Modelling of a piled raft foundation as a plane strain model in PLAXIS 2D A geotechnical case study of Nordstaden 8:27 Master of Science Thesis in the Master’s Programme Infrastructure and Environmental Engineering JOEL ALGULIN BJÖRN PEDERSEN Department of Civil and Environmental Engineering Division of GeoEngineering Geotechnical Engineering Research Group CHALMERS UNIVERSITY OF TECHNOLOGY Göteborg, Sweden 2014 Master’s Thesis 2014:131 joal Ögonblicksbild MASTER’S THESIS 2014:131 Modelling of a piled raft foundation as a plane strain model in PLAXIS 2D A geotechnical case study of Nordstaden 8:27 Master of Science Thesis in the Master’s Programme Infrastructure and Environmental Engineering JOEL ALGULIN BJÖRN PEDERSEN Department of Civil and Environmental Engineering Division of GeoEngineering Geotechnical Engineering Research Group CHALMERS UNIVERSITY OF TECHNOLOGY Göteborg, Sweden 2014 Modelling of a piled raft foundation as a plane strain model in PLAXIS 2D A geotechnical case study of Nordstaden 8:27 Master of Science Thesis in the Master’s Programme Infrastructure and Environmental Engineering JOEL ALGULIN BJÖRN PEDERSEN © JOEL ALGULIN & BJÖRN PEDERSEN, 2014 Examensarbete / Institutionen för bygg- och miljöteknik, Chalmers tekniska högskola 2014:131 Department of Civil and Environmental Engineering Division of GeoEngineering Geotechnical Engineering Research Group Chalmers University of Technology SE-412 96 Göteborg Sweden Telephone: + 46 (0)31-772 1000 Cover: Pore pressure distribution below cross-section K after ten years of consolidation and an additional construction of two floors. Chalmers Reproservice Göteborg, Sweden 2014 I Modelling of a piled raft foundation as a plane strain model in PLAXIS 2D – A geotechnical case study of Nordstaden 8:27 Master of Science Thesis in the Master’s Programme Infrastructure and Environmental Engineering JOEL ALGULIN BJÖRN PEDERSEN Department of Civil and Environmental Engineering Division of GeoEngineering Geotechnical Engineering Research Group Chalmers University of Technology ABSTRACT The aim of this report has been to, through a case study, investigate if a composite foundation, consisting of a piled raft, is possible to model in a satisfying way with the finite element computer software PLAXIS 2D, as well as investigate if an additional construction of storeys would be possible on the existing foundation. For the case study, a building in the shopping centre Nordstan in Gothenburg has been used. Documentation in form of construction drawings, soil tests and reports regarding the foundation of Nordstan has been used for the calculations. The soil model Soft Soil has been used since it is suitable for modeling deformations of clay, like the one present at the site of the case study. The structural element embedded pile row, which provides the opportunity to set the out-of-plane distance in spite of the two- dimensional modelling, has been used to model the piles. Different loading scenarios have been used in order to predict settlements for addition of different number of storeys. Comparisons between the soil models Soft Soil and Soft Soil Creep have been performed as well as comparisons between rafts with and without piles. In the conclusion it is stated that it seems possible to model the case study in a way that gives reasonable results regarding settlements, which indicates that a two-dimensional model can be a good and time efficient way to get a rough estimation of the capacity of a piled raft foundation. The embedded pile row element has a reasonable behaviour in the calculations, but comparisons to real testing of piles are needed. For further studies new soil tests are also needed. The results indicate that construction of additional storeys meets the demands regarding differential settlements and that deformations at connections to surrounding streets more likely will set the limits of design. Key words: Piled raft, Plaxis 2D, Excavation, Settlements, Vertical soil deformations, Soft Soil, Gothenburg, Nordstan, Östra Nordstaden, Embedded pile row II Modellering av en samverkansgrundläggning som ”plane strain” model i PLAXIS 2D – En geoteknisk fallstudie av Nordstaden 8:27 Examensarbete inom masterprogrammet Infrastructure and Environmental Engineering JOEL ALGULIN BJÖRN PEDERSEN Institutionen för bygg- och miljöteknik Avdelningen för geologi och geoteknik Forskargruppen för geoteknik Chalmers tekniska högskola SAMMANFATTNING Denna rapports ändamål har varit att, genom en fallstudie, undersöka huruvida en samverkansgrundläggning, bestående av en platta på pålar, går att modellera på ett bra sätt i det finita element-datorprogrammet PLAXIS 2D samt om en eventuell tillbyggnad av våningar skulle vara möjlig på den befintliga grundläggningen. Som fallstudie har en byggnad i köpcentret Nordstan i Göteborg använts. Dokumentation i form av konstruktionsritningar, jordtester samt rapporter om Nordstans grundläggning har använts för beräkningar. Jordmodellen Soft Soil har använts eftersom den är lämplig för att modellera sättningsbeteende i lerjordar likt den som finns vid fallstudien. Konstruktionselementet ”embedded pile row”, vilket ger möjlighet att ställa in avstånd i djupled trots tvådimensionell modellering, har använts för att modellera pålarna. Olika lastscenarion har använts i beräkningar för att förutsäga sättningar för olika antal våningar vid en eventuell tillbyggnad. Jämförelse mellan jordmodellerna Soft Soil och Soft Soil Creep har utförts liksom en jämförelse mellan plattor med och utan pålar. I rapportens slutsatser framkommer att fallstudien verkar gå att modellera på ett sätt som ger rimliga resultat i form av sättningar, vilket indikerar att en tvådimensionell modell kan vara ett bra och tidseffektivt sätt att få en grov uppfattning av en samverkansgrundläggnings kapacitet. Pålelementet har ett rimligt beteende i beräkningarna, men behöver jämföras med verkliga påltester. För fortsatta studier behövs det även utföras nya jordtester. Resultat indikerar att eventuell tillbyggnad klarar kraven för differentialsättningar och att sättningar vid förbindelser med omkringliggande gator snarare kommer bli dimensionerande. Nyckelord: Samverkansgrundläggning, Plaxis 2D, Schaktning, Sättningar, Vertikala jorddeformationer, Soft Soil, Göteborg, Nordstan, Östra Nordstaden, Embedded pile row CHALMERS Civil and Environmental Engineering, Master’s Thesis 2014:131 III Contents ABSTRACT I SAMMANFATTNING II CONTENTS III PREFACE VII NOTATIONS VIII 1 INTRODUCTION 1 1.1 Background 1 1.2 Aim 1 1.3 Limitations 2 1.4 Methodology 2 2 BUILDING FOUNDATIONS ON SOFT COHESIVE SOIL 3 2.1 Raft foundation 3 Contact pressure and settlements 3 2.1.1 2.2 Compensated foundations 4 2.3 Piled foundations 5 Friction piles 6 2.3.1 Negative skin friction - Down drag 6 2.3.2 Neutral plane 6 2.3.3 Settlements for piled foundations 7 2.3.4 2.4 Composite foundation - Piled raft 9 The creep pile principle 10 2.4.1 2.5 Magnitude of allowable settlements for foundations on soft cohesive soil 11 3 CASE STUDY OF NORDSTADEN 8:27 12 3.1 History of the area 12 3.2 Geotechnical conditions 13 Geology 13 3.2.1 Hydrogeological conditions 14 3.2.2 Soil properties - parameter evaluation 14 3.2.3 3.3 Foundation of Nordstan 22 3.4 Principles behind the foundation method of building 6 26 Bearing capacity of the soil 27 3.4.1 Bearing capacity of the piles 28 3.4.2 Settlements readings 29 3.4.3 3.5 Loads acting on the foundation 29 4 NUMERICAL ANALYSES. MODELLING IN PLAXIS 2D 31 CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 IV 4.1 Introduction to PLAXIS 2D 31 4.2 Soil models 32 Linear elastic (simplification of top layers) 32 4.2.1 Soft Soil (SS) 32 4.2.2 Soft Soil Creep (SSC) 33 4.2.3 4.3 Structural elements 35 Plate element 35 4.3.1 Embedded pile row element 36 4.3.2 4.4 Loads in PLAXIS 2D 39 5 VERIFICATION OF SOIL PARAMETERS AND SOIL MODELS 40 5.1 Soil tests performed in PLAXIS 2D 40 Axisymmetric model, Stepwise oedometer test 40 5.1.1 Triaxial soil test 41 5.1.2 5.2 Evaluating results 42 Stepwise oedometer simulations 42 5.2.1 Triaxial test simulations 46 5.2.2 6 MODELLING 47 6.1 Geometry and simplifications 47 6.2 Soil Model 50 6.3 Structural elements 51 Embedded pile row element 51 6.3.1 Plate element 52 6.3.2 6.4 Loads 53 Load scenarios 53 6.4.1 6.5 Mesh optimization 54 6.6 Phases 54 6.7 Validation analysis 55 6.8 Sensitivity analysis 55 7 RESULTS 57 7.1 Results from PLAXIS analyses 57 Excess pore water pressure 58 7.1.1 Settlements 60 7.1.2 Pile interaction 69 7.1.3 7.2 Sensitivity analyses results 71 7.3 Hand calculations 78 Stress distribution 78 7.3.1 Design demands 79 7.3.2 8 DISCUSSION 81 CHALMERS Civil and Environmental Engineering, Master’s Thesis 2014:131 V 9 CONCLUSIONS 83 10 REFERENCES 84 CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 VI CHALMERS Civil and Environmental Engineering, Master’s Thesis 2014:131 VII Preface This Master of Science Thesis has been conducted at the unit for geotechnical engineering at ELU, Gothenburg, between January 7 th and June 18 th in 2014. The project was initiated by ELU employees Bo Jansson and Lars Hall. The authors would like to mention a number of people who have been of great help and made this project possible: We would like to thank our supervisor at ELU, Lars Hall, and ELU employee Therese Hedman for support during the spring in 2014. Furthermore we would like to thank the rest of the employees at ELU, especially Bo Jansson, Hans Lindewald, Mehras Shahrestanakizadeh, Fredrik Olsson, Anders Beijer and Anna Iversen. We would also like to thank Torbjörn Pettersson at Vasakronan, Malin Klarquist at the Urban Planning Department of Gothenburg and Björn Petersson at WSP for providing us with useful information about the building Nordstaden 8:27. Likewise we would like to thank Professor Emeritus Sven Hansbo, responsible for the foundation of the case study building, for explaining questions regarding his, at the time unconventional, foundation method. Lastly we would like to direct our appreciation to Professor Minna Karstunen at Chalmers Univeristy of Technology for providing us with feedback as well as always taking time to answer question and discuss different kinds problems encountered during the process. Gothenburg, June 2014 Joel Algulin and Björn Pedersen CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 VIII Notations Roman upper case letters A cross section area of pile B width of raft v C coefficient of consolidation c C compression index s C swelling index  C creep index D depth of raft below closest adjacent surface E Young’s modulus ck E characteristic Young’s modulus for concrete EA normal stiffness 1 EA normal stiffness for plate element in PLAXIS 2D EI flexural rigidity s G specific gravity NC K 0 earth pressure coefficient for normally consolidated soil OC K 0 earth pressure coefficient for over consolidated soil L length of raft p L length of pile pilei L length of pile part i in Figure 3.18 spacing L pile spacing perpendicular to the model plane N bearing capacity of pile toe O circumference of pile OCR over consolidation ratio R bearing capacity of pile i R bearing capacity of pile part i in Figure 3.18 max T skin resistance of embedded pile row element max,top T skin resistance at pile top for embedded pile row element max,bot T skin resistance at pile bottom for embedded pile row element CHALMERS Civil and Environmental Engineering, Master’s Thesis 2014:131 IX Roman lower case letters b width of plate element 'c cohesion for Mohr Coulomb criteria u c corrected undrained shear strength eq d equivalent thickness of plate element i d diameter at pile part i in Figure 3.18 pile d diameter of pile e void ratio 0 e initial void ratio h height of plate element p h depth from +3.5 in Figure 3.18 k permeability y k vertical permeability x k horisontal permeability v m coefficient of volume compressibility 'p mean effective stress ' p p effective preconsolidation pressure POP over consolidation formulated as POP = ' c  - ' 0  oilexcavateds q weight of excavated soil ground q bearing capacity of the ground gnewbuildin q load from new building piles q bearing capacity of piles/area per pile water q uplifting water pressure ou r dry density of timber u r real density of timber u moisture content i u circumference at pile part i in Figure 3.18 pile u expression for circumference of lower pile part in Figure 3.18 plate w weight of plate element material L w liquid limit N w natural water content x length along raft from left to right z depth from level y CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 X Greek lower case letters  adhesion factor rp  ratio of load carried by piles for a piled raft pile  unit weight of pile material soil  unit weight of soil w  unit weight of pore water  one-dimensional strain v0  initial volumetric strain e v0  initial volumetric strain during elastic response v  volumetric strain c v  change of creep rate in time e v  volumetric strain during elastic response *  modified swelling index *  modified compression index *  modified creep index  correction factor for undrained shear strength  Poisson’s ratio concrete  Poisson’s ratio of concrete ' 0  in-situ effective earth pressure ' 1  effective vertical earth pressure ' 3  effective horisontal earth pressure ' c  effective preconsolidation pressure ' creep  effective creep pressure m  bearing capacity of raft  reference time for oedometer test fu  undrained shear strength of the soil '  friction angle  dilatancy angle CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 1 1 Introduction In 1970’s the shopping centre Nordstan was completed. Professor Sven Hansbo implemented a new method when designing the foundation of the building. The foundation method constitutes of a composite foundation with a piled raft, combined with effects of uplifting water pressure and compensated weight of excavated soil. Today, about 40 years later, the property owner, Vasakronan, is looking at the possibility of expanding the building, by adding floors. To investigate if this is possible, they have hired the consultancy company ELU. This Master thesis was initiated with the belief that the foundation of Nordstan was designed according to the creep pile principle. That kind of foundation method is rather unusual today, which made ELU interested in the design and theory behind the foundation method as well as whether or not it was possible to construct additional floors. 1.1 Background The shopping centre Nordstan is situated in the northern part of central Gothenburg. It is one of the largest shopping centres in Europe and consists of nine buildings, numbered 1-9 according to Figure 1.1, with a total gross floor of approximately 300 000 m 2 . The buildings are connected by streets and a roof. They also share a common basement, where there are streets and loading docks. Nordstan was built between 1965 and 1976 (Fritz, 1997). Figure 1.1 Overview of Nordstan shopping centre, including object numbering of the buildings. (Svensson, 1993) The building Nordstaden 8:27, which is in focus of the case study of this report, is also known by the object number 6. The building is owned by Vasakronan and the storeys of the house mainly consist of bank offices and department stores. 1.2 Aim The aim of this project is to investigate the foundation principle of a piled raft and how well this can be modelled with numerical analysis, using a plane strain model in the computer software PLAXIS 2D. A case study model has been made of the building Nordstaden 8:27. CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 2 The aim of the case study model in PLAXIS 2D, can be divided into the objectives listed below:  Determine to what extent it is possible to model a piled raft, with the complexity of Nordstan, as a plane strain problem in PLAXIS 2D.  Determine to what extent the structural element embedded pile row is working when modelling a piled raft.  Determine what geotechnical effects increasing loads, due to additional construction, would have in terms of settlements. 1.3 Limitations When constructing on soft soil, deformations generally sets the limits for how large loads can be applied to the foundation and is therefore the focus of this thesis. The numerical calculations have been limited to 2D and only the building itself have been taken into consideration for the numerical modelling. No consideration has been taken to for example surrounding streets and buildings. Construction drawings from before construction have been used as a basis for the modelling and no consideration has been taken to any reconstruction. The property owner states that the loads on acting on the foundation should be more or less the same today as after reconstruction of the building 1 . 1.4 Methodology In order to perform this investigation a literature survey regarding foundation methods, commonly used on soft soil, have been carried out. Also a literature survey of the foundation of the building, in the case study of Nordstaden 8:27, has been carried out through articles, construction drawings, existing soil tests and documentation of the building process. There was little documentation found regarding the details of the design of building 6. However, such documentation was found for building 5, which foundation was designed in a similar manner (Hansbo, Hoffman and Mosesson, 1973). Numerical analyses, with the finite element computer software PLAXIS 2D, have been performed with focus on the real case scenario from Nordstan. The soil models used in the case study model have been calibrated to match with existing soil tests. A literature survey on different soil models and structural elements in PLAXIS has also been made. Elevation values mentioned in this thesis are corresponding to the local coordinate system of Gothenburg used during the 20th century. In this system the datum line is situated about 10 m below sea level. 1 Torbjörn Petterson, technical manager at Vasakronan, interviewed 14-02-20 CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 3 2 Building foundations on soft cohesive soil This chapter contains information about different foundation methods for constructing buildings on clay. The main purpose of a foundation is to transmit loads to the underlying soil. This results in a soil-structure interaction. The foundation method which is most suitable depends on the properties of the soil and the functional requirements of the building. Since structural parts of a building often have higher stiffness and strength than underlying soil, support is generally done by the use of shallow foundations (Hansbo, 1989). An example of this is enlarged ground plates (or slabs) which distributes the loads over a larger area. However, if the soil stratum near the surface is not capable to give sufficient support, deep foundations as piles or caissons may be used to transfer the loads to larger depths, where the soil often has higher strength and stiffness (Craig and Knappet, 2012). 2.1 Raft foundation A large single slab which supports the structure as a whole is called a raft. Raft foundations are used to distribute structural loads when the bearing capacity of the underlying soil is low. A slab can cover the entire bottom area of the building or several smaller ones can be strategically placed below pillars or walls (Hansbo, 1989). A single raft is preferable in order to reduce differential settlements or when there are local parts of the soil where the strength deviates. The raft can have an even thickness or have stiffer parts where structural loads from walls or pillars are transmitted. It can be designed with a stiffness large enough for the contact pressures to be assumed equally distributed throughout the plate. Otherwise the distribution will depend on the relative stiffness between plate and soil (Bergdahl, Malmborg and Ottosson, 1993). Contact pressure and settlements 2.1.1 The distribution of the contact pressure depends on the mechanical properties of the soil in combination with the stiffness of the foundation plate. The flexural rigidity of a slab, resting on soil, is often very large compared to the deformability of the material below (Hansbo, 1989). As to be expected, the settlements are uniform for a completely rigid foundation slab. However the contact pressure is not. When a rigid foundation slab is placed directly on cohesive soil, and a uniform load is applied, the contact pressure at the edges reaches high values that causes plastic deformation, see Figure 2.1. The shear stress under the edge of the foundation reaches, but cannot exceed, the shear strength of the clay, i.e. the contact pressure at the edges reaches a limit based on the shear strength of the clay. As the load on the foundation slab gradually increases, the zone of plastic deformation grows towards the centre of the slab. Thus, the contact pressure distribution depends on the shear strength of the clay as well as the applied load (Hansbo, 1989). The contact stress distribution for a flexible raft is uniform and the settlement distribution is largest in the middle, according to Figure 2.2 (Holtz, 1991). CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 4 Figure 2.1 Contact stress distribution and settlements for a rigid raft (Holtz, 1991). Figure 2.2 Contact stress distribution and settlements for a flexible raft (Holtz, 1991). A gradual equalization of the contact pressure can be expected over time. With this in mind, the errors are presumed to be negligible when designing a foundation slab with evenly distributed pressure (Jendeby, 1986a). 2.2 Compensated foundations Excavations are often performed to such a large depth that the weight of the excavated soil exceeds the weight of the building. The building is constructed with a single slab and “floats” on the soil like a raft on water. This kind of foundation can be suitable when constructing buildings on thick homogenous layers of silt or clay (Hansbo, 1989). When constructing these kinds of foundations on clay the slab is often situated below the groundwater table, which adds an uplifting water pressure on the slab. Even if the slab is made of watertight concrete there is still a small permeability in the same magnitude as clay. This results in a water flow directed upwards through the slab and consequently a lowering of the pore water pressure in the clay. This risk can be eliminated if a highly permeable layer of sand or gravel were to be placed between the “watertight” slab and a layer of concrete casted directly on the clay. Groundwater will then be able to flow freely through this layer and the water level will be at least the same as in the surrounding clay. If the building, or parts of it, is encircled by sheet pile walls, different parts of the pore water pressure can be controlled. This makes it possible to reduce differences in effective stress on the slab. Water pressure can be controlled, with respect to the size of the loads on different parts of the slab, in order to not fall short of respectively exceed a certain value (Hansbo, 1989). CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 5 2.3 Piled foundations When designing foundations with piles, the two main aspects to take into consideration are bearing capacity and settlements. For a foundation on clay, settlements are almost exclusively the limiting factor (Jendeby, 1986a). The main reason for using piles in a foundation design is to transfer applied loads to a greater depth of the soil. Deeper layers of the soil, due to their stress history, normally have higher strength and stiffness compared to more shallow layers and therefore would have greater resistance to settlement. When a pile is subjected to a vertical force at the top of the pile, the pile head, shear stresses are mobilised in the ground that surrounds the pile. If the created shear stress exceeds the shear strength of the soil, ground failure will occur. Two different parameters decide the capacity: 1. Shear stress that is developed in the soil around the pile toe 2. Shear stress that is developed at the interface between the shaft and the surrounding soil. This leads to two types of pile classification; end bearing piles and shaft bearing piles, see Figure 2.3. However, this classification describes special cases. In the normal case, the pile resistance depends on both end and shaft resistance (Alén, 2012). Figure 2.3 Principal skis of how a shaft respective end bearing pile work (Alén, 2012). The usual long and slender dimension of a pile makes axial loading the most beneficial way to use them. The failure load of a pile is defined as the load acting on a pile when the soil no longer can carry the transmitted load. The creep load of a pile is defined as the biggest load that can be applied to the pile, without achieving a substantial increase of settlements (Holm and Olsson, 1993). Piled foundations are, almost exclusively, constructed as a group of piles. A group has the dual effect of both carrying the load down to deeper layers of the soil as well as reinforcing the soil. A failure of the group can either occur as a failure of a single pile or as a failure of the whole reinforced block of soil. Block failure is in general more likely to happen with close spacing of the piles (Flemming et al., 1992). The capacity of a single pile in a group may be lower than a single isolated pile. This is due to the fact that the capacity of each single pile within a group may be affected CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 6 by the remoulding of surrounding soil, when other piles are installed in close proximity (Flemming et al., 1992). Friction piles 2.3.1 A friction pile utilises the shaft bearing principle, according to Figure 2.3 above. A foundation which includes friction piles can act differently depending on the duration of the load. Thus, the bearing capacity should be controlled with regards to both short- term and long-term loads. For the settlements calculation, only the long-term load is considered in a normal case (Eriksson et al., 2004). Negative skin friction - Down drag 2.3.2 Due to settlements, soil surrounding the pile can start to move downward relative the pile. This creates negative skin friction. The negative skin friction acts as down drag, an extra load on the pile. Thus, it is the relative movement between the pile and the soil that determines the size of the additional load. The action effect in the pile equals the sum of the negative skin friction and the loading at the pile head (Alén, 2012). The shaft friction is considered to be fully developed with a relative movement of 2-5 mm. Common practice is to take the effect into consideration along the part of the pile where the soil settles 5 mm more than the pile (Eriksson et al., 2004). A simplified evaluation of the risk of down drag can be made by using the same relationship as when evaluating the risks for long term settlements, creep, described in equation 3.8. With this approach, negative skin friction is considered along the pile, where the vertical stress is bigger than the creep limit. Neutral plane 2.3.3 The neutral plane is defined as where the relative movement between the soil and the pile is zero, i.e. the pile and the soil settle equally (Fellenius, 2004). For this to happen, the pile needs to be in equilibrium state. The equilibrium state is when the sum of all external loads on the pile as well as the down drag equals the bearing capacity of the pile. This means that on a certain depth, the down drag of the pile changes into friction resistance (Eriksson et al., 2004). This is illustrated in Figure 2.4. Figure 2.4 Description of the neutral plane for shaft bearing piles (Alén, 2012). CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 7 The neutral plane principle is based upon an assumption of ongoing settlements in the ground, i.e. the pile is subjected to negative skin friction, or down drag. In a real case scenario, this might not be the case. However, as described above, relative movements as small as 2-5 mm are required to develop full friction between the soil and the pile shaft. If despite that, no settlements would occur below a certain depth, no additional loading by down drag can occur below that depth. This creates a zone of equal strain that “pushes” the neutral plane further down, see Figure 2.5. Thus, the concept of the neutral plane is on the safe side (Alén, 2012). Figure 2.5 Behaviour of the neutral plane due to zone of equal strain (Alén, 2012). Settlements for piled foundations 2.3.4 Settlements of a pile foundation are caused by an increase of effective stress in the soil. The neutral plane governs the settlement analysis of a piled foundation. When calculating settlements on a piled foundation, the applied loads can be transferred to an “equivalent footing” placed at the location of the neutral plane, i.e. the loading from the upper levels are transmitted through the piles and distributed downwards from the neutral plane. The settlement of the whole piled foundation is considered to be the same as for the equivalent footing, Figure 2.6 (Fellenius, 2004). For a large group of piles, the reinforcing effect of the piles to the surrounding soil must be taken into consideration, when calculating settlements for the equivalent footing. This can be done by combining the stiffness moduli of the soil and piles into a combined modulus. The new modulus is applied between the neutral plane level and the pile toe level. The combined modulus is usually so large that the settlements between the neutral plane level and the pile toe level can be neglected. Therefore, a simplified approach can be made by placing the equivalent footing at the pile toe level (Fellenius, 2004). CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 8 Figure 2.6 Placement of the simplified equivalent footing (Fellenius, 2004). Bearing capacity of friction piles Settlement calculations are based on the bearing capacity of the piles. In Sweden, the geotechnical bearing capacity for friction piles is usually decided with the α-method (Eriksson et al., 2004). In soft soils, α stands for the relationship between the undrained shear stress that can be developed between the shaft area and the surrounding soil, and the shear strength of the soil. According to Alén (2012) α can be set to 1.2 for timber piles with an upward increasing section area. As illustrated above, the resistance of a pile, R, is decisive for where the neutral plane is located. R is described by equation 2.1 (Eriksson et al., 2004). ∫ (2.1) where: Lp = length of the pile α = adhesion factor O = pile circumference cu = corrected undrained shear strength N = bearing capacity factor for the pile toe A = pile cross section area For toe resistance to be fully developed, a considerable larger deformation than 2-5 mm is needed. An approximated value is 10 % of the pile width. Thus, due to the large deformations required, it might not be possible to account for the complete end resistance of the pile, when using the formula above. Therefore, the end bearing resistance of a friction pile in soft soil is usually neglected (Alén, 2012). CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 9 2.4 Composite foundation - Piled raft According to Eriksson et al. (2004) there are three different design methods for piled rafts:  The “conventional case”. Foundations where all load is carried by friction piles. In a case like this, the piles have to acquire sufficient bearing capacity as well as reduce the settlements.  Foundations where the load distribution is divided between the friction piles and the contact pressure from the soil on a foundation slab. Used when the weight of the excavated soil only covers part of the applied load. The piles main function here is to reduce settlements. The creep pile principle can be applied for such foundations.  Foundations where all applied load can be carried by the contact pressure against the foundation slab. In such cases, the friction piles are placed under concentrated loads and their primary function are to decrease the dimensions of the overlying constructions, such as the foundation slab. This is suitable when all applied loads can be compensated by excavating soil. Most foundations constructed on clay are within the limits from a bearing capacity perspective without the use of piles (Jedenby, 1986b). The main reason for adding pile elements to the raft is usually not to carry the major part of the loads but to reduce average and differential settlements (Kulhawy and Prakoso, 2001). Therefore, the piles are designed to act both as soil reinforcing and settlement reducing elements, as well as to take care of concentrated loads acting on the raft. The distribution and number of piles is decided upon these criteria. This enables the design of the foundation to be optimized and the number of piles to be reduced, which generally is the most cost effective approach (Hansbo and Källström, 1983). The load sharing mechanism of a piled raft, as well as its stiffness and resistance, is regulated by the soil structure interactions between the load bearing components of the foundation, i.e. the piles, the raft and the soil (Giretti, 2009). The raft is often designed to carry loads of the same size as the preconsolidation pressure (Jendeby, 1986a). As illustrated in Figure 2.7, a piled raft foundation can be assumed to have four kinds of interactions. Each interaction is governed by the parameters of the three elements, for example stiffness, shear strength of the soil, pile spacing and pile length. The pile- soil and pile-raft interactions are described in earlier in this chapter. The pile-pile interaction can be defined as additional settlements of a pile, caused by a loaded adjacent pile, and the pile-raft interaction can be defined as additional settlement of the raft caused by supporting piles (Nguyen, Jo and Kim, 2013). CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 10 Figure 2.7 The four different interactions of a piled-raft foundation (Katzenbach, Gutberlet and Bachmann, 2007). The creep pile principle 2.4.1 The use of a relatively high safety factor when designing a piled foundation could result in a scenario where the surrounding soil settles more than the foundation, which would mean that no contribution from contact pressure between soil and raft could be accounted for. The principle of a piled raft foundation is to distribute the loads between the raft and the piles. To achieve this, the design of the factor of safety of the piles is close to unity, which means that the neutral plane is designed to be located at or close to the bottom of the raft (Fellenius, 2004). With the piled raft method, the piles can be designed to make the potential settlements of the foundation be the same as the settlements of the surrounding soil. This is done through a better utilisation of the piles, by designing them to be exposed of a load equal to their creep load, causing a state of creep failure (Fredriksson and Rosén, 1988). The design should ensure that the contact stress is uniformly distributed across the raft (Fellenius, 2004). The ability of a construction to distribute forces horisontally is especially governed by the stiffness of the construction (Eriksson et al., 2004). Since there is pressure acting on the raft, it will generally have to be thicker and more reinforced than in a conventional piling case. The theory behind the principle is to take advantage of the compensation in effective stress created by the excavated soil. A certain percentage (Q1) of the total applied load (Q), can be carried without piles, due to the compensation. The remaining part of the load (Q-Q1) has to be carried by the pile system. For example, if a raft can carry 80% of the load without causing substantial settlements, the piles has to carry the remaining 20% of the load. Thus, the purpose of using the creep pile principle is to maximize the pile capacity in order to control that a certain part of the load will be carried by the raft. The pile spacing is chosen to regulate the amount of load carried by piles (Hansbo and Jedenby, 1998). CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 11 The load-settlement behaviour for different design approaches, concerning a piled raft, is presented in Figure 2.8. Curve 0 represents the behaviour of a raft acting alone. Curve 1 represents the conventional design approach. Curve 2 illustrates the “creep pile principle”, in which the piles are designed with a lower factor of safety. Curve 3 represents the use of full utilization of the piles at the design load, by strategically placing the piles as settlement reducers. The reduction in number of piles for curve 2 and 3, results in a larger amount of load carried by the raft. Fewer piles results in a more economical design (Poulos, 2001). Figure 2.8 Load-settlement behaviour for a piled raft, comparing different design approaches (Poulos, 2001). 2.5 Magnitude of allowable settlements for foundations on soft cohesive soil A settlement analysis should involve more than just an upper boundary. Both total amount of settlements as well as differential settlements needs to be evaluated. The magnitude of acceptable settlements varies with the size and type of structure (Fellenius, 2006). The differential settlement ratio is calculated as the difference in settlement of two edges of a section, divided by the length between them. In Appendix E, allowable settlement limits for structures, according to Holtz (1991), are presented. It underlines that the settlement demands varies depending on the type of structure and its function. CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 12 3 Case study of Nordstaden 8:27 This chapter contains information about the case study building and its surroundings. It also contains information about geotechnical conditions at the site, in form of evaluations made from test documentation. 3.1 History of the area The district Östra Nordstaden is situated north of Stora Hamnkanalen and east of Östra Hamngatan and was earlier a district of emigrant hotels, storehouses and brasseries. This is also the place where “Chalmer’s crafting school” once started in the first half of the 19th century. Most of the buildings were from the late 18th or early 19th century. Since the 1970’s, this area is totally dominated by the shopping centre Nordstan. (Fritz, 1997). Figure 3.1 Map of Östra Nordstaden from around 1860. The location where Nordstan shopping centre later was erected is marked by thick lines. The top corner of this marking is where Chalmers Crafting School was located at the time (Fritz, 1997). In the middle of the 20th century, the existing buildings were in a rather bad condition (Fritz, 1997). It was deemed not economically justified to reconstruct or restore them. In November 1959 it was therefore decided that, in order to prevent the ongoing deterioration into slum of the northern part of central Gothenburg, a redevelopment of Östra Nordstaden was to take place. The old buildings were to be torn down and a modern shopping centre to be erected in their place (Hansbo, Hoffman and Mosesson, CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 13 1973). The first buildings, 1 and 2, were constructed during the years 1965-68, while buildings 3 to 9 were constructed during the years 1970-76. 3.2 Geotechnical conditions The geological data used for the case study of this thesis come from investigations performed by AB Flygfältsbyrån and Jacobson & Widmark AB (J&W AB) in 1966, during planning of the reconstruction. The tests consist of in-situ testings as Field Vane Tests (FVT) and Cone Penetration Tests (CPT), as well as standard laboratory tests, consisting of stepwise oedometer tests and fall cone tests. Oedometer tests were performed on soil from two boreholes, 1 and 17b, in the area and down two a depth of 25 meters. Boreholes used for the tests are presented in Figure 3.2. Figure 3.2 Plan of boreholes from the investigation performed by AB Flygfältsbyrån and J&W AB. Boreholes 1 and 17b, where samples for the oedometer tests have been taken, are marked by ellipses. Geology 3.2.1 The ground level at building 6 is approximately at +12.1. It consists of 1.5-3 m fill on top of a deep layer of clay. In the southwest corner the depth of the clay layer is 49 m. CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 14 Below there is a 2 m thick layer of frictional soil resting on the bedrock. In the other three corners the clay and friction soil layers has a thickness of approximately 90 and 10 m respectively. Sampling of soil has been made to a depth of 40 m (Svensson, 1993). Hydrogeological conditions 3.2.2 The mean groundwater level for the area is approximately at level +10.1. There is a hydrostatic overpressure of 20-30 kPa at a depth of 20 m. There is however no information on what level this overpressure starts (Svensson, 1993). Soil properties - parameter evaluation 3.2.3 This chapter presents parameters evaluated from the obtained tests as well as assumptions made regarding other parameters that will be of importance for this thesis. Unit weight - γsoil The volume weight is uniform with depth and has an approximate value of 1.6 t/m 3 . The data is transformed into unit weight, γsoil [kN/m 3 ]. A graph of the unit weight plotted versus level can be seen in Appendix C. Natural water content - wN The natural water content, wN, is obtained from standard tests in laboratory, and is plotted versus level in Figure 3.3. The graph indicates a homogeneous layer of clay, apart from the highlighted area, which implies that there is a section with higher water content. CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 15 Figure 3.3 Natural water content plotted versus level. Initial void ratio - e0 If the soil is assumed to be fully saturated, the initial void ratio can be calculated according to equation 3.1 (Wood, 1990). The specific gravity, Gs, is assumed to 2.71. (3.1) Liquid limit - wL The liquid limit is relatively constant with depth at approximately 70%. A graph of the liquid limit plotted versus level can be seen in Appendix C. Corrected undrained shear strength - cu The shear strength, τfu, is evaluated from data obtained through field vane tests for samples from 8 boreholes and at multiple levels. As vane tests are not as much subject to sample disturbance, they are likely to be more accurate than cone tests, therefore only data from vane tests have been used, even though cone tests were available. The undrained shear strength is overestimated if the liquid limit, wL, is high. To consider this, equations 3.2 and 3.3, has been used to obtain the corrected undrained shear strength, cu (Helenelund, 1977). ( ) (3.2) -32,9 -27,9 -22,9 -17,9 -12,9 -7,9 -2,9 2,1 7,1 12,1 30% 40% 50% 60% 70% 80% 90% 100% Le ve l [ -] Natural water content, wN [%] Borehole 8 Borehole 1 Borehole 2319 Borehole 2319 Borehole 24 Borehole 2452 Borehole 2322 Borehole 2321 Borehole 60 Borehole 2320 Borehole 17b CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 16 (3.3) Corrected undrained shear strength is plotted versus level in Figure 3.4 and an approximation is described by equation 3.4. ( ) kPa (3.4) where: z = meters of depth starting at level 3.5. Figure 3.4 Undrained shear strength plotted versus level. Vertical and horisontal permeability - ky and kx The behaviour over time for the consolidation process can be decided with the consolidation coefficient Cv, presented in equation 3.5. (3.5) where: k = permeability mv= coefficient of volume compressibility -30 -25 -20 -15 -10 -5 0 5 10 15 0,0 20,0 40,0 60,0 80,0 Le ve l [ -] cu[kPa] Borehole 8 Borehole 2319 Borehole 36 Borehole 24 Borehole 2322 Borehole 60 Borehole 2320 Borehole 17b CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 17 γw = Unit weight water Cv and mv are evaluated from the oedometer tests. The vertical permeability, ky, is evaluated from equation 3.5 and is presented for different depths in Figure 3.5. No data are available for the horisontal permeability, kx. Due to previous buildings in the area which probably have caused an anisotropic stress state and fabric, kx is assumed according to equation 3.6. (3.6) Figure 3.5 Vertical permeability ky plotted versus depth. Compression, swelling and creep indices The compression index, swelling index and creep index are evaluated from oedometer tests. The inclination of the virgin compression line equals the compression index Cc, see Figure 3.6, and thus, Cc can be described by equation 3.6. Cc is decisive for the consolidation settlements (Craig and Knappet, 2012). ( ) (3.7) -25 -20 -15 -10 -5 0 5 0 0,000005 0,00001 0,000015 0,00002 Le ve l [ -] Permebility [m2/day] ky - bh 1 ky - bh 17b CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 18 Figure 3.6 Principal skis of a stepwise oedometer test curve with compression and swelling indices (Craig and Knappet, 2012). In Figure 3.7, the compression indices for the two evaluated boreholes are plotted versus level. Both compression index curves seem to follow a similar pattern. Figure 3.7 Compression index plotted versus level. The swelling index Cs (also known as expansion index), is evaluated by approximating a straight line between the unloading and reloading curves, see Figure 3.6, which makes it decisive for the swelling of the soil as well as the elastic settlements. It can, like Cc, be described by equation 3.6. In Figure 3.8, the swelling indices for the two evaluated boreholes are plotted versus level. The two curves diverge at the deepest samples. Ideally the swelling index is determined at the stress level where any unloading due to excavation process are expected to take place. Unfortunately this is not often done and hence (just like in this case) the values relate to the unloading at the end of the test. -15 -10 -5 0 5 10 0,00 0,50 1,00 1,50 2,00 Le ve l[ -] cc [-] Cc, borehole 1 Cc, borehole 17b CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 19 Figure 3.8 Swelling index plotted versus level Creep index The rate of secondary compression, or creep index Cα, is evaluated as the inclination of the final part of the semi-logarithmic graph in figure Figure 3.9. Figure 3.9 Oedometer test plotted as logarithmic time versus strain/void ratio (Olsson, 2010). In Figure 3.10 the creep index for the two evaluated boreholes are plotted versus level. Both creep index curves seem to have similar patterns, but with the data from borehole 17b reaching higher values. -15 -10 -5 0 5 10 0 0,05 0,1 0,15 Le ve l [ -] cs [-] Cs, borehole 1 Cs, borehole 17b CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 20 Figure 3.10 Creep index plotted versus level Stress analysis The preconsolidation pressure, , is obtained from the oedometer test according to Casagrande’s method. A tangent is drawn at the point where the radius of the curve is smallest. A horisontal line is drawn from the same point and thereafter a bisector of the angle between the two lines. The “straight part” of the oedometer curve is extended upwards. Where the extended line intersects with the bisector corresponds empirically to the preconsolidation pressure, see Figure 3.11. (Larsson, 2008). Figure 3.11 Principal skis of how to use Casagrande’s method to obtain preconsolidation pressure from an oedometer test (Larsson, 2008). Stress analyses of both in situ conditions and current conditions, caused by the existing building, are presented in Figure 3.12. The threshold limit for creep is also -15 -10 -5 0 5 10 0 0,02 0,04 0,06 0,08 Le ve l [ -] Cα [-] Cα, borehole 1 Cα, borehole 17b CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 21 shown in the graph. Tests performed on Swedish clays show that the secondary compression is rather low until the compression corresponds with an effective vertical stress according to equation 3.8 (Larsson, 1986). (3.8) Figure 3.12 In situ, preconsolidation and creep stresses plotted versus level. The change in stress from the construction is also plotted Since no triaxial tests from the site are available, the values for parameters υ, ϕ’, ψ and c´ have all been assumed. The assumed values of these properties are presented in Table 3.1. υ = Poisson´s ratio ϕ’ = Friction angle ψ = Dilatancy angle c´ = Cohesion Table 3.1 Assumed values for soil parameters due to lack of triaxial tests. υ ϕ’ ψ c´ 0.15 30° 0 1 -10 -5 0 5 10 15 0 50 100 150 200 Le ve l [ -] σ'v [kPa] σ´o σ´c σ´o+Δσz σ´creep CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 22 Earth pressure coefficients - and at rest For normally consolidated soils, the value of can be obtained by using the friction angle, ϕ’, according to equation 3.9, proposed by Jaky in 1944 (Craig and Knappet, 2012). (3.9) For overconsolidated soils, depends on the stress history of the clay, which can be taken into consideration with equation 3.10, proposed by Mayne and Kulhawy in 1982 (Craig and Knappet, 2012). ( ) ( ) (3.10) 3.3 Foundation of Nordstan Due to the local building rules, the height of the building complex was restricted to 28 m. Thus, to have more capacity, it was beneficial to place the foundation of the building as deep as possible into the ground to gain extra area from floors below ground. The optimum depth was decided to be two basement floors, requiring a maximum depth of excavation of about 8 m. All buildings in the complex have a common roof and also share a common basement with a total area of 58 700 m 2 (Svensson, 1993). Buildings 1-3 are founded on individual footings with spliced timber piles with a length of 30 m (Hansbo, Hoffman and Mosesson, 1973). The piles are concentrated in groups below the columns of the building above. The weight of these buildings is not compensated by the excavated soil. The foundations of buildings 4-9 is carried out with a combination of the compensation principle, the use of underlying water pressure and friction piles. This is further explained below (Svensson, 1993). The level of the raft for the different sections are presented in Figure 3.13 (ök = upper edge, uk = lower edge). The foundation level differs among the sections between +5.90 and +7.30. Buildings 6 and 9 both contain a bank vault, where the foundation level has been lowered to +4.50 m and +5.60 m respectively. The ground level is situated at about 12.1 m (Svensson, 1993). CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 23 Figure 3.13 Rough sketch of raft levels for the buildings of Nordstan shopping centre (Svensson, 1993). Below lighter areas, basement parts which consists of streets or have courtyards above, the groundwater has to maintain a level between +8.90 and +9.60. This is to prevent great loads from hydraulic uplift. As mentioned above, the foundation principle for building 6, Nordstaden 8:27, is a combination of the compensation principle, the use of underlying water pressure and the utilisation of friction piles. The building is positioned so deep that full compensation is obtained. To compensate for the relatively heavy weight from a bank vault and the higher parts of the building, the south-east corner of the ground plate consists of caissons. Compared to the rest of the building the foundation level is lower there, which results in a higher degree of compensation and a higher water pressure acting on the raft. The excavation level is +5.8 under areas without caissons, and +4.25 under areas with them. Figure 3.14 Drawing of building 6. The location of the caissons is seen in the down right corner (Hansbo, Hoffman and Mosesson, 1973). The raft is made of waterproof concrete. The dimensions of the plate are obtained from Figure 3.15. The major part of the ground plate, i.e. the part which does not include the caissons, has a height of 1150 mm of concrete. The total height of the caissons is approximately 3000 mm. CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 24 Figure 3.15 Details of the raft including underlying material (concrete K75, plastic foil, gravel (2 – 20 mm), concrete K75, gravel, clay). All dimensions are given in [mm]. Since the groundwater level is located above the foundation level, the loads from the building is partly carried by water pressure, acting on the raft from below. In order to maintain a high groundwater pressure below heavier parts and reduce it below lighter parts, groundwater conditions are regulated. Beneath the raft there is a 10 cm thick permeable layer of gravel. Wooden sheet piles create watertight sections and separate the ground beneath the object, and even parts within the object itself. Because of this the level of the groundwater table varies between different areas. Each encircled area has a regulated water level, controlled by pumps, which automatically handles refill and overflow when needed. There are four different watertight sections beneath building 6. Their positions are presented in Figure 3.16. CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 25 Figure 3.16 Water reservoirs below building 6. The borders of the four different reservoirs are marked with thicker red lines and adjacent names. As can be seen in Table 3.2, there is a difference between the level set as a limit in the design and the measured water level in the main reservoir. This is due to problems in maintaining the set level. The owners could not tell for how long the level has been this low 2 . 2 Torbjörn Petterson, technical manager at Vasakronan, interviewed 14-02-20 CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 26 Table 3.2 Reservoir levels for building 6 Reservoir Date Set water level Measured water level Water level according to construction drawing Gården (Yard) 1974, 1975 +9.08 - +9.5 +10 2003-08-18 +9.47 +9.47 2003-10-20 +9.47 +9.47 2012-02-xx +9.73 Huvudmagasin (Main reservoir) 1974, 1975 +10.06 - +10.3 +11 2003-08-18 +9.92 +9.86 2003-10-20 +9.92 +9.80 2012-02-xx +9.86 Postgatan 1974, 1975 +9.41 - +9.57 +9.6 2003-08-18 +9.40 +9.56 2003-10-20 +9.40 +9.38 2012-02-xx +9.44 Spannmålsgatan 1974, 1975 +8.78 - +9.39 +9.6 2003-08-18 +9.47 2003-10-20 +9.47 2012-02-xx +9.73 The piles are made of timber and have a length of 20 m. The tip diameter is about 0.125 m with an increase of 0.8 cm per m. The pile spacing varies between 1.5-2.4 m, depending on the weight of the building above. Due to the theory of contact pressure for a rigid raft on cohesive soil, discussed in section 2.1.1, the pile spacing is smaller at the edges, since the pressure is higher there. 3.4 Principles behind the foundation method of building 6 Below information is presented on how the design was performed before construction. As can be seen when evaluating the design demands below, see equations 3.11-3.14, the raft alone should be sufficient to carry the building. As stated by Hansbo (1973), the main reason for using friction piles under the raft was mainly to eliminate the risk of differential settlements. Many of the former buildings at the site were founded on timber piles. The unknown amount of remaining piles in the soil could act as reinforcement of the soil, creating great variations in modulus of the subsoil. For the same reason, there were difficulties to estimate the heave of soil during the excavation phase. Thus, a mat of friction piles under a raft was deemed as an appropriate solution. With this foundation method, the disturbance effects caused by installation of the piles as well as heave of the soil during excavation could both be ignored (Hansbo, Hoffman and Mosesson, 1973). CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 27 The design demands which the foundation were based on are presented below: 1. (3.11) 2. (3.12) 3. (3.13) 4. (3.14) where: = load from the new building = uplifting water pressure = weight of excavated soil = bearing capacity for the ground = bearing capacity of the piles/area per pile Since the bearing capacity of the piles is divided by the area covered by each pile to obtain qpiles, the pile spacing was designed to obtain the safety factor of 2. According to Hansbo, this was the first time foundation design was based on interactivity between friction piles and pressure against the raft. The safety factor used against failure according to conventional methods at the time was set to three. In this case, which can be seen in demands 3 and 4 above, a safety factor of two was used. Thus, the foundation of Nordstan can be seen as an introduction to the creep pile principle, implementing a better utilisation of the piles 3 . Bearing capacity of the soil 3.4.1 During the design of the foundation the bearing capacity of the soil was calculated with equation 3.15, according to Svensk Byggnorm 67 (Statens planverk, 1968). ( ) ( ) (3.15) if D/B ≤ 2.5 where: D = depth of raft below closest adjacent surface B = width of raft L = length of raft = undrained shear strength of the soil = unit weight of the soil 3 Sven Hansbo, Professor Emeritus, interviewed 14-02-24 CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 28 D was chosen as zero. was set to its minimum value of 2.5 MP/m 2 . (2.5 MP/m 2 was the minimum shear strength from the parameter evaluation made in 1966, where correction factor of shear strength was not considered). The bearing capacity was calculated to 5.1 MP/m 2 (approximately 51 kPa). Figure 3.17 Definitions of D and B for equation 3.15 (Statens planverk, 1968). Bearing capacity of the piles 3.4.2 During the design of the foundation the bearing capacity of the piles was calculated with equations 3.16 – 3.20, according to Pålnormer sbn-n 23:6. The equation only takes the shaft resistance into consideration and is based on Figure 3.18. It should be noted that values in the figure does not consider the building in the case study, but the principle however is accurate. (3.16) (3.17) ∫ (3.18) ( ) (3.19) (3.20) where: R = bearing capacity of pile Ri = bearing capacity of pile part i di = diameter at pile part i upile = expression for circumference of lower pile part in Figure 3.18 ui = circumference at pile part i Lpilei = length of pile part i = undrained shear strength of the soil CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 29 hp = depth from +3.5 in Figure 3.18. (written as h in the figure) The shear strength is constant with a value of 2.5 MP/m 2 (approximately 25 kPa) down to the level of 3.5 m. From that level it is increasing with 0.18 MP per m (appriximately 1.8 kPa/m). The pile is divided into two sections according to Figure 3.18 Bearing capacity of the piles was calculated to 45.9 MP. Figure 3.18 Principal skis of how calculations of pile bearing capacity was made during design. Settlements readings 3.4.3 Settlement readings for the building have been performed on continuous basis, since 1978, and are presented in Appendix F. The maximum settlement measured is about 15 mm and the maximum heave about 10 mm. The settlements are quite evenly distributed. Due to water leakage, the water supply was shut down during a major part of 2007. During this period, the settlements increased rapidly. When the water levels were restored the building heaved to its previous position. The lowest level of the water during this period was not recorded. 3.5 Loads acting on the foundation The applied loads from the building have been assessed, using the construction drawings in Appendix A. In the construction drawings, the loads for each floor are specified. The loads transferred down through the building are divided into dead- weight load and working load. For settlements, it is the long-term loads that needs to be considered. The working load is transformed into permanent load based on the ongoing activity on each floor. The permanent load addition from department stores CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 30 can be approximated as 60% of their working load, whereas 30 % percent of the office load is considered as permanent load 4 . When the building was erected, the three lower floors were used both as department stores and offices, in this thesis, they are considered as department stores. The rest of the floors were used as offices, which they also are considered to be in this thesis. The facade consists of lightweight material (Gustafsson et al., n.d.). Therefore, the load contribution from the facade is considered to be negligible. The load contribution from pillars is approximated as 10 kN per floor. This is considered to be included in the dead weight of each floor. The snow load is neglected due to the long-term perspective 4 . The loads are summarized for each pillar, and is presented in Appendix B. The weight of the raft is calculated with the input parameters in Table 3.3. Table 3.3 Unit weight of materials at raft foundation. Material Unit weight [kN/m 3 ] Saturated macadam (Larsson, 2008) 21 Unsaturated macadam (Larsson, 2008) 18 Concrete 4 25 Characteristic loads are used as input for PLAXIS. Therefore, no partial factors have been applied on the loads. The total long term load of the building, including the weight from both pillars and raft, is calculated to 96 kPa. The weight of the excavated soil is approximated to 104.8 kN/m/m. The water pressure acting on the raft is approximated to 43 kPa. 4 Hans Lindewald, Structural Engineer at ELU, interviewed 14-03-17 CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 31 4 Numerical analyses. Modelling in PLAXIS 2D This chapter contains information about the finite element computer software PLAXIS 2D. 4.1 Introduction to PLAXIS 2D PLAXIS 2D is developed for analysis of deformation and stability problems for different types of geotechnical situations in two dimensions. A geometry model is created in the x-y plane of the global coordinate system, with the z-axis as the out of plane direction, see Figure 4.1. Despite the fact that it is a two dimensional application, stresses are based on the 3D Cartesian coordinate system, according to Figure 4.1. According to the sign convention, compressive stresses are negative (PLAXIS, 2014b). Figure 4.1 Definition of coordinate systems in PLAXIS 2D (PLAXIS, 2014b). Real scenarios can be modeled with a plane strain or an axisymmetric model, see Figure 4.2. The plane strain model is suitable to implement with a relatively uniform cross-section, loading scheme and a great extent in the z-direction. Normal stresses in the z-direction are fully considered but the displacements and strains are assumed to be zero. The axisymmetric model is suitable when modelling circular structures with a relative uniform radial cross section and loading scheme around the central axis. The stress state and deformations are considered to be equal in any direction (PLAXIS, 2014b). Figure 4.2 Comparison between plane strain and axisymmetric models in PLAXIS 2D (PLAXIS, 2014b). 15- and 6-node triangular elements are available for modelling volume clusters. Material properties are assigned to each volume cluster. In order to perform CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 32 calculations on the created model, the geometry needs to be divided into finite elements. The finite elements are the above described triangular elements as well as other special elements for e.g. plates, which together create a mesh. PLAXIS has the ability to automatically create a mesh. However, the automatically created mesh may not be accurate enough to perform an acceptable numerical analysis. To prevent this, the mesh can be manually refined, both as a whole and in areas with large stress and strain concentrations or gradients. 4.2 Soil models A brief description of the models used for the case study, as well as methods for evaluation of the input parameters, is given below. Linear elastic (simplification of top layers) 4.2.1 This is a relatively simple model which has a linear elastic behavior. According to the model the soil will never reach failure. Soft Soil (SS) 4.2.2 The Soft Soil model is suitable for near-normally consolidated clays, clayey silts and peat. These are materials which have a high degree of compressibility (PLAXIS, 2014a). When using the Soft Soil model the stiffness depends on the stress level. The compression behaviour is logarithmic and the model makes a distinction between primary loading and unloading-reloading. Pre-consolidation stress is taken into account and the failure behavior is modelled according to the Mohr-Coulomb criterion (PLAXIS, 2014a). The logarithmic behaviour during isotropic compression is formulated as: ( ) (4.1) where p’ is the mean effective stress and is the volumetric strain. λ* is the modified compression index which determines the compression during primary loading (virgin compression). During isotropic unloading-reloading the relation is formulated as: ( ) (4.2) where κ* is the modified swelling index which determines the compression during this phase. The strain denotations, ε, have the superscript e is because the response from the soil in this phase is assumed to be elastic. CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 33 Soft Soil model parameter evaluation The modified compression and swelling indices, λ* and κ*, are evaluated from triaxial tests. The modified compression and swelling indices can be obtained from a plot of the logarithmic mean effective stress, p’, as a function of the volumetric strain, . The first as the slope of the primary loading line and the latter as the slope of the unloading-reloading line, see Figure 4.3. Figure 4.3 Definitions of indices λ* and κ* (PLAXIS, 2014a). These parameters can also be obtained from a one-dimensional oedometer test since there is a relationship between λ*/κ*, and the parameters for one dimensional compression and recompression Cc/Cs (PLAXIS, 2014a). In PLAXIS either could be used as input value. Since only oedometer tests were available for this project parameters Cc and Cs were evaluated and then transformed by using relationships described below. Modified compression index, λ* The modified compression index λ* is obtained from the relationship with the compression index, Cc, in equation 4.3 (PLAXIS, 2014a). ( ) (4.3) Modified swelling index, κ* The modified swelling index, κ*, is obtained from the relationship with the swelling index, Cs, in equation 4.4 (PLAXIS, 2014a). ( ) (4.4) Soft Soil Creep (SSC) 4.2.3 While the Soft Soil model is a suitable tool for modeling clays, it does not consider the secondary compression (creep). The parameters and principles of the both models CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 34 coincide well with each other apart from the modified creep index, µ*, which takes the time aspect into consideration (PLAXIS, 2014a). Similar to the Soft Soil model, the Soft Soil Creep model distinguish between primary loading and unloading/reloading. The difference is that for the Soft Soil Creep model, the limit between the two loading states is not only determined by the maximum stress state that has been reached in the past, but also by the time aspect (PLAXIS, 2014a). The Soft Soil Creep model assumes a reference time, τ, of 1 day, which cannot be altered. This is to be used in conjunction with a preconsolidation pressure corresponding to 24 hours load step. For other load/strain rates, the input value of OCR or POP needs to be scaled accordingly (Leoni, Karstunen and Vermeer, 2008). Creep is formulated using the concept of constant volumetric creep strain rate, which is inversely proportional to OCR*. OCR* is the OCR defined by mapping the normal consolidation surface and current stress state surface to preconsolidation pressure, p’, see Figure 4.4 (Leoni, Karstunen and Vermeer, 2008). Figure 4.4 Anisotropic creep model in triaxial stress space. NCS = Normal Consolidation Surface. CSS = Current State Surface (Leoni, Karstunen and Vermeer, 2008). The modified creep index, µ*, equals to the creep rate after one day. In combination with λ* and κ*, the change of creep rate in time can be defined according to equation 4.5. ( ) (4.5) Evaluation of creep index parameter, µ* The modified swelling index, µ*, is obtained from the relationship with the swelling index, Cα, in equation 4.6 (PLAXIS, 2014a). CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 35 ( ) (4.6) When applying a load step, both consolidation and creep will occur simultaneously. For a proper parameter evaluation of the creep parameter, µ*, when plotting the strain versus the natural logarithm of time, the time period needs to be long enough for the inclination of settlement curve to be straight, i.e. after full consolidation. This makes the consolidation settlement contribution from µ* minor compared to the contribution of creep (Waterman and Broere, 2005). 4.3 Structural elements The structural elements that are used in this thesis are presented below. Plate element 4.3.1 Plate elements are structural objects used to model slender structures. They are often suitable to use when simulating the influence of walls or plates. In the plane strain model the plate extends in the out-of-plane direction. The plates in the plane strain model have two translational degrees of freedom (ux, uy) and one rotational degree of freedom (ϕz). The plate elements are based on Mindlin’s beam theory which allows for deflections due to bending as well as shearing. The plate element can also change length when axial force is applied. When a prescribed maximum bending moment or axial force is exceeded the element becomes plastic (PLAXIS, 2014b). In order to allow for a proper modeling of soil-structure interaction, an interface can be applied to a structural element (PLAXIS, 2014b). Plate element parameters The general properties are: deq: Equivalent thickness of the plate. Automatically calculated from stiffness parameters EA and EI, see Stiffness properties. [m] wplate: Weight of the plate material per unit of length per unit of width in the out-of-plane direction [kN/m/m] The stiffness properties are: EI: The flexural rigidity, or bending stiffness, for a rectangular cross section is calculated according to equation 4.8. CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 36 (4.8) EA: The normal stiffness, for a rectangular cross section is calculated according to equation 4.9. (4.9) For equations 4.8 and 4.9 b and h are chosen according to Figure 4.5. Figure 4.5 Definitions for b and h in equations 4.8 and 4.9 (Waterman, 2006). deq: The element thickness deq (h in Figure 4.5) is calculated according to equation 4.10. √ (4.10) υ: Poisson’s ratio Embedded pile row element 4.3.2 It is of course difficult to model piles realistically in a two-dimensional plane strain model, since the stress state and deformation pattern is fully three-dimensional. In PLAXIS 2D there is a feature called embedded pile row element which is a simplified approach to deal with out-of-plane directed pile rows in a two-dimensional plane strain model (PLAXIS, 2014b). Earlier analyses comparing 3D and 2D models indicate that this element is able to represent the pile behaviour in a 2D model better than node-to-node anchors or plates (PLAXIS, 2012). The pile is represented by a beam element which is superimposed on the mesh rather than being in it, which a plate element would be. The mesh is thus continuous and the soil can “flow through” the embedded pile row. The beam is connected with the CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 37 underlying soil element by an out-of-plane interface, as can be seen in Figure 4.6 (PLAXIS, 2014b). Since there are special interface elements included in the embedded pile row feature, there is no need to create additional interface elements for the piles. The embedded pile row element have three different connection options: Free, Hinged and Rigid. If it shares a geometry point with a structure and both elements are active, the node created at the connection is by default rigid. If however the structural element is not active the point has a hinged connection to the soil. When there is an interface between the plate and the soil the embedded pile row can be connected to either the structure or the soil (PLAXIS, 2014b). The line elements which compose the embedded pile rows have two translational degrees of freedom (ux, uy) and one rotational degree of freedom (ϕz). The elements are based on Mindlin’s beam theory which allows for deflections due to bending as well as shearing. The elements can also change length when axial force is applied (PLAXIS, 2014b). To consider skin resistance, line-to-line interface elements along the shaft and perpendicular to the model plane, are used as connection between the pile and the surrounding soil. These consists of springs and a slider in the longitudinal direction and springs also in the transverse direction (PLAXIS, 2014b), see Figure 4.6. There is also the option of involving a point-to-point interface at the pile base to consider the base resistance. Figure 4.6 Embedded pile row interaction with soil (PLAXIS, 2014b). The embedded pile row element is supposed to combine features of earlier modelling methods, where node-to-node anchors and plates have been used (Sluis et al., 2013), such as:  Soil-structure interaction due to line-to-line interfaces and a continuous mesh (the soil can “flow through” the element);  Axial stiffness can be applied; CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 38  Bending stiffness can be applied;  Structural forces in piles can be obtained;  Unrealistic shear planes are not introduced. Embedded pile row element parameters The embedded pile row feature differs somewhat to most finite element methods since the bearing capacity (skin friction) is considered to be an input parameter rather than the result of calculation. The input value of this is preferably based on representative data from pile load testing. It is advised to compare the behaviour from a calibration with the results from the pile load test. The group action of the pile row must be taken into account when defining the pile bearing capacity (PLAXIS, 2014b). The single pile material properties: E: Young’s modulus. [kN/m 2 ] γpile: Unit weight of pile material. [kN/m 3 ] The geometric properties of the embedded pile row: Pile type: Predefined or User defined can be chosen Predefined pile type: Massive circular pile, Circular tube or Massive square pile can be chosen. dpile: For Massive circular pile, the pile diameter is defined and determines the size of the elastic zone where soil behaviour is excluded. [m] User-defined piles are defined by the pile cross section area, A, and moment of inertia, I. Lspacing: Pile spacing perpendicular to the model plane. [m] The interaction properties of the embedded pile row: In order to describe the behaviour of the special interface element, an elastic-plastic model is used. The elastic behaviour accounts for the difference in average soil displacements and the displacements of piles in the out-of-plane direction and depends on the pile diameter in relation to Lspacing. The plastic behaviour is regarded CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 39 by skin resistance Tmax [kN/m], defined at the pile top and bottom, Ttop,max and Tbot,max, and Base resistance [kN]. These values are automatically recalculated per unit of width in the out-of-plane direction (PLAXIS, 2014b). For the interface to remain elastic the shear force t.s must be lower than Tmax. When it is exceeded the behaviour is plastic. The pile bearing capacities are automatically recalculated per unit of width in the out-of-plane direction by using the Lspacing input (PLAXIS, 2014b). 4.4 Loads in PLAXIS 2D A point load are created in a similar manner as geometry points and given the input value in force per unit of width [kN/m] in the direction perpendicular to the model plane. In the 2D plane strain model the point load thus is a line load. Also in the axisymmetric model the point load is a line load, in this case on a circle section, if not located at x = 0, where it is a real point load and the input value is given in the unit of force [kN] (PLAXIS, 2014b). Distributed loads are created in a similar manner as geometry lines. Like the point load, the distributed load extends in the out-of-plane direction and thus has the input value of force per area [kN/m2]. In the input window for distributed loads the input values for the two geometry points at each end of the load line can be applied. The load can be uniform if the same value is given to the two points. If there is a difference between the input values the load is linear along the line (PLAXIS, 2014b). Characteristic values of the loads are used as input for PLAXIS. CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 40 5 Verification of soil parameters and soil models This chapter contains information about how evaluated parameters have been adjusted to give an accurate representation of the soil in the PLAXIS 2D model. 5.1 Soil tests performed in PLAXIS 2D An important aspect of creating models using numerical software is to be able to validate that the model is acting as anticipated. In order to verify that the soil model created in PLAXIS is able to express the actual behaviour of the in situ soil, it is possible to simulate different kinds of soil tests in PLAXIS. Soil test results from real laboratory tests can be compared with the results from simulated tests in PLAXIS and thus show if the model corresponds to the real case in a realistic way. Based on the comparison, the input parameters could be calibrated to find the optimal input values. For this thesis the stepwise oedometer tests carried out in 1966, used to evaluate the soil parameters, have been simulated using an axisymmetric model as described below. To compare the shear strength, triaxial test simulations have also been carried out. The oedometer tests from 1966 were not fully performed according to the recommended practice, with the time for each loading step set to one day. Several load steps have been applied for shorter periods. This has been taken into account in the soil test simulations by using the same length of time steps, as in the oedometer tests from 1966. As is described in section 6.1, the clay below the excavation bottom is in this thesis divided into three different layers. Soil tests simulations, both oedometer and triaxial, with the Soft Soil model have been performed for each of the three layers. The Soft Soil Creep model has only been evaluated with an oedometer simulation and only for Clay 1. The Soft Soil Creep simulation is made as a comparison with the Soft Soil model. Therefore, the curve of the Soft Soil Creep has not been modified. Axisymmetric model, Stepwise oedometer test 5.1.1 A stepwise oedometer test is simulated in PLAXIS as an axisymmetric scale model with a closed consolidation boundary and dimensions according to Figure 5.1. When performing the soil test simulations by scale modelling rather than the Soil Test feature in PLAXIS 2D, the possibility to set time is given. This should be the preferred way to model, especially for Soft Soil Creep which is time dependent. CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 41 Figure 5.1 Principal sketch of the axisymmetric model in PLAXIS for a stepwise oedometer test. Dashed line means closed boundary (Olsson, 2010). In both the Soft Soil model and the Soft Soil Creep model, the stiffness is stress dependent. This means that since the top layer of the soil profile is subjected to zero vertical stress, the stiffness in the top of the soil profile will be very small. This causes large deformations to occur in the beginning, when the soil is loaded. To prevent this from happening in a soil test simulation, an initial stress can be applied to the soil specimen. This is done by applying a layer of elastic soil on top of the test sample with a corresponding overburden effective stress to the real test sample (Olsson, 2010). The test is simulated by calculation phases where a distributed load is increased according to the test documentation from 1966. Consolidation for each phase is calculated and the time is set to the corresponding value from 1966, for each load step. Triaxial soil test 5.1.2 The triaxial soil test in the Soil Test application is used to simulate shear strength at failure. Since no triaxial tests have been done for the site the input values have to be calculated. The horisontal pressure is calculated according to equation 5.1. * (5.1) The test is performed in undrained conditions. CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 42 5.2 Evaluating results Since settlements are the focus of this thesis, the most important parameters to match with the soil test simulations are λ*, κ* and the OCR, which all have a big influence on the predicted deformation of the soil. Due to the lack of triaxial tests, the parameters in Table 5.1 are assumed and will be constant during all soil test simulations. Table 5.1 Assumed values for the soil models. υ [-] [-] c' [kPa] ɸ' [°] 0.15 0.5 1 30 Stepwise oedometer simulations 5.2.1 If the curve from the simulated oedometer test does not fit sufficiently well, when compared to the curve from the laboratory test, the parameters are adjusted until the fit is estimated to represent the behaviour of the soil in a realistic way. Presented below in Figure 5.2, Figure 5.4 and Figure 5.5 are the oedometer curves from 1966, plotted together with the soil test simulations, which have been adjusted until as a sufficiently good fit is reached. In Figure 5.3, the strain is plotted versus time for the load step 160-320 kPa, which is the load step that µ* is being evaluated from. The curves in the strain versus time graph have not been modified to match better. The input parameters are presented in Table 5.2, Table 5.3 and Table 5.4. Since λ*, κ* and OCR are the most important parameters to match, the whole curve does not need to have a good fit. Thus, the inclinations of the curves as well as where the preconsolidation pressure is reached is where focus of the comparison should be. The inclination of the different curves, prior to reaching the preconsolidation pressure, does not fit well. However, the input value for the κ* value is evaluated from the unloading-reloading curve, of which the fit is good. CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 43 Clay Layer 1 Figure 5.2 Oedometer test from 1966 compared to simulated oedometer tests in PLAXIS for Soft Soil model and Soft Soil Creep model. The oedometer tests represents clay layer 1. Figure 5.3 Strain plotted versus time for the load step 160-320 kPa. The oedometer test from 1966 is compared to soil test simulations in PLAXIS for Soft Soil model and Soft Soil Creep model. 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 1 10 100 1000 ε [- ] σ'v [kPa] Oedometer 66 Scale model SS Scale model SSC 0 0,02 0,04 0,06 0,08 0,1 0,12 1 10 100 1000 10000 100000 ε [- ] Time [s] Oedometer 66 Scale model SS Scale model SSC CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 44 Table 5.2 Input parameters for clay layer 1 λ* [-] κ* [-] [-] OCR [-] e0 [-] [kPa] ky [m/day] kx [m/day] 0.153 0.02797 0.547 1.14 1.87 82 1.62E-5 2.44E-6 Clay layer 2 Figure 5.4 Oedometer test from 1966 compared to simulated oedometer tests in PLAXIS for Soft Soil model. The oedometer tests represents clay layer 2. Table 5.3 Input parameters for clay layer 2 λ* [-] κ* [-] [-] OCR [-] e0 [-] [kPa] ky [m/day] kx [m/day] 0.198 0.0189 0.54 1.167 1.84 140 1.71E-5 2.57E-5 0 0,05 0,1 0,15 0,2 0,25 1 10 100 1000 ε [- ] σ'v [kPa] Oedometer 66 Scale model CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 45 Clay layer 3 Figure 5.5 Oedometer test from 1966 compared to simulated oedometer tests in PLAXIS for Soft Soil model. The oedometer tests represents clay layer 3. Table 5.4 Input parameters for clay layer 3 λ* [-] κ* [-] [-] OCR [-] e0 [-] [kPa] ky [m/day] kx [m/day] 0.185 0.025 0.543 1.18 2.03 170 5.6E-6 8.46E-6 0,00% 5,00% 10,00% 15,00% 20,00% 25,00% 30,00% 35,00% 1 10 100 1000 ε [- ] σ'v [kPa] Oedometer 66 Scale model CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 46 Triaxial test simulations 5.2.2 The input data and the borehole used for each soil layer is the same as in the oedometer simulations presented above. Figure 5.6 Shear strength obtained from vane tests from 1966 compared with shear strength from a triaxial test simulation performed in PLAXIS As mentioned above, triaxial tests are simulated in order to investigate the evaluated shear strength of the soil. The results differ from the measured values from 1966, which can be seen in Figure 5.6. The curves do not have a good fit relative each other and the inclinations are different, but these differences can partly be explained by different modes of failure, as vane tests does not correspond to undrained failure in triaxial compression. Unfortunately there is no real triaxial test to compare it with, and hence it is pointless to attempt to calibrate parameters for a better fit. -20 -15 -10 -5 0 5 10 15 0,0 20,0 40,0 60,0 Le ve l [ -] Shear strength [kPa] Vane test average Simulated triaxial test CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 47 6 Modelling This chapter contains information about how the modelling for the case study was performed. The case study of Nordstaden 8:27 is modelled using the plane strain model. Thus, a whole cross section can be investigated. According to Prakoso and Kulhawy (2001) this type of model can somewhat overestimate settlements, but can still provide reasonable results and the possibility to analyse large piled rafts with relatively low computing time. Initially, loads and dimensions from multiple cross sections were to be investigated to compensate for the simplifications when designing a 3D-problem in 2D. However, due to a tight time frame and the difficulty of modelling the caissons in 2D, only one cross-section is modelled. Also, the caissons make the bottom plate stiffer, which is beneficial in terms of settlements. The cross-section is chosen over the short side of the building at line K, see Figure 3.16, in order to make the plane strain conditions better utilised. The settlement analyses are performed after the additional loading with all prior displacements being reduced to zero. This is done since it has been deemed that the settlements of interest are the ones resulting from the construction of additional floors. 6.1 Geometry and simplifications The geometry model, which can be seen in Figure 6.1 and Figure 6.2, is based on construction drawings for Nordstaden 8:27 and the soil parameter evaluations. In the geometry input the elevation on the y-axis has been given the same values as in the local coordinate system of Gothenburg. The ground level is located at y = 12.1, the excavation bottom is located at y = 5.8. Coordinates for the embedded pile row elements are obtained from construction drawings, where piles closest to line K have been regarded. Point loads are located at gridlines 1-8 in the construction drawings. For construction drawings see Appendix A. CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 48 Figure 6.1 Overview of the model geometry. Coordinates for corners (clockwise from the top left corner): (-240,12.1),(320,12.1),(320,-80) and (-240, -80). Figure 6.2 Zoom in of the geometry for the construction. The excavation and plate are located between x-coordinates 0 and 79.2. The groundwater head is placed at +10.1. The assumption is made that the water pressure acting on the raft is set to the same level. No consideration is made regarding the difference in groundwater pressure below the raft. The shape of the compression index curves as well as the creep index curves indicate that the properties of the soil change with depth. This can also be seen in the permeability-level graph. Based on this, a sectioning of three layers is suitable, see Table 6.1. Furthermore, the natural water content diverges at approximately the same levels as the indices, indicating that the soil properties have altered there. For the swelling index, no such pattern is found. The unloading-reloading curve of borehole 17b - 25 m, has an odd shape, which indicates that this might be due to sample disturbance. Appropriate borehole and depth is used for each layer, see Table 6.1. Based on the compression index curves, it would be appropriate to use borehole 17b at a depth of 25 m for soil layer three. However, due to the potential sample disturbance at that depth discussed above, the input data would be to dubious to use. Therefore, borehole 1 at a depth of 20 is better to use. CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 49 Table 6.1 Levels for the layers modelled as Linear Elastic (LE) and Soft Soil and sample used for the corresponding input parameters for the Soft Soil layers. Start level, y End level, y Borehole and depth LE layer 1 (fill) +12.1 +10.1 - LE layer 2 +10.1 +5.8 - Clay layer 1 +5.8 +2 Borehole 1, 8m Clay layer 2 +2 -6 Borehole 17b, 16m Clay layer 3 -6 -90 Borehole 1, 20 m The stress-void ratio curves, evaluated from the soil tests, in Figure 6.3, show two distinct trends. This might imply that there would be sufficient with two layers for the model. However, only the compression indices for the chosen two deeper layers are similar. The rest of the parameters differ too much to model it as one layer. CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 50 Figure 6.3 Vertical stress plotted versus void ratio for oedometer tests from holes 1 and 17b. The building is surrounded by streets and other large buildings which in reality of course affect the foundation and ground conditions. This has not been considered in the analyses of this thesis. The model expands to a relatively large distance in the x- direction, on both sides of the building, to prevent influence from the fixed boundary. 6.2 Soil Model To represent the settlement behaviour of the soft clay in Gothenburg the Soft Soil model has been chosen to model the clay below excavation level. The top layer, which represents the fill, has been modelled as linear-elastic with a thickness of 2 m 0,70 0,90 1,10 1,30 1,50 1,70 1,90 2,10 2,30 10 100 1000 V o id r at io , e [ -] σ'v [kPa] Bh 1, 3 m Bh 1, 4 m Bh 1, 8 m Bh 1, 12 m Bh 1, 20 m Bh 17b, 6 m Bh 17b, 10 m Bh 17b, 16 m Bh 17b, 25 m CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 51 and a unit weight of 18kN/m 3 . The clay layer down to the excavation depth has also been modelled as linear-elastic, but with a unit weight of 16 kN/m 3 . The choice of modelling these as linear elastic is to simplify the excavation process for the model. Since settlements under the foundation are the focus of the investigation, the two upper soil layers only need to contribute with unit weight and permeability. The model Soft Soil Creep is included in the investigations as, a comparison to the Soft Soil model, to see if the behaviour over time can be considered in a reasonable manner. 6.3 Structural elements If not stated otherwise, the input parameters are based on construction drawings. Embedded pile row element 6.3.1 The piles are modelled by using the embedded pile row element in PLAXIS 2D. Construction drawings are used to obtain the pile spacing for each strip. The strength class of the timber is assumed to be K12, which has a Young’s modulus E of 2200 MPa (Carling et al, 1992). In reality the timber piles have a conical shape, which cannot be modelled by the embedded pile row element in PLAXIS. Therefore a diameter has been approximated. The diameter is assumed to be 0.205 m, which is the diameter at half the pile length. The weight, real density, ru, of the timber piles was calculated to 12 kN/m 3 , according to equation 6.1. ( ) (6.1) where: rou = dry density, approximated as 400 kg/m 3 (Carling et al, 1992). u = moisture content. Since the piles are located below the groundwater level the moisture content is considered to be at its maximum, which equals to 200 % (Carling et al, 1992). When calculating the skin resistance, Tmax, for pile top and bottom, equation 6.2 is used. The equation is the based on the bearing capacity of a pile without considering the circumference of the pile. Toe resistance is neglected. (6.2) where: α = adhesion factor 1.2 for timber piles CHALMERS, Civil and Environmental Engineering, Master’s Thesis 2014:131 52 cu = undrained shear strength at the top respectively bottom of the pile, according to equation 3.4. Table 6.2 Input parameters for the embedded pile row element. Parameter Size unit E 2.2E6 kN/m 2 γpile 12 kN/m 3 Predefined pile type Massive circular - Diameter 0.205 m Lspacing 1.5 m Ttop,max (cu = 22 kPa) 26.40 kN/m Tbot,max (cu = 40.9 kPa) 49.1 kN/m The connection between pile and raft is chosen as Rigid. Plate element 6.3.2 The building is simulated by the use of plate elements. The ground plate has been given input values for normal stiffness and flexural rig