Connection roof and outer wall Stress distribution at the point of the connection with the outer wall and the roof is given in figure 122. As there can be seen two stress concentration spots can be identified. In which the orange/red is the tensile stress and green/blue the compressive stress. A closer look is first taken at the upper tensile spot. Since the concrete tensile strength is low, tensile cracks will appear in the concrete tensile section. As there can be recalled from the previous sections, this was also taken into account for the capacity calculations in which the concrete tensile force was neglected. From the perspective of durability there can be stated that the cracks in the tensile section are not a problem since the concrete is in a confined space enclosed by steel. Intrusion of water or minerals in concrete will not take place. In figure 122 also the strain distribution can be observed. Also for the tensile zone there can be concluded that the tensile strain of concrete is exceeded. On the other side the compressive stresses locally exceed the design compressive stress of concrete, which is fcd 20 N/mm2. As a result of this local concrete plasticity and crushing of concrete might occur in the lower part of the concrete. From the strain distribution of the cross section there can be seen that indeed the highest strains are at the intersection of the roof with the wall. As a result of the tensile and compressive cracks in concrete the slip between the steel and concrete connection will increase, this will eventually lead to a reduction of the shear stiffness of the connection. Kubilay Bekarlar - Master Thesis - 99 - August – 2016 Figure 122: Stress (left) and strain (right) distribution of roof – outer wall connection Mid span roof For the mid span of the roof element there can be seen that on the upper side there are high compressive stresses and the lower side tensile stresses. Again the tensile stresses and strain at the bottom of the concrete exceed the low value of the concrete tensile strength. This will result in tensile cracks at the lower part of the concrete. These tensile cracks were also expected to occur. At the upper part of the concrete core the compressive stress is high, however the compressive design stress is not exceeded. The applied concrete class C30, with a characteristic compressive stress value of 30 N/mm2 and a compressive design stress value of 20 N/mm2. In figure 123 below, at the upper side of the concrete there can be seen that the compressive stress reaches as value of 17 N/mm2. Due to this no cracks / crushing will occur in the compressive zone as well. As there can be seen in the strain distribution over the cross section, the highest compressive strain happen at the top of the roof element and the highest tensile strain happened at the lower part. Figure 123: Stress (upper) and strain (lower) distribution of roof mid span Connection roof with the inner wall The location where the roof element connects with the inner wall also stress concentration points can be observed, see figure 124. The tensile stresses at the upper side of the concrete core show that the concrete tensile strength is exceeded. In other words tensile cracks will appear at this part of the concrete. On the other side high compressive stresses can be observed at the connection of the roof with the inner wall. The compressive stresses here exceed the concrete design stress and nearly reach the characteristic concrete compressive stress. There can be concluded that the concrete in these cells will be in a plastic state and local crushing of concrete will occur in the Kubilay Bekarlar - Master Thesis - 100 - August – 2016 compressive zone. This stress distribution is confirmed by the strain distribution over the cross section at the intersection as well, see figure 98 (lower picture). Figure 124: Stress (upper) and strain (lower) distribution of connection roof – inner wall 15.2.2 Stress distribution in the floor Connection floor and outer wall Stress and strain distribution of the connection between the floor and the outer wall is given in figure 125. From the stress and strain distribution of the corner cells there can be seen that the concrete will crack in the concrete tensile zone. At the upper side of the concrete core a high compressive stress and strain zone can be identified. Here the design concrete compressive stress is exceeded, which means that locally concrete plasticity and crushing of concrete will occur in the concrete compressive zone. Figure 125: Stress (left) and strain (right) distribution of floor – outer wall connection Floor mid span The stress and strain distribution at the mid span of the floor element is given in figure 126. As Kubilay Bekarlar - Master Thesis - 101 - August – 2016 there can be seen the concrete tensile stress and strain exceeds the design value. As a result the concrete is cracked in the tensile section. On the bottom side of the floor element an increasing compressive stress and strain can be identified. This stress is high but it does not exceed the design value of the concrete compressive stress. As a result no cracks / crushing will appear in the concrete compressive zone. Figure 126: Stress (upper) and strain (lower) distribution of floor mid span Connection floor with the inner wall figure 127 below the stress and strain distribution of the location where the floor is connected with the inner wall is given. The tensile section given in orange/brown, shows that the concrete tensile strength is exceeded here as well. It means that tensile cracks will occur at the lower part of the concrete core. During the calculations of the cross section this was also assumed to happen, since the concrete tensile strength is low. However what was not taken into account are the cracks that will occur at the concrete compressive section. Since there are high stresses and strain in the concrete compressive zone that will exceed the design value of the concrete compressive strength. Kubilay Bekarlar - Master Thesis - 102 - August – 2016 Figure 127: Stress (upper) and strain (lower) distribution of connection floor – inner wall 15.2.3 Stress distribution in the walls The vertical stress and strain distribution in the walls will be analysed in this part. First the outer wall will be investigated, see figure 128 (left). There can be seen that tensile stresses and strain are present at the outer side and the compressive stresses in the inner side. From this figure there can be seen that the concrete tensile stresses exceeds the concrete tensile strength, which denotes that concrete in these parts are cracked. As for the part that is exposed to compressive stresses there can be noted that the stress approaches the design value and at some places exceeds it. This is the case in the top and bottom cells of the outer wall. As a result concrete will be in the plastic state and crushing might occur, only locally. For the inner walls there can be stated that the stress in these elements are smaller. Some cracks will occur due to exceedance of the concrete tensile stresses, but the design concrete compressive stresses will not be exceeded. This can be observed in figure 128 (right) below. Figure 128: Stress (left) and strain (right) distribution of the outer and inner wall Kubilay Bekarlar - Master Thesis - 103 - August – 2016 15.2.4 Stress distribution in steel parts In this part the stress and strain distribution of the steel plates are discussed. There will be focused on the positions of high stresses and strains and there will be checked whether the steel will yield due to exceedance of its tensile /compressive strength. The stress and strain distribution of the steel is given respectively in figure 129 and figure 130 below. As expected, the high tensile and compressive zones are at the same positions as discussed in the section of concrete stresses and strain. From the distribution of the tensile stresses and strain in the steel there can be concluded that at no position in the steel structure the elastic tensile / compressive stresses and strain will be exceeded. Since the maximum tensile and compressive stresses respectively are 124 N/mm2 and 143 N/mm2. This is below the applied design yield strength of steel 322,7 N/mm2. Figure 129: Stress distribution of the steel Figure 130: Strain distribution of the steel 15.3 Principal vector stress analysis of concrete core The principal stresses are the components of the stress tensor when the basis is changed in such a way that the shear stress components become zero. Yielding occurs when the largest principal stress exceeds the yield strength. The principal stress analysis is in particularly useful for brittle material, like the concrete core. With the principal stress analysis a more accurate analysis of the concrete inner core has been made. The described distribution of the earlier stress analysis does coincide with the principal stress analysis, but this time with more detail and accuracy. For the roof – inner wall connection there can be seen that the tensile principal stresses at the upper side of the concrete core show that the concrete tensile strength is exceeded, figure 131. In other words tensile cracks will appear at this part of the concrete. On the other side also locally high compressive principal stresses can be observed. From the results of this analysis there was obtained that the highest compressive Kubilay Bekarlar - Master Thesis - 104 - August – 2016 stress is 29 N/mm2. This means that cracks will go to the plastic state and local crushing of concrete will occur, at the position illustrated in dark blue below. There can also be observed that the vectors are oblique due to the high shear forces at the connection with the inner walls. Figure 131: Roof – inner wall connection For the roof element at mid span there can be seen that vectors are horizontal due to the low shear forces, see figure 132. At the lower side of the mid span the concrete tensile strength is exceeded, which will cause cracks in the concrete. At the upper side of the roof element the concrete compressive stress is not exceeded. This indeed coincides also with the earlier stress analysis. Figure 132: Roof mid span Again there can be observed that the principal stress vectors at the connection with the outer roof are oblique due to the large shear forces. On the upper side of the connection with the outer wall there can be seen that the tensile strength of the concrete is exceeded. This means that cracks will occur in the concrete at this position figure 133. On the other hand there can be observed that there are two positions of compressive stress concentration. The principal stresses here locally do exceed the concrete compressive strength. This will result in local concrete plastic state and crushing of the concrete. Figure 133: Roof – outer wall connection Kubilay Bekarlar - Master Thesis - 105 - August – 2016 For the floor – inner wall connection there can be seen that the principal stresses are oblique, figure 134. In the lower part of this connection the concrete tensile strength is exceeded, which will cause tensile cracks. For the upper part of this connection there can be observed that on three positions the concrete compressive strength is exceeded. This will cause local concrete plasticity and crushing of concrete. Figure 134: Floor – inner wall connection Again the principal stress vectors at the mid span are horizontal due to small shear forces, see figure 135. As a result of exceedance of the tensile strength of concrete cracks will occur at the upper side of this element at the mid span. While the compressive principal stresses don’t exceed the design compressive strength of concrete. This means that no cracks will occur at the lower part of this element. Figure 135: Floor mid span For the connection of the floor element with the outer wall there can be seen that the tensile principal stress exceeds the concrete tensile strength so cracks will occur. While the concrete compressive strength will only be locally exceeded, at one point. This position is denoted in dark blue, see figure 136. Figure 136: Floor – outer wall connection Kubilay Bekarlar - Master Thesis - 106 - August – 2016 15.4 Conclusions of the stress analysis As there was seen at some spots the design concrete compressive stress is exceeded and the characteristic compressive stress value is approached. These spots can be seen in the cells where the roof and floor elements are connected with the inner and outer walls. The cracks in the tensile zone of the concrete are permissible because the concrete is in a confined space. As for the local crushing and cracking in the compressive zone, they will be compressed by the compressive force which will prevent the cracks from growing further. On the few places where the yielding strength is exceeded the internal forces will be redistributed. The cracks however may have impact on the degree of connection between the steel and concrete. Due to the cracks the shear stiffness of the steel and concrete connection can decrease. This may have impact on the overall stiffness of the structure. From the durability point of view these cracks have no impact on the durability of the structure since the concrete is situated in a confined space. On the other side the exceedance of the stress is only locally, which will result in a redistribution of forces. 16 ULTIMATE MOMENT CAPACITY INTERACTION AXIAL FORCE – MOMENT 16.1 Interaction axial force and bending moment The results of the detailed SCS model were first verified with the simplified model and the hand calculation. From these results there can be concluded that the detailed model is correct. One of the biggest advantages of such detailed model is that it gives a detailed insight in the distribution of the internal forces. It means that the design forces are determined more accurately and the uncertainties are less, which means that the structure can be designed more optimal. High water and soil pressures acting on the structure result in large axial forces in the elements. Taking these axial forces into consideration, new moment capacities can be determined that are higher since large axial forces result in an increase of the concrete compressive force, consequently also the moment capacity. In this section there will be checked whether the design can be optimized after gathering detailed insight in the internal force distribution. In order to do so first the additional moment capacity will be determined for each element due to the large axial loading. For the elements where large axial forces and moments are present, an interaction diagram should be made in order to determine the ultimate moment capacity for a certain axial force. This will be done for the roof, floor and wall element. 16.1.1 Roof element – Outside part (inclination) For the first element the steps for the interaction diagram will be discussed for each step. Since the interaction diagram is an iterative process there is chosen for a four point M – N interaction diagram which will give the required insight in the development of the moment capacity. Point A For this point the bending moment is zero and the roof is exposed to pure axial loading. ( ( )) ( ) Point B The axial loading for this point is zero, where the roof is exposed to pure bending moment, see figure 137. Kubilay Bekarlar - Master Thesis - 107 - August – 2016 Figure 137: Forces working on a cross section for pure bending moment Point C Compared with point B, for the determination of point C the neutral axis is mirrored relative to the central axis of the cross section. The extra compressive stresses in the concrete don’t contribute to the moment since those are symmetric around the central axis. This means that the Mrd,C = Mrd, B. However the extra compressive force adds to the axial force, see figure 138. ( ) Figure 138: Forces working on a cross section with bending moment and axial loading Point D For point D the neutral axis coincides with the central line of the cross section. The stresses in the steel plates do contribute to the normal force due to the difference in thickness, they could be left out of the equation if they were equally thick, see figure 139. On the other hand all stresses contribute to the internal moment. Figure 139: Forces working on the cross section when the neutral axis coincides with the central line Kubilay Bekarlar - Master Thesis - 108 - August – 2016 This way the values (4 points) for the interaction diagram of the roof element has been obtained. Now the diagram can be plotted, see figure 140. Figure 140: Interaction diagram N – M for the roof element at the inclination New moment capacity with the axial force acting on the element: 17196,7 + 326,6 = 17523,3 kNm The steps above are repeated for each element for the inclination and the mid span, values and diagrams can be observed below. 16.1.2 Roof element – Mid span Table 99: Roof element per meter width - Mid span Roof element per meter width - Mid span Point A Point B Point C Point D Mrd 0 kNm Mrd 12667 kNm Mrd 12667 kNm Mrd 21122 kNm Nrd 50164 kN Nrd 0 kN Nrd 25340 kN Nrd 12173 kN x 308 mm x - new 1292 mm Figure 141: Interaction diagram N – M for the roof element at mid span Kubilay Bekarlar - Master Thesis - 109 - August – 2016 New moment capacity with the axial force acting on the element: 12667 + 1076,5 = 13743,7 kNm 16.1.3 Floor element – Outside part (inclination) Table 100: Floor element per meter width - Mid span Floor element per meter width - Mid span Point A Point B Point C Point D Mrd 0 kNm Mrd 20209 kNm Mrd 20209 kNm Mrd 25110 kNm Nrd 54650 kN Nrd 0 kN Nrd 29920 kN Nrd 23290 kN x 369 mm x - new 1531 mm Figure 142: Interaction diagram N – M for the floor element at inclination New moment capacity: 20209 + 400 = 20609 kNm 16.1.4 Floor element – Mid span Table 101: Floor element per meter width - Mid span Floor element per meter width - Mid span Point A Point B Point C Point D Mrd 0 kNm Mrd 12086 kNm Mrd 12086 kNm Mrd 25110 kNm Nrd 54650 kN Nrd 0 kN Nrd 30220 kN Nrd 13609 kN x 369 mm x - new 1531 mm Kubilay Bekarlar - Master Thesis - 110 - August – 2016 Figure 143: Interaction diagram N – M for the floor element at mid span New moment capacity: 12086 + 1682 = 13768 kNm 16.1.5 Wall element - Outside part (inclination) Table 102: Floor element per meter width - Mid span Floor element per meter width - Mid span Point A Point B Point C Point D Mrd 0 kNm Mrd 11669 kNm Mrd 11669 kNm Mrd 16019 kNm Nrd 43622 kN Nrd 0 kN Nrd 23680 kN Nrd 16164 kN x 291 mm x - new 1209 mm Figure 144: Interaction diagram N – M for the wall element at inclination New moment capacity: 11669 + 915 = 12584 kNm Kubilay Bekarlar - Master Thesis - 111 - August – 2016 16.1.6 Wall element – Mid span Table 103: Floor element per meter width - Mid span Floor element per meter width - Mid span Point A Point B Point C Point D Mrd 0 kNm Mrd 9537 kNm Mrd 9537 kNm Mrd 16019 kNm Nrd 43622 kN Nrd 0 kN Nrd 23780 kN Nrd 12937 kN x 291 mm x - new 1209 mm New moment capacity: 9537 + 1704 = 11241 kNm Figure 145: Interaction diagram N – M for the wall element at mid span 17 OPTIMIZATION OF THE DESIGN USING DETAILED LINEAR STRUCTURAL ANALYSIS 17.1 Optimization due to detailed analysis of the internal forces In the previous section the new moment capacity is determined as a result of the interaction between the bending moment and the axial force. There can be seen from the interaction diagrams for each element that the moment capacity increases with an increasing axial force up to a certain level. After exceeding this level the moment capacity decreases again, which can be observed as a kink in the interaction diagram. The new design moment for each element is given in table 104 below. Table 104: Design moment, new moment capacity and unity check Roof Floor Wall Out In Out In Out In N [kN] 1550 1550 1900 1900 3400 3400 M design [kNm] 12000 9500 13000 11000 10000 7500 M new capacity [kNm] 17523 13744 20609 13768 12584 11241 Unity check 0,68 0,69 0,63 0,79 0,79 0,67 Kubilay Bekarlar - Master Thesis - 112 - August – 2016 In this table above there can be seen that with the detailed model and interaction between moment and axial loading, the moment capacity check is reduced. The values for the unity checks are around 70%, this means that the tunnel has a considerable rest capacity. This is why there will be checked whether the design can be more optimized for the moment capacity. The results in table 105 give the new determined steel thicknesses, the overall height of the element and the corresponding moment capacity. Table 105: New determined steel thickness Roof Floor Wall Out In Out In Out In tsc new [mm] 20 25 20 25 20 20 tst new [mm] 25 20 25 20 20 20 h new [mm] 1600 1600 1900 1900 1500 1500 Nsc [kN] 6455 8068 6455 8068 6455 6455 Nst [kN] 8068 6455 8068 6455 6455 6455 N [kN] 1550 1550 1900 1900 3400 3400 Ncu [kN] 1614 1614 1614 1614 0 0 x [mm] 311 311 371 371 292 292 M cap new [kNm] 12916 10996 15530 13218 10794 10794 As there can be seen the results give a reduction of the steel used. This resulted in a higher value of the unity check which now is around 0,85 - 0,9, see table 106. Which is a more optimal value for the unity check, than the previously determined value around 0,7, see table 104. In other words by getting to know the distribution of the internal forces more accurately the SCS tunnel structure can be designed more optimal. Table 106: Unity check of the moment capacity for the new steel thicknesses Roof Floor Wall Out In Out In Out In N [kN] 1550 1550 1900 1900 3400 3400 M design [kNm] 12000 9500 13000 11000 10000 7500 M capacity [kNm] 12916 10996 15530 13218 10794 10794 Unity check 0,93 0,86 0,84 0,83 0,93 0,69 This is the optimization step taken for the moment capacity check. The same can be done for the shear capacity. This will be governing for the concrete core and the steel diaphragms that connect the steel plates with each other. In table 107 below the new shear capacity per meter width of the cross section for each element is given. Kubilay Bekarlar - Master Thesis - 113 - August – 2016 Table 107: Calculations of the shear capacity for the new steel dimensions Dimensions Roof Floor Walls outside inside outside inside outside inside h [mm] 1600 1600 1900 1900 1500 1500 b [mm] 1500 1500 1500 1500 1500 1500 hc [mm] 1455 1455 1655 1655 1460 1460 tweb [mm] 15 15 15 15 10 10 ctc web [mm] 1500 1500 1500 1500 1500 1500 τrd,c,min [N/mm ] 0,54 0,54 0,54 0,54 0,54 0,54 Vrd,c [kN] 1180 1180 1342 1342 1184 1184 hs,web [mm] 1455 1455 1655 1655 1460 1460 Av,s [mm ] 21825 21825 24825 24825 14600 14600 Vrd,s [kN] 4067 4067 4626 4626 2720 2720 Vrd,c+s [kN] 5247 5247 5968 5968 3904 3904 Vrd new [kN/m1] 3498 3498 3979 3979 2603 2603 2 2 If the new shear capacities of the elements are compared with the previously determined shear capacities there can be concluded that the new shear capacities are smaller. Since the thickness of the diaphragm denoted as tweb in table 107 above has been reduced. The thickness of the diaphragms in the roof and floor was 20 mm, has become 15 mm. Design shear force has been determined in detail with the detailed analysis, which leaves the shear capacity check to be performed. The results can be observed in table 108. Table 108: Unity check of the shear capacity Roof Floor Wall Out In Out In Out In V design [kN] 3100 3100 3400 3400 1200 1200 Vrd new [kN/m1] 3498 3498 3979 3979 2603 2603 Unity check 0,89 0,89 0,85 0,85 0,46 0,46 The unity check for the shear force previously was around a value of 0,6. This means that the structure had a rest capacity which is considerable high. In other words the design was not optimized. After the internal forces are known in detail with the help of the detailed linear analysis, the optimization step could be made. As there can be seen in table 108, the unity check has now gone up to 0,85 – 0,90. This is a more optimal value for a design. Since the tunnel cross section has now been optimized for the moment and shear capacity checks, now the total quantity of steel can be determined per meter in the axial direction of the tunnel. These optimized values may not look significant at the first sight however they will be significant since these values are only done for one meter in the axial direction of the tunnel. Considering that immersed tunnel projects range from several hundred meters to several kilometres, it means that this type of optimization will be highly important. In table 109 below on the left side, the amount of steel applied for the tunnel designed by making use of framework program Matrixframe and hand calculations, denoted as old. On the right side the new determined dimensions of the steel plates are given by making use of a detailed FEM analysis. Kubilay Bekarlar - Master Thesis - 114 - August – 2016 There can be concluded that the total amount of steel applied for the design using the detail analysis is reduced significantly. Where in the previous design the applied steel in the cross section was 11,96 m2, has now reduced to 9,45 m2. This is a reduction of the steel applied with 21 %. In absolute values, this is a reduction of 2,51 m3 per meter in the axial direction. The optimization which leads to reduction of the steel applied with 21% is a significant improvement, since the steel is an expensive material and is one of the major expenses of a SCS tunnel project because it is applied on a large scale. Table 109: Steel area in the old situation (left) and new situation (right) Steel Area Old New 2 2 t [mm] l [mm] A[mm ] t [mm] l [mm] A[mm ] Outer side floor 35 63050 2206750 25 63050 1576250 Inner side floor 20 57250 1145000 20 57250 1145000 Outer side roof 35 63050 2206750 25 63050 1576250 Inner side roof 25 57250 1431250 20 57250 1145000 Outer side outer wall 25 11400 570000 20 11400 456000 Inner side inner wall 20 7900 316000 20 7900 316000 Outer side inner wall 20 7900 316000 20 7900 316000 Inner side inner wall 20 7900 316000 20 7900 316000 Web plate - ctc 1500 20 3450100 15 Total steel area 2604750 2 11957850 [mm ] 11,96 [m ] 2 2 9451250 [mm ] 9,45 [m ] 2 The amount of concrete applied in a SCS immersed tunnel is not further optimized because that amount is needed for the immersion and floating balance. In other words, if the amount of concrete in the SCS structure is reduced, than it has to be applied as ballast concrete in the cross section. Another reason is that the thickness of the concrete has impact on the moment capacity since the internal level arm of the forces in the steel become larger which correspondents with a higher moment capacity. This is the reason why no further optimization of the amount of concrete will take place. In the preliminary study of this research project there was made clear that there should be a balance between immersion and floating of the tunnel element. This means that with the new dimensions of the steel plates, checks need to be performed whether the tunnel element still fulfils the floating and immersion conditions. The results for the floating and immersion conditions are given in table 110 below. Table 110: Immersion and floating balance calculations Immersion calculation Old 3 New 3 3 3 Total areas [m ] [kN/m ] [kN] [factor] [m ] [kN/m ] [kN] [factor] Concrete 257,9 23,2 5984 1 267,2 23,2 6198 1 Steel 11,95 77 643 1 9,45 77 508 1 Ballast 50,2 23,2 1165,1 1 50,2 23,2 1165,1 1 Earth 0 7,5 0 1 0 7,5 0 1 Hydrostatic load 718,8 10,35 7439,3 1 718,8 10,35 7439,3 1 Kubilay Bekarlar - Master Thesis - 115 - August – 2016 Check 1,06 >1 Check 1,06 >1 Floating calculation 3 3 3 3 Total areas [m ] [kN/m ] [kN] [factor] [m ] [kN/m ] [kN] [factor] Concrete 257,9 23,5 6061 1 267,2 23,5 6277,9 1 Steel 11,95 77 920 1 9,45 77 727,7 1 Ballast 0 23,5 0 1 0 23,5 0 1 Hydrostatic load 711,5 10 7115 1 718,8 10 7187,7 1 Check 0,98 <1 Check 0,98 <1 From these results there can be concluded that the new SCS tunnel cross section fulfils the floating and immersion conditions. Kubilay Bekarlar - Master Thesis - 116 - August – 2016 Design and cost comparison of tunnel variants Kubilay Bekarlar - Master Thesis - 117 - August – 2016 18 TRANSVERSE PRESTRESSED (POST TENSIONED) REINFORCED CONCRETE TUNNEL 18.1 Roof element During the study of the base case design there was concluded that a large span of 27m is not feasible for a reinforced concrete tunnel element for which the maximum reinforcement ratio is applied. The limit for the maximum span is around 19 m. This has to do with the fact that the crack width of concrete exceeds the maximum allowable crack width. In order to make a valid comparison between a SCS sandwich tunnel and a reinforced concrete tunnel for a large span of about 27m, there has to be investigated which measures have to be taken for the reinforced concrete tunnel in order to make a span of 27m. The crack width can be reduced by increasing the axial force in the roof and floor element. This can be realized by applying prestressed tendons in the transverse direction of the tunnel. As it is known the longitudinal prestressed cables are cut after the immersion of the tunnel element. But the transverse tendons will remain in place after immersion. Aspects of attention are the protection of the prestressed tendons from the marine environment. This because the loss of a tendon can have great impact on the prestressed members since their ability to sustain load relies on the tensile strength on the tendons2. Also the friction of the concrete with the tendon will be reduced due to the attack of the tendon. This is the reason why the application of transverse prestressing of tunnel elements is not that common. First the moment distribution of the statically indeterminate system will be determined for the axial, prestress and variable loading. A computer program will be used to determine the moment line distribution, see figure 146, figure 147 and figure 148. Figure 146: Roof self-weight 2 Corrosion protection and steel concrete bond improvement of prestressing strand. M. Anderson, M. Oliva, M. Tejedor. December 2012. Kubilay Bekarlar - Master Thesis - 118 - August – 2016 Figure 147: Roof variable Figure 148: Roof total The tendon layout and force should be chosen such that the tensile strength of concrete should not be exceeded at t = 0. On the other hand the prestressing force should be high enough to prevent too high stresses tensile stresses in t = ∞. The layout of the tendon is given in figure 149 and table 111 below. Figure 149: Layout of the prestressed tendon Table 111: Dimensions of the roof and tendon Dimensions roof and tendon Height 1,6 m Width 1,0 m Ac 1,6 m 2 4 I 0,34 m z 0,8 m W 0,427 m 3 Kubilay Bekarlar - Master Thesis L1 - length big span 28,4 m f1 drape 0,615 m R1 – radius 1 163,9 m L2 – length short span 4,7 m f2 - drape 0,07 m R2 – radius 2 39,8 m - 119 - August – 2016 The radius of the tendon should have a minimum value of 15 – 20 m. From the tendon profile the radius can be calculated as follows: . In figure 150, the layout including the radius of the tendon profile is give. Figure 150: Prestressed tendon layout and the radius of the tendon profile Now the distributed loading due to prestressed tendon can be calculated. . The results are given in table 112 below. Table 112: Loading and the specifications concrete and tendon Loading and specifications qp1 – prestress loading big span 7,32 kN/m fck 35 N/mm 2 qp2 – prestress loading small span 30,19 kN/m fcd 23,33 N/mm 2 Self-weight 47,5 kN/m Es 210000 N/mm 2 External loading long term 140 kN/m Ec 34000 N/mm 2 Pm0 – initial prestress force 1200 kN Ep 195000 N/mm 2 fct 1,44 N/mm 2 As 2880 mm 2 The moment line distribution due to the prestress loading of an initial prestress force Pm0 of 1200 kN is given in figure 151. Figure 151: Roof prestress loading Kubilay Bekarlar - Master Thesis - 120 - August – 2016 The next step is the determination of the minimum and maximum tensile forces for the roof element. At t = 0 the prestressing force is at its maximum (no losses). The first calculation is done for point A, which is at the mid span of the roof element. For the working prestressing force Pm∞, there is assumed that Pm∞ = 0,85 Pm0, loss of 15%. Point A t=0 Bottom Top Point A t=∞ Bottom Top Now the governing prestressing force can be determined from the results presented above. The prestressing force should be in the range 17941 kN ≥ Pm0 ≤ 59516 kN. The results for position A and B (where the roof connects with the inner wall) gathered with a spreadsheet program are presented in table 113 and table 114. Table 113: Results of the prestress calculation in point A Roof - Point A t=0 Self weight t=0 Ma 2431 kNm Bottom Pm0 ≥ 3077 kN Mb 3406 kNm Top Pm0 ≤ 59516 kN t=0 Prestress t=∞ Ma 378 kNm Bottom Pm0 ≥ 17941 kN Mb 512 kNm Top Pm0 ≤ 168707 kN t = ∞ Variable loading Kubilay Bekarlar - Master Thesis - 121 - August – 2016 Ma 7167 kNm Mb 10040 kNm Table 114: Results of the prestress calculation in point B Roof - Point B t=0 Self weight t=0 Ma 2431 kNm Bottom Pm0 ≤ 25128 kN Mb 3406 kNm Top Pm0 ≥ 4026 kN Ma 378 kNm Bottom Pm0 ≤ 101009 kN Mb 512 kNm Top Pm0 ≥ 21273 kN t=0 Prestress t=∞ t = ∞Variable loading Ma 7167 kNm Mb 10040 kNm For spot B the prestressing force should be in the range 21273kN ≥ Pm0 ≤ 25128 kN. In the next stage the number of strands will be calculated. Since the prestressing force in point B is governing, this load will be used for further design of the prestressed tendon. The minimum prestressing force is known, which means that the required prestress tendon area can be determined, table 115. Table 115: Results of the required tendon area and the amount of strands to be applied Steel type Y1860S7 fpk 1860 N/mm 2 Pm0 21773 kN σ pm0 1395 N/mm 3 Ap 15607,89 mm Characteristic diameter 15,2 mm n strands in tendon 109,7 n 2 tendons 55 strands Cross section of steel 139 mm 2 2 Figure 152: Position of the tendon in the concrete cross section Kubilay Bekarlar - Master Thesis - 122 - August – 2016 From these calculations there can be observed that two tendons of 55 strands Y1860S7 has to be applied. The 55 strand tendon anchor is illustrated in table 115. Figure 153: Data and layout of a 55 strand tendon of Y1860S7 18.2 3 Floor element The hydraulic loading of the floor element works in the opposite direction of the loading on the roof element. If a curved tendon profile would be applied, than the large prestressed loading and the loading due to self-weight will act in the same direction. This means that in the initial situation, t=0 both loads will cause tensile stresses in the concrete tensile zone. Since there is no opposing load in the initial stage t=0, the concrete will eventually be cracked. This is the reason why an axial tendon will be applied, rather than a curved tendon profile. There will be examined whether to apply a centrically or an eccentrically prestressing tendon. The advantage of an eccentrically prestressing tendon is that there is also a moment introduced, which works favourable. For the floor element first the moment distribution due to self-weight and external hydraulic loading will be determined. This is again needed for the determination of the maximum and minimum prestress force value. The dimensions of the floor element are given in table 116. Table 116: Dimensions of the roof and the loading Dimensions roof and loading Height 1,9 m Self-weight 47,5 kN/m Width 1,0 m External loading long term 240 kN/m Eccentricity - e 0,25 m Ac 1,9 m 2 4 I 0,57 m z 0,8 m W 0,6 m 3 The moment line distribution of the floor due to dead load and hydraulic loading is given respectively in figure 154 and figure 155 below. 3 Data and picture from Freyssinet Prestressing, April 2010 Kubilay Bekarlar - Master Thesis - 123 - August – 2016 Figure 154: Moment line distribution of the floor due to dead load Figure 155: Moment distribution of the floor due to hydraulic loading Now the boundaries of the applied prestressing force are determined. There are two governing locations where the checks should be done. Position A at the mid span of the floor element and position B at the intersection of the floor element with the inner wall. Checks will be done for t=0 and t=∞. For the working prestressing force Pm∞, there is assumed that Pm∞ = 0,85 Pm0, loss of 15%. The check will be done for A and B simultaneously with a spread sheet program in order to determine the force and eccentricity which results in the smallest prestressing force. This is an iterative process. Again the tensile strength of concrete should not be exceeded. Eccentricity, e = -0,06 m (below the neutral axis) Pm0 = 41500 kN, the calculation of this prestress force is not presented here, rather in Appendix (28.5). Kubilay Bekarlar - Master Thesis - 124 - August – 2016 In figure 156 below a possible position of the tendon in the floor element is given. Figure 156: Possible position of the tendon in the floor element As stated before the tendon is placed slightly eccentrically (figure 157), which requires the smallest prestressing force. Now the minimum required amount of prestressing steel can be calculated. For the prestressing steel Y1860S7 with a σp0 of 1395 N/mm2 will be applied. The area prestressing steel is calculated as follows: Figure 157: Final position of the tendon The number of strands that have to be applied for the cross section is determined as follows, table 117. The position of the tendon in the concrete cross section is given in figure 158. Table 117: Results of the required tendon area and the amount of strands to be applied Steel type Y1860S7 fpk 1860 N/mm 2 Pm0 41500 kN 3 Ap 29749 mm n strands in tendon 214 N 4 tendons 55 strands σ pm0 1395 N/mm Characteristic diameter 15,2 mm Cross section of steel 139 mm Kubilay Bekarlar - Master Thesis 2 - 125 - 2 August – 2016 Figure 158: Position of the tendon in the concrete cross section Figure 159: Curved and eccentrically prestressed tendon layout for the roof and floor element Conclusion prestressed (post tensioned) immersed tunnel From the new design of a concrete tunnel element there can be concluded that a span of 27 m is not feasible with prestressed (post tensioned) roof and floor elements. In the initial reinforced concrete tunnel design there was seen that the crack width was the limiting factor. By adding prestressed tendons no cracks will occur. However the prestress tendons to be applied have a dimension of 510 mm by 420 mm. This makes it impossible to fit several of 55 strands of Y1860S7 tendons per meter width of the cross section. If those tendons were able to fit the cross section, there was seen that the moment and shear force capacity is also smaller than the design moment and shear force in ULS. On the other side there was seen from the analysis that large axial forces were present. In order to bear these large axial forces, high strength concrete is required. From this analysis there is seen that a transversely prestressed reinforced concrete tunnel is not a feasible solution for a tunnel with a large span in the transverse direction. Kubilay Bekarlar - Master Thesis - 126 - August – 2016 19 STEEL SHELL TUNNEL 19.1 Variant 1 In this section there will be investigated if a span of 27 m is feasible for a steel shell tunnel. If a span of 27 m is not feasible with a normal steel shell tunnel, there should be investigated which measures there need to be taken in order to fulfil the condition for a large span. But first the steel shell tunnel element will be described in little more detail. As the name of the steel shell tunnel says so, the tunnel consists of a steel shell on the outer side. This is also the first part of the tunnel that will be constructed, see figure 160. After the steel shell has been constructed the reinforced concrete inner section will be constructed. Some roof elements of a steel shell tunnel are designed as a reinforced concrete part without a steel shell on the outer side. However this would be no different for the length of the span from that of a reinforced concrete tunnel element as was seen for the base case design. Figure 160: Construction of the steel shell of a steel shell tunnel element. In order to see the difference between the steel shell and a reinforced concrete tunnel element, also the roof element is designed as a steel shell element. Doing so the boundary condition that the concrete cover has to be 75 mm can be ignored, since the concrete is not exposed to marine conditions. The reinforced concrete part is exposed to normal humid conditions. In table 118 below the environmental class and material properties are given. Table 118: Environmental class and the material properties Environmental class XC1 / XS2 fcd = 30,0 N/mm² εc;3 = 1,75 ‰ Concrete class C35/45 fyd = 434,78 N/mm² εu;3 = 3,5 ‰ Reinforcement steel B500B Es = 200000 N/mm² εud = 45 ‰ wmax 19.1.1 0,3 mm Floor element First the floor element is designed. The dimensions of the floor element and the design forces in ULS and SLS are given in table 119 below. Table 119: Dimensions of the floor element and the loading on the floor element Dimensions and loading Width 1000 Kubilay Bekarlar - Master Thesis mm - 127 - August – 2016 Height ULS SLS 1900 mm Md 16620 kNm/m Nd -2040 kN/m Vd 3078 kN/m Nd,vd -2040 kN/m Mrep 12976 kNm/m Nrep -1774 kN/m Tensile zone As stated before, the steel shell tunnel has a steel shell on the outer side of the tunnel element and reinforced concrete on the inner side. In table 120 the amount of reinforcement applied on the inner side of the tunnel. Table 120: Amount of steel applied on the inner side Layer 1st layer 2nd layer 3rd layer Amount Diameter 10,00 Ø 10,00 Ø 10,00 Ø Position 40 mm distance layers 50 mm distance layers 50 mm 40 mm 40 mm Total Area 1773,0 [mm] 12566 [mm²] 1683,0 [mm] 12566 [mm²] 1593,0 [mm] 12566 [mm²] 37699 [mm²] 1683,0 [mm] Compressive zone In table 121 the thickness of the steel plate and the total steel area per meter width is given. Further in table 122 the amount of stirrups applied is given. Table 121: Dimension of the steel plate Thickness plate Steel shell Area 30 [mm] 30000 [mm²] Table 122: Amount of stirrups applied Stirrups 1st Ø 16 mm - 150 mm 2 pcs Asw;1 2,68 mm²/mm Asw,tot 2,68 mm²/mm Normal stress check The first check is whether the normal stresses in the cross section does or does not exceed the normal stress capacity of the cross section. From the result in table 123 there can be stated that the maximum capacity of the cross section is not exceeded by the design force. Kubilay Bekarlar - Master Thesis - 128 - August – 2016 Table 123: Normal stress check Normal stresses Calculation of stresses σc;top fcd -28,7 N/mm² -30 N/mm² Unity check 0,96 Moment capacity check Now the moment capacity check is performed. In table 124, the compression zone height in ULS is given along the strains in the cross section. Furthermore the strain and force distribution in ULS over the cross section can be seen in figure 161. Table 124: Results of strains calculation Calculation of strains xu 237,41 e'c;u mm -3,5 ‰ es1 22,63 ‰ es2 21,31 ‰ es3 19,98 ‰ es4 -3,48 ‰ Figure 161: Strain distribution and force distribution in ULS of the cross section Since the forces in the cross section are known, now the moment capacity of the cross section can be calculated. The results are given in table 125. Table 125: Moment capacity calculation of the cross section and the unity check Calculation of forces Calculation of internal equilibrium Effective depths N'cd;1 -5341,94 kN MN'cd;1 -493,22 kNm Ns1 5463,63 kN MNs1 9687,03 kNm ds1 1773 mm Ns2 5463,63 kN MNs2 9195,30 kNm ds2 1683 mm Kubilay Bekarlar - Master Thesis - 129 - August – 2016 Ns3 5463,63 kN MNs3 8703,57 kNm ds3 1593 mm Ns4 -13089 kN MNs4 -13,08 kNm ds4 1 mm Nd 2040 kN MNd 1938 kNm ds5 22,25 mm Total 0 kN MRd 29017,61 kNm Unity check 0,58 Shear capacity check The shear capacity check for the situation with and without shear reinforcement is given in table 126 below. Table 126: Results of the shear forces calculation in combination with normal forces Shear forces in combination with normal forces Acting forces Bearing capacity cross section without stirrups VEd 3078 kN CRd,c 0,12 Nd,Vd -2040 kN k 1,34 ρl 0,02 Bearing capacity cross section with stirrups k1 0,15 cot θ = 2,14 scp 1,074 N/mm² VRd,c 1420 kN Unity check 2,17 θ 25 ° a 90 ° VRd,s 3876 kN VRd,max 7151 kN Unity check 0,79 Crack width control Finally the crack width control will be performed for the steel shell tunnel. The results of the calculation can be seen in table 127. Table 127: Results of the crack width calculation Calculation of crack width εsm - εcr 0,914751 ‰ s1 100 mm s1,max 555 mm 407,2538 mm ae 5,555556 - sr,max ρp,eff 0,069491 - k1 0,8 - mm k2 0,5 - mm² k3 3,4 - 0,425 - heff 542,5 Ac,eff 542500 fct,eff 3,795447 N/mm² k4 ξ1 1 - φeq 40 kt 0,4 - kx 1 wk Kubilay Bekarlar - Master Thesis 0,372536 - 130 - mm mm August – 2016 wmax 0,3 mm Unity Check 1,24 From the calculations there can be seen that the steel shell tunnel element does not fulfil the condition of crack width control. Several steps were taken in order to fulfil this condition. By increasing the reinforcement ratio the crack width becomes smaller, doing so the maximum reinforcement ratio is exceeded. The reinforcement needed is 3%, which is too high and not permitted in order to prevent brittle failure. Another aspect that influences the crack width is the diameter of the reinforcing steel. By increasing their number and decreasing the diameter, there was tried to fulfil the crack width condition. However there was seen that still the crack width condition was not met. A concrete cover of 91 mm is applied, which is the 75 mm cover and the additional 16 mm of the stirrup diameter. This is a boundary condition demanded by the client (reference project). If the cover would be reduced to 60 mm the crack width control check would fulfil the precondition. The steel plates for a steel shell are applied on the outer side of the floor and wall elements. As stated before, the roof element which is normally executed as a reinforced concrete element will also be designed with a steel plate on the outer side. This way the concrete side is only exposed to the inner environment. This also means that the client would drop the demand of a 91 mm cover on the reinforcing steel. Table 128: Exposure class related to environmental conditions in accordance with EN 206-1 (table 4.1) 2 Corrosion induced by carbonation XC1 Dry or permanently wet Concrete inside buildings with low air humidity. Concrete permanently submerged in water XC2 Wet, rarely dry Concrete surfaces subject to long-term water contact. Many foundations XC3 Moderate humidity Concrete inside buildings with moderate or high air humidity. External concrete shelter from rain XC4 Cyclic wet and dry Concrete surfaces subject to water contact, not with exposure class XC2 Table 129: Values of minimum cover Cmin, dur requirements with regard to durability for reinforcement steel in accordance with EN 10080 (Table 4.4N) Environmental requirement for Cmin,dur [mm] Exposure class according to table 4.1 Structural X0 XC1 XC2/XC3 XC4 class S5 15 20 30 35 S6 20 25 35 40 XD1/XS1 XD2/XS2 XD3/XS3 40 45 45 50 50 55 Now the new concrete cover can be determined. The new thickness of the concrete cover is 35 mm + 16 mm = 51 mm this will be rounded up to 60 mm. Now the crack width check is performed again and the result is given in table 130 below. Kubilay Bekarlar - Master Thesis - 131 - August – 2016 Table 130: Results of crack width calculation Calculation of crack width εsm - εcr 0,930643 ‰ s1 100 mm ae 5,882353 - s1,max 400 mm ρp,eff 0,081073 - sr,max 287,8747 mm heff 465 mm k1 0,8 - Ac,eff 465000 mm² k2 0,5 - fct,eff 3,209962 N/mm² k3 3,4 - ξ1 1 - k4 0,425 - kt 0,4 - φeq 40 mm kx 1 - wk 0,267909 mm wmax 0,3 mm Unity Check 0,89 Now the same calculation steps are performed for the roof element. 19.1.2 Roof element The same steps as been performed above for the floor element are now performed for the roof element. Table 131: The dimensions and the forces acting on the roof element Dimensions and forces C50/60 B500B Width 1000 mm Height 1800 mm Md 16342 kNm Nd -1295 kN ULS Vd 3027 kN -1295 kN Mrep 13316 kNm Nrep -1126 kN Nd,vd SLS Table 132: Layout and amount of the reinforcement Tensile zone 1st layer 12 Ø 40 2nd layer 9 Ø mm distance between layers: 50 40 mm Kubilay Bekarlar - Master Thesis - 132 - ds;i As;i [mm] [mm²] 1713 15079,64 1623 11309,73 mm August – 2016 distance between layers: 50 3rd layer 10 Ø 32 mm mm Totals 1537 8042,477 1642,328 34431,86 Table 133: Thickness and area of the steel plate applied Compressive zone Thickness plate Area Steel shell 30 30000 [mm] [mm²] Table 134: Amount of stirrups applied Stirrups 1st Ø 16 mm - 150 mm 2 pcs Asw;1 = 2,68 mm²/mm Figure 162: Strain distribution and force distribution in ULS of the cross section Table 135: Overview of the results of the unity checks Unity Checks MSd 16419,7 kNm MRd 25580,52 kNm VEd 3027 kN VRd,c 1273 kN VRd,s 3695 kN VRd,max 6816 kN wk 0,276031 mm wmax 0,3 mm σc;top -30,9824 N/mm² fcd -33,3333 N/mm² Kubilay Bekarlar - Master Thesis xu uc= 0,64 127,5484 mm ε'bu -3,5 ‰ εs1 43,50569 ‰ uc= 2,38 Stirrups required uc= 0,82 Θ 25 ° Α 90 ° x 581,4342 mm σs;1 250,9991 N/mm² uc= 0,92 uc= 0,93 - 133 - August – 2016 Now the floating and immersion check will be done, see Table 136 and Table 137. Table 136: Results of the immersion calculation Immersion calculation Total areas Concrete Steel Ballast Earth Hydrostatic load 3 [m ] 3 [kN/m ] [kN] [factor] 285,44 23,20 6622,09 1,00 6,01 77,00 462,47 1,00 61,02 23,20 1415,66 1,00 0,00 7,50 0,00 1,00 760,49 10,35 7871,02 1,00 [kN] [factor] height 1,13 Check 1,08 >1 Check 0,94 <1 Table 137: Results of the floating calculation Floating calculation Total areas Concrete 3 [m ] 3 [kN/m ] 285,44 23,50 6707,72 1,00 Steel 6,01 77,00 462,47 1,00 Ballast 0,00 23,50 0,00 1,00 760,49 10,00 7604,85 1,00 Hydrostatic load By increasing the height of the roof element the crack width condition is met. The new height of the roof element is 1,8 m instead of 1,6 m. This however has impact on the immersion and floating conditions. Due to this change the floating and immersion conditions are initially not met. Which means that the cross sectional dimensions has to be adjusted. In order to fulfill the floating and immersion conditions the amount of air in the tunnel cross section has to be increased. This also means that the height of the tunnel will be increased. The inner height of the tunnel increased from 7,9 m to 8,4 m. Doing so the total height of the tunnel has become 12,1 m. There can be seen that by adjusting the tunnel dimensions to the new conditions the floating and immersion conditions are fulfilled again. However there should be taken into account that more ballast has to be applied to fulfill the condition. The weight of ballast concrete/water that has to be applied for the new condition is 1416 kN. This means that during the immersion process 142 m 3 ballast water has to be applied. It accounts to 71 m3 water in each side of the tunnel. This can be realized by a ballast tank of 6 x 6 x 2 m. The designed steel shell tunnel element is illustrated in figure 163 and figure 164. Kubilay Bekarlar - Master Thesis - 134 - August – 2016 Figure 163: Drawing of the cross section of a steel shell tunnel element (half of the cross section until the symmetry axis) Figure 164: Detail of a steel shell tunnel, floor element 19.1.3 Amount of materials applied variant 1 Now the amount of materials applied for the steel shell tunnel will be quantified. First the length over which the shear reinforcement has to be applied will be calculated. These results are given in table 138 and figure 165 below. Table 138: Length over which stirrups will be applied Length of stirrup Roof Floor Shear capacity without stirrups 1273 kN Design shear force 3027 kN Length over which stirrups needed 7,8 m Shear capacity without stirrups 1420 kN Design shear force 3078 kN Length over which stirrups needed 7,3 m Kubilay Bekarlar - Master Thesis - 135 - August – 2016 Figure 165: Illustration of the length over which stirrups will be applied Since the length over which the stirrups are needed is known, now the amount of stirrups to be applied can be calculated. The quantity and the specifications of the stirrups applied for each element is given in table 139. Table 139: Amount of stirrups applied Amount of stirrups applied Roof Length over which stirrups needed Ø 16 – 150 Floor 2 pcs h roof 1800 mm Volume per stirrup 1125936 mm Amount of stirrups applied 208 Total stirrup area 0,234 m Length over which stirrups needed 7,3 m Ø 16 – 150 Walls 7,8 m 3 2 pcs h floor 1900 mm Volume per stirrup 1166159 mm Amount of stirrups applied 208 Total stirrup area 0,233 m Length over which stirrups needed 1,6 m Ø 16 – 150 3 3 2 pcs b wall 1500 mm Volume per stirrup 1005309 mm Kubilay Bekarlar - Master Thesis 3 - 136 - 3 August – 2016 Amount of stirrups applied 22 Total stirrup area 0,044 m Total amount stirrup reinforcement /m 0,52 m 3 3 After the amount of stirrups is determined the amount of tensile reinforcement will be determined. The amount and specifications of the tensile reinforcement is given in table 140 below. Table 140: Amount of tensile reinforcement applied Amount of tensile reinforcement applied Floor Tensile reinforcement 10 - Ø 40 x 3 Total area 37699 mm 2 Total reinforcement volume 2,04 m Roof 3 Tensile reinforcement 12 - Ø 40 9 - Ø 40 10 - Ø 32 Total area 34432 mm 2 Total reinforcement volume 1,86 m Walls 4 - Ø 32 Total area 3217 mm 3 2 Total reinforcement volume 0,35 m 3 3 Total amount tensile reinforcement /m Total reinforcement volume 4,25 m /m The amount of steel plate applied is given in table 141. Table 141: Amount of steel plate applied Amount of steel plate applied Thickness Volume Roof 30 mm 1,89 m 3 Floor 30 mm 1,89 m 3 Walls 30 mm 0,48 m 3 3 Total amount of steel plate applied/m 4,25 m /m The quantity of concrete applied to this tunnel is given in table 142. Table 142: Amount of concrete applied Amount of concrete applied Thickness Volume Roof 1900 mm 119,7 m 3 Floor 1800 mm 113,4 m 3 Walls 1500 mm 45,82 m 3 Kubilay Bekarlar - Master Thesis - 137 - August – 2016 3 Total amount of concrete applied /m 278,92 m /m The dimensions and the quantity of the stiffeners applied are given in table 143 below. Table 143: Amount of steel stiffeners applied Amount of steel stiffeners applied h×l×t Volume Roof 100 × 60 × 30 mm 0,40 m 3 Floor 100 × 60 × 30 mm 0,40 m 3 Walls 100 × 60 × 30 mm 0,135 m 3 3 Total amount of steel stiffeners applied /m 0,935 m /m Finally the amount of studs applied per meter is given in table 144. Table 144: Amount of shear studs applied Amount of shear studs applied Roof Diameter Height Min. ctc Max. ctc Height stud head 12 mm Volume 1440 mm Diameter stud head 45 mm 30 mm 360 mm 45 mm 0,41 m 3 Floor 30 mm 360 mm 45 mm 1440 mm 45 mm 12 mm 0,41 m 3 Walls 32 mm 384 mm 48 mm 1536 mm 48 mm 12,8 mm 0,214 m 3 Total amount of shear studs applied /m 19.2 3 1,04 m /m Variant 2 As there was seen in the previous variant of the steel shell tunnel with a maximum reinforcement ratio of close to 2% the height of the roof element had to be adjusted. Which also meant that the cross sectional dimensions of the tunnel element had to be adjusted. In order to fulfill the immersion condition more ballast has to be added. 19.2.1 Roof element Another option for the design of a steel shell tunnel is by applying a steel cover on the inner side, this way the crack width is not the limiting factor anymore. Doing so the cross sectional dimensions don’t have to be adjusted and the applied reinforcement can be reduced. In other words the moment, shear or normal force capacity will be governing. In table 145 below the design loads for the roof element is given. Table 145: Dimension and design loads on the roof element Dimensions and forces C60/75 B500B ULS Width 1000 mm Height 1600 mm 16342 kNm Md Kubilay Bekarlar - Master Thesis - 138 - August – 2016 SLS Nd -1295 kN Vd 3027 kN Nd,vd -1295 kN Mrep 13316 kNm Nrep -1126 kN The amount of reinforcement, steel thickness and stirrups applied is given in table 146, table 147 and table 148 below. Table 146: Amount and position of the tensile reinforcement Tensile reinforcement 1st layer 11 Ø 32 mm distance between layers: 2nd layer 10 Ø 32 10 Ø 32 mm 50 mm mm distance between layers: 3rd layer 50 mm Totals ds;i As;i [mm] [mm²] 1517 8847 1427 8042,4 1345 8042,4 1437,6 24932 Table 147: Amount of steel shell applied Compressive zone Thickness plate Area Steel shell 30 30000 [mm] [mm²] Table 148: Amount of stirrups applied Stirrups 1st 16 mm - 95 mm 4 pcs Asw;1 = 8,47 mm²/mm Now the checks for the roof element can be performed and the results are given in table 149. Table 149: Overview of the results of the unity checks Unity Checks MSd 16411,07 kNm MRd 16585 kNm uc= 0,99 VEd 3027 kN Stirrups required VRd,c 1289 kN uc= 2,35 VRd,s 4775,912 kN 11800 kN VRd,max wk wmax 0,47 mm 0,3 mm Kubilay Bekarlar - Master Thesis uc= 0,64 uc= 1,57 - 139 - August – 2016 αc;top -39,1109 N/mm² -40 N/mm² fcd uc= 0,98 Steel plates are placed on the inner side, which makes the crack width check irrelevant. This way the crack width control is not the limiting factor anymore, since the concrete is not exposed to external environment. Where the reinforcement ratio of the previous case was close to 2,0% in the roof element, this value has now been reduced to 1,55% and the thickness of the roof element still remains 1,6 m. Eventually the final analysis will reveal which variant is more feasible from the material / cost point of view. 19.2.2 Floor element The same calculations will be performed for the floor element of the steel shell tunnel variant 2. In table 150 the design loads for the floor element can be observed. Table 150: Dimension and design loads of the floor element Dimensions and forces C45/55 B500B ULS SLS Width 1000 mm Height 1900 mm Md 16620 kNm Nd -2040 kN Vd 3077 kN Nd,vd -2040 kN Mrep 12976 kNm Nrep -1774 kN The amount of reinforcement, thickness steel plate and the stirrups is given in table 151, table 152 and table 153. Table 151: Amount and position of the tensile reinforcement Tensile reinforcement 1st layer 9 Ø 2nd layer 9 Ø 3rd layer 9 Ø 32 mm 32 mm 32 mm distance between layers: 50 distance between layers: 50 ds;i As;i [mm] [mm²] 1817 7238 1735 7238 1653 7238 1735 21715 mm mm Totals Table 152: Amount of steel shell applied Compressive zone Thickness plate Area Steel shell 30 30000 Kubilay Bekarlar - Master Thesis [mm] - 140 - [mm²] August – 2016 Table 153: Amount of stirrups applied Stirrups 1st 16 mm - 95 mm 4 pcs Asw;1 = 8,47 mm²/mm Now the checks are performed for the floor element and the results can be observed in table 154. Table 154: Overview of the results of the unity checks Unity Checks MSd 16749 kNm MRd 18284 kNm uc= 0,92 VEd 3077 kN Stirrups required VRd,c 1348 kN uc= 2,28 VRd,s 5748 kN 11524 kN VRd,max wk 0,42 mm wmax 0,30 mm αc;top -28,7 N/mm² -30 N/mm² fcd uc= 0,54 uc= 1,41 uc= 0,96 From the results of the checks there can be seen that all checks fulfill the boundary condition except the crack width check. Since this variant is a steel shell with steel plates covering the concrete surface the crack width check is not the limiting aspect anymore. In other words the concrete layer is not exposed to the environment anymore. This means that all relevant checks fulfill the boundary conditions. Figure 166: Drawing of the cross section of a steel shell tunnel element (half of the cross section until the symmetry axis) Kubilay Bekarlar - Master Thesis - 141 - August – 2016 Figure 167: Detail of a steel shell tunnel, floor element 19.2.3 Amount of materials applied variant 2 The amount of stirrups and its specifications are denoted for each element in the table 155. Table 155: Amount of stirrups applied Amount of stirrups applied Roof Length over which stirrups needed Ø 16 – 150 Floor 2 pcs Amount of stirrups applied 208 Total stirrup area 0,234 m Length over which stirrups needed 7,3 m Ø 16 – 150 Walls 7,8 m 2 pcs Amount of stirrups applied 208 Total stirrup area 0,233 m Length over which stirrups needed 1,6 m Ø 16 – 150 3 3 2 pcs Amount of stirrups applied 22 Total stirrup area 0,044 m Total amount stirrup reinforcement /m 0,52 m 3 3 The amount of tensile reinforcement per element is given in table 156 below. Table 156: Amount of tensile reinforcement applied Amount of tensile reinforcement applied Floor Tensile reinforcement 9 - Ø 32 x 3 Total area 21715 mm 2 Total reinforcement volume 1,36 m Roof 3 Tensile reinforcement 11 - Ø 32 10 - Ø 32 10 - Ø 32 Total area 34432 mm 2 Total reinforcement volume 1,57 m Walls 4 - Ø 32 Kubilay Bekarlar - Master Thesis Total area 3217 mm - 142 - 3 2 August – 2016 Total reinforcement volume 0,35 m 3 3 Total amount tensile reinforcement /m Total reinforcement volume 3,25 m /m The amount of steel plate applied for variant 2 is given in table 157. Table 157: Amount of steel plate applied Amount of steel plate applied Thickness Volume Roof 30 mm + 10 mm 2,52 m 3 Floor 30 mm + 10 mm 2,52 m 3 Walls 30 mm + 10 mm 0,48 m 3 3 Total amount of steel plate applied/m 5,52 m /m The calculated amount of concrete to be applied in this tunnel is given in table 158. Table 158: Amount of concrete applied Amount of concrete applied Thickness Volume Roof 1900 mm 119,7 m 3 Floor 1600 mm 100,8 m 3 Walls 1500 mm 45,82 m 3 3 Total amount of concrete applied /m 266,32 m /m The dimensions of the stiffeners and the amount is given in table 159 below. Table 159: Amount of steel stiffeners applied Amount of steel stiffeners applied h×l×t Volume Roof 100 × 60 × 30 mm and 100 × 60 × 15 mm 0,61 m 3 Floor 100 × 60 × 30 mm and 100 × 60 × 15 mm 0,61 m 3 Walls 100 × 60 × 30 mm and 100 × 60 × 15 mm 0,28 m 3 3 Total amount of steel stiffeners applied /m 1,50 m /m Now the dimensions and the amount of studs are calculated. The results are given in table 160. Table 160: Amount of shear studs applied Amount of shear studs applied Roof – Inside Diameter Height Min. ctc Max. ctc 15 mm 180 mm 22,5mm Roof - Outside 30 mm 360 mm Floor – Inside 15 mm Floor - Outside 30 mm Kubilay Bekarlar - Master Thesis Height stud head 6 mm Volume 720 mm Diameter stud head 22,5 mm 0,05 m 3 45 mm 1440 mm 45 mm 12 mm 0,41 m 3 180 mm 22,5mm 720 mm 22,5 mm 6 mm 0,05 m 3 360 mm 45 mm 1440 mm 45 mm 12 mm 0,41 m 3 - 143 - August – 2016 Walls – Inside 15 mm 180 mm 22,5mm 720 mm 22,5 mm 6 mm 0,04 m 3 Walls - Outside 30 mm 360 mm 45 mm 1440 mm 45 mm 12 mm 0,14 m 3 3 Total amount of shear studs applied /m 19.3 1,1 m /m Critical span steel shell tunnel Since there will be a comparison of the steel shell tunnel with the SCS sandwich tunnel, it is also important to know what the critical span is for the steel shell tunnel. In the tables below the calculation for the critical span for a steel shell tunnel is given. The unity checks for a span of 28 m are given in table 161 and for 29 m table 162. Table 161: Unity checks of a steel shell tunnel for a span of 28 m Unity Checks MSd 18002 kNm MRd 29568 kNm uc= 0,61 VEd 3192 kN Stirrups required VRd,c 15574 kN uc= 2,05 VRd,s 7712 kN VRd,max 9454 kN wk 0,28 mm wmax 0,30 mm αc;top -28,7 N/mm² -30 N/mm² fcd uc= 0,41 uc= 0,95 uc= 0,96 Table 162: Unity checks of a steel shell tunnel for a span of 29 m Unity Checks MSd 19302 kNm MRd 29568 kNm uc= 0,65 VEd 3306 kN Stirrups required VRd,c 1557 kN uc= 2,12 VRd,s 7712 kN VRd,max 9454 kN wk 0,31 mm wmax 0,30 mm Kubilay Bekarlar - Master Thesis uc= 0,43 uc= 1,03 - 144 - August – 2016 αc;top -32,94 N/mm² fcd -33,33 N/mm² uc= 0,99 From these calculations there is seen that the critical span for a steel shell tunnel is 28 m. There can be seen that the normal, shear and moment capacity is higher than the design forces applied on the structure. However the crack width for a span of 29 meters becomes larger than the permissible 0,30 mm. So now also for the inner environment the crack width is the limiting factor. This evaluation is important because will be essential in the comparison of the types of tunnels for a large span in the cross direction. 20 SCS SANDWICH The SCS sandwich tunnel that was designed in the earlier stage of this research and analysed with a FEM program, will now be expressed in the quantity of the materials used. Doing so the amount of steel used for the plates of the SCS tunnel is given in table 163. Table 163: Amount of steel plate applied Amount of steel plate applied Thickness Volume of steel applied Roof outside 25 mm 1,575 m Roof inside 20 mm 1,26 m Floor outside 25 mm 1,575 m Floor inside 20 mm 1,26 m 3 Walls outside 20 mm 0,63 m 3 Walls inside 20 mm 0,63 m 3 Diaphragm 15 mm 2,69 m 3 Perpendicular diaphragm 15 mm 1,17 m 3 3 3 3 3 Total amount of steel plate applied/m 10,79 m /m Hereafter the amount of self-compacting concrete is calculated, from which the results are given in table 164. Table 164: Amount of concrete applied Amount of concrete applied Thickness Volume Roof 1600 mm 100,8 m 3 Floor 1900 mm 119,7 m 3 Walls 1500 mm 45,82 m 3 3 Total amount of concrete applied /m 266,32 m /m The amount and dimensions of the stiffeners is given in table 165 below. Table 165: Amount of steel stiffeners applied Amount of steel stiffeners applied h×l×t Volume Roof – Outside 100 × 60 × 25 mm 0,34 m 3 Roof – Inside 100 × 60 × 20 mm 0,27 m 3 Kubilay Bekarlar - Master Thesis - 145 - August – 2016 Floor – Outside 100 × 60 × 25 mm 0,34 m 3 Floor – Inside 100 × 60 × 20 mm 0,27 m 3 Walls - Outside 100 × 60 × 20 mm 0,09 m 3 Walls - Inside 100 × 60 × 20 mm 0,19 m 3 3 Total amount of steel stiffeners applied /m 1,50 m /m Finally the designed dimensions and quantity of the applied studs is given in table 166. Table 166: Amount of shear studs applied Amount of shear studs applied Roof - Outside Diameter Height Max. ctc 360 mm Min. ctc 45 mm Height stud head 12 mm Volume 1440 mm Diameter stud head 45 mm 30 mm 0,35 m 3 Roof – Inside 25 mm 300 mm 38 mm 1200 mm 38 mm 10 mm 0,24 m 3 Floor - Outside 30 mm 360 mm 45 mm 1440 mm 45 mm 12 mm 0,35 m 3 Floor – Inside 25 mm 300 mm 38 mm 1200 mm 38 mm 10 mm 0,24 m 3 Walls - Outside 25 mm 300 mm 38 mm 1200 mm 38 mm 10 mm 0,08 m 3 Walls – Inside 25 mm 300 mm 38 mm 1200 mm 38 mm 10 mm 0,17 m 3 3 Total amount of shear studs applied /m 1,43 m /m 21 COMPARE THE COSTS OF VARIANTS 21.1 Comparing the material quantities In order to compare the tunnel variants, the amount of materials to be applied for each variant is summed in table 167 below. Table 167: Comparing the tunnel variants for the amount of materials used per m1 Prestressed Tunnel Steel Shell variant 1 Steel Shell variant 2 Not feasible Stirrups 0,52 m /m Tensile reinforcement 4,25 m /m Steel plate 4,25 m /m Stiffeners 0,94 m /m Kubilay Bekarlar - Master Thesis SCS Sandwich Tunnel 3 Stirrups 0,52 m /m 3 Tensile reinforcement 3,25 m /m 3 Steel plate 5,52 m /m 3 Stiffeners 1,50 m /m - 146 - 3 3 3 Steel plate 10,8 m /m 3 Stiffeners 1,50 m /m August – 2016 3 3 3 Studs 1,10 m /m 3 Concrete 266 m /m Studs 1,04 m /m Concrete 278,9 m /m 3 Studs 1,43 m /m 3 3 Concrete 266 m /m 3 As there was concluded in the previous section about the transversely prestressed concrete tunnel, this method is not a feasible solution for large span tunnels. This is why the materials are not further quantified. Comparing the amount of materials applied for the two steel shell tunnel variants there can be observed that amount of stirrups applied for both variants is the same. As for the tensile reinforcement there can be seen that more is applied for variant 1. On the other hand the amount of steel plates applied for variant 2 is larger. This has to do with the fact that steel plates are also placed in the inner side of the steel shell tunnel. Further there can be seen that the amount of stiffeners applied for variant 2 is larger, this also has to do with the fact that steel plates are also placed on the inner side of the tunnel. Since steel plates on the inner side also need to be stiffened, which explains the difference in values. The same holds for the steel studs to be applied, in which variant 2 requires more. Also due to the steel plates on the inner side which need to be connected with the concrete inner core by studs. Further, the amount of concrete to be applied for variant 1 is slightly larger because the dimensions of the elements are slightly larger. Comparing the quantity of materials applied for the steel shell tunnel with the SCS tunnel, the following can be seen. First of all no stirrups and tensile reinforcement is needed for the SCS tunnel. The amount of steel plates applied for the SCS is larger than for the steel shell variant 1 and 2. This due to the fact that for a SCS tunnel steel plates are applied on both sides of the concrete and in between there are diaphragm’s placed. That is why the steel plates applied to the SCS tunnel are about twice as high as the steel shell tunnel. The amount of stiffeners applied to the SCS tunnel is the same as for the steel shell tunnel variant 2. On the other side there can be observed that the amount of stiffeners to be applied for the steel shell tunnel variant 1 is less than steel shell variant 2 and the SCS tunnel. From the quantity of studs applied to the tunnels there can be seen that the volume of studs for the SCS tunnel is the highest. Same as stated above the reason for this larger amount is that steel plates are on both sides of the concrete and both plates need to be connected with the concrete. The same holds for the steel shell tunnel variant 2. Since the overall thickness of the steel plates is less, this results in less stud volume to be applied for the steel shell tunnel variant 2 in comparison with the SCS tunnel. For the steel shell tunnel variant 1 there can be seen that the volume of studs to be applied is the least of the three variants. This is explainable by the fact that the steel is applied at only one side of the concrete, where the inner side is made out of reinforced concrete. Finally the concrete quantity will be discussed. There can be seen that the amount is nearly same for all variants. Only for variant 1 the concrete to be applied is slightly more. This is because of the extra concrete to be applied as a cover on the reinforcing steel. 21.2 Comparing the costs In order to make a costs comparison the material quantities need to be multiplied with the unit prices4, see table 168. These unit prices include labour costs. 4 Data obtained from construction costs specialist at Royal Haskoning DHV, February 2016 Kubilay Bekarlar - Master Thesis - 147 - August – 2016 Table 168: Unit price per material Unit prices per material Unit Price / kg Unit Price / m3 or m2 Steel plates 2,50 Euro/kg 19500,00 Euro/m3 Reinforcing Steel 1,10 Euro/kg 8580,00 Euro/m3 Steel Studs 3,00 Euro/kg 23400,00 Euro/m3 Prestressing Steel 5,50 Euro/kg 42900,00 Euro/m3 125,00 Euro/m3 125,00 Euro/m3 20,00 Euro/m2 20,00 Euro/m2 Formwork Walls 75,00 Euro/m2 75,00 Euro/m2 Formwork Roof 150,00 Euro/m2 150,00 Euro/m2 Concrete Formwork Floor Since the material quantities and the unit prices are determined, now the total price for each type of tunnel per meter width can be calculated. With these costs per tunnel variant, the tunnel variants can be compared with each other. These costs include the costs for labour as well. As stated before the prestressed immersed tunnel is not a feasible solution, which is why that variant was not further elaborated. There was seen that the steel shell tunnel variant 1 was a feasible solution for a large span tunnel of 27m. The results for the costs calculation of this variant can be observed in table 169. Table 169: Results of the cost calculation of the steel shell tunnel variant 1 Costs Floor Element incl labour Stirrups Costs Roof Element incl labour Costs Walls incl labour 2007,7 Euro Stirrups 2007,7 Euro Stirrups Tensile reinforcement 17503,2 Euro Steel plates 51597,0 Euro Stiffeners 10920,0 Studs Tensile reinf 15958,8 Euro Steel plates 51597,0 Euro Euro Stiffeners 10920,0 Euro 15990,0 Euro Studs 15990,0 Concrete 14742,0 Euro Concrete Formwork 11358,0 Euro Formwork Sum 124117,9 Total 377,5 Euro Tensile reinf 3003,0 Euro Steel plates 13104,0 Euro Stiffeners 3685,5 Euro Euro Studs 8346,0 Euro 15561,0 Euro Concrete 6873,0 Euro 35967,0 Euro Formwork 7110,0 Euro 148001,5 42499,0 315 000,0 Euro/m tunnel From these results there can be seen that the costs of the steel shell tunnel variant 1 is 315 000 euros per meter length. There was also seen that the steel shell tunnel variant 2 was a feasible solution for a large span of the tunnel for 27m. The results of the cost calculation can be seen in table 170 below. Table 170: Results of the cost calculation of the steel shell tunnel variant 2 Costs Roof Element incl labour Costs Floor Element incl labour Costs Walls incl labour Stirrups Tensile reinforcement Stirrups Tensile reinf 2007,7 Euro 11668,8 Euro Kubilay Bekarlar - Master Thesis 2007,7 Euro Stirrups 13470,6 Euro Tensile reinf - 148 - 377,5 Euro 3003,0 Euro August – 2016 Steel plates 68796,0 Euro Stiffeners 16653,0 Euro Steel plates Stiffeners Studs 17940,0 Euro Concrete 15561,0 Euro Formwork 30288,0 Euro Sum 162914,5 Total 351 000 68796,0 Euro Steel plates 13104,0 Euro 16653,0 Euro Stiffeners 7644,0 Euro Studs 17940,0 Concrete 13104,0 Euro Studs 7020,0 Euro Euro Concrete 5956,6 Euro Formwork 11989,0 Euro Formwork 7110,0 Euro 143960,3 44215,1 Euro/m tunnel These results show that the costs for the steel shell tunnel variant 2 is 351 000 euros. This value is higher than value for the costs of variant 1. Finally the results of the cost calculation for the SCS tunnel is given in table 171. Table 171: Results of the cost calculation of the SCS tunnel Costs Roof Element incl labour Costs Floor Element incl labour Costs Walls incl labour Steel plates 112476 Euro Steel plates Stiffeners 16653 Euro Studs 23010 Concrete 11088 Sum 163227,0 Total 421 000 112476 Euro Steel plates Stiffeners 16653 Euro Euro Studs 23010 Euro Concrete 13167 165306,0 69615 Euro Stiffeners 7644 Euro Euro Studs 9750 Euro Euro Concrete 5040 Euro 92049,2 Euro/m tunnel From these results there can be seen that the costs for the SCS tunnel per meter length is the highest with 421 000 euros. Kubilay Bekarlar - Master Thesis - 149 - August – 2016 Conclusion & Recommendations Kubilay Bekarlar - Master Thesis - 150 - August – 2016 22 CONCLUSION AND RECOMMENDATIONS 22.1 Conclusions In this chapter the most important conclusions drawn from the performed research are described. In the second part some recommendations are given to provide a direction for further research on this topic. Design of a reinforced concrete, SCS sandwich immersed tunnel and determining the critical span: In order to determine the critical span for a reinforced concrete tunnel and a SCS tunnel a base case design was made. For the reinforced concrete tunnel there was seen that with the maximum reinforcement ratio applied, the maximum span for the roof element is around 18-19m. While for the floor element this critical span is 21 m. There was seen that for the reinforced concrete tunnel not the moment-, shear- or normal force capacity was the determining factor, but the crack width was. This meant that the reinforced concrete tunnel was not able to make the desired span of 27m meters (reference project). However for the SCS tunnel the crack width is no limiting factor since the concrete remains inside the steel casing and is not exposed to the environment. As well as the amount of steel applied for the SCS tunnel does not have a maximum steel ratio that might be applied, which holds for the reinforced concrete tunnel. With these characteristics for a SCS tunnel, there was seen that a span of 27m is feasible. Schematization and modelling of a SCS sandwich elements in a FEM program: The schematization of the SCS tunnel was started with a simplified model first. For the simplified model the SCS shape was idealized to a line element in order to reduce the computation time. So for the roof, floor and wall element a three node plain strain element CL9PE is applied. The choice for this element is applied since it gives good insight in the stress and strain distribution. From these stresses and strains the internal forces can be calculated by integrating over the length of the element. Another aspect for choosing this element was that it is infinitely long in the axial direction. The subsoil was schematized with the interface element CL12I. Finally the bedding was constraint in two directions, X and Y. This model was validated by hand calculations. There was seen that the simplified model coincides with the hand calculations, which meant that the model is correct. After the simplified model was validated, a detailed model was made. This model was made as the SCS is designed in reality. This means that the steel parts for the inner side and outer side of the roof, floor and wall element have a specified thickness. The same holds for the diaphragms that connect the inner and outer steel plates. The steel inner, outer and the diaphragm parts will be modelled by using the plain strain element CL9PE. This is a three node plain strain element. This shell element is chosen for the steel since it has a small height compared with its length, just like the steel plates applied. Another point is that the plain strain elements also have an infinite length in the axial direction. These elements give a good stress and strain distribution from which the internal forces can be calculated. The concrete inner core of a SCS sandwich cell is modelled with the CQ16E element, which is an eight node plain strain element. This element is square shaped and can be applied for all kind of analysis including linear, nonlinear and cracking. Also this element has a length which is infinitely long in its axial direction. The stiffeners and studs which connect the steel and concrete aren’t modelled physically, rather by making use of interface elements. For these interface elements a stiffness is given. The stiffness resembles the degree of connection between these two elements. The applied interface element is CL12I. Kubilay Bekarlar - Master Thesis - 151 - August – 2016 Detailed analysis of the internal forces (stresses) over the SCS sandwich tunnel element (Tracing the stress concentration in the structure) Stress distribution in concrete core For the stress distribution over the concrete core layer three critical spots were identified for the roof and floor element. On the left hand side the connection with the outer wall, in the middle of the span and at the connection with the inner wall. These spots are critical since there are higher stresses at these locations than the rest of the cross section. When looked at these locations in more detail, there was seen for the roof, floor and wall elements have stress / strain concentration points. Since the concrete tensile strength is low, so this was exceeded and tensile cracks appeared in the concrete tensile section. From the perspective of durability there can be stated that the cracks in the tensile section is not a problem because the concrete is in a confined space enclosed by steel. Intrusion of water or minerals in concrete will not take place. There was also seen that the design concrete compressive stress is exceeded locally and the characteristic compressive stress value is approached. These spots can be seen in the cells where the roof and floor elements are connected with the inner and outer walls. As a result of this the concrete will be locally in the plastic state and local concrete crushing might occur. On the few places where the yielding strength is exceeded the internal forces will be redistributed. The cracks however may have impact on the degree of connection between the steel and concrete. Due to the cracks the shear stiffness of the steel and concrete connection can decrease. This may have impact on the overall stiffness of the structure. From the durability point of view these cracks have no impact on the durability of the structure since the concrete is situated in a confined space. On the other side the exceedance of the stress is only locally, which will result in a redistribution of forces. Stress distribution in steel parts From the stress / strain analysis of the steel elements, there was seen that the high tensile and compressive zones are at the same positions as discussed in the section of concrete stresses and strain. From the distribution of the stresses and strain in the steel there was be concluded that at no position in the steel structure the elastic tensile / compressive stresses and strain was exceeded. Optimization of the SCS sandwich tunnel design with a detailed FEM analysis: From the detailed model accurate insight in the distribution of the internal forces was obtained. In other words, the design forces were determined more accurately and the uncertainties were less, which meant that the design of the structure was further optimized. Also the high water and soil pressures acting on the structure result in large axial forces in the elements. Taking these axial forces into consideration, new moment capacities can be determined that are higher since large axial forces result in an increase of the concrete compressive force, consequently also the moment capacity. For these elements where large axial forces and moments are present, interaction diagrams were made in order to determine the ultimate moment capacity for a certain axial force. This was done for the roof, floor and wall element. From the detailed analysis of the internal forces (FEM) and also the taking into consideration the large axial forces by using the interaction diagram, the design was optimized. The unity checks for the moment capacity that used to be around 70%, was raised to 85-90%. The same was also done for the shear capacity, which used to be around 60%, was also raised to 85-90%. There was seen that the total amount of steel applied for the design using the detail analysis is reduced significantly. Where in the previous design the applied steel in the cross section was 11,96 m2, has now reduced to 9,45 m2. This is a reduction of the steel applied with 21 %. In absolute values, this is a reduction of 2,51 m3 per meter in the axial direction. The optimization which leads to reduction of the steel applied with 21% is a significant improvement. These optimized values may not look significant at the first sight however they will be significant since these values are only done for one meter in the axial direction of the tunnel. Considering that immersed tunnel Kubilay Bekarlar - Master Thesis - 152 - August – 2016 projects range from several hundred meters to several kilometres, it means that this type of optimization will be highly important. Since the steel is an expensive material and hence one of the major expenses of a SCS tunnel project because it is applied on a large scale. The amount of concrete applied in a SCS immersed tunnel was not further optimized because that amount was needed for the immersion and floating balance. In other words, if the amount of concrete in the SCS structure is reduced, than it has to be applied as ballast concrete in the cross section. Another reason is that the thickness of the concrete has impact on the moment capacity since the internal level arm of the forces in the steel become larger which correspondents with a higher moment capacity. This is the reason why no further optimization of the amount of concrete will take place. Analysis whether a prestressed (post tensioned) reinforced concrete tunnel and a steel shell tunnel is a feasible solution for a tunnel with a large span in the cross direction: From the new design of a concrete tunnel element there can be concluded that a span of 27 m is not feasible with prestressed roof and floor elements. In the initial reinforced concrete tunnel design there was seen that the crack width was the limiting factor. By adding prestressed tendons the crack width becomes small enough. However the prestress tendons to be applied have a dimension of 510 mm by 420 mm. This makes it impossible to fit several of 55 strands of Y1860S7 tendons per meter width of the cross section. If those tendons were able to fit the cross section, there was seen that the moment and shear force capacity is also larger than the design moment and shear force in ULS. On the other side there was seen from the analysis that large axial forces were present. In order to bear these large axial forces, high strength concrete is required. From this analysis there is seen that a transversely prestressed reinforced concrete tunnel is not a feasible solution for a tunnel with a large span in the transverse direction. For the steel shell tunnel two variants were researched. One normal steel shell tunnel with steel shell on the outer side and reinforced concrete on the inner side. The second variant also has a steel shell on the outer side and a steel cover plate on the inner side, which will seal the concrete from the inner environment of the tunnel. For the first steel shell variant, the new exposure class for the concrete is moderate humid. This leads to a reduction of the concrete cover to 60 mm. There was seen for the first variant that all checks were fulfilled including the crack width. For the second variant on the other side the crack width is not relevant, since the concrete is sealed on the inner side with a steel plate and there is the steel shell on the outer side. This means that the other checks are relevant such as, moment-, shear- and normal force capacity. All these checks also fulfilled the conditions. Which lead to the conclusion that both steel shell variants are feasible solutions for tunnels with large spans in the cross direction up to 27 m. Comparison of a SCS immersed tunnel with other types of tunnels, for large spans in terms of cost and materials: In order to make a cost comparison for the variants, first the amount of material required per meter length for each variant was determined. From the amount of materials, the costs per variant was determined, including labour. Since the presetressed reinforced concrete tunnel is not a feasible solution, it is not in this comparison. On the other side there was seen that the steel shell tunnel variant 1 was a feasible solution for a large span tunnel (27 m). From the costs analysis there was seen that steel shell tunnel variant 1 would cost 315 000 euros per meter length. This is the costs including labour. Also the steel shell tunnel variant 2 was a feasible solution for a large span of 27 m. This variant was slightly more expensive then variant 1. The costs for this tunnel per meter length is 351 000 euros. The same analysis was performed for the SCS tunnel. This variant is with 421 000 euros per meter length, more expensive than the other two steel shell tunnel variants. Kubilay Bekarlar - Master Thesis - 153 - August – 2016 Is a SCS sandwich immersed tunnel the most ideal solution for tunnels with large span in the cross direction? (Main research question) In terms of costs a reinforced concrete tunnel is the most ideal solution for tunnels with a span up to 18 / 19 m. This is also the limiting span for a reinforced concrete tunnel. Also a transversely prestressed (post tensioned) reinforced tunnel was investigated in detail, however the conclusion was drawn that it is not a feasible option. On the other had a span of 18 / 19 m is not considered a large span for the cross section. For the reference project (Sharq Crossing) which initiated this research project a large span was desired of around 27 m. With this research project there was seen that a large span up to 27 m is feasible with a SCS sandwich tunnel as well as a steel shell tunnel. However in terms of costs a SCS tunnel is not the most ideal solution for a tunnel with a large span which is around 27m. From the costs analysis there was seen that the SCS tunnel is around 34% more expensive than steel shell variant 1 and 20% more expensive than the steel shell tunnel variant 2. In other words, for a tunnel span in the cross direction of between 19 till 28 m a steel shell tunnel is the most ideal solution in terms of costs. The amount of costs that can be reduced is significant. The higher costs for a SCS sandwich tunnel have to do with the fact that more steel is applied. However a detailed FEM analysis needs to be performed for a steel shell tunnel for a large span. This way insight will be gathered how the steel shell will respond to loading due to a large span. However choosing for a SCS sandwich tunnel a span shorter than 29 m, has also several advantages. One advantage is that the shear force capacity and moment capacity of a SCS tunnel is larger than a steel shell tunnel. This advantage can be important for changing boundary conditions or accidental loading on the tunnel structure. One can think of an explosion, sunken ship on top of the tunnel or extra loading due to sedimentation on top of the tunnel or erosion below the tunnel floor. Another aspect worth mentioning separately is the loading on the structure due to earthquake. If the construction area is in a region where the risks for earthquakes are significant, then the SCS sandwich is the most ideal solution. This is the case for the reference project the Sharq Crossing (Qatar), risks for an earthquake in that part of the Arabian Peninsula is significant 5. Since the design lifetime of a tunnel is up to 100 years, conditions and loadings may change. In that case a SCS tunnel might be an ideal solution. Another aspect is the safety. As stated before a SCS tunnel is a stronger and more rigid structure then other tunnel types. Since in a SCS tunnel more steel has been applied, a higher rest capacity is present and the structure will behave more ductile if the ultimate strength would be exceeded. This is in particular important for the safety of the people making use of the tunnel. Which is less the case for structures that show failure closer to brittle failure. Another conclusion is that the SCS sandwich tunnel becomes the most ideal solution for a span 28 m or larger. Since for spans larger than 28 m the SCS tunnel is the only feasible solution. This has to do with the fact that at a span of 29 m the steel shell tunnel does not hold the crack width condition for the inner environment. While for a SCS tunnel the crack width is not a limiting condition. The points mentioned above are summarized in table 172. Table 172: Overview of ideal solution for a certain span in the cross direction Length of span Reinforced Concrete Tunnel Steel Shell Tunnel Steel Concrete Steel Sandwich Tunnel < 19 m Most ideal solution Not ideal Not ideal 19 – 28 m Not feasible Ideal solution Ideal solution >28 m Not feasible Not feasible Only feasible solution 5 Earthquake hazard zonation of Eastern Arabia: Jamal A. Abdalla and Al-Homoud 2004 Kubilay Bekarlar - Master Thesis - 154 - August – 2016 22.2 Recommendations The effect of the uneven soil settlement on the design optimization of a SCS tunnel. The effect of uneven soil settlement on the design is important for further research because it might have impact on the detailed design of a SCS sandwich tunnel. A reinforced concrete tunnel consists of segments which form an element. These segments are prestressed with prestress cables during the transport to its final location. After immersed on its final location the prestress cables are cut off, which enables the tunnel segments to adjust to the subsoil. This will prevent the creation of large spans beneath the floor element. As for a SCS tunnel, this tunnel consists of one big element, without any segments. In other words, scour underneath the structure may introduce extra loading on the structure. Studying this phenomenon and describing the impact on the detailed design of a SCS tunnel is a research on its own. Nonlinear analysis For this thesis only linear elastic material behaviour is assumed. By using the nonlinear analysis more insight will be gathered regarding the development of the cracks as well as the failure mechanisms. This way more information will be gathered about the ductile behaviour of a SCS tunnel due to extreme loading. Detailed analysis of structural response of a SCS tunnel to loading due to explosion or fire. In this research loading due to an explosion inside the tunnel was briefly analysed with the FEM program. There was seen that the structure did not collapse due to this load. However there are more things included such as fire. There are certain things that should be investigated as the response of the steel and concrete sandwich structure to heat inside the tunnel. Also the fire protection is an important aspect regarding this topic. Research whether a fibre reinforced concrete tunnel a feasible solution is for a tunnel with a large span in the transverse direction. There was concluded with this research that a reinforced concrete tunnel has its limits regarding a large span. The limiting condition was the crack width. However fibre reinforced concrete has several advantages like reducing the crack width and improving the structural strength, compared with normal concrete. After the feasibility study also a comparison in costs should be made in order to compare it with the other tunnel types. Detailed FEM Analysis of a steel shell tunnel for large spans After this research among other aspects, also detailed insight in the structural response of a SCS tunnel has been gathered. The same needs to be done for a steel shell tunnel to see how it will respond to loading on a large span. Stress / strain concentration points needs to be identified and analysed. Kubilay Bekarlar - Master Thesis - 155 - August – 2016 Appendix Kubilay Bekarlar - Master Thesis - 156 - August – 2016 23 LITERATURE Book: Immersed Tunnels Authors: Richard Lunniss, Jonathan Baber Lecture notes: Bored and Immersed Tunnels – TU Delft Author: Dr. Ir. K. J. Bakker Lecture slides: Concrete Science and Technology Author: Prof. Dr. Ir. K. van Breugel Report: Double skin composite construction for submerged tube tunnels – Phase3, 1997 Author: European Commission for Technical Steel Research Report: “Stalen en composiet staalbeton tunnelconstructies – Staalbeton sandwichelementen, Deel 2: Modelvorming en rekenregels” English: “Steel and composite steel concrete tunnel constructions – Steel concrete sandwich elements” – 2000 Author: Centrum Ondergronds Bouwen Paper: Immersed Tunnels in Japan: Recent Technological Trends - 2002 Authors: Keiichi Akimoto, Youichi Hashidate, Hitoshi Kitayama, Kentaro Kumagai Paper: Development of sandwich structure submerged tunnel tube production method Authors: Hideo Kimura, Hiroo Moritaka, Ichio Kojima Paper: Self-compacting concrete - 2003 Authors: Hajime Okamura, Masahiro Ouchi Paper: The challenges involved in concrete works of Marmaray immersed tunnel with a service life of 100 years - 2009 Authors: Ahmet Gokce, Fumio Koyama, Masahiko Tsuchiya, Turgut Gencoglu Paper: “Finite element analysis of steel concrete steel sandwich beams” – 2007 Author: N. Foundoukos, J.C. Chapman Paper: Behaviour of composite segment for shield tunnel – 2010 Authors: Wenjun Zhang, Atsushi Koizumi Kubilay Bekarlar - Master Thesis - 157 - August – 2016 24 APPENDIX A Immersed Tunnels General 24.1 Introduction One of the options to cross a waterway is by an immersed tunnel. As the name says these tunnel elements can be transported over great distances and be immersed at its final location. Immersed tunnels consist of a large pre-cast concrete or concrete-filled steel tunnel elements fabricated in the dry and installed under water. At the moment there are about 180 immersed tunnels built ever since 1893. Compared with the other types of tunnel this number is rather low. This also means that this technique is still in its infancy. An immersed tunnel can be preferred over a bridge, bored tunnel or a cut and cover tunnel due to its several advantages. The disadvantage of a bridge is that it limits the air draft of the ships passing under the bridge. A solution would be a moveable bridge, but still this has some disadvantages as waiting times and limited cross section to pass under. Bored tunnels on the other side are not possible to execute in soft alluvial sandy soils. Since the bored tunnels need a cover layer of about one time the tunnel diameter (to prevent uplift), the bored tunnels are normally more expensive. Also with very deep tunnels bored tunnels are not the most economical solution. The biggest disadvantage of a cut and cover technique is that the waterway will be reduced to half of its capacity. At some frequently used waterway this is not a preferred choice. Another advantage is that immersed tunnel elements are fabricated in convenient lengths on shipways, in dry docks or in improvised floodable basins where they can be floated out. Bulkheads are needed to create a watertight tunnel element which can be floated. Immersed tunnel elements are usually floated to the site using their buoyant state. However, sometimes additional external buoyancy tanks attached to the elements would be used if necessary. They are then towed to their final location where the tunnel elements will be lowered into their location after adding either temporary water ballast or tremie concrete. After the tunnel is immersed into a trench and joined to previously placed tunnel elements, foundation works will be completed and the trench around the immersed tunnel is backfilled and the water bed reinstated. The countries where the immersed tunnels are constructed more often are the US, the Netherlands and Japan. There is a significant difference between the immersed tunnels constructed in these countries. In the US the immersed tunnels are constructed more often with a single or double steel shell. As for the Netherlands the traditional tunnel is built out of reinforced concrete segments. In Japan reinforced concrete, steel plate or steel concrete steel composite (sandwich) tunnels are constructed more often. This type of tunnel will be described in more detail below with the emphasis on steel concrete steel immersed tunnel elements. 24.2 Types of tunnels 24.2.1 Single shell immersed tunnel The single shell immersed tunnels consists of a stiffened outer shell. This steel shell is stiffened in the longitudinal and transverse direction. It is normally manufactured by using 10 mm thick steel plate. The steel shell provides strength and water tightness. On the inner side of the steel shell a reinforced concrete lining is placed. This reinforced concrete acts compositely with the steel and the inner lining is about 700 mm thick, figure a- 1. The steel shell which is exposed to the marine environment is most commonly protected by a cathodic protection system. Kubilay Bekarlar - Master Thesis - 158 - August – 2016 A big advantage of the steel shell tunnels is that the steel shell can be built in small facility or a shipping yard. Nearly all countries have these types of shipyards where the shells can be constructed. Another advantage is that the concrete can be casted in a steel shell while it is afloat. For this, the tunnel element will be towed to a jetty, where the concrete will be cast. The small draft of a steel shell makes it possible to execute an immersed tunnel in shallow waters. This would certainly not be the case with reinforced concrete immersed tunnels where the draft is large. In order to give the steel shell resistances against deforming, stiffeners are attached in the longitudinal and transverse directions. The shear studs which are connected on the inner side of the steel shell connect the steel with concrete. This way the steel and concrete will act compositely. Figure A- 1: Left: single shell tunnel and right: construction of a single shell To prevent extreme loading on the single steel shell tunnel during launching of the tunnel from a slipway, these tunnels are launched sideways. This way the internal stresses will be minimized. Otherwise the tunnel elements would have to be designed more robustly. Before launching, the reinforcement for the inner concrete lining is placed together with other internal equipment and a certain amount of keel concrete is also placed to increase the draft of the element and to give it stability while afloat. Bulkheads are applied at the ends which prevents the water from entering the tunnel element. This way the element can be transported over water to its final position. 24.2.2 Double steel shell immersed tunnel This tunnel consists of two steel shell layers, one on the inner side and the other on the external. Compared with a single steel shell, the inner shell is thinner (about 8 mm). These steel shells provide strength and water tightness. External diaphragms are added at intervals between the inner and external steel shell, also known as a form plate. On the inner side of the steel shell reinforced concrete lining is placed. This lining will act compositely with the steel shell. Around the inner shell there is an outer shell also known as form plate. This outer plate is slightly thinner than the inner plate, about 6 mm. The space between the two shells is filled with concrete, which acts as ballast and also protects the inner steel shell against corrosion. In figure a- 2 there is a cross section of a double shell immersed tunnel element. The construction method is similar to that of a single steel section. Fabrication of the steel shell is done from a series of modules then assembled on a slipway and launched. It is then towed to an outfitting site and the concrete is placed while the element is afloat. Kubilay Bekarlar - Master Thesis - 159 - August – 2016 Figure A- 2: Double shell immersed tunnel element 24.2.3 Concrete immersed tunnels The reinforced concrete immersed tunnel is predominantly used in the European countries, in particular the Netherlands. The main driving reason for this is that the steel prices in Europe are relatively high. Because of the fact that the Dutch waterways are not that deep, rectangular shaped reinforced concrete elements were constructed. An advantage of the rectangular shape is that it matches the rectangular traffic envelope belter. Some rough dimensions of a concrete immersed tunnel are about 1 m for the floor and roof and the inner and outer wall all the way from 0,3m to 0,7m. An important aspect is the foundation of the immersed tunnel. The foundation should provide uniform bedding for the tunnel element. If this is not the case, high local stresses will be generated. In order to prevent this some techniques were provided such as sand jetting and sand flow. Sand jetting where a water sand mixture was jetted under the tunnel had the disadvantage that the jetting plant was an obstacle in the waterway. Sand flow happens through pipes casted in the tunnel element. In this case the water sand mixture flows slowly under the tunnel without obstructing the waterway. Tunnel elements used to be built as 100 m long monolithic reinforced concrete structures, figure a3. The disadvantage of these types of long concrete structures is that due to thermal shrinkage cracking can occur. As a result water could leak into the tunnel. In order to prevent thermal cracking, engineers in the Netherlands divided element of over 100 m into several smaller segments of 20 – 25 m. An element is not cast in one pour, first the base is cast where after the walls and roof are cast. The temperature development during the second cast is controlled closely and measures are taken if necessary to prevent significant thermal differences between the base and wall slabs. By cooling concrete during curing cracking could be prevented and the need for a waterproof membrane was eliminated. Omission of a waterproofing layer results in a reduction of construction time and money. On the other hand, the individual segments have to be connected by prestressing to form a continuous element while being towed towards its final location. After the concrete elements are immersed the prestress tendons are cut off. Figure A- 3: Cross section reinforced concrete tunnel Even though water tight concrete was produced by segmenting the concrete tunnel element, the weakness was that more joints were introduced. The joints are potential sources of leakage. In order to make the segment joints watertight, a continuous water stop is placed in the joint. These Kubilay Bekarlar - Master Thesis - 160 - August – 2016 water stops were developed so that grout could be injected around the ends so that any porosity in the concrete near the tips of the water stop could be sealed. 24.2.4 Monolithic concrete tunnel element As stated before the concrete tunnel element can either be executed as a segmental or as a monolithic tunnel element. The monolithic tunnel element is made as a continuous structure. Reinforced concrete tunnels constructed before 1960 -1970 were constructed as monolithic elements. As stated before, the cracking is the main cause of problem for a monolithic structure. To prevent this thermal control measures are taken as well as a waterproof layer is placed on top of it. For a monolithic concrete tunnel, this is considered to provide the best long-term solution for water tightness and hence durability. Reinforcing steel is used to account for the tensile stresses in the slabs and walls. A typical dimension of a monolithic tunnel element is about 100 m to 200 m long. The base, walls, and roof are all rigidly connected together with the reinforcement throughout the section and across the construction joints. The monolithically constructed tunnel elements provide great flexibility for the designer, since it can provide variation in the height width of the tunnel cross section as well as in the length direction. This is useful if the width varies or an emergency lane has to be provided. At the joints between the monolithic elements shear keys are provided where the shear is transferred and which also makes sure that the elements remain in alignment. Since the tunnel element is exposed to fresh or saline water it needs to be protected against corrosion as well. This is usually done by applying a bituminous coating or a protective epoxy layer. Even this may not be enough to protect the tunnel for a life time of 100 years. The extra security is provided by cathodic protection. Cathodic protection for the steelwork provides this additional security. This can either be a sacrificial anode protection system or an impressed current cathodic protection system. The sacrificial anode system, which usually consists of zinc anodes fixed to the outside of the steel membrane, is designed to make up the difference between the expected life of the protective coating and the design life of the tunnel, with an additional allowance made for a possible percentage of defects in the coating. An impressed current system can be installed at the outset, or provision can be made to retrofit one later if subsequent monitoring of the steelwork corrosion shows that it is needed. Another way to protect the tunnel element is by applying some additional thickness to the steel membrane. This way the steel membrane will still have the required thickness at the end of the design life of the tunnel. A newly applied technique is the plastic membrane instead of steel. This is a more cost efficient solution than the steel membrane. The monolithic immersed tunnel could also be designed as a prestressed monolithic element. The advantage of this is that the amount of longitudinal reinforcement would be reduced. Also sometimes transverse prestress is considered. When the span in the cross section increases due to requirements, then the reinforced concrete sections become uneconomic. A disadvantage however is that the anchorages of the prestress tendons are positioned on the outside of the tunnel element and should be protected well against the environment. 24.2.5 Segmental concrete tunnel The segmental concrete tunnel was developed from the monolithic tunnel in order to omit the waterproofing layer on the structure. As stated before the main cause of leakage in a monolithic tunnel element is due to thermal cracks created by thermal differences, between the freshly poured concrete on the already hardened concrete. These cracks create a path for water to go from the Kubilay Bekarlar - Master Thesis - 161 - August – 2016 outside towards the inside of the tunnel. Measures are taken to reduce the cracks in a monolithic tunnel element but nevertheless completely crack free element cannot be guaranteed. To encounter the crack problem with the monolithic element, the segmental tunnel element was introduced by the Dutch engineers. They limited the tunnel size to segments of 22 – 25 m this way crack free tunnel segments could be manufactured. The segment was cast roughly in two sessions, first the base was casted where after the walls and roofs were. A typical segment joint detail can be observed in figure a- 4. Figure A- 4: Segment joint – detail segmental concrete tunnel The temperature of the second pour is carefully controlled to prevent the concrete from cracking as it cools. As for the tensile stresses, this is kept below the developing tensile strength of concrete. A way to achieve it is by a concrete mix design, controlling of temperature and insulating of the formwork. All these controlled the temperature gradient in the boundary of the existing and fresh concrete. External insulation was applied to the shutters to prevent the concrete from cooling too quickly. These measures control the development of the stresses in concrete such that it does not exceed the tensile strength of the poured concrete. Through these techniques it possible to cast a crack free cross section. A watertight external membrane becomes unnecessary. As stated before a tunnel element consists of several segments. These segments are connected with joints where after they are clamped together with longitudinal prestress, such that they behave as a single homogeneous tunnel element for transporting and placing. Prestressing cables are cut after the element has been placed into its final location. 24.2.6 SCS sandwich composite immersed tunnel Steel concrete steel composite sandwich construction is a relatively new application in the immersed tunnel engineering. This technique is mostly used in Japan. Roughly stated it is constructed from steel plates connected by shear plates and diaphragms. In between the steel plates self-compacting concrete is poured. The unreinforced concrete gives the structure stiffness and connects the steel plates with each other. This results in concrete acting compositely with the steel. The steel concrete connection is provided by steel studs welded on the steel plates. These steel studs also account for the longitudinal shear stress between the concrete and steel plates, figure a- 5. Placing this concrete and ensuring sufficient compaction and complete filling of the void between the plates, is one of the main challenges of this method. This is why self-compacting concrete is applied rather than conventional concrete which it is not possible to compact in a confined space. Due to the ideal configuration of the steel and concrete parts of a SCS sandwich tunnel slabs, these slabs will be designed more slender. However the envelope of free space for the traffic will remain the same as for a reinforced concrete tunnel for example. So a lighter structure with the same upward force can cause a balance problem. If the mass of the tunnel element is not in the structural section as part of the load carrying members, it has to be applied elsewhere as internal ballast or on the roof. Kubilay Bekarlar - Master Thesis - 162 - August – 2016 Figure A- 5: Steel concrete steel sandwich element with shear studs A major advantage of the SCS sandwich tunnel element is that it behaves ductile when the ultimate capacity is exceeded. The structure will show large deflections rather than a brittle failure. In case of dynamic loading this property of a SCS composite sandwich tunnel makes it favourable, dynamic loading such as explosion or earthquake. As stated before, the studs that connect the steel with the concrete also accounts for the shear force between the steel and concrete. To be effective at resisting shear, these studs have to extend through the full depth of the section and must be anchored in the compression zone. Another function of the shear studs is to prevent the steel plate in the compression zone from buckling. The spacing between the studs can be reduced to prevent the steel plate to buckle. The composite tunnel is an elegant solution to a structural problem. Since the steel and the concrete are used efficiently a strong and light element is created. A lighter tunnel element has a shallower draught which enhanced the application of it delta regions with shallow waters. There can also be opted for the casting of concrete close to the location of the tunnel. Then first the steel shell will be constructed and this will be towed to the final tunnel location. Two layers of steel create a double watertight layer which is an important advantage of this type of tunnel, because preventing water leakage into the tunnel is critical. Another advantage is that this design does not need formwork to cast the concrete in. This has to do with the fact that the steel shells are used as permanent formwork and it will cut down the costs for extra materials and labour. In figure a- 6 below, there is a 3 dimensional schematization of a SCS sandwich tunnel. Figure A- 6: Schematization of a SCS sandwich tunnel element Another major advantage of a SCS sandwich tunnel compared with reinforced concrete tunnel is that the SCS tunnel doesn’t has an upper / lower limit of reinforcement ratio unlike the reinforced concrete tunnel. The reinforcement ratio limit of 2% for reinforced concrete structures is against Kubilay Bekarlar - Master Thesis - 163 - August – 2016 brittle failure, concrete cracking at smaller deflection and difficult concrete casting around the steel. These aspects don’t hold for SCS structures since the steel is on the outer side of the element and it can be thicker if needed. That is why there is no upper steel ratio limit. As stated before, the SCS sandwich tunnel element is not easy to execute. Especially casting of the concrete is challenging. The self-compacting concrete is poured into the steel casing by using nozzles or tremie-pipe either in the top or bottom steel plate. Pouring the concrete through the bottom plate with a nozzle makes it able for the self-compacting concrete reaches the voids better. Air holes are placed in the corners of the steel shell where the trapped air can get out and the voids can be filled. Vibrating elements are placed on top of the steel shell which helps to release the trapped air. Ensuring a complete fill is essential for a good bond between the steel studs and the concrete. Fires inside a SCS sandwich tunnels is of bigger concern than for other types of tunnels. This has to with the high heat absorption of steel. Because of the fact that the steel is on the outer side of the structure it is more vulnerable for heat development inside the tunnel. In case of a reinforced concrete tunnel this is a smaller problem since the steel bars are covered in concrete. This problem for the SCS sandwich tunnel is solved by applying a fire resistant layer on the steel outer shell. 25 APPENDIX B Variants of composite sandwich tunnels Immersed tunnels can be divided into three main groups: reinforced concrete tunnels, steel shell tunnels and composite sandwich tunnels. The composite sandwich tunnels can also be subdivided. There are full sandwich tunnels, open sandwich tunnels and a combination of both. 25.1 Full sandwich tunnel element In case of a full sandwich tunnel all elements of the tunnel are made out of SCS sandwich members. Steel plates on both sides are provided with steel studs and or stiffeners and are interconnected with self-compacting concrete. The shear reinforcement and diapragms connect both steel plates with eachother. Because of the outer steel plates, which accounts for the tensile stresses no reinforcement is needed. In figure a- 7, a schematization is given of a tunnel cross section where all elements are designed as full sandwich. The first application of the full sandwich immersed tunnel is the Okinawa Naha Port Tunnel in Japan because all members are made as a SCS sandwich member. This tunnel is a road tunnel of which the immersed part is 724 m long. It consists of 8 elements with a height of 8,7 m. Because of the fact that no suitable casting yard was near the tunnel location, the engineers were forced to construct the steel shell and cast while it was afloat. The biggest advantage of a SCS full sandwich tunnel element compared with the open sandwich tunnel element is that the full sandwich tunnel can be built in a shorter time period. Further since all members are SCS sandwich members this variant is also lighter than the open sandwich tunnel. Kubilay Bekarlar - Master Thesis - 164 - August – 2016 Figure A- 7: Steel - Concrete - Steel full sandwich tunnel 25.2 Open sandwich tunnel element The immersed tunnel is an open sandwich tunnel if at least one member is made as an open sandwich and the other elements are of reinforced concrete. An open sandwich member is made out of a steel plate on the outer side which is connected to concrete by shear studs. On the inner side of the member reinforced concrete is applied. The other members will be made of reinforced concrete, figure a- 8. Therefore there are different configurations possible for an open composite immersed tunnel. Compared with the reinforced concrete tunnel, the open sandwich tunnel allows the total weight of the structure to be reduced. But compared with the full sandwich it is still heavier. An advantage of this variant compared with a full sandwich is that it is more cost efficient, since less steel is used. Conventional concrete can be applied for the bottom slab which is from the executional point of view advantageuos, easy casting. Further just like the full sandwich tunnel the concrete can also be casted while it is afloat. The Osaka Port Sakishima tunnel is an application of an open sandwich member for the floor slab and reinforced concrete for the roof and inner walls. This tunnel consists of 10 elements with a height of 8,5 m and a width of 35,2 m. The length of a tunnel element is 103 m. Figure A- 8: Steel concrete open sandwich tunnel Kubilay Bekarlar - Master Thesis - 165 - August – 2016 25.3 Combination of full sandwich and open sandwich members A combination of open and full sandwich tunnel has also been designed. In that case some members will be open sandwich members and the others will be full sandwich members, see figure a- 9. The bottom slab is often designed as an open sandwich element with a steel plate on the outer side and reinforced concrete on the inner side, as described above. On the other side the roof slab and the outer walls are designed as full sandwich members. An advantage of this variant is that the full sandwich members can be designed more slender, which will reduce the overall weight compared with the open sandwich tunnel. Reduction of the weight would reduce the draught which will be an executional advantage. Another aspect is that the full sandwich roof and walls are important to prevent brittle failure in case the ultimate bearing capacity is exceeded, the same holds for the full sandwich tunnel. So this variant is a solution in between the two earlier mentioned. Osaka Port Yumeshima Tunnel is an example of a combination of full sandwich and open sandwich tunnel members. The immersed tunnel consists of 8 immersed tunnel elements of 8,6m height and 35,4m in width. The length of the element varies from 93,1 m to 103,5 m. Figure A- 9: Composite tunnel consisting as a combination of open and full sandwich members 25.4 Elements in a SCS sandwich members The SCS sandwich member consists of several members such as: upper skin plate, lower skin plate, stiffeners, shear connectors, diaphragm and shear reinforcement, see figure a- 10. Kubilay Bekarlar - Master Thesis - 166 - August – 2016 Figure A- 10: Schematization of a SCS sandwich tunnel element with all members 25.4.1 Shear Studs In a SCS sandwich tunnel project hundreds of thousands of shear studs are applied on the steel plates. The studs are normally made with a length which is less than 200mm. In case of a full sandwich member the studs are placed on the top and bottom steel plate. Studs are extended till the compression zone. As stated before these shear studs are a connection between the steel and concrete and account for the longitudinal shear force. Spacing of the studs can be adjusted depending to prevent buckling of the compression steel plate and shear failure. Shear studs can be attached either automated or manually. There is not much difference in the price however, since the automated system has to suit the design specifications. 25.4.2 Steel plates The steel plates form the border of a SCS sandwich compartment. Stiffeners give these plates rigidity, which is essential during concrete casting. These structural plates account for the tensile forces acting on the cross section. Besides the structural function of these plates, they also provide two watertight layers. This is an essential aspect for the tunnels. 25.4.3 Shear reinforcement plates Shear reinforcement are steel plates in the transverse direction of a SCS sandwich member. These plates account for the shear stresses in the member. Because it connects both steel plates with each other it gives stiffness to the plates and prevents it from deforming during concrete pouring. 25.4.4 Diaphragm The diaphragm is installed in the tunnel axis direction to create the compartments. It also accounts for the shear stresses. Also the diaphragms connect both steel plates with each other it gives the steel shell stiffness to prevent it from deforming during concrete pouring. 25.4.5 Self-Compacting concrete The part of the cross section that connects all members with each other is the concrete. Because of the enclosed steel compartment conventional concrete cannot be used, since compacting by vibrating is not possible. This is why self-compacting concrete is applied. Self-compacting concrete is poured in after which the concrete compacts by itself due to its typical composition. 25.4.6 Stiffeners In order not to deform during towing of the steel shell, stiffeners are attached on the steel plates. These stiffeners will make the steel shells robust enough to float. They also provide stiffness which is essential during pouring of concrete which helps it not to deform. Stiffeners have to be applied in the longitudinal and transverse direction. Different shapes could be used for stiffeners, such as Ishape, T-shape or L-Shape. Kubilay Bekarlar - Master Thesis - 167 - August – 2016 26 APPENDIX C Identified topics 26.1 Self-compacting concrete Because the self-compacting concrete is an essential part of the SCS sandwich tunnel and a relatively new technique, this topic is dealt with in more detail. In order to create durable concrete adequate compacting is needed. This would mean that when concrete is not well compacted the quality is reduced. To prevent concrete durability depending on the degree of compaction, selfcompacting concrete was developed. Self-compacting concrete has a special composition which enables it to compact into every corner of the formwork, purely by means of its own weight. These are the main reasons why self-compacting concrete is applied in SCS sandwich tunnel elements. The prototype of self-compacting concrete was first completed in 1988 in Japan. Besides the high deformability property of self-compacting concrete, it also has a high resistance against segregation. Dropping the concrete paste from several meters high will not cause any problem. Paste is viscous in order to be able to flow around the obstacles. High deformability is achieved by applying superplastizer. In the figure a- 11 below the composition of self-compacting concrete is compared with normal concrete. Figure A- 11: Composition of normal and self-compacting concrete, where S fine aggregate, G coarse aggregate and W water There can be seen that self-compacting concrete has an aggregate content which is lower than the conventional concrete. In figure a- 12 there is a sketch which summarizes how self-compacting concrete can be achieved. The ratio of coarse aggregate in self-compacting relative to the total solid volume is 50%, this to reduce interaction between coarse agregate particles when concrete deforms. Whereas the degree of fine aggregates in self-compacting concrete mortar is 60%, see figure a- 13. The viscosity of self-compacting concrete paste is higher than the conventional concrete because of its low water powder ratio. Figure A- 12: Achieving self-compatibility Kubilay Bekarlar - Master Thesis - 168 - August – 2016 Ratio of coarse aggregate volume to the total solid volume given and the ratio of the fine aggrgate volume to the total solid volume are given in the figure below both for self-compacting concrete (SCC) and conventional concrete (Normal). The figure on the right hand side gives a comparison of the water powder ratio of self-compacting concrete and normal concrete. Figure A- 13: Coarse and fine aggregate ratio and water powder ratio of normal and SCC Another important component of self-compacting concrete is the superplasticizer. Superplasticizer in combination with a low water powder ratio will keeps the concrete paste highly deformable. Depending on the properties of the powder, the water powder ratio is assumed around 0,9 – 1,0. The flow ability of fresh concrete depends on coarse aggregate and on the spacing of obstacles (studs). Sufficient deformability of the mortar is needed so the concrete paste can be compacted by its self-weight into all edges of the structure. In figure a- 14 below the normal stresses in the mortar due to approaching of coarse particles is given. Figure A- 14: Mortars shear resistance schematization and test schematization Besides of the function of the mortar as a fluid as stated before it also has a function as solid particle. This property is called the pressure transferability, which acts on the coarse particles as normal stresses when these particles approach each other. The mortars shear resistance is schematized in the figure above. Further self-compacting concrete saves costs of vibrating compaction. However the total costs cannot always be reduced. In figure a- 15 below a practical application of self-compacting concrete can be seen for a steel concrete composite tunnel element. Figure A- 15: Application of self-compacting concrete in steel concrete composite tunnel Kubilay Bekarlar - Master Thesis - 169 - August – 2016 26.2 Loading The loading on the immersed tunnel can be divided into two categories: - 26.2.1 Loading which induces internal forces in the plane of the tunnel walls such as, dead load, hydrostatic load and backfill pressure. Loading resulting in internal forces in the longitudinal direction of the tunnel such as, jacking force and differential forces due to settlement of the subsoil. Dead load Dead load of the tunnel includes the weights of concrete, steel plate, studs, spacers and ballast. Dead weight acts in the gravity direction, but can be resolved into axial and transverse components for the analysis of the tunnel cross-section. The dead loads can act with or against the hydrostatic and backfill loading. 26.2.2 Hydrostatic load and backfill Hydrostatic and backfill pressures constitute the major component of the loading. Both pressures can be assumed to increase linearly with depth. The hydrostatic pressure Pw at any depth h below the water surface is given by: The ρw is the unit weight of water. The pressure is at the top of the tunnel roof is x , at the underside of the tunnel it is ( + D)x ρw. Hydrostatic pressure acts equally in all directions, hw is determined from the height of the maximum water level above zero level. Variations in the water level as a result of waves, tides, river flows, and atmospheric conditions should be taken into account. The pressure can be divided into three components: 26.2.3 Pressure on the tunnel roof Pressure on the side walls Pressure on the floor Pressure on the tunnel roof Pressure on the roof Pr is given by: Pr = hw x ρw + hb (ρsat – ρw) + hs (ρsat – ρw) Pr = hw x pw + hb (ρsub) + hs (ρsub) The ρsat is the saturated unit weight and ρsub is the submerged unit weight of the backfill. The designer should note that the depth of the backfill can change as a result of sedimentation or the movement of sediment. An appropriate allowance for this, hs, should be made in the design. It should also be noted that, for the roof, self-weight loads are additive to the hydrostatic and backfill loading. 26.2.4 Pressure on the side walls The pressure on the side walls is given by: Ph = (hw + hf) ρw + k (hb + hf) ρsub + k hs ρsub Kubilay Bekarlar - Master Thesis - 170 - August – 2016 In this formula k is the effective lateral earth pressure coefficient. This value lies between the active and passive coefficient. The is the angle of internal friction. Because the backfill is under water the angle of friction may be assumed =0 which results in k = 1. That is why the horizontal pressure below the tunnel roof can be calculated as follows: Ph = (hw + hr) ρw + (hb + hr) ρsub + hs ρsub A more accurate value for k may be adopted for k if more reliable data about the lateral earth pressure is available. But for the initial design the earlier assumption is sufficient. 26.2.5 Pressure on the floor The pressure acting on the base is the hydrostatic pressure. Since the tunnel will normally have negative buoyancy, the extra weight of the tunnel will be resisted by the soil on which the tunnel rests. The submerged weight of the backfill on the tunnel roof and any skin friction on the sides of the tunnel section must be resisted. These are additional pressures on the base of the tunnel. It can be assumed that these additional load components are reacted by the soil as uniformity distributed loads. The hydrostatic pressure on the base is given as: Base pressure due to hydrostatics = (hw + D) ρw The weight of the tunnel can be determined from BF2. The base pressure due to the weight of the tunnel can be calculated as follows. Base pressure due to tunnel net weight = (D ρw / BF2) – D ρw Backfill and sedimentation loads will be transferred via the tunnel cross-section to the tunnel base. The pressure acting on the base can be calculated as follows: Base pressure due to backfill = hbc ρsub + hs ρsub The skin friction acts on both sides of the tunnel. It can be calculated from the horizontal earth pressure forces by multiplying by tan φ where φ is the effective angle of friction. Note that tan φ should not be less than 0.5. If skin friction is caused by backfill settlement, then skin friction forces act downward on the base. This gives a tunnel base pressure as follows: Base pressure due to skin friction = (2 hs + 2 hb + hr) Combining the above expression gives the total pressure on the tunnel base: Ρb = (hw ρw ) + (D ρw / BF2) + (hb + hs) ρsub + (2 hs + 2hb + hr) When calculating internal forces in the tunnel base, it should be noted that the self-weight of the base acts in the opposite direction to the above pressure. Kubilay Bekarlar - Master Thesis - 171 - August – 2016 26.2.6 Loading due to placing The tunnel elements are placed on hydraulic jacks that can be adjusted. This way a concentrated end reaction is applied by the jack on the tunnel element. When there is only one jack supporting the tunnel element then torsion is exerted on the tunnel element 26.2.7 Loading due to subsoil settlement When the tunnel is resting on uniformly supported subsoil, no longitudinal moments are generated. However if the subsoil under the tunnel element settles, then there is no uniform support of the subsoil. This way concentrated load will act on the tunnel which will result in high local stresses. 26.2.8 Wave loading The waves, tides and high and low pressure conditions can lead to to variations in the height of the water surface. This causes on its turn variations in hydrostatic pressure on the immersed tunnels. Variations should be considered to determine the maximum hydrostatic pressure. In general, immersed tube tunnels are constructed in sheltered waters, and the influence of wave loading is likely to be small compared with the influence of forces due to jacking and differential settlements. If tunnel elements are to be floated across open sea from fabrication yards remote from the tunnel site, then wave loading needs to be considered more rigorously. The waves will cause additional bending moments in the tunnel element. When wavelength and the length of a tunnel are of the same order, then the most critical situation may be estimated as the Wave length L is identical with the length of an element. The tunnel element will be loaded by a sinusoidal distributed lateral force with its highest action upwards at the ends of the caisson and the larges downward forces in the middle of the element figure a- 16. Figure A- 16: Wave loading on a tunnel element 26.2.9 Thermal loading The loading is caused by loads induced during service due to small temperature gradients. It is assumed that material properties are unchanged. Fire response analysis requires a different approach. Normally under service conditions the temperature of immersed tunnels remains approximately constant and the effects of temperature differences are small. However, thermal forces are induced by a relatively small, linear thermal gradient between the inside and outside of the tunnel wall and this should be assessed. 26.2.10 Sunken ship loading The chance for a concentrated load on the tunnel due to a sunken ship is relatively small. Nevertheless the tunnel should fulfill the safety requirements for resisting the loads if such an event happens. This means that the governing (heaviest) ship should be taken into account in the calculations. Kubilay Bekarlar - Master Thesis - 172 - August – 2016 26.2.11 Traffic loading The traffic loading amounts approximately for 5-10% of the upward loading on the floor slab of the tunnel. This will be balanced by the increased foundation pressure. Due to the thickness of the floor slab and the ballast concrete layer, the influence of the traffic loading on the forces acting on the cross section will be limited. That is why the traffic load is neglected in most cases. 26.2.12 Load combinations The governing situation is that several loads act simultaneously in-plane and longitudinal. Most unfavorable loading combination is taken in order to calculate the internal forces acting on a tunnel. 26.3 SCS Sandwich Elements Laboratory Test Results Experiments were carried out at the University of Wales in Cardiff regarding SCS sandwich elements in 1985. Various aspects of structural performance of SCS elements were investigated. The purpose of these tests were to validate the conclusions of the first test series to obtain a clearer and more thorough understanding of the structural behaviour of SCS and to produce a published design guide specific to SCS construction. In the initial program several tests were conducted. There has to be stated that there are differences between the SCS tunnels elements made in Japan and the elements tested in the UK. The biggest difference is that the tested beams at the University of Wales don’t have diaphragms and shear reinforcement. First the ultimate load tests were carried out. For these tests SCS sandwich beams, columns, radius, joints and tunnel cross sections were used. Also fatigue tests were carried out. Parameters as plate thickness, shear connection, stud length, loading and concrete strength were examined. The test results of the beams showed that all beams except one exhibit ductile behaviour. One suddenly collapsed due to failure of tension plate connectors. Slip was the cause of failure for three beams. The fatigue test showed that all the beams failed on cracking of the tension plate connectors at the weld affected zone. Also there could be seen that that with an increase in the loading, the number of cycles to failure decreased. For the columns two of the three test pieces showed ductile behaviour with yielding of the tension plate and reduction of the carrying capacity. The other columned showed also ductile behaviour where the buckling of the compression plate resulted in a reduction of the load carrying capacity. There was limited slip between the steel and concrete which concludes that there was a proper connection between these elements. There were four radius specimen tested. All four specimen exhibited ductile behaviour. Two failure modes were distinguished, yielding of the inner plate and stud pull-out. Therefore there was concluded that an increase in the loads would result in the strengthening in the inner plate. Also the tension connection with concrete needed to be increased by increasing the length of the studs and reducing the spacing. Two of the four tested T-junctions had radius plates and the other two had right angled plates. Under transverse loading there was only little difference between these two joints. Overall junctions with radius joints were able to withstand a load which is three to four times more than the straight plates. There was concluded that for T-joints with straight plates the arrangement of studs is a crucial factor. In flexural conditions joints fail due to studs pulling out and the right angled joints straighten out. Kubilay Bekarlar - Master Thesis - 173 - August – 2016 Tunnel cross sections were subjected to horizontal and vertical loads. The tunnel section also showed ductile behaviour. Collapse of the tunnel section was due to shear failure of the concrete. The tunnel was repaired by injecting epoxy in the cracked concrete. This confirmed the application of repairs to these types of SCS composite elements. Tests revealed that where collapse was caused by failure of concrete than it is possible to carry out repairs. To summarize these experiments, the following failure modes can be identified, figure a- 17: - yielding of the tension steel plate yielding or buckling of the compression steel plate crushing of concrete in compression shear failure of the concrete horizontal or slip failure of the stud connectors pull out failure of connectors Figure A- 17: Failure modes of SCS composite sandwich elements The behaviour of the test elements showed agreement with the design models. One of the main conclusions of this research program was that SCS sandwich elements could be designed with conventional methods for composite construction. 27 APPENDIX D Project Sharq Crossing The reason why the Sharq crossing project in Doha Qatar is related to this research is that TEC (Tunnel Engineering Consultants) and Royal Hoskoning DHV engineers designed a steel-concrete-steel immersed tunnel. The knowledge gathered from this research will give a better insight in the limits of the design rules as well as the optimization of the design. TEC (a joint venture between Witteveen+ Bos and RoyalHaskoningDHV), together with Santiago Calatrava Engineers and Architects worked on the validation of the original concept design of five tunnels for the Sharq Crossing, figure a- 18. TEC designed in total five tunnels for the Sharq crossing. Two are immersed tunnels of 3.1 and 2.8 km and three are cut-and-cover tunnels with a length of approx. 950-1250 m each connecting the bridges to the Figure A- 18: Map of the Sharq Crossing and immersed tunnel Kubilay Bekarlar - Master Thesis - 174 - August – 2016 Marine Interchange of approx. 600 m, connecting the two immersed tunnels and one of the bridges. Besides the tunnels TEC also works on the bridge foundations, roads, utilities, mechanical, electrical and plumbing systems, the integral safety concept including ventilation and construction schedule. The sandwich immersed tunnel designed for the Sharq crossing will be the first sandwich tunnel designed by TEC as well as the first sandwich immersed tunnel is this region of the world. This explains the relation between this research and the Sharq crossing project. 28 APPENDIX E 28.1 Hand calculation design forces Table 173: Hand calculation of the design forces for different spans Design forces 15m Span Design forces 20 Span Internal Forces - approximation – ULS Internal Forces - approximation – ULS Med - roof 5043,825 kNm Med - roof 8966,8 kNm Med - floor -5129,55 kNm Med - floor -9119,2 kNm V-roof 1681,275 kN V-roof 2241,7 kN V-floor -1709,85 kN V-floor -2279,8 kN N-roof 1294,513 kN N-roof 1294,513 kN N-floor 2040,044 kN N-floor 2040,044 kN Internal Forces - approximation – SLS Internal Forces - approximation – SLS Med - roof 4109,85 kNm Med - roof 7306,4 kNm Med - floor -4004,78 kNm Med - floor -7119,6 kNm V-roof 1369,95 kN V-roof 1826,6 kN V-floor -1334,93 kN V-floor -1779,9 kN N-roof 1125,679 kN N-roof 1125,679 kN N-floor 1773,968 kN N-floor 1773,968 kN Design forces 25 Span Design forces 27 Span Internal Forces - approximation – ULS Internal Forces - approximation – ULS Med - roof 14010,63 kNm Med - roof 16341,99 kNm Med - floor -14248,8 kNm Med - floor -16619,7 kNm V-roof 2802,125 kN V-roof 3026,295 kN V-floor -2849,75 kN V-floor -3077,73 kN N-roof 1294,513 kN N-roof 1294,513 kN N-floor 2040,044 kN N-floor 2040,044 kN Internal Forces - approximation – SLS Med - roof 11416,25 Kubilay Bekarlar - Master Thesis Internal Forces - approximation – SLS kNm Med - roof - 175 - 13315,91 August – 2016 kNm Med - floor -11124,4 kNm Med - floor -12975,5 kNm V-roof 2283,25 kN V-roof 2465,91 kN V-floor -2224,88 kN V-floor -2402,87 kN N-roof 1125,679 kN N-roof 1125,679 kN N-floor 1773,968 kN N-floor 1773,968 kN Structural calculation software Matrixframe is used to check the hand calculations for the ULS case. The bedding is assumed to be uniform. This analysis is done for spans of 15m, 20m, 25m, and 27m. The results are illustrated in figure 168 below. Internal forces - Span 15 m Internal forces - Span 20 m Kubilay Bekarlar - Master Thesis - 176 - August – 2016 Internal forces - Span 25 m Kubilay Bekarlar - Master Thesis - 177 - August – 2016 Internal forces - Span 27 m Figure 168: Internal forces (ULS) for different spans from Matrixframe. 28.2 Capacity calculations for the floor element for a span of 20 m Moment capacity – span 20 m (ULS) Also for the floor first the amount of tensile, compressive reinforcement and the stirrups should be determined. The same steps as described for the roof element are made in order to determine the moment capacity. But first the strains need to be determined. The only unknown is the compression zone height in ULS. This is calculated from the spreadsheet, which is 743,5 mm. Results for the floor element are given in table 174 below. Table 174: Layout reinforcement, area and the strains Kubilay Bekarlar - Master Thesis - 178 - August – 2016 Distances ds Tensile reinforcement Compressive reinforcement 2 1st layer 2 2nd layer 1st layer 1773 [mm] 1st layer 10053 [mm ] 2nd layer 1683 [mm] 2nd layer 10053 [mm ] 3th layer 1593 [mm] 3th layer 10053 [mm ] 4962 2 [mm ] 2 [mm ] 2 Stirrups 1st layer d eff 1683,0 [mm] Total 30159 2 804,2477 [mm ] Asw 8,47 [mm /mm] 2 [mm ] Stirrups Effective depths Strains ε'cu,3 -0,350% ds1 1773 [mm] εs1 0,485% ρtensile 1,59 % ds2 1683 [mm] εs2 0,442% ρcompressive 0,26 % ds3 1593 [mm] εs3 0,400% ds4 91 [mm] εs4 -0,307% 2 After the strains are calculated, the next step is determining the forces in the reinforcement. With all forces known the design moment resistance Mrd can be calculated by multiplying these loads with their eccentricities towards the reference point. This value will be checked with the design moment Med, table 175. There can be concluded from the calculations that for this span of 20 m the design moment is smaller than the moment resistance of the cross sections. Table 175: Moment capacity check Steel, concrete forces N'cd;1 Moment resistance -13011,25 [kN] MN'cd;1 -3763,13 [kNm] Ns1 4371,23 [kN] MNs1 7750,19 [kNm] Ns2 4371,23 [kN] MNs2 7356,78 [kNm] Ns3 Ns4 4371,23 [kN] MNs3 6963,36 [kNm] -2157,57 [kN] MNs4 -196,34 [kNm] Ns5 0,00 [kN] MNs5 0,00 [kNm] Nd 2040,04 [kN] MNd 1938,04 [kNm] ΣF 0,00 [kN] ΣMRd 20048,90 [kNm] eccentricity e0 Med 0,06 9248,40 U-check 4.3.3.2 - Normal stress capacity – span 20 m check (ULS) Again the compressive stress check will be done, this time for the roof element. ( ) In which: Kubilay Bekarlar - Master Thesis - 179 - August – 2016 [m] [kNm] 0,46 N is the normal force in the floor element Ac,eff is the effective cross sectional area of the floor M is the design moment W is the sectional modulus Table 176: Normal stress check Normal stresses 2 fcd -23,33 [N/mm ] σc,top -16,23 [N/mm ] 2 U-check 0,695 The unity check in Table 176 shows that the roof element holds the condition of not exceeding the concrete compressive stress. 4.3.3.3 - Shear force capacity – span 20 m check (ULS) Just like the roof element also the floor will be checked for not exceeding the shear capacity. This is first done for the case without shear reinforcement (stirrups). Therefor the following formula is applied, to calculate the shear resistance of concrete (without stirrups). [ ( ) ] In which: √ These calculations are made for all the spans that are investigated. The results for a span of 20 m are listed in table 29 below. As can be seen the cross section is not able to bear the shear force in case no shear reinforcement is applied. This means that shear reinforcement has to be applied and the shear capacity check has to be done again, now for the shear reinforced cross section. ( ) In which: The minimum value of the two calculated shear force resistances will be used to calculate the unity check. ( ) The unity check for the shear capacity for the cross section with 8,47 mm 2/mm of shear reinforcement, shows that for a span of 20 m the working shear force can be carried, Table 177. Kubilay Bekarlar - Master Thesis - 180 - August – 2016 Table 177: Shear force resistance check with and without shear reinforcement Shear resistance Ved 2279,8 [kN] Nd 2040,0 [kN] Bearing capacity without stirrups Bearing capacity with stirrups Crd,c 0,12 [-] Θ 45 ⁰ αcw k 1,34 [-] Α 90 ⁰ V1 k1 0,15 [-] cot θ ρ1 0,0179198 σcp 1,07 [-] 1 Asw 8,47 5578,5 1 0,6 tan θ 1 2 [mm /mm] 2 [N/mm ] Vrd,c 1350,1 [kN] Vrs,d Ved 2279,8 [kN] Vrd,max Ved U-check ≤ [kN] 10602,9 [kN] 2279,8 [kN] 1,688 U-check 0,41 4.3.3.4 - Crack width control floor (SLS) The next check is the crack width control check. This is a serviceability limit state (SLS) check, which means that the moments and normal forces in SLS will be used. In order to calculate the crack width, first the concrete compression zone is determined. The same steps as for the roof element will be repeated for the floor element. Results are shown in table 178 below. Table 178: Strain, forces, moments and steel stress Serviceability limit state Nrep 1774,0 [kN] Eccentricities Mrep,sls -7119,6 x Strains e'c3 ec 677 [mm] ε'c -0,66 ‰ es1 823 [mm] εs1 0,76 ‰ es2 733 [mm] εs2 0,69 ‰ es3 643 [mm] εs3 0,62 ‰ es4 859 [mm] εs4 -0,58 ‰ es5 950 [mm] εs5 -0,66 ‰ Forces -5395,0 kN MN'c 3649,9 [kNm] Ns1 1535,2 kN MNs1 1263,5 [kNm] Ns2 1390,2 kN MNs2 1019,0 [kNm] Ns3 1245,1 kN MNs3 800,6 [kNm] Ns4 -580,2 kN MNs4 498,4 [kNm] 0,0 kN MNs5 0,0 [kNm] 1774,0 kN Mrep -7119,6 [kNm] Nrep 0,00175 Moments N'c Ns5 820,4 Kubilay Bekarlar - Master Thesis - 181 - August – 2016 [mm] ΣF 0,0 kN ΣM 0 [kNm] σs 152,715 Since the stress in the reinforcing steel has been determined, the crack width that will occur can be calculated. In order to do so the following formula is used: ( ) ( ) These calculation steps have been carried out by making use of a spread sheet program and the results are given in table 179 below. Table 179: Crack width control Crack width εsm -εcm 0,6103256 ‰ 2 s1 125 [mm] wk wmax αe 5,8823529 [n/mm ] s1,max 535 [mm] ρp,eff 0,0555926 [-] sr,max 407,26 [mm] heff 542,5 [mm] k1 0,8 [-] k2 0,5 [-] Ac,eff 542500 2 [mm ] 2 fct,eff 3,21 [n/mm ] k3 3,4 [-] ξ1 1 [-] k4 0,425 [-] kt 0,4 [-] φeq 32 [mm] kx 1 [-] U-check 0,248558 [mm] 0,3 [mm] 0,83 As there can be seen from the unity check in table 31 above, the occurring crack width exceeds the maximum allowed crack width. This is valid for a span of 20 m and current reinforcement ratio of ρtensile :1,59 % ρcompression :0,26%. 28.3 Capacity calculations for the outer wall element for a span of 20 m 4.3.4.1 - Moment capacity – span 20 m (ULS) The same steps as described for the roof element are made in order to determine the moment capacity. But first the strains need to be determined. The only unknown is the compression zone in ULS. This is calculated from the spreadsheet, which is 503 mm. Results for the floor element are given in table 180 below Table 180: Reinforcement layout, area and strains Distances ds Tensile reinforcement Compressive reinforcement 2 1st layer 2 2nd layer 1st layer 1373 [mm] 1st layer 10053 [mm ] 2nd layer 1283 [mm] 2nd layer 10053 [mm ] 3th layer 0 [mm] 4962 2 [mm ] 2 [mm ] 2 3th layer [mm ] Stirrups 1st layer Kubilay Bekarlar - Master Thesis - 182 - 804,25 August – 2016 2 [mm ] d eff 1328,00 [mm] Total 2 20106 [mm ] Stirrups Effective depths Strains Asw 8,47 2 [mm /mm] ε'cu,3 -0,350% ds1 1373 [mm] εs1 0,605% ρtensile 1,35 % ds2 1283 [mm] εs2 0,543% ρcompression 0,33 % ds3 0 [mm] εs3 ds4 91 [mm] εs4 ds5 0 [mm] εs5 -0,287% With the strains known, the forces in the reinforcement and the concrete compressive zone can be calculated. With the eccentricities the design moment resistance Mrd will be determined, table 181. Table 181: Moment capacity check Steel, concrete forces N'cd;1 Moment resistance -8802,50 [kN] MN'cd;1 -1722,36 [kNm] Ns1 4371,23 [kN] MNs1 6001,69 [kNm] Ns2 4371,23 [kN] MNs2 5608,28 [kNm] Ns3 0,00 [kN] MNs3 0,00 [kNm] Ns4 -2157,57 [kN] MNs4 -196,34 [kNm] Ns5 0,00 [kN] MNs5 0,00 [kNm] Nd 2203,00 [kN] MNd 1652,25 [kNm] ΣF 0,00 [kN] ΣMRd 11343,53 [kNm] eccentricity e0 Med 0,05 5504,25 U-check [m] [kNm] 0,485 As shown above the design moment occurring at a span of 20 m is smaller than the design moment resistance. 4.3.4.2 - Normal stress capacity – span 20 m check (ULS) The compressive stress check will be done once more: ( ) Table 182: Normal stress check Normal stresses 2 fcd -23,33 [N/mm ] σc,top -15,85 [N/mm ] xu 503,00 [mm] Kubilay Bekarlar - Master Thesis 2 U-check - 183 - 0,679411 August – 2016 Table 182 shows, that the normal stress occurring in the outer wall is smaller than the concrete compressive yield stress. 4.3.4.3 - Shear force capacity – span 20 m check (ULS) First the shear capacity will be checked for the case when there is no shear reinforcement (stirrups) applied. Therefor the following formula is applied to calculate the shear resistance of concrete (without stirrups), table 183. As can be seen the cross section is not able to bear the shear force in case no shear reinforcement is applied. This means that shear reinforcement has to be applied and the shear capacity check has to be done again, now for the shear reinforced cross section. The unity check for the shear capacity for the cross section with 8,47 mm2/mm of shear reinforcement, shows that for a span of 20 m the working shear force can be carried, table 183. Table 183: Shear force capacity check Shear resistance Ved 1684,3 [kN] Nd 2203,0 [kN] Bearing capacity without stirrups Bearing capacity with stirrups Crd,c 0,12 [-] θ 45 ⁰ αcw k 1,39 [-] α 90 ⁰ V1 k1 0,15 [-] cot θ ρ1 0,0151401 [-] Asw 8,47 σcp 1,47 1 0,6 tan θ 1 2 [mm /mm] 2 [N/mm ] Vrd,c 1123,4 [kN] Vrs,d 4401,8 ≤ [kN] Ved 1684,3 [kN] Vrd,max 8366,4 [kN] Ved 1684,3 [kN] U-check 1 1,499273 U-check 0,38 4.3.4.4 - Crack width control floor (SLS) Now the crack width control check will be performed. The same steps as for the roof and floor element will be repeated for the outer wall element. Again the stress in the steel in the serviceability limit state needs to be calculated first, where after the crack width can be determined. Results are shown in table table 184 and table 185. Table 184: Strains, forces, moments and the steels stress Serviceability limit state Nrep 2000,0 [kN] Eccentricities Mrep,sls -4395 x Strains e'c3 ec 536 [mm] ε'c -0,68 ‰ es1 623 [mm] εs1 0,77 ‰ es2 533 [mm] εs2 0,68 ‰ es3 -750 [mm] εs3 -0,68 ‰ Kubilay Bekarlar - Master Thesis - 184 - 641,5 0,00175 August – 2016 [mm] es4 659 [mm] εs4 -0,58 ‰ es5 750 [mm] εs5 -0,68 ‰ Forces Moments N'c -4339,0 kN MN'c 2326,4 [kNm] Ns1 1550,7 kN MNs1 966,1 [kNm] Ns2 1359,9 kN MNs2 724,8 [kNm] Ns3 0,0 kN MNs3 0,0 [kNm] Ns4 -576,0 kN MNs4 379,6 [kNm] Ns5 0,0 kN MNs5 0,0 [kNm] 2000,0 kN Mrep -4395,0 [kNm] 0,0 kN ΣM 0 [kNm] Nrep ΣF σs 154,255 Table 185: Crack width control Crack width εsm - εcr 0,596 ‰ 2 s1 125 [mm] wk 0,254 [mm] wmax 0,3 [mm] U-check 0,85 αe 5,882 [n/mm ] s1,max 535 [mm] ρp,eff 0,046 [-] sr,max 425,74 [mm] heff 430 [mm] k1 0,8 [-] k2 0,5 [-] Ac,eff 430000 2 [mm ] 2 fct,eff 3,21 [n/mm ] k3 3,4 [-] ξ1 1 [-] k4 0,425 [-] kt 0,4 [-] φeq 32 [mm] kx 1 [-] As there can be seen in table 185 the cross section with the current dimensions and reinforcement layout also holds for the crack width. The outer wall with these dimensions also fulfils all other checks. There can be concluded that the outer wall can be applied. 28.4 Calculation of the composed modulus of elasticity Table 186: Calculation of the composed modulus of elasticity and height of the floor element Floor Inner steel plate Concrete core t [mm] 20 b [mm] 1000 2 E [N/mm ] z [mm] Outer steel plate Composed 1845 35 1900 1000 1000 1000 210000 34000 210000 10 922,5 17,5 950 2 A [mm ] 20000 1845000 35000 1900000 4 1,67E+09 1,5375E+11 2,92E+09 1,58E+11 4 1,74E+10 5,23E+11 3,09E+10 5,72E+11 4,20E+09 6,27E+10 7,35E+09 7,43E+10 3,50E+14 5,23E+15 6,13E+14 6,19E+15 Ixx [mm ] Iyy [mm ] EA [N] 2 EIxx [N mm ] Kubilay Bekarlar - Master Thesis - 185 - August – 2016 2 EIyy [N mm ] 3,65E+15 1,78E+16 h* 2124,63 Exx* 34961,36 [N/mm ] Eyy* 34961,36 [N/mm ] 6,50E+15 2,79E+16 [mm] 2 2 Table 187: Calculation of the composed modulus of elasticity and height of the roof element Roof Inner steel plate Concrete core Outer steel plate Composed 25 1540 35 1600 1000 t [mm] b [mm] 2 E [N/mm ] z [mm] 1000 1000 1000 210000 34000 210000 12,5 770 17,5 800 2 A [mm ] 25000 1540000 35000 1600000 4 2,08E+09 1,28333E+11 2,92E+09 1,33E+11 4 1,53E+10 3,04E+11 2,17E+10 3,41E+11 Ixx [mm ] Iyy [mm ] EA [N] 5,25E+09 5,24E+10 7,35E+09 6,50E+10 2 4,38E+14 4,36E+15 6,13E+14 5,41E+15 2 3,21E+15 1,03E+16 4,56E+15 1,81E+16 EIxx [N mm ] EIyy [N mm ] h* 1829,65 [mm] Exx* 35503,98 [N/mm ] Eyy* 35503,98 [N/mm ] 2 2 Table 188: Calculation of the composed modulus of elasticity and height of the wall element Wall Inner steel plate Concrete core Outer steel plate Composed 20 1455 25 1500 1000 t [mm] b [mm] 2 E [N/mm ] z [mm] 1000 1000 1000 210000 34000 210000 10 727,5 12,5 750 2 A [mm ] 20000 1455000 25000 1500000 4 1,67E+09 1,2125E+11 2,08E+09 1,25E+11 4 1,09E+10 2,57E+11 1,37E+10 2,81E+11 Ixx [mm ] Iyy [mm ] EA [N] 4,20E+09 4,95E+10 5,25E+09 5,89E+10 2 3,50E+14 4,12E+15 4,38E+14 4,91E+15 2 2,28E+15 8,73E+15 2,88E+15 1,39E+16 EIxx [N mm ] EIyy [N mm ] h* 1681,77 [mm] Exx* 35034,57 [N/mm ] Eyy* 35034,57 [N/mm ] 2 2 These values will be used for the definition of the material properties and physical properties of the SCS sandwich cross section in Diana. Kubilay Bekarlar - Master Thesis - 186 - August – 2016 28.5 Calculation of the prestress force in the floor element Point A t=0 Bottom Boundary condition fulfilled Top Boundary condition fulfilled Point A t=∞ Bottom Boundary condition fulfilled Top Boundary condition fulfilled The same steps are performed for point B. Point B t=0 Bottom Kubilay Bekarlar - Master Thesis - 187 - August – 2016 Boundary condition fulfilled Top Boundary condition fulfilled t=∞ Bottom ( ) ( ) Boundary condition fulfilled Top ( ) ( ) Boundary condition fulfilled 29 APPENDIX F 29.1 FEA model 29.1.1 Introduction In the previous studies done for this research project there was concluded that there should be investigated whether a SCS sanwdwich tunnel design could be optimized. In order to do so insight needs to be gathered in the structural response to the loadings in servicability limite state (SLS) and ultimate limt state (ULS). This can either be done for the linear and nonlinear analysis. However due to the number of equations that needs to be solved, a Finite Element Analysis (FEA) software program will be used to do the detailed structural analysis. The FEA program that will be used is DIANA. Dimensions of the earlier designed “Base Case” of the SCS sandwich tunnel will be used for the model. In order to reach the goal of achieving reliable results from the FEA program, the following steps are performed. First the problem is described. Here after there should be investigated what types Kubilay Bekarlar - Master Thesis - 188 - August – 2016 analysis there are, when they should be used and what type of output there will be generated. The next step is the idealisation of the SCS sandwich tunnel element into a simplified engineering problem that can be solved with the FEA program DIANA. Here for studying DIANA elements is essential to apply the elements with the best charachteristics for this particular problem. The second phase is modelling of the SCS tunnel element. Initially the schematized structure geometry will be constructed. Here after a proper mesh will be applied to the structure. The next step will be the application of the material properties / material models. Material models to be used depend on the type of analysis that will be made as well as the type of material. This means that a study should be done on the most suitable material models for the steel and concrete in a SCS sandwich tunnel element. Finally the loading on the structure and the boundary conditions will be applied. All these steps will be executed in iDIANA pre-processor. The next phase takes place in DIANA MeshEdit. Here the analysis types will be specified, where after the analysis will be run. The final phase in the post-processing, which will be analyzing the results from DIANA. All these steps are schematized in figure 169 below. Figure 169: Schematization of the steps to be performed for the FEA of the SCS sandwich tunnel element 29.1.2 Linear and Non-Linear FEA analysis The structural analysis can be divided into three broad categories. These are hand analysis, linear FEA and non-linear FEA. With the hand analysis, the order of magnitude of the internal forces can be determined. This will allow dimensions to be selected for detailed analysis. For detailed structural analysis linear and non-linear analysis should be preferred. There are three types of nonlinearities. Material (physical) nonlinearity, geometrical nonlinearity and boundary (contact) nonlinearity. The geometrical non-linearity is the change of geometry due to large displacement. Material non-linearity is the non-linear relation between stress and strain. The contact non-linearity is caused by the impact on the structures. 29.1.3 Linear analysis Linear analysis is an acceptable approximation of the reality, where the material behaviour is assumed to be perfectly linear for a certain loading. This way less material constants are used. So the linear FEA is performed if there is expected that the structure will behave linearly, according to the Hook’s Law where the stress is proportional to the strain. The induced displacements are so Kubilay Bekarlar - Master Thesis - 189 - August – 2016 small that the change in geometry and material properties is negligible. After the load is removed, the structure will return to its original configuration. This is the fundamental principle of linear structural analysis. In figure 170 a linear elastic material model is given. Figure 170: Linear elastic material model Throughout the process of loading and unloading in which the structure deforms, the structure will retain its initial stiffness. This can be simplified by the following equation: [ ] [ ] [ ] In which: [F] is the vector of nodal force [K] is the stiffness matrix [d] is the vector of nodal displacement The stiffness matrix [K] depends on the material, geometry and boundary conditions. For the linear analysis the stiffness does not change. This means that the equations are just solved once. This also explains why the computation time is short. 29.1.4 Nonlinear analysis For a more realistic assessment of the structural response nonlinear analysis should be performed. Full nonlinear analysis covers the complete loading from nonlinear behaviour in SLS to nonlinear behaviour ULS which results in collapse. Nonlinear FEA is performed to investigate the behaviour of the structure beyond the elastic limit of the material. In this case the loading produces a significant change in the stiffness. Since the element is exposed to plastic deformation it will not return to its original configuration. The most important difference with the linear analysis is that the nonlinear analysis does not assume a constant stiffness. In contrary, the stiffness changes during deformation of the structure. It means that the stiffness matrix [K] must be updated during the iterative calculation process. This explains the much longer calculation time for the nonlinear FEA program. Since the structure generally does not collapse after the appearance of the first crack or local crushing, that is why the linear elastic analysis is a step back with respect to the limit state. This is also the reason why a nonlinear analysis should be performed for the full understanding of the structural behaviour. The nonlinear analysis can be subdivided into material nonlinear analysis, geometrical nonlinear analysis and contact nonlinear analysis. 7.2.2.1 - Material (physical) nonlinear analysis In case the stiffness changes during the loading due to the changing material properties, than it is a material nonlinearity problem. Engineering materials show a linear stress-strain relationship up to Kubilay Bekarlar - Master Thesis - 190 - August – 2016 a certain stress level. This is the linear elastic domain of the material. The maximum stress level of this domain is called the design yield stress. Beyond this stress-stress strain relationship becomes nonlinear, also known as the plastic domain. In figure 171 below the elastic perfectly plastic stressstrain curve is given for concrete and steel. This is the most simple nonlinear material model. Figure 171: Elastic perfectly plastic stress-strain curves of concrete and steel The elastic perfectly plastic model does not take into account the plastic strength of the material, also known as hardening. There is assumed that after reaching the yield strength the structure will collapse. However after exceeding the yield stress the material will resist the higher stresses in its plastic state. This given real stress-strain diagram of steel and concrete in figure 172. The material nonlinear stress strain relationship can cause the structure to behave nonlinearly. The factors that may influence the material stress-strain relationship are the load history, environmental conditions (temperature) and the time that a certain load is applied (creep). Figure 172: Actual stress-strain diagram for steel and concrete 7.2.2.2 - Geometrical nonlinear analysis As stated before, nonlinear analysis is necessary when the stiffness changes during the loading process. If the stiffness changes due to change in the shape, than the nonlinearity is defined as geometrical nonlinearity. These changes in the shape that cause a different stiffness are large deformations. A rule of thumb that gives an indication when to use a nonlinear geometrical analysis is when the deformation is 1/20th of the largest dimension. In figure 173 below a nonlinear response of a structure exposed to loading can be seen. Kubilay Bekarlar - Master Thesis - 191 - August – 2016 Figure 173: Geometrical nonlinearity Another aspect of large deformations is that the direction of the force will also change during the loading process. The FEA program has two options regarding this aspect: following and nonfollowing load. In case a following load is chosen, the load remains its orientation towards the structure where the non-following load remains its initial direction, see figure 174. Figure 174: Schematization of a following and a non-following load Changes in stiffness can also occur when the deformations are small. However with small deflection and small strain there is assumed that the resulting stiffness changes are insignificant. 7.2.2.3 - Boundary (contact) nonlinear analysis This nonlinear analysis is of importance when there is contact between two or more components. In civil engineering problems this is the interaction between the structure and the support (boundary). A normal force contacting the surfaces acts on the two bodies where they touch each other. In case there is friction between the surfaces, shear forces may be created. The aim of this analysis is to identify the surfaces that are in contact and to calculate the pressures that are generated. 7.2.2.4 - Choice of analysis First there should be started with a simple model of the SCS sandwich tunnel element. This way there could be checked whether the outcome of the model is in accordance with hand calculation results. If the hand calculation results and the output of the simple model coincide, then it means that the applied boundary conditions are realistic. The analysis type that will be used in the initial stage is the linear elastic analysis. This way there can be seen whether some elements already yield in this stage. In other words, if there are some problem areas present these can already be identified in the linear elastic stage. But it does not give a decisive answer whether the structure will fail. For this the nonlinear analysis should be performed. Kubilay Bekarlar - Master Thesis - 192 - August – 2016 After the linear analysis the nonlinear analysis can be performed depending on the results of the linear elastic analysis. The nonlinear analysis will be performed if in large parts of the structure the limit stresses and strains are exceeded. 29.2 DIANA elements In this section some of the relevant Diana elements which can be used for the SCS sandwich tunnel model, will be explained in more detail. The study of the Diana elements is essential in order to choose the most appropriate element for this SCS sandwich tunnel model. This is necessary since the better the elements represent the reality the more realistic the output of the model will be. 29.2.1 Beam Elements The beam element is a bar which fulfils the condition that the height d is small in relation to its length l, see figure a- 18. These elements can be exposed to axial deformation Δl, shear deformation γ, curvature κ and torsion. That is why this element can describe axial forces, shear forces and moments. Beam elements are used to do 2-D and 3-D analysis. This element can be subdivided into three classes. Class-I These are the classical beam elements with directly integrated cross sections. They can be used for linear analysis and the geometrical nonlinear analysis. For the physical nonlinear analysis it only gives a limited stress-strain diagram. Class-II The elements in the second class are fully numerical integrated classical beams. Linear analysis, geometrical and physical nonlinear analysis can be performed with these elements. Class-III The third class is the fully numerical integrated Mindlin beam element. This can also be used for linear analysis and nonlinear analysis (geometrical and physical). Figure A- 19: Beam element For the beam elements the variables are the displacements, translation and the rotation. Diana can calculate from these variables the forces, moments and Cauchy stresses in the node. For class I, II and III Diana derives the deformation from the displacement in the node. From these deformations it derives the strains, stress, forces and the moments The beam elements result in a simple model, which leads to a reduced computation time. This element will give insight in the occurring forces and the behaviour. Also modelling with these elements is rather easy. However a disadvantage of this element that it does not give sufficient information about the stresses on a detailed level. Kubilay Bekarlar - Master Thesis - 193 - August – 2016 29.2.2 Plane stress elements The plane stress element is characterized by the element nodes being in one flat plane. Which means that the thickness t must be small, compared with the b, see figure a- 18. Whereas the loading must be in the plane of the element. Figure A- 20: Plane stress element Diana has also 3-D plane stress elements available. The loads can be defined in the plane of the element as well as perpendicular to the plane. Since these elements don’t have stiffness in the transverse direction, this is why loads perpendicular can only be carried when the element is connected to another element that has stiffness in this direction. One of the characteristics of the plane stress elements is that the stress components perpendicular to the face σ xx = 0. These elements can be applied if there is no bending outside the plane of the structure. From the deformations Diana derives the strain. Where after it calculates the Chauchy stress and generalized forces. 29.2.3 Plane strain elements The plane strain elements must be positioned in the XY-plane, where the Z coordinate of the nodes must be zero. Similar as the plane stress element also here the loading F must be in the plane of the element, see figure a- 21. One of the characteristics of the plane strain elements is that the thickness t is equal to unity. Another characteristic is that the strain component perpendicular to the face of the element εzz = 0. The following plane strain elements are available in Diana: - Standard plane strain elements with triangular and quadrilateral cross section. Nonlinear analysis can be performed with this element. Another element is the infinite shell element which has a thickness that is small compared with its length. The complete plane strain element is an element which can be applied for 3-D models. The variables for the plane strain elements are the translations of the nodes. These translations cause deformation of the elements. From these deformations the strains are determined, which on its turn results in the derivation of the Cauchy stresses. Kubilay Bekarlar - Master Thesis - 194 - August – 2016 Figure A- 21: Plane strain element 29.2.4 Plate bending element The plate bending elements must fulfill the condition that the element nodes must be in the flat XY plane. The dimension of this element is characterized by the fact that the thickness t is small relative to the width b. There can be stated that the loading on this element must be perpendicular to the element plane and the moment must act around an axis of the element. This can be observed in figure a- 22 below. Figure A- 22: Plate bending element Another characteristic of the plane bending element is that the stress component perpendicular to the plate face is zero, σzz = 0. Variables of the plate bending element is the translation Uz, which is perpendicular to the element plane and rotation φx and φx. The nodal displacements result in the deformations ∂Ux, ∂Ux and ∂Uz. From these deformations Diana derives the strains, generalized moments, forces and Cauchy stresses are calculated by Diana. 29.2.5 Flat shell elements The flat shell elements are a combination of plane stress elements and plate bending elements. Just like the previous elements the nodes should be in a flat plane, the XY plane. If this is not the case and the nodes are not in the XY plane than the curved shell element should be applied. The element should be thin, in other words the thickness t should be small compared with the width b of the element. This can be seen in figure a- 23 below. Kubilay Bekarlar - Master Thesis - 195 - August – 2016 Figure A- 23: Flat shell element The forces can act on this element from in all directions, whereas the moment should act in plane of the element. Diana offers three flat shell elements: regular element, elements with drilling rotation and the spline element. Regular elements have three translations and two in plane rotations in each node. The element with the drilling rotation has an additional rotation φz in each node. As for the spline element, this element is useful for the analysis of post-buckling of prismatic structures. Variables in the nodes of these elements are the translations Ux, Uy and Uz and the rotations φzx and φy. From these deformations the strains are calculated, where after the generalized moments, forces and Cauchy stresses are calculated. 29.2.6 Curved shell elements As the name of this element says so, this element is ideal for curved structures. For flat models the flat shell elements should be preferred. The curved shell element nodes have five degrees of freedom, three translations Ux, Uy, Uz and rotations φx and φy. Other characteristic of this element is that they must be thin (thickness t small compared with width b). Further the load can act in any direction of the element, see figure a- 24 below. The moment should act around an axis of the element. Figure A- 24: Curved shell element The displacements cause deformations to the elements. From these deformations Diana derives the strains. This way the output of this element will be given which is: Cauchy stress, moments and forces. Kubilay Bekarlar - Master Thesis - 196 - August – 2016 29.2.7 Solid elements When the solid elements are applied, the computation time becomes longer since these elements produce a larger system of equations. That is the reason why this element should be used when other elements are not suitable or when the output is not accurate. One of the characteristics of the solid element is that the stress situation is 3-D. The loading on this element may be arbitrary. Applications of this element are voluminous structures such as concrete foundations, walls, floors and soil masses. In figure a- 25 below a solid element is schematized. Figure A- 25: Solid element The solid elements in Diana can be used to determine the Cauchy stresses. Herewith the moment and forces can also be derived. 29.2.8 Interface elements Diana offers three types of interfaces elements structural interface elements, contact elements and fluid-structure interface. For the scope of this research project only the first element type is of importance. Applications of the interface element are: elastic bedding, nonlinear-elastic bedding, discrete cracking, friction between surfaces and joints in rock. With respect to shape and connectivity there are four types of structural elements: - 30 Nodal interface element Line interface element Line-solid connection interface element Plane interface element APPENDIX G PAPERS AND REPORTS ON SCS SANDWICH TUNNELS AND COMPOSITE FEM ANALYSIS Paper: Immersed Tunnels in Japan: Recent Technological Trends - 2002 Authors: Keiichi Akimoto, Youichi Hashidate, Hitoshi Kitayama, Kentaro Kumagai This paper gives general information about the recent technology on steel-concrete-steel composite sandwich tunnels and what type of variants there are. The differences between the variants are Kubilay Bekarlar - Master Thesis - 197 - August – 2016 further highlighted. Here after it focusses on several SCS tunnel projects that were built in the last few decennia in Japan. Further the joint between the elements is discussed. Conclusions of the paper: Recent years there is an increase in SCS sandwich tunnels constructed in Japan. SCS sandwich tunnels can be divided into full sandwich and open sandwich element. Bellows joints consist of steel leaf springs and expansion and contraction of the leaf springs absorbs the displacement of the joints. Crown seal joint consists of a dewatering rubber piece called a crown and is provided with an opening inside. This paper was used in the initial literature study stage to get general information about the full sandwich tunnel, open sandwich tunnel and the combined full and open sandwich tunnel. It gave insight in the conventional joint as well as the joints used for recent SCS sandwich tunnel projects in Japan, such as bellow joints and crown seal. The joints in Japan are provided with coupler cables which make sure that the joint opening doesn’t widen. Paper: Self-compacting concrete - 2003 Authors: Hajime Okamura, Masahiro Ouchi This paper highlighted the development of self-compacting concrete. Here after it focusses on the mechanisms which give the self-compacting concrete its self-compatibility. Comparisons are being made with the conventional concrete. Especially what the advantages and disadvantages are and how they are created. Concrete elements made out of self-compacting concrete were also thoroughly tested before being used. These test results are also discussed in this paper. Further the current status of self-compacting concrete is explained. Conclusion: The author states that the main obstacle for the wide range use of self-compacting concrete has been taken out by the large number of tests carried out. Now it is time for the engineers to make use the concrete and its construction. In addition new structural systems making use of self-compacting concrete need to be introduced. When self-compacting concrete becomes widely used such that it will be seen as normal concrete rather than special concrete, this will be a big step in acquiring durable and reliable structures. Paper: The challenges involved in concrete works of Marmaray immersed tunnel with a service life of 100 years - 2009 Authors: Ahmet Gokce, Fumio Koyama, Masahiko Tsuchiya, Turgut Gencoglu This paper focusses initially on the waterproofing and corrosion protection of the Marmaray immersed tunnel. It highlights what measures were taken and why. Also discussed is the execution sequence of the concrete work, namely the pre-concreting, casting and post concreting. Conclusion: One of the successful outcomes of the Marmaray immersed tube tunnel project was the controlled concrete works ensuring the long term durability requirements of the owner. This was achieved by combining effective design principles, relevant standards, codes, specifications and expertise of the multidisciplinary specialist in the conception phase. Report: Double skin composite construction for submerged tube tunnels – Phase3, 1997 Author: European Commission for Technical Steel Research This report consists of three phases. Phase one the Cardiff tests where different SCS sandwich elements were tested on failure. The test results were analysed and the main failure mechanisms were acquired. In phase two the loads and existing design guidelines are discussed in detail. This Kubilay Bekarlar - Master Thesis - 198 - August – 2016 chapter gives a good image how to calculate the loads and how to design the SCS sandwich composite elements. In the third and last phase the Cardiff fatigue test is discussed. In the first phase the elements tested were beams, columns, radius, joints and tunnel cross sections. Nearly all beam elements showed ductile behaviour, except one which showed brittle failure. Failure due to failure of shear connectors and slip were the main causes for the beam models. All test columns showed ductile behaviour where yielding of the tension plate and buckling of the compression plate was the main failure mechanism. The three radiuses tested showed also ductile behaviour. Failure mechanisms for these test pieces were, yielding of the inner plate and the pullout of the studs. The main conclusion of joints tests was that the radius joints were able to bear three to four times more load than the joint with straight plates. Ductile behaviour was also observed for the tunnel cross section. The collapse of the tunnel was due to shear failure of the concrete. This report is useful for the research on SCS sandwich immersed tunnels, since it gives insight in the failure mechanisms that occurred with the different specimen. In a later stage of this research the model output could be compared with the test results obtained in Cardiff. Besides experimental insight, this report also gives information how to design SCS sandwich tunnels and which checks should be done, what loads should be used and which safety factors should be applied. There is also an example of a SCS immersed tunnel being worked out. Report: “Stalen en composiet staalbeton tunnelconstructies – Staalbeton sandwichelementen, Deel 2: Modelvorming en rekenregels” English: “Steel and composite steel concrete tunnel structures – Steel concrete sandwich elements” - 2000 Author: Centrum Ondergronds Bouwen This research focuses on an alternative type of SCS sandwich elements. Commonly used sandwich element consists of shear studs attached to the steel plate at only one side. The other side with a flat had is embedded in the concrete compression zone. An alternative is to apply shear connectors attached to the steel plates with both sides. One side will be welded on the upper steel plate and the other side on the lower steel plate. The aim of this report is to determine design rules for a statically determined SCS sandwich beam, which has shear studs that are connected on both sides. In order to reach this goal result of SCS sandwich elements were used. Also an analytical and a numerical model are worked out. The numerical model is used to predict the non-linear behaviour of the element. From the numerical model there is seen that the shear force is carried by a truss system. In which the compression diagonals arise in the concrete and the tensile forces in the studs. Besides this truss contribution to bear the shear force, a part of the shear force also goes directly to the support. Paper: “Finite element analysis of steel concrete steel sandwich beams” - 2007 Author: N. Foundoukos, J.C. Chapman This paper is about finite element analysis of a bi-steel beam. A bi-steel beam is a beam which consists of steel plates connected with steel studs. For this analysis ABAQUS FEM program has been used. First the force deflection curves for different beams have been obtained with the FEM Kubilay Bekarlar - Master Thesis - 199 - August – 2016 program. This showed good agreement with the test results. The same has been done for the axial forces and the slip. With the model insight has been obtained about the cracking pattern that will occur in the concrete. The failure modes of the FEM model show good agreement with the tested beam. The first conclusion of this paper is that the load deflection curves of the FEM model show good agreement with the tests. Also the ultimate failure load is close to the observed value of the tests. The same holds for the failure modes observed, which also show good agreement. The horizontal shear forces show agreement with the truss model. This force is resisted by the shear connectors and the friction between the steel and concrete. Cracking pattern obtained with the FEM model showed agreement with the experimental results. The slip is mainly affected by concrete cracking and shear stud yielding. Further there is concluded that the parametric studies showed good agreement design guide for transverse shear capacity. This supports the use design equations for the transverse shear resistance. Paper: Behaviour of composite segment for shield tunnel – 2010 Authors: Wenjun Zhang, Atsushi Koizumi This paper focusses on composite elements in shield tunnels. The purpose of this research is to study the behaviour of composite segments by results of experiments and a FEM analysis. With this analysis the failure models of the composite elements will be investigated. First the author discusses the results of the experiments carried out. After this stage the FEM analysis starts. From these analysis graphs of moment / curvature and force / deflection is obtained. These graphs for the experiments and the FEM analysis show good agreement. One of the conclusions of the authors regarding their research is that, the composite shield elements with steel studs failed due to the crushing of the concrete within the composite element. On the other hand the composite elements without shear studs failed due to buckling of the top steel plate. There were also composite elements carried out with weak studs. For these elements there was observed that they failed either because of failure of concrete crushing or buckling of the top plate. This study also showed that the skin plate has a significant contribution to the ultimate limit capacity of the composite element. Finally there was also concluded that the segments showed ductile behaviour after exceeding the ultimate yield strength and that the experimental results and the FEM analysis showed good agreement. Kubilay Bekarlar - Master Thesis - 200 - August – 2016
