Excavation in Soft Clay Class A prediction of excavation in central Gothenburg Master’s thesis in Master Program Infrastructure and Environmental Engineering MATILDA HARLÉN GABRIELLA POPLASEN Department of Architecture and Civil Engineering CHALMERS UNIVERSITY OF TECHNOLOGY Master’s thesis ACEX30-19-44 Gothenburg, Sweden 2019 Master’s thesis ACEX30-19-44 Excavation in Soft Clay Class A prediction of excavation in central Gothenburg MATILDA HARLÉN GABRIELLA POPLASEN Department of Architecture and Civil Engineering Division of Geology and Geotechnics Geotechnics Research Group Chalmers University of Technology Gothenburg, Sweden 2019 Excavation in Soft Clay Class A prediction of excavation in central Gothenburg MATILDA HARLÉN GABRIELLA POPLASEN © MATILDA HARLÉN & GABRIELLA POPLASEN, 2019. Supervisor: Industrial Doctoral Student Johannes Tornborg, Department of Archi- tecture and Civil Engineering Examiner: Senior Lecturer Mats Karlsson, Department of Architecture and Civil Engineering Department of Architecture and Civil Engineering Division of Geology and Geotechnics Geotechnics Research Group Chalmers University of Technology SE-412 96 Gothenburg Telephone +46 31 772 1000 Cover: Picture of studied excavation (Tornborg, 2018) Typeset in LATEX Department of Architecture and Civil Engineering Gothenburg, Sweden 2019 iv Excavation in Soft Clay Class A prediction of excavation in central Gothenburg MATILDA HARLÉN GABRIELLA POPLASEN Department of Architecture and Civil Engineering Division of Geology and Geotechnics Chalmers University of Technology Abstract The densification of urban areas implies a higher demand on sustainable infras- tructure, where deep excavations play an important role. Therefore, satisfactory modelling of the unloading response of clay, both in short and long term perspec- tive, is of importance. To capture the complex behaviour of soft clay and include the effect of surrounding structures, numerical modelling is essential to ensure an adequate level of design. The purpose of this thesis is to perform a Class A prediction of an excavation for the Hisings bridge project in Gothenburg. The area of the studied excavation is a busy area, adding to the complexity of the project. An advanced numerical model, Creep-SCLAY1S, was chosen for several reasons. It is an effective stress based visco- plastic model, which accounts for creep, anisotropy, bonding and destructuration. Thus, many properties inherent to Scandinavian clays are taken into account. The excavation design in Plaxis 2D was already finalized by Skanska Teknik, but with NGI-ADP, a total stress based elasto-plastic model, that also accounts for anisotropy. In addition to the Class A prediction with Creep-SCLAY1S, a comparison with the results from the NGI-ADP model is also made. The result shows that both numerical models, Creep-SCLAY1S and NGI-ADP, pre- dict similar unloading response. The difference between the model results lies in the magnitude of the predicted values, where Creep-SCLAY1S gives larger values for displacements and lower values for structural forces/bending moments. When comparing to some preliminary results from field measurements, both models seem to overestimate deformations. Even though NGI-ADP tends to give a reasonable prediction for the short term (undrained) case, it could be for the wrong reason. In comparison to NGI-ADP, it is clear that Creep-SCLAY1S predicts the development of deformations/stresses with time in a more realistic way. Further, there may be many reasons for the difference in model results, such as not incorporating installa- tion effects, lack of 3D effects or using incorrect stress state in the soil. In conclusion, numerical modelling is a very useful tool when modelling soil be- haviour, but it should be used as an indication on the expected behaviour more than for prediction of definite answers. Another thing that is important to con- sider when using different numerical models is what purpose the study has. Both studied numerical models have their advantages and drawbacks. Creep-SCLAY1S seemingly incorporates many aspects of Scandinavian clay behaviour, in comparison v to NGI-ADP. By allowing for consolidation analysis which could be crucial for de- sign of excavations, the Creep-SCLAY1S model has an obvious advantage. However, the complexity of Creep-SCLAY1S is a drawback which could lead to uncertainties. Finally, if modelling long-term performance of excavations (or other underground structures) and their surroundings, rate-dependent models such as Creep-SCLAY1S that account for effects of on-going background creep settlements should be used. Keywords: Creep-SCLAY1S, soft clay, creep, numerical modelling, bottom heave, deep excavation, sample disturbance, small strain stiffness, total stress based model, effective stress based model vi Acknowledgements We would like to thank our supervisor Johannes Tornborg and our examiner Mats Karlsson for introducing us to the subject and for guidance and contribution with expertise throughout the whole process. We would also like to thank everyone at Skanska Teknik (Geoteknik) in Gothenburg, that have shown interest in our thesis. A special thanks to Anders Kullingsjö, David Ekstrand, Robert Oskarsson and Torbjörn Edstam at Skanska for valuable thoughts and discussions during the project. Matilda Harlén & Gabriella Poplasen Gothenburg, June 2019 viii x Contents List of Figures xvii List of Tables xxi 1 Introduction 1 1.1 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Aim and Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 Area Description 7 2.1 History of the Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Geology and Hydrogeology . . . . . . . . . . . . . . . . . . . . . . . . 8 3 Theoretical Background 11 3.1 Behaviour of Soft Clay . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.1.1 Creep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.1.2 Deep Excavations in Soft Clay . . . . . . . . . . . . . . . . . . 15 3.1.2.1 Bottom Heave . . . . . . . . . . . . . . . . . . . . . 16 3.2 Soil Modelling and Numerical Modelling . . . . . . . . . . . . . . . . 19 3.2.1 Total Stress vs Effective Stress Based Model . . . . . . . . . . 21 3.2.2 Small Strain Stiffness . . . . . . . . . . . . . . . . . . . . . . . 22 3.3 Creep-SCLAY1S Model . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.3.1 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.3.1.1 Initial Stress Parameters . . . . . . . . . . . . . . . . 28 3.3.1.2 Conventional Parameters . . . . . . . . . . . . . . . 29 3.3.1.3 Anisotropic Parameters . . . . . . . . . . . . . . . . 30 3.3.1.4 Bonding and Destructuration Parameters . . . . . . 31 3.3.1.5 Creep Parameters . . . . . . . . . . . . . . . . . . . 32 3.4 NGI-ADP Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.5 Sample Disturbance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4 Technical Specifications 39 4.1 Soil Profile and Properties . . . . . . . . . . . . . . . . . . . . . . . . 41 4.2 Numerical Modelling of Excavation . . . . . . . . . . . . . . . . . . . 44 4.2.1 Existing Contractor Design with NGI-ADP . . . . . . . . . . . 44 4.2.2 Modified Design with Creep-SCLAY1S . . . . . . . . . . . . . 46 xi Contents 5 Results 49 5.1 Soil Displacements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 5.1.1 Distribution of Bottom Heave . . . . . . . . . . . . . . . . . . 50 5.1.2 Point A - Center of Excavation Bottom . . . . . . . . . . . . . 52 5.1.3 Point B - 1.5 m Beside Excavation . . . . . . . . . . . . . . . 56 5.1.4 Point C - Left Tram Lane on Embankment . . . . . . . . . . . 59 5.2 Structural Entities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 5.2.1 Sheet Pile Wall . . . . . . . . . . . . . . . . . . . . . . . . . . 60 5.2.2 Struts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 5.3 Sensitivity Analysis Creep-SCLAY1S . . . . . . . . . . . . . . . . . . 65 5.3.1 Sensitivity of OCR . . . . . . . . . . . . . . . . . . . . . . . . 66 5.3.2 Sensitivity of Permeability, k . . . . . . . . . . . . . . . . . . . 68 5.3.3 Sensitivity of Modified Swelling Index, κ* . . . . . . . . . . . 70 5.3.4 Sensitivity of KNC 0 and K0 . . . . . . . . . . . . . . . . . . . . 72 5.4 Validation of Simulation . . . . . . . . . . . . . . . . . . . . . . . . . 74 5.5 Effect of Piles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5.6 Comparison with Measured Values . . . . . . . . . . . . . . . . . . . 81 6 Discussion 83 6.1 Sources of Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 7 Conclusion & Recommendations 89 7.1 Further Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 Bibliography 91 A Appendix: Foundation Type I B Appendix: Soil Properties III C Appendix: Parameters for Numerical Model XI D Appendix: Soil Test XV D.1 Calibration of Tests at Depth 7-8 m . . . . . . . . . . . . . . . . . . . XV D.2 Calibration of Tests at Depth 10-11 m . . . . . . . . . . . . . . . . . XVII D.3 Calibration of Tests at Depth 19-20 m . . . . . . . . . . . . . . . . . XIX E Appendix: Construction Sequence XXI F Appendix: Result XXIII F.1 Displacements in Soil . . . . . . . . . . . . . . . . . . . . . . . . . . . XXIII F.2 Bending Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XXIX F.3 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . XXX F.4 Effect of Piles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XXXI xii Nomenclature Roman letters as Swelling index [-] b Load factor for which swelling exceeds creep [-] c′ Cohesion intercept [kPa] c′ref Reference cohesion intercept [kPa] cu Undrained shear strength [kPa] cuk Corrected undrained shear strength [kPa] Cα Secondary compression index [%] e Void ratio [-] e0 Initial void ratio [-] E ′ Drained Young’s modulus [kPa] E ′50 Drained Young’s modulus at 50% of peak strength [kPa] E Young’s modulus [kPa] Eoed Oedometer modulus [kPa] Eu Undrained Young’s modulus [kPa] EA Axial stiffness [kN/m] EI Bending stiffness [kNm2/m] G Shear modulus [kPa] G0 Small strain shear modulus [kPa] Gur Unloading/reloading shear modulus [kPa] Gur/s A u Ratio unloading/reloading shear modulus over (plane strain) active shear strength [-] k Permeability [m/s] K ′ Drained bulk modulus [kPa] K Bulk modulus [kPa] K0 Coefficient of lateral earth pressure at rest [-] KNC 0 Coefficient of lateral earth pressure at rest for normally consolidated state [-] Ku Undrained bulk modulus [kPa] Lspacing Out-of-plane spacing [m] m Ratio between Me & Mc [-] M ′ Stiffness increase at large strains from oedometer curve [-] M Stress ratio at critical state [-] M0 Elastic stiffness (δσ/δε) from oedometer curve [kPa] Mc Stress ratio at critical state in triaxial compression [-] Me Stress ratio at critical state in triaxial extension [-] Med Bending moment [kNm/m] ML Stiffness (δσ/δε) for compression after σ′c from oedometer curve [kPa] xiii Contents Mp Maximum bending moment [kNm/m] Mre Reloading modulus [kPa] Mul Unloading modulus [kPa] Np,1 Maximum force in 1D [kN/m] Np,2 Maximum force in 2D (anisotropy) [kN/m] p′ Mean effective stress [kPa] p′eq Mean effective stress at Current state surface [kPa] p′m Mean effective stress at Normal compression surface [kPa] p′mi Mean effective stress at Intrinsic compression surface [kPa] q Deviator stress [kPa] rs Time resistance number (or creep number) [-] rsi Intrinsic time resistance number (or intrinsic creep number) [-] R Time resistance [s] Rinter Strength reduction factor [-] s′ Principal effective stress in the plane of shearing (centre of Mohr circle) [kPa] sDSSu /sAu Ratio of direct simple shear strength over (plane strain) active shear strength [-] sPu /S A u Ratio of (plane strain) passive shear strength over (plane strain) active shear strength [-] sAu,inc Increase of shear strength with depth [kN/m2/m] sAu,ref Reference (plane strain) active shear strength [kN/m2] St Sensitivity [-] t0 Initial time [s] t Maximum shear stress in the plane of shearing (radius of Mohr circle) [kPa] t Time [s] tr Reference time [s] u Pore pressure [kPa] Ved Shear force [kN] Vp Pressure wave velocity [m/s] Vs Shear wave velocity [m/s] w Specific weight of plate [kN/m/m] w Water content [%] wL Liquid limit [%] wN Natural water content [%] wP Plastic limit [%] yref Reference depth [m] xiv Contents Greek letters α0 Initial anisotropy [-] αs Creep parameter or secondary compression index [-] χ0 Initial bonding [-] δW Increment in work [kPa] δWd Increment in distortional work [kPa] δWv Increment in volumetric work [kPa] ∆χ Destructuration or degradation of bonding [-] ∆ε Relative strain [-] ∆εcr Relative creep strain [-] ∆εcp Relative volumetric viscoplastic strain [-] ∆εcq Relative deviatoric viscoplastic strain [-] ∆e/e0 Relative void ratio [-] ∆t Relative time [-] ε̇ Total strain rate [1/s] ε̇cp Volumetric creep strain rate [1/s] ε̇ep Volumetric elastic strain rate [1/s] ε̇cq Deviatoric creep strain rate [1/s] ε̇eq Deviatoric elastic strain rate [1/s] ε̇c Creep strain rate [1/s] ε̇e Elastic strain rate [1/s] εcr Creep strain [%] εp Volumetric strain [%] εq Deviatoric strain [%] η Stress ratio [-] ηK0 Initial stress ratio [-] γ Unit weight [kN/m3] γCf Shear strain at failure in triaxial compression [%] γDSSf Shear strain at failure in direct simple shear [%] γEf Shear strain at failure in triaxial extension [%] γsat Saturated unit weight [kN/m3] γunsat Unsaturated unit weight [kN/m3] κ∗ Modified swelling index [-] λ∗ Modified compression index [-] λ∗i Modified intrinsic compression index [-] µ∗ Modified creep index [-] µ∗i Modified intrinsic creep index [-] ν ′ Poisson’s ratio [-] νu Undrained Poisson’s ratio [-] ω Absolute effectiveness of rotational hardening [-] ωd Relative effectiveness of rotational hardening [-] φ′ Friction angle [°] φ′c Friction angle at critical state in compression [°] φ′cv Critical state friction angle [°] φ′e Friction angle at critical state in extension [°] ψ′ Dilatancy angle [°] xv Contents ρ Density [kg/m3] σ′1=σ′2=σ′3 Principal effective stresses [kPa] σ′c Apparent preconsolidation pressure [kPa] σ′h Effective horisontal stress [kPa] σ′h0 Effective horisontal in-situ stress [kPa] σ′v Effective vertical stress [kPa] σ′v0 Effective vertical in-situ stress [kPa] τ Reference time [days] τ0/s A u Initial mobilization [-] θ Lode angle [rad] ∧̇ Visco-plastic multiplier [-] ξ Absolute rate of destructuration [-] ξd Relative rate of destructuration [-] Abbreviations CADC Consolidated Anisotropic Drained Compression CRS Constant Rate of Strain CSL Critical State Line CSS Current State Surface ESP Effective Stress Path FEM Finite Element Method ICS Intrinsic Compression Surface IL Incremental Load MCC Modified Cam Clay NC Normally Consolidated NCS Normal Compression Surface OC Over Consolidated OCR Over Consolidation Ratio POP Pre-Overburden Pressure SPW Sheet Pile Wall SQD Specimen Quality Designation TSP Total Stress Path YS Yield Surface xvi List of Figures 1.1 Location of the studied area (Google Maps, 2019). . . . . . . . . . . . 1 1.2 Visualization of location and section of the ramp (Ekholm, 2017) (red=new bridge, grey=future buildings, white=existing). . . . . . . . 2 1.3 Methodology for this thesis. . . . . . . . . . . . . . . . . . . . . . . . 4 2.1 Maps of studied area from different time periods, where the studied excavation is marked with red or black (Google Maps, 2019; Lantmä- teriet, 2019; Stadsbyggnadskontoret, 2019). . . . . . . . . . . . . . . . 8 2.2 Regional maps of soil type and depth to bedrock (SGU, 2019). . . . . 9 3.1 Evaluation of secondary compression (creep) indices (Olsson, 2010). . 13 3.2 Variation of αs with strain (Meijer & Åberg, 2007). . . . . . . . . . . 14 3.3 Time resistance with time during one Oedometer load step (Svanø, 1991). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.4 Simplified example of wall deformation and slip surface (Knappet & Craig, 2012). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.5 Illustration of bottom heave mechanism (Knappet & Craig, 2012). . . 17 3.6 Unloading modulus related to stress behaviour in laboratory test (Larsson, 1986). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.7 Simplified model for unloading modulus (Larsson, 1986). . . . . . . . 18 3.8 Different constitutive models (Karstunen & Amavasai, 2017). . . . . . 19 3.9 Visualization of principal stresses (Knappet & Craig, 2012). . . . . . 20 3.10 Illustration of TSP and ESP for NC clays (Knappet & Craig, 2012). . 22 3.11 Strain ranges and stiffness variation for geotechnical structures (Clay- ton, 2011). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.12 Illustration of 3D reference surface for the Creep-SCLAY1S model (Sivasithamparam, 2012). . . . . . . . . . . . . . . . . . . . . . . . . 25 3.13 Illustration of yield and reference surfaces. a) MCC, b) S-CLAY1, c) S-CLAY1S, d) Creep-SCLAY1S . . . . . . . . . . . . . . . . . . . 26 3.14 Relation between different swelling and compression parameters. a) Swedish designation b) Creep-SCLAY1S . . . . . . . . . . . . . . . . 29 3.15 Illustration of Lode angle dependency in π-plane (Sivasithamparam, Karstunen, & Bonnier, 2015). . . . . . . . . . . . . . . . . . . . . . . 30 3.16 Effect of destructuration (Grimstad, Degago, Nordal, & Karstunen, 2010). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.17 Definition of modified creep index (Karstunen & Amavasai, 2017). . . 32 xvii List of Figures 3.18 Failure criterion for the NGI-ADP model (Grimstad, Andresen, & Jostad, 2012). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.19 Effect of sample disturbance (Karstunen & Amavasai, 2017). . . . . . 34 3.20 Example of comparison of block and piston sampling (Karlsson, Bergström, & Dijkstra, 2015). a) CRS b) CADC . . . . . . . . . . . . . . . . . . 35 3.21 Effect of different test conditions (Leroueil, 2006). a) Strain rate, b) Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.22 Assessment of sample quality using volumetric strain change and nat- ural water content (Larsson et al., 2007). . . . . . . . . . . . . . . . . 37 4.1 Overview of the studied section and main boreholes. . . . . . . . . . . 39 4.2 The studied section showing the finished construction as well as a road embankment with existing wooden piles beneath. . . . . . . . . 40 4.3 Methodology for retrieving soil profile and parameters. . . . . . . . . 41 4.4 Soil profile with properties. . . . . . . . . . . . . . . . . . . . . . . . . 42 4.5 Section of NGI-ADP model design in Plaxis 2D. . . . . . . . . . . . . 45 4.6 Section of Creep-SCLAY1S model design in Plaxis 2D. . . . . . . . . 46 5.1 Chosen points, sections and structures for analysis. . . . . . . . . . . 49 5.2 Distribution of bottom heave for final excavation depth (phase 10). . 50 5.3 Difference in stiffness between Creep-SCLAY1S and NGI-ADP. . . . . 51 5.4 Comparison of heave in point A with Creep-SCLAY1S and NGI-ADP. 52 5.5 Prediction of vertical displacement in section A for all construction phases, with Creep-SCLAY1S and NGI-ADP. . . . . . . . . . . . . . 53 5.6 Comparison of vertical displacement in section A. . . . . . . . . . . . 54 5.7 Comparison of heave in section A between Creep-SCLAY1S, NGI- ADP and analytical estimation using Mul. . . . . . . . . . . . . . . . 55 5.8 Comparison of horizontal displacements in point B with Creep-SCLAY1S and NGI-ADP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 5.9 Horizontal displacement of section B for all construction phases, with Creep-SCLAY1S and NGI-ADP. . . . . . . . . . . . . . . . . . . . . . 57 5.10 Comparison of horizontal displacement in section B. . . . . . . . . . . 58 5.11 Comparison of settlements in point C with Creep-SCLAY1S and NGI- ADP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.12 Horizontal displacement of right-hand SPW with Creep-SCLAY1S and NGI-ADP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 5.13 Comparison of horizontal displacement for critical phase. . . . . . . . 61 5.14 Bending moment of right-hand SPW using Creep-SCLAY1S and NGI- ADP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 5.15 Comparison of bending moment for critical phase (phase 10). . . . . . 63 5.16 Satellite measurement of settlements in studied area with studied excavation marked in black (courtesy to Trafikverket). . . . . . . . . . 74 5.17 Points for comparison of p′m and p′eq. . . . . . . . . . . . . . . . . . . 75 5.18 Position of piles in studied excavation. . . . . . . . . . . . . . . . . . 77 5.19 Bottom heave for the final excavation depth (phase 10). . . . . . . . . 78 5.20 Comparison of heave in point A with Creep-SCLAY1S and Modified Creep-SCLAY1S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 xviii List of Figures 5.21 Comparison of vertical displacement in section A. . . . . . . . . . . . 80 5.22 Comparison of heave predictions in section A for phase 8 (heave = positive). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 6.1 Comparison of stress in 2D and 3D using the analytical 2:1 method. . 86 6.2 Heap of soil in the studied excavation. . . . . . . . . . . . . . . . . . 87 6.3 Cracks on excavation bottom in studied excavation. . . . . . . . . . . 88 A.1 Foundation types in the nearby area with excavation marked in red (Trafikverket, 2016c). . . . . . . . . . . . . . . . . . . . . . . . . . . . I B.1 Shear strength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III B.2 Density. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV B.3 Water content. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V B.4 Liquid and plastic limit. . . . . . . . . . . . . . . . . . . . . . . . . . VI B.5 Permeability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII B.6 Sensitivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII B.7 Compilation of σ′c with OCR trend-lines, chosen layers marked with black lines. The triangular markers are the values closest to the exca- vation, followed by the rectangular markers and then by the circular markers which are furthest away. . . . . . . . . . . . . . . . . . . . . IX D.1 Calibration against triaxial test, level -5.26 m. . . . . . . . . . . . . . XV D.2 Calibration against IL Oedometer test, level -4.1 m. . . . . . . . . . . XVI D.3 Calibration against CRS test, level -4.1 m. . . . . . . . . . . . . . . . XVI D.4 Calibration against triaxial test, level -8.24 m. . . . . . . . . . . . . . XVII D.5 Calibration against IL Oedometer test, level -7.1 m. . . . . . . . . . . XVIII D.6 Calibration against CRS test, level -7.1 m. . . . . . . . . . . . . . . . XVIII D.7 Calibration against triaxial test, level -16.1 m. . . . . . . . . . . . . . XIX D.8 Calibration against IL Oedometer test, level -17 m. . . . . . . . . . . XX D.9 Calibration against CRS test, level -16 m. . . . . . . . . . . . . . . . XX F.1 Total displacements for last excavation stage using Creep-SCLAY1S model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XXIII F.2 Total displacements for last excavation stage using NGI-ADP model. XXIV xix List of Figures xx List of Tables 3.1 Drained and undrained stiffness parameters (Clayton, 2011). . . . . . 23 3.2 Input parameters to the Creep-SCLAY1S model (Amavasai, Siva- sithamparam, Dijkstra, & Karstunen, 2018). . . . . . . . . . . . . . . 27 3.3 Assessment of sample quality using volumetric strain and void ratio change (Lunne, Berre, & Strandvik, 1997; Terzaghi, Peck, & Mesri, 1996). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.1 Chosen parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.2 Construction sequence with Creep-SCLAY1S in Plaxis 2D. . . . . . . 47 5.1 Comparison of predicted strut forces. . . . . . . . . . . . . . . . . . . 64 5.2 Sensitivity analysis of OCR on uy in point A and C. . . . . . . . . . 66 5.3 Sensitivity analysis of OCR on Mmax and N . . . . . . . . . . . . . . . 67 5.4 Sensitivity analysis of k on uy in point A and C. . . . . . . . . . . . . 68 5.5 Sensitivity analysis of k on Mmax and N . . . . . . . . . . . . . . . . . 69 5.6 Sensitivity analysis of κ* on uy. . . . . . . . . . . . . . . . . . . . . . 70 5.7 Sensitivity analysis of κ* on Mmax and N . . . . . . . . . . . . . . . . 71 5.8 Sensitivity analysis of KNC 0 and K0 on uy in point A and C. . . . . . 72 5.9 Sensitivity analysis of KNC 0 and K0 on Mmax and N . . . . . . . . . . 73 5.10 Change of reference surface between phase 1 and phase 3. . . . . . . . 76 C.1 Calculated parameters for Creep-SCLAY1S model. . . . . . . . . . . . XI C.2 Classification of sample quality for IL Oedometer tests. . . . . . . . . XI C.3 Classification of sample quality for CRS tests. . . . . . . . . . . . . . XII C.4 Parameters for clay layers in NGI-ADP model. . . . . . . . . . . . . . XII C.5 Properties of filling material. . . . . . . . . . . . . . . . . . . . . . . . XIII C.6 Properties of sheet pile walls. . . . . . . . . . . . . . . . . . . . . . . XIII C.7 Properties of struts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . XIII C.8 Parameters for Soft Soil interfaces. . . . . . . . . . . . . . . . . . . . XIV E.1 Construction sequence with NGI-ADP in Plaxis. . . . . . . . . . . . . XXI F.1 Bottom heave in point A (center of excavation bottom) with Creep- SCLAY1S and NGI-ADP. Displacements are reset to 0 after Phase 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XXV xxi List of Tables F.2 Horizontal displacement in point B (location of inclinometer) with Creep-SCLAY1S and NGI-ADP. Displacements are reset to 0 after Phase 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XXVII F.3 Settlement in point C (tram track closest to excavation) with Creep- SCLAY1S and NGI-ADP. Displacements are reset to 0 after Phase 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XXVIII F.4 Horizontal displacement in right-hand sheet pile wall with Creep- SCLAY1S and NGI-ADP. . . . . . . . . . . . . . . . . . . . . . . . . XXIX F.5 Bending moment in right-hand sheet pile wall with Creep-SCLAY1S and NGI-ADP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XXX F.6 Increased values for KNC 0 and K0. . . . . . . . . . . . . . . . . . . . . XXX F.7 Parameters for steel and concrete piles. . . . . . . . . . . . . . . . . . XXXI F.8 Parameters for axial skin resistance. Steel piles: 0.5·cuk Concrete piles: 0.7·cuk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XXXI F.9 Bottom heave in point A (center of excavation bottom) with Creep- SCLAY1S and Modified Creep-SCLAY1S. Displacements are reset to 0 after Phase 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XXXII xxii 1 Introduction As cities densify and the demand for sustainable infrastructure is increasing, there will also be a higher demand for underground constructions. Consequently, satisfac- tory modelling of the unloading behaviour of clay will come to play a more important role. Especially since deep and complex excavation works may stay open a longer time period than previously. Thus, the modelling of time-dependent response of clay will be important since the stability of excavations often gets more critical with time. To be able to capture the complex behaviour of clay and include the effect of surrounding structures, numerical modelling is essential to ensure adequate design. It is of extra importance to get reliable predictions in urban areas since there often are high demands on safety and restrictions of deformations. Therefore, it is of interest to further investigate how numerical models perform considering unloading behaviour. 1.1 Case Study This study investigates a deep excavation located in the central parts of Gothen- burg, see Figure 1.1. To build excavations in Gothenburg, and larger buildings/in- frastructure in general, is rather complicated due to the difficult ground conditions. A characteristic ground profile in Gothenburg consists of thick layers of soft and sensitive clay which leads to challenges with ongoing creep settlements. Figure 1.1: Location of the studied area (Google Maps, 2019). 1 1. Introduction The construction site is located between Nordstan and Nils Ericson terminalen, see Figure 1.2. The area is highly exploited and busy, which in addition to the ground conditions adds to the complexity of the project. The excavation is carried out in order to construct a ramp, where the upper part is connected to the new Hisings bridge and the lower part is a loading ramp going into Nordstan, see Figure 1.2. The studied excavation will be up to 7 m in the deeper parts. Figure 1.2: Visualization of location and section of the ramp (Ekholm, 2017) (red=new bridge, grey=future buildings, white=existing). The ramp is a part of the new Hisings bridge project, which itself is a part of the “Västsvenska paketet”. The project is ordered from the city of Gothenburg, and their vision is to facilitate and increase the capacity of public travelling which will allow for a growth of western Sweden (Trafikverket, 2016b). The companies responsible for the Hisings bridge project (including the excavation for the ramp) are Skanska and MT Højgaard. This thesis will be conducted in collaboration with Skanska Teknik. The design of the retaining structure for the excavation has already been finalized by Skanska Teknik using analytical Rankine earth pressures and nu- merical (FEM) analysis with the NGI-ADP model in Plaxis 2D. However, since the NGI-ADP model is total stress based, it does not include time-dependent response. Another interesting aspect of clay is the bonding and destructuration effects. It would therefore be of interest to study the response of a more advanced numerical model that is effective stress based and that includes these aspects. Therefore, it is chosen to analyze the designed system with the Creep-SCLAY1S model. 2 1. Introduction 1.2 Aim and Objectives The aim of this Master’s thesis is to make a Class A prediction for the excavation located between Nordstan and Nils Ericsson terminalen, which is preparing for the new Hisings bridge ramp. The prediction will be performed by numerical analysis, using Plaxis 2D with the Creep-SCLAY1S model. Both short and long term perfor- mance will be assessed. Further, the study aims at mapping important behaviour of soft clay and understand how the model affects the results. It also aims at identify- ing uncertainties when modelling deep excavations and approaches to reduce those. The following objectives are set: • Create a soil profile and retrieve parameters for the Creep-SCLAY1S model which are representative for the soil behaviour • Validate the Creep-SCLAY1S model • Study how deformations and structural forces develop with time – Which magnitude of bottom heave could be expected? – Which magnitude of settlement could be expected? • Compare and evaluate the main differences between the results of the Creep- SCLAY1S and NGI-ADP model – What are the main limitations of the studied models, and what effect does it have? • Asses which parameters that have large influence in the Creep-SCLAY1S model • Analyze what could be improved in order to get more reliable results 1.3 Limitations As always, it is not possible to replicate reality and get exact predictions. The following are the main limitations that are identified for this thesis: • The geometry of the excavation and the properties of the retaining structure in Plaxis 2D is designed by Skanska Teknik • Only one section of the excavation is considered • By using 2D plane strain, it does not account for corner effects and other 3D-effects like step-wise excavation • The soil profile and properties are retrieved from a limited number of boreholes, which may not be representative for the soil surrounding the excavation • Limitations with modelling soil with Creep-SCLAY1S: – the isotropic elastic behaviour is modelled as linear – does not account for small strain stiffness – does not describe non-linear variation of OCR (or strength) with depth • Installation effects from piles and sheet pile walls are not be considered 3 1. Introduction 1.4 Method The main steps of the Method used in this thesis are presented in this section. Figure 1.3 shows an overview of the steps that are described. Figure 1.3: Methodology for this thesis. First, a literature review was executed to get a better understanding on the subject of this thesis. Both printed books and online scientific databases were used. In addition to this, information about the studied area was retrieved to get an under- standing of the soil in the area, expected behaviour and problems that could occur. The description of the area and the literature review, can be found in Chapter 2 and 3, respectively. Before the laboratory test data was analyzed, a sample quality assessment was performed in order to only include representative data. After that, the screened laboratory tests together with the borehole data were analyzed to retrieve a soil profile. In addition to this, the remaining input parameters to the Creep-SCLAY1S model were calculated. All model specific parameters were then calibrated with soil test in PLAXIS 2D. Further information about the input parameters for the Creep- SCLAY1S model can be found in Section 3.3. A more detailed description of the parameter retrieval and soil profile, can be found in Section 4.1. 4 1. Introduction After this, the NGI-ADP model design by Skanska Teknik, was modified to be able to use the Creep-SCLAY1S model parameters. The changes done were alterations in the soil profile and changing plastic calculation to consolidation calculation. Fur- ther, the original boundaries of the models were changed in order to avoid boundary effects. More detailed information about the PLAXIS 2D modelling can be found in Section 4.2. The main results consist of a comparison of the results from the Creep-SCLAY1S and NGI-ADP model. In the soil, vertical and horizontal displacements were ana- lyzed in points of interest, while bending moment and normal forces were analyzed for the structural entities. Further, a sensitivity analysis was performed in order to validate the accuracy of the results from the Creep-SCLAY1S model. The results and sensitivity analysis can be found in Chapter 5. To further improve the prognosis for the studied excavation (and also make it more similar to reality), piles beneath the excavation bottom were added to the Creep- SCLAY1S simulation in PLAXIS 2D. The results for this can be found in Section 5.5. In addition to this, measured data on the bottom heave from the studied exca- vation was compared to all numerical predictions. The comparison can be found in Section 5.6. 5 1. Introduction 6 2 Area Description The purpose of this chapter is to give a background on the history of the excavation area as well as a description of the local ground conditions. Thus, giving a picture of the expected soil characteristics and behaviour. 2.1 History of the Area The northern part of central Gothenburg or more specifically the areas of Vallgraven and Nordstaden (where the excavation is located), are the oldest parts of the city and have been populated since 1620 (Stadsmuseet, 1999). From then and until the beginning of the 1800’s, Gothenburg was a fortificated city. Figure 2.1 shows the evolution of the city from year 1809 until today. From 1806 Gothenburg was not a fortificated city anymore, and large areas were converted into land mass and piled to make space for new buildings. Thus, the Göta älv river started to resemble today’s appearance more and more. The studied area was before 1840 a reed area, where the Göta älv river was much wider than it is today. From 1855 and further on, a major expansion of the railway system was executed. In Figure 2.1 under year 1872, it can be seen that there was a building, more precise a train storage and workshop, located at the studied excavation site. During early excavation of the studied area, the foundation wall and 8 m long wooden piles from this building were found and have now been removed. Between the 1950’s and 1960’s, Gothenburg was a fast growing city, where some of the most extensive changes in the area of the studied excavation were made. 7 2. Area Description Figure 2.1: Maps of studied area from different time periods, where the studied excavation is marked with red or black (Google Maps, 2019; Lantmäteriet, 2019; Stadsbyggnadskontoret, 2019). 2.2 Geology and Hydrogeology The geological history of the Gothenburg region is rather complex, consisting of different kinds of deposits, both glacial and post-glacial (SGU, 2019; Trafikverket, 2016a). Gothenburg’s topography consists of lowland valleys including rivers with surrounding mountain-landscape. The soil in the valleys generally consists of a top layer of filling, followed by a thick layer of clay deposit. The clay could be assumed to be illite, which has rather strong bonding. Although, since the clay has been deposited in saltwater, the microstructure is more open resulting in a highly compressible deposit (Rankka, 2003). The bedrock consists mainly of felsic magmatic rock, such as gneiss and quartz-rich granite. Furthermore, glacial clay composes the largest share of the soil, where some is covered by post-glacial clay or post-glacial sand (SGU, 2019). The limit between glacial and post glacial clay is around 19 m ± 1m below sea level (T. Wood, 2015). In Figure 2.2 the location of the excavation is marked on regional maps showing soil type (Quaternary map) and depth to bedrock. It can be seen from the Quaternary map that the excavation is located on the converted reed area close to the old shoreline. Further, the Quaternary map shows that the top layers (the fill) consist of artificial fill and an underlying bed of young fluvial sediment. The thickness of the filling material in the area of the excavation varies between 3.6-4.7 m (Skanska Teknik, 2018a). The bottom 0.5-1.5 m of the filling are found to consist of mainly clay, with elements of sand, silt and bricks. Further, clay makes up the remaining soil, down to approximately 90 m 8 2. Area Description below ground surface, where a thin layer of friction material is found on top of solid bedrock. From the second map in Figure 2.2, it can also be seen that the excavation is located in a lowland area (valley), where some of the thickest clay deposits in the region are located. Figure 2.2: Regional maps of soil type and depth to bedrock (SGU, 2019). Investigations from the area indicate on a homogeneous clay which is slightly over- consolidated (OCR around 1.1-1.4). No intermediate permeable layers of sand or silt have been identified (Skanska Teknik, 2018b). The topography in connection to the excavation is rather flat, except for an embankment for the existing Göta älv bridge next to it, resulting in a variation in ground surface level. In general the ground surface is located at +3 m above sea level, and the groundwater table is located at +1 m above sea level (Skanska Teknik, 2018b). The clay has a water content of 60-90% and a sensitivity around 10-30 (Skanska Teknik, 2018b), which is classified as medium sensitivity according to Rankka et al. (2004) (Swedish defini- tion). One challenge with excavating in these conditions, except the stability, is to prevent deformations of nearby structures, which will be extra challenging due to the urban location. A potential problem will be the risk of lowering the groundwa- ter table which could damage foundations due to consolidation or an acceleration of degradation processes (due to extra contact with oxygen). The potential risk of damage will depend on proximity to the excavation and the foundation type (Trafikverket, 2016c). A building which will be in the risk zone is Nordstan which is a large building close to the excavation where wooden piles have been used for the foundation. To see foundation types for buildings in the area, see Figure A.1 in Appendix A.1. Another structure in the risk zone would be the road embankment next to the excavation, where the tracks for the trams are sensitive to deformations. 9 2. Area Description 10 3 Theoretical Background In this chapter the main findings from the literature review are presented. The chap- ter starts with explaining important characteristics and behaviour of clay, with focus on soft clay and unloading response. Then, different ways of simplifying (model) the soil behaviour are introduced, where numerical modelling is explained. Further, the difference between effective and total stresses based models are made clear since the studied models differ in this aspect. Also, small strain stiffness is included since it has not been incorporated in the studied models but is expected to influence the results. At last the used models, Creep-SCLAY1S and NGI-ADP are described in more detail, where Creep-SCLAY1S is the main focus. 3.1 Behaviour of Soft Clay Soil particles naturally have different shapes, where clay particles are mostly flat and platy which implies a low ability to resist deformations (D. M. Wood, 1990). In contrast to more coarse grained soils, clay particles are not held together by di- rect contact. Instead they are held together by molecular forces, allowing for a soil structure with a large void ratio (Sällfors, 2013). The voids are filled with pore fluids, most commonly air and water. Due to the large share of voids and the poor contact between the particles, clay tends to exhibit large irrecoverable deformations (D. M. Wood, 1990). The low stiffness and large deformation is extra prominent in soft clay, where the void ratio (and water content) is larger. The deformation of soils consists of both change in volume and shape, and the magnitude varies in different directions due to the anisotropic properties of clay. Further, the magnitude of defor- mation is dependent on properties like density, water content, mineral composition and organic content (Larsson, 2008). It is also dependent on the current stress state as well as the stress history. Volume change in soils occurs most commonly when it is sheared, where this mechanism is called dilatancy (D. M. Wood, 1990). When the volume changes, the pore fluid will move as well. Here, the permeability, k, indicates how easy it is for the water to move through the soil. As clays are com- posed mostly of very small particles, the permeability will be very low as opposed to coarse grained soils, such as sand. The flow of water in the soil is governed by excess pore pressures that are created if equilibrium of the pore water is disturbed. The response of the soil is thus dependent on the effective stresses that the soil is experiencing. 11 3. Theoretical Background One important mechanism of soft clays is the consolidation process (Knappet & Craig, 2012). Consolidation is a volume reduction by dissipation of excess pore pressure from saturated soils, i.e. change in effective stress. The opposite mechanism is called heave, where an increase in volume is incorporating dissipation of negative excess pore pressure. The classical theory of consolidation (1D) was first introduced by Terzaghi (1923) and assumes that time is independent of the relationship between effective stress and strain. Although, it has later been shown, by for instance Larsson (1986), that this theory is not valid for e.g. Swedish clays by analyzing measured settlements and pore pressures. Another important, also time-dependent, process to consider when modelling soft clay behaviour is creep (Persson, 2004), which is described in more detail in the next section. 3.1.1 Creep Deformations can be both elastic and plastic and are also either instantaneous or time-dependent (Larsson, 2008). Instantaneous deformations in undrained satu- rated soils consist only of shape change, while time-dependent deformations include consolidation and creep. The consolidation process is, as mentioned, driven by the gradient due to the excess pore pressures, while the creep is defined as a time- dependent volume change under constant effective stress. Further, creep can be described as the rearrangement of soil particles to a more stable state, and can in- clude both change in volume and shape (Knappet & Craig, 2012). Šuklje (1957) was first to introduce a model where creep is incorporated in the whole consolidation process as opposed to that it only could occur when excess pore pres- sures have dissipated. This implies that primary and secondary compression (con- solidation and creep) are not separate processes, but rather occur simultaneously. According to Hansbo (1960), creep occurs most likely due to viscous deformations in microstructural fracture zones which originate from the primary compression. Due to the stress increment that arises, a rearrangement of particles with time occurs. If the rearrangement is followed by a volume increase, the soil dilates (Larsson, 2008). If the rearrangement is followed by a volume decrease, the soil contracts. The re- arrangement of soil particles leads to an increased deformation resistance or bulk modulus, resulting in that the creep rate decreases with time (Hansbo, 1960). To quantify the creep rate, there are several parameters to describe creep. Ex- amples are the parameters Cα, αs and rs which all describe a linear relationship between time and creep deformations if the time axis is logarithmic. Taylor (1942) introduced a secondary compression index, Cα, which is most commonly used inter- nationally. In Sweden it is more common to use αs (Olsson, 2010). The difference between them is that αs is described with strain and Cα with the void ratio (Claes- son, 2003). Janbu (1969) presented the time resistance number, rs, which just like αs is described with strain, but with the natural logarithm instead. In Equations (3.1)-(3.3) the definitions of the creep parameters can be seen. 12 3. Theoretical Background Cα = ∆e ∆log(t) (3.1) αs = ∆εcr ∆log(t) (3.2) 1 rs = ∆εcr ∆ln(t) (3.3) The relationship between αs and rs can be described with Equation (3.4). αs = ln10 rs ≈ 2.3 rs (3.4) Cα and αs can be derived from the slope of the consolidation/compression in an Incremental load, IL, Oedometer test when all excess pore pressures have dissipated, see Figure 3.1 (Claesson, 2003; Olsson, 2010). Figure 3.1: Evaluation of secondary compression (creep) indices (Olsson, 2010). Creep deformations are strongly dependent on the effective stress during increasing strain (Meijer & Åberg, 2007). An illustration of this can be seen in Figure 3.2, where αs starts to increase significantly when approaching σ′c. Thus, the highest probability of creep occurrence is in normally consolidated, NC, and slightly over consolidated, OC, clays. 13 3. Theoretical Background Figure 3.2: Variation of αs with strain (Meijer & Åberg, 2007). The time resistance, R, explains the stress- and time-dependent soil behaviour dur- ing compression, swelling and recompression (Olsson, 2010). R is evaluated from a single load step in an Oedometer test. If time is seen as an act and deformation as its response, R can be described with Equation (3.5). R = ∆t ∆ε (3.5) Figure 3.3 shows that R increases linearly with time at t0 (Olsson, 2010), which corresponds to when excess pore pressures have dissipated. Figure 3.3: Time resistance with time during one Oedometer load step (Svanø, 1991). 14 3. Theoretical Background Here, the relationship between R and t is linear and only “pure” creep is occur- ring. The gradient of the linear relationship can be defined with the time resistance number, rs, which can be described with Equation (3.6). R = rs(t− tr) (3.6) The creep strain due to linear time resistance can be expressed by integrating over a time-span, t0 to t, see Equation (3.7). ∆εcr = 1 rs t∫ t0 dt (t− tr) = 1 rs ln t− tr t0 − tr (3.7) 3.1.2 Deep Excavations in Soft Clay The main factor adding to the difficulty of excavation design is an increment in complexity with depth (Wang, Liu, & Liu, 2009). Especially soft clay is more chal- lenging when designing and constructing deep excavations, due to its low stiffness (Kempfert & Gebreselassie, 2006). Its low stiffness can cause large deformations, both inside and outside the excavation, which is particularly problematic in urban areas. Also, urban areas are a more complex environment for excavations as current structures exist and must be dealt with (Kullingsjö, 2007). Thus, the design needs to be executed properly, as large settlements or collapse could occur, leading to damage of infrastructure or injuries of individuals (Ahmad, 2017). An example of a severe collapse, is the excavation of Nicoll Highway in Singapore, which except adding to large economic losses, caused 4 deaths and was cutting of traffic and electricity in large areas (COI, 2005). With increased depth of excavation, an increased yielding of soil is occurring if no support is present (Knappet & Craig, 2012). Therefore, a support system is installed, which most commonly consists of a retaining wall, and struts or anchors to keep the wall in place. For a deep excavation, struts at several levels is commonly used. If the retaining structure is not designed adequately, a slip surface could form as plastic equilibrium is reached in the lower part of the excavation, for an example see Figure 3.4. Normally, failure of a braced excavation is due to failure in one strut (Knappet & Craig, 2012). 15 3. Theoretical Background Figure 3.4: Simplified example of wall deformation and slip surface (Knappet & Craig, 2012). There are several factors that affect the performance of the retaining system, such as soil behaviour, stiffness of the support system, geometry of the excavation and distance to adjacent structures (Kullingsjö, 2007). However, the soil response is the most complex. When studying the unloading of soil, it is crucial to know the stress history of the soil in order to understand the response (Ladd & Foott, 1974). Fur- ther important soil characteristics when studying unloading, are non-linear stress strain response, anisotropy, rate-effects and hysteresis behaviour. However, all these aspects are rarely taken into account when designing retaining systems (Kullingsjö, 2007). The stress changes that occur when excavating will be both due to the loss of lateral support and due to the vertical unloading (Kullingsjö, 2007). This in turn leads to different drainage conditions around the excavation, which will cause different effective stresses. The effective stresses may change "more or less" with time after excavation depending on the consolidation process. The drainage conditions could be either ideally drained (no excess pore pressures), ideally undrained (constrained volume change in soil and excess pore pressure) or more likely partly drained (excess pore pressure dissipates over time). All excavations are theoretically most similar to the third drainage type, but due to the low permeability, clay is often treated as undrained. Although, this could lead to underestimation of stability since the effective stresses decrease with time as the excess pore pressure equalizes. 3.1.2.1 Bottom Heave When excavating, the soil will experience a stress relief which in turn results in heave of the excavation bottom. The heave in clay is induced by the negative excess pore pressures which are created when the soil is unloaded. The bottom heave is a crucial design factor for deep excavations, especially in urban areas as large deformations could cause damage to nearby structures and softening in sensitive clays (Karlsrud & Andresen, 2008). It is extra important to consider bottom heave 16 3. Theoretical Background in soft clays due to its low shear strength (Ergun, 2008). The heave mechanism can be described as an upward vertical displacement, due to soil expansion caused by unloading (Knappet & Craig, 2012). Heave is a reverse consolidation process and is governed by the unloading modulus, Mul (Persson, 2004). The mechanism is induced by the weight of the excavated soil and surcharge next to the excavation, which results in upward movement of the bottom, see Figure 3.5. If the shear strength of the soil is not sufficient to withstand deformations, the soil can fail due to the bottom heave mechanism. Thus, these potential problems should be constantly monitored. Figure 3.5: Illustration of bottom heave mechanism (Knappet & Craig, 2012). Like the process of consolidation settlement, the heave in low permeable soils is hydrodynamically delayed in time (Tornborg, 2017). As stated before, the unloaded soil will initially experience negative excess pore pressures. Those pore pressures will even out with time and thereby also gradually decrease the effective stress. Swelling, which often is confused with heave, is a similar mechanism which instead of unloading gives an upward vertical displacement due to changes of chemicals or water content in the clay. Swelling is however not of interest in this study. Larsson (1986) did several IL Oedometer tests on Swedish clay and found that loading stresses near the preconsolidation pressure gave very large Mul due to creep effects. Also, unloading of OC clays gives lower Mul than for NC clays (Persson, 2004). Figure 3.6 shows that according to the Larsson (1986) model, Mul decreases linearly if vertical stress decreases in relation to 80% of the preconsolidation pres- sure. Figure 3.7 shows that for σ′v>0.8σ′c, the unloading instead becomes infinitely large. The unloading modulus is stress dependent and can simplified be described with Equations (3.8)-(3.9) (Persson, 2004). 17 3. Theoretical Background Figure 3.6: Unloading modulus related to stress behaviour in laboratory test (Lars- son, 1986). Figure 3.7: Simplified model for unloading modulus (Larsson, 1986). Mul = σ′v as for σ′v ≤ bσ′c (3.8) Mul →∞ for σ′v ≥ bσ′c (3.9) where as=swelling index [-] b=load factor for which swelling exceeds secondary compression [-] Further, Karlsrud (2003) showed that a non-linear relationship for the unloading modulus, where stiffness relates to the stress level of the soil and preconsolidation pressure should be more accurate. Also, a reloading modulus, Mre, was defined using reload steps in the IL tests. 18 3. Theoretical Background Persson (2004) also performed IL Oedometer tests, but also triaxial tests and field measurements as well, where the unloading behaviour of soft Gothenburg clay was studied. Similar behaviour as for the results from Larsson (1986) and Karlsrud (2003) was observed. The relationship for Mul proposed by Persson (2004) is pre- sented in Equation (3.10). Mul = 35σ′c e 3.5 OCR (3.10) 3.2 Soil Modelling and Numerical Modelling When dealing with geotechnical structures it is of importance to be able to predict deformations and to ensure stability, especially in urban areas (Karstunen & Amava- sai, 2017). Due to the complexity of the interaction between the soil, the structure and the surroundings, the system has to be idealized. To simplify the behaviour of the soil there exist several different constitutive models (Karstunen & Amavasai, 2017). In Figure 3.8 four different constitutive models are shown. Figure 3.8: Different constitutive models (Karstunen & Amavasai, 2017). The rigid-perfectly plastic model implies that soil is not deforming until failure oc- curs (Karstunen & Amavasai, 2017). The elasto-plastic perfectly-plastic model, i.e. Mohr-Coulomb model, has linear elastic behaviour until failure occurs. Neither the rigid-perfectly plastic nor the elasto-plastic perfectly plastic model are suitable for simulating the behaviour of soft clay, which is NC or slightly OC, since this type of clay tends to have a significant change in volume during shearing. For soft clays, the elasto-plastic hardening or elasto-plastic softening models are more suitable. The elasto-plastic hardening model accounts for increase of undrained shear strength during consolidation of NC clay. The elasto-plastic softening model accounts for degradation of mobilised shear strength, which is common in sensitive soft clay. Most common in geotechnical modelling is to use isotropic elasto-plastic soil models, for instance those in Figure 3.8 (Wheeler, Näätänen, Karstunen, & Lojander, 2003). However, soft clays are mostly anisotropic due to the clay particles’ platy shape, the deposition process and the consolidation history of the deposit (Karstunen & Koskinen, 2008). 19 3. Theoretical Background The simplified behaviour of soils is usually described with principal stresses in either s′-t plane or in p′-q plane (D. M. Wood, 1990). The principal stresses are explained in Figure 3.9 while the definitions of s′ & t and p′ & q are presented in Equation (3.11) and Equation (3.12), respectively. Figure 3.9: Visualization of principal stresses (Knappet & Craig, 2012). s′ = σ′1 + σ′3 2 t = σ′1 − σ′3 2 (3.11) where σ′1, σ′2 and σ′3 = principal effective stresses s′ = principal effective stress in the plane of shearing (center of Mohr circle) t = maximum shear stress in the plane of shearing (radius of Mohr circle) p′ = σ′1 + σ′2 + σ′3 3 q = σ′1 − σ′3 (3.12) where σ′1, σ′2 and σ′3 = principal effective stresses p′ = mean effective stress q = deviator stress Changes in the soil during different processes can according to D. M. Wood (1990) be described with increment in work, see Equation (3.13). p′ is here linked to volumetric work, while q is linked to distortional work (shape change). δW = δWv + δWd = p′δεp + qδεq (3.13) Altogether, there are three possible methods to solve idealized problems: empirical, analytical and numerical (Petalas, 2018). If possible, it is best to solve the problem analytically, however due to complexity of the system it is not always possible to 20 3. Theoretical Background solve the problem analytically. Further, empirical methods would require extensive knowledge of similar previous projects or much resources such as time and money. Due to the limitations of analytical and empirical methods, numerical methods are more suitable for predictions of complex structures in urban areas. The numer- ical approach often involves using Finite element methods, FEM, which is based on discretizing the continuous soil (Karstunen & Amavasai, 2017). The discretized elements are then assigned the same properties for the whole element. Further, the elements are connected by nodes where the parameters and values of interest could be evaluated (Plaxis, 2018c). The number of nodes can be adjusted according to the desired level of accuracy. In short, the infinite amount of soil particles and their bonding is reduced to a finite amount of nodes with 2 or 3 degrees of freedom (de- pending on if modelling in 2D or 3D). A common commercial software for modelling geotechnical structures is Plaxis. Although software such as Plaxis are handy and useful tools, the results could be misleading if proper care is not taken (Karstunen & Amavasai, 2017). It is important to remember that the prediction can never be better than the input data and that the choice of constitutive model in combination with the experience of the engineer are major factors affecting the results. 3.2.1 Total Stress vs Effective Stress Based Model In numerical modelling, there exist different kinds of material models. Depending on the material model chosen and in turn the drainage type used, there exist different types of analyses (Plaxis, 2018b). The most common analysis types are total stress analysis and effective stress analysis, respectively (Jamal, 2017). The total stress analysis is used when the soil is considered to behave undrained, i.e. for short term conditions in low permeable soils. In total stress analysis the soil is as- sumed to be a one-phase material, and thus pore pressures, u, are not distinguished from the stresses. Therefore both total strength (cu, φ=0, ψ=0) and total stiffness parameters (Eu, νu) are used (Jamal, 2017; Plaxis, 2018b). Even though cu is an input value, the analysis does not give an increase or decrease in shear strength with time, as consolidation is not analyzed (Plaxis, 2018b). A further drawback with the total stress analysis is that the rate-dependent response of soil is not accounted for. The effective stress analysis is used when the soil is considered to behave drained, i.e. for long-term conditions (Jamal, 2017). In effective stress analysis, u is accounted for, and changes in excess pore pressures are analyzed. Here, effective strength (c’, φ′, ψ’=0) and effective stiffness (E50’, ν’) parameters are used (Jamal, 2017; Plaxis, 2018b). The development of excess pore pressures is used to obtain the effective stress path, ESP (Plaxis, 2018b). However, a drawback with the effective stress analysis is that the wrong undrained shear strength may be predicted, as it is based on the effective strength parameters. An advantage with the effective stress analysis is that an increase (hardening) or decrease (softening) of shear strength is accounted for. In Figure 3.10 the total stress path, TSP and ESP are illustrated. 21 3. Theoretical Background Figure 3.10: Illustration of TSP and ESP for NC clays (Knappet & Craig, 2012). 3.2.2 Small Strain Stiffness Today, there is no existing constitutive model that accounts for all characteristics of Swedish soft clay, such as structure/destructuration, anisotropy (in elastic and plas- tic regions), small strain stiffness (and its degradation) and creep (T. Wood, 2016). However, T. Wood (2016) claims it to be necessary for the construction projects that are ahead in Sweden. The stiffness is the resistance to withstand deformations under applied force. Small strain stiffness is important since it has been shown that field stiffness is much larger than the one derived from laboratory tests, when look- ing at back-analysis of constructions, meaning that conventional laboratory tests underestimate soil stiffness (Clayton, 2011; Persson, 2004). For urban excavations which are designed to be far from failure state, strains in the ground are small (Clayton, 2011). Clayton (2011) claims that especially for these cases, it is important to account for small strain stiffness to obtain more realistic ground movement predictions, as this can affect adjacent buildings or un- derlying structures. Small strains are considered to lie below 10−5%, and to have an elastic behaviour with no plastic deformations (Persson, 2004; T. Wood, 2016). Skeletal stiffness of unconsolidated soil depends on the effective stress (Clayton, 2011). Therefore, for saturated soils, two different parameter sets may be needed; parameters for the “undrained” or “short-term” case and the “drained” or “long- term” case. For isotropic soil, the most common stiffness parameters can be seen in Table 3.1. 22 3. Theoretical Background Table 3.1: Drained and undrained stiffness parameters (Clayton, 2011). Case Parameter set 1 Parameter set 2 Undrained Undrained Young’s modulus, Eu Undrained Poisson’s ratio, νu Shear modulus, G Undrained bulk modulus, Ku Drained Effective Young’s modulus, E ′ Effective Poisson’s ratio, ν ′ Shear modulus, G Drained bulk modulus, K ′ Parameter set 1 can be obtained from a triaxial tests (assuming isotropy) (Clayton, 2011). Parameter set 2 is convenient as the shear modulus, G, is the same for the drained and the undrained case. The relationships between drained and undrained shear modulus, Young’s modulus, Poisson’s ratio and bulk modulus for assuming isotropic conditions can be seen in Equations (3.14)-(3.16). G = E ′ 2(1 + ν ′) = Eu 2(1 + νu) (3.14) K ′ = E ′ 3(1− 2ν ′) (3.15) Ku = Eu 3(1− 2νu) (3.16) It is practical to consider stiffness parameters as constant at very small strains, but usually the stiffness reduces as strains increase above those levels (Clayton, 2011), see Figure 3.11. Figure 3.11: Strain ranges and stiffness variation for geotechnical structures (Clay- ton, 2011). 23 3. Theoretical Background Strain levels around geotechnical structures like tunnels, foundations and retaining walls are generally small, which can be seen in Figure 3.11 (Clayton, 2011). To anal- yse this, both parameters at very small strain levels, preferably reference strains like G0, and stiffness parameters are needed (Clayton, 2011; T. Wood, 2016). These can be obtained from field methods like seismic geophysical methods and laboratory tests such as triaxial apparatus with bender elements and resonant column tests. However, none of these methods are ideal, as they give different results since layering of the soil, the testing procedure and sample disturbance have an impact. Never- theless, compared to field tests, laboratory tests can give a greater range of stiffness data. Laboratory tests could also be used to derive stiffness degradation with strain. 3.3 Creep-SCLAY1S Model Creep-SCLAY1S is an advanced constitutive model which can be used in PLAXIS 2D or 3D. It originates from the elasto-plastic Modified Cam Clay model, MCC, but in addition includes anisotropy, destructuration, bonding and creep (rate-dependency), which all are important aspects to include when modelling natural soft clay (Grim- stad et al., 2010; Karstunen & Amavasai, 2017). The model is an elastic-viscoplastic constitutive model, where the total strain rate can be described with Equation (3.17)-(3.20) (Karstunen & Amavasai, 2017; Leoni, Karstunen, & Vermeer, 2008). The total strain rate contains an elastic part based on Hooke’s law, and an inelastic part that represents irreversible and time-dependent strains i.e. creep (Leoni et al., 2008). ε̇ = ε̇e + ε̇c (3.17) where ε̇e = ε̇ep + ε̇eq = ṗ′ K + q̇ 3G (3.18) and ε̇c = ε̇cp + ε̇cq = ∧̇ δp′eq δp′ + ∧̇ δp′eq δq (3.19) where ∧̇ is the visco-plastic multiplier ∧̇ = µ∗i τ ( p′eq p′m )β ( M2 c − α2 0 M2 c − η2 K0 ) where β = λ∗i − κ∗ µ∗i (3.20) The Creep-SCLAY1S model is able to model reliable stress strain behaviour for natural clays which are NC or slightly OC and is therefore suitable for modelling Gothenburg clay, see for example Dijkstra, Karstunen, Gras, and Karlsson (2015); Karstunen and Amavasai (2017). Since Creep-SCLAY1S considers creep effects it 24 3. Theoretical Background is also suitable for modelling deformations in urban environments, especially the long-term performance can be analyzed (Karstunen & Amavasai, 2017). In contrast to elasto-plastic models, Creep-SCLAY1S does not have a conventional yield surface since it does not have a purely elastic region. Instead of a yield surface the model has a Normal compression surface, NCS, which is the transition between small and large irrecoverable creep strains, and is defined by the preconsolidation pressure (Amavasai et al., 2018). The NCS for Creep-SCLAY1S is visualized in general stress space in Figure 3.12. Equation (3.21) shows the equation for NCS in triaxial space (Karstunen & Amavasai, 2017). Figure 3.12: Illustration of 3D reference surface for the Creep-SCLAY1S model (Sivasithamparam, 2012). fNCS = (q − p′)2 − (M(θ)2 − α2)[p′m − p′]p′ = 0 (3.21) Since the model does not include any consistency condition it is possible to go out- side the NCS. Although, the "price" for going outside the NCS is large permanent strains. Except the NCS there are two more reference surfaces (which are defined in the triaxial space): the Current state surface, CSS, and the Intrinsic compres- sion surface, ICS. All reference surfaces for Creep-SCLAY1S are illustrated in the triaxial space in Figure 3.13 d). Figure 3.13 also includes the yield surfaces for the "predecessors" (MCC, SCLAY1 and SCLAY1S) (a-c) of Creep-SCLAY1S, in order to visualize what happens with the yield surface when adding anisotropy, bonding/de- structuration and rate-dependency. 3.13 a) represents the yield surface of the MCC model, which is the simplest of the models, assuming isotropic behaviour, and as can be seen the surface is symmetric around the p’-axis. In contrast to the MCC model, S-CLAY1 model includes anisotropy which can be seen by the inclined sur- face. In the S-CLAY1S model, the bonding and destructuration is also included, which relates to the appearance of the ICS. 25 3. Theoretical Background Figure 3.13: Illustration of yield and reference surfaces. a) MCC, b) S-CLAY1, c) S-CLAY1S, d) Creep-SCLAY1S Since Creep-SCLAY1S accounts for many aspects of soft clay behaviour, it involves many parameters, which are not always straight forward to derive or calibrate. Therefore, the following sections will present the input parameters and their mean- ing. In Table 3.2 all input parameters to the model are summarized. 26 3. Theoretical Background Table 3.2: Input parameters to the Creep-SCLAY1S model (Amavasai et al., 2018). Type Parameters Symbol Required tests Initial stress parameters Apparent preconsolidation pressure σ′c Oedometer IL (alt. CRS test) Lateral earth pressure at rest for NC state KNC 0 See eq. (3.22) Lateral earth pressure at rest K0 See eq. (3.23) Overconsolidation ratio OCR Oedometer IL test Pre-overburden pressure POP Oedometer IL test (Inital void ratio e0 Oedometer IL test) Conventional parameters Poisson’s ratio ν ′ Triaxial test Modified intrinsic compression index λ∗i Oedometer IL (alt. CRS test) Modified swelling index κ∗ Oedometer IL (alt. CRS test) Stress ratio at critical state in triaxial compression Mc Triaxial compression test Stress ratio at critical state in triaxial extension Me Triaxial extension test Anisotropic parameters Initial anisotropy α0 See eq. (2.6) Absolute effectiveness of rotational hardening ω Triaxial extension test Relative effectiveness of rotational hardening ωd See eq. (2.7) Bonding and Destructuration parameters Initial bonding χ0 Estimated from sensitivity Absolute rate of destructuration ξ Back calculated from CRS and Triaxial tests Relative rate of destructuration ξd Back calculated from CRS and Triaxial tests Creep parameters Modified intrinsic creep index µ∗i Oedometer IL (creep) test Reference time (days) τ Average time step used in Oedometer tests 27 3. Theoretical Background 3.3.1 Parameters In this section the input parameters for the Creep-SCLAY1S model are presented. 3.3.1.1 Initial Stress Parameters The apparent preconsolidation pressure, σc’, is an important parameter in geotech- nical design as it distinguishes the elastic and reversible deformations from the in- elastic and partially irreversible deformations (Yang, Jia, Liu, & Shan, 2009). It also indicates the point where high compressibility of the soil starts. As OCR and POP depend on this parameter and are input parameters into the Creep-SCLAY1S model, it is crucial to estimate the preconsolidation pressure correctly (Karstunen & Amavasai, 2017). In addition to this, the model response is very sensitive to those parameters, adding to its importance. When retrieving the preconsolidation pressure from laboratory tests, the value obtained also depends on the strain rate used, as higher strain rates result in a higher preconsolidation pressure. Therefore, it is not advised to use constant rate of strain, CRS, tests for this model. Thus, incremental load, IL, Oedometer tests are needed. The OCR and POP are cal- culated using the in-situ vertical effective stress, σv’, together with the apparent preconsolidation pressure. The coefficient of lateral earth pressure at rest for the NC state, KNC 0 , and for the OC state, K0, are retrieved with equation (3.22) and (3.23), respectively (Karstunen, Krenn, Wheeler, Koskinen, & Zentar, 2005). KNC 0 = 1− sinφ′cv (Jaky’s formula) (3.22) K0 = (1− sinφ′cv)OCR sinφ′ cv (3.23) where φ′cv is the friction angle at critical state. K0 is valid during expansion and not recompression (Karstunen & Amavasai, 2017). Another method of estimating K0 proposed by Larsson et al. (2007) is presented in Equation (3.24)-(3.25). K0 = KNC 0 OCR0.55 (3.24) where KNC 0 = 0.31 + 0.71(wL − 0.2) (3.25) This relationship is empirical, and is like most such relationships for clays, based on the liquid limit, wL (Larsson et al., 2007). The liquid limit is often used as a general measure of the influence of for example clay minerals, depositional environ- ment, chemistry of pore water at deposition and changes in it. Therefore, it is of importance to use this empirical relationship only on soils with as similar as possible properties as the soil used in the retrieval of the empirical relationship. In this case, the relationship in Equation (3.24)-(3.25) is only valid for homogeneous clay layers with properties representative for Swedish clays. 28 3. Theoretical Background The initial void ratio, e0, is not an required input parameter to the model, but is needed in consolidation analysis if taking account for change in permeability, k, as a function of change in void ratio (Karstunen & Amavasai, 2017). 3.3.1.2 Conventional Parameters The Creep-SCLAY1S model uses similar parameters to the ones used in the MCC model (Sivasithamparam et al., 2015). Among them are Poisson’s ratio, ν ′, stress ratio at critical state, M, modified compression index, λ*, and modified swelling index, κ*. One difference is that this model uses the modified intrinsic compression index, λi* instead (Karstunen & Amavasai, 2017). It is derived in the same way as λ*, but with reconstituted clay preferably. If reconstituted clay is not available, IL Oedometer tests on natural clay at a high strain level enough to destroy all effects of apparent bonding can be used. For clarification of Swedish conventional designation and the modified swelling and compression indices, see Figure 3.14. Figure 3.14: Relation between different swelling and compression parameters. a) Swedish designation b) Creep-SCLAY1S The stress ratio at critical state, M, is defined for triaxial compression, Mc, and for triaxial extension, Me (Karstunen & Amavasai, 2017). Incorporating Lode angle dependency, gives a smooth yield surface as opposed to the Mohr-Coulomb failure surface (Sivasithamparam, 2012). By using a Lode angle dependent yield surface, corners are avoided and numerical computations are made easier. In Figure 3.15, the Lode angle dependency is shown for different m-values. The m-value is the ratio betweenMe andMc, where m=1 corresponds to the Drucker-Prager failure criterion (used in the MCC model without α0-inclination/anisotropy). 29 3. Theoretical Background Figure 3.15: Illustration of Lode angle dependency in π-plane (Sivasithamparam et al., 2015). Including Me allows for more accurate predictions when modelling unloading sit- uations. Equation (3.26) and (3.27) show how to determine Mc and Me from φ′cv (D. M. Wood, 1990). Mc = 6 sinφ′cv 3− sinφ′cv (3.26) Me = 6 sinφ′cv 3 + sinφ′cv (3.27) where φ′cv is derived from compression respectively extension tests. If no triaxial extension tests are conducted, Me can be redeemed from Equation (3.28), using the friction angle at critical state in compression, φ′c, i.e. for Mohr Coulomb failure (Karstunen & Amavasai, 2017). However, this would likely under- estimate Me. sinφ′c = 3Me 6−Me (3.28) 3.3.1.3 Anisotropic Parameters In natural clays the anisotropy is an important aspect to consider when modelling the response of loading (Grimstad et al., 2010). The anisotropy in clay is a result of the shape of clay particles, the process of deposition and the history of consolidation (Karstunen & Koskinen, 2008). In Creep-SCLAY1S the initial anisotropy of the soil is described by the parameter α0, which corresponds to the inclination of the reference surface, see Figure 3.13 (Karstunen & Amavasai, 2017). If assuming that the soil mainly has been exposed to one dimensional consolidation, resulting in close to NC clay and horizontal layering, the initial anisotropy could be estimated with Jaky’s formula resulting in an α0 according to Equation (3.29) (Leoni et al., 2008). α0 = η2 K0 + 3ηK0 −M2 c 3 where ηK0 = 3Mc 6−Mc (3.29) 30 3. Theoretical Background If the soil is subjected to plastic straining, the initial anisotropy will be changed which is represented by change of the inclination/position of the reference surface. The change in position of the reference surface is determined by so called rotational hardening laws (Sivasithamparam et al., 2015). In Creep-SCLAY1S, the evolution of anisotropy is represented by the parameters ω (rate of rotation) and ωd (rate of rotation due to deviatoric stress) (Karstunen & Amavasai, 2017). ωd and ω can be estimated with Equation (3.30) and (3.31), respectively. Even though it is possible to estimate ω, it will require calibration against laboratory test data. ωd = 3 8 (4M2 c − 4η2 K0 − 3ηK0) (η2 K0 −M2 c + 2ηK0) (3.30) ω ≈ 1 (λ∗i − κ∗) ln ( 10M2 c + 2α0 ωd M2 c + 2α0 ωd ) (3.31) 3.3.1.4 Bonding and Destructuration Parameters The bonding between the clay particles and the degradation of bonding are also important effects to consider when studying the response of clay (Grimstad et al., 2010). The interparticle bonding for a natural soil (initial bonding) is dependent on the composition of minerals and porewater when the soil was deposited (Karstunen et al., 2005). The bonding gives additional strength/resistance to the soil and allows for a higher void ratio during deposition. However, when the soil is exposed to plastic straining, the particles will slip and rearrange which will cause degradation of bonding, i.e. the process called destructuration (Karstunen et al., 2005). If the soil is sensitive enough, and if the rate of destructuration is larger than the rate of plastic straining, the soil could exhibit a loss in shear strength during compression (Karstunen et al., 2005). An example where the effects of destructuration can be seen is presented in Figure 3.16. Figure 3.16: Effect of destructuration (Grimstad et al., 2010). 31 3. Theoretical Background To model the bonding and the destructuration, Creep-SCLAY1S has three parame- ters: χ0, ξ and ξd (Karstunen & Amavasai, 2017). χ0 is the initial bonding and can be estimated with the sensitivity of the soil, see Equation (3.32). χ0 = St − 1 (3.32) The destructuration (degradation of bonding) is calculated with Equation (3.33), where ξ and ξd are constants which need to be calibrated against laboratory tests (Karstunen & Amavasai, 2017). As can be seen in Equation (3.33), the destructura- tion is dependent on both volumetric and deviatoric strain. Further, the constant ξ represents the absolute rate of destructuration and ξd represents destructuration linked to the deviatoric viscoplastic strain (Sivasithamparam et al., 2015). ∆χ = −ξχ [ |∆εcp|+ ξd ( ∆εcq )] (3.33) 3.3.1.5 Creep Parameters In order to model rate-dependency, Creep-SCLAY1S incorporates the parameters µi* and τ (Karstunen & Amavasai, 2017). The modified intrinsic creep index, µi*, is derived in the same way as the modified creep index, µ*, for the Soft Soil Creep model, i.e. from a particular stress increment stage in an IL Oedometer test, see Figure 3.17. Figure 3.17: Definition of modified creep index (Karstunen & Amavasai, 2017). µi* is related to “pure” creep as all bonding is destroyed by using either a recon- stituted sample, or doing the test using a high enough stress level to destroy all bonding (Karstunen & Amavasai, 2017). A parameter that is related to µi* is the intrinsic time resistance number, rsi, which is a more common parameter in Swedish practice (Olsson, 2013). Equation (3.34) describes the relationship further. rsi = 1 µ∗i (3.34) Furthermore, the reference time, τ , is related to the duration of a load step in the IL Oedometer test, which gives the apparent preconsolidation pressure (Amavasai et al., 2018). 32 3. Theoretical Background 3.4 NGI-ADP Model The Creep-SCLAY1S model is the main focus of this thesis, and therefore the NGI- ADP model is just briefly described. For more detailed information see Grimstad et al. (2012); Plaxis (2018a). The NGI-ADP model is a total stress based elasto-plastic constitutive model suited for undrained behaviour of clay and modelling undrained loading (Grimstad et al., 2012). There is a direct input of undrained shear strength as opposed to Creep-SCLAY1S that is effective stress based. The model also ac- counts for anisotropy of undrained shear strength and stiffness. Within geotechnical engineering, isotropic undrained shear strength is represented by Tresca’s yield criterion i.e. a hexagonal prism in 3D principal total stress space (Grimstad et al., 2012). To account for differences in undrained shear strength in compression and extension, the NGI-ADP model uses a modified Tresca criterion. More precise it uses the Tresca approximation after Billington (1988) in combina- tion with von Mises plastic potential function (Mises, 1913), see Figure 3.18. This avoids possible corner problems for numerical calculations. The plastic potential and yield function in this model are independent of mean stress, and thus no volu- metric strains develop. The plastic potential and yield functions in this model are not strictly isotropic hardening plasticity and thus increased mobilization changes the shape of the yield curve. Figure 3.18: Failure criterion for the NGI-ADP model (Grimstad et al., 2012). The NGI-ADP model accounts for differences in failure shear by using a non-linear stress path dependent relationship for hardening from direct input of failure strains in three directions of shearing: triaxial compression (α = 0◦), direct simple shear (α ≈ 30◦) and triaxial extension (α = 90◦) (Grimstad et al., 2012). These are translated to the design profile of undrained shear strength, i.e. active (A), direct simple shear (D) and passive (P) modes of loading. 33 3. Theoretical Background 3.5 Sample Disturbance In order to make a good prediction of soil stability and deformations, it is important to obtain reliable test data. However, when the soil is extracted from the ground, transported, stored and prepared for the test, the soil will be disturbed, which will give parameters differing from the in-situ soil conditions (DeGroot, Poirier, & Lan- don, 2005). The degree of disturbance will depend on which sampling method that is used and how the sample is handled, but will also depend on the characteristics of the soil. Soils that are extra sensitive to sample disturbance are clays with low plasticity, low OCR and a high level of structure (T. Wood, 2016). Examples of such soils are Scandinavian soft clays, where problems with sample disturbance have been noticed for a long time (T. Wood, 2016). The sample disturbance will affect important design parameters such as stiffness and strength, more specific, distur- bance tends to reduce the preconsolidation pressure and the initial stiffness, while it tends to increase the post yield stiffness (T. Wood, 2016). A visualization of how a disturbed sample could differ from in-situ conditions can be seen in Figure 3.19. Figure 3.19: Effect of sample disturbance (Karstunen & Amavasai, 2017). One major influence on sample quality is the sampling method. The sampling method which is considered to give least disturbance is block sampling. However, this is a time consuming and expensive method, and therefore the method most commonly used in Sweden for soft clays is piston sampling (STI & STII) (T. Wood, 2016). The accuracy with piston samplers, and other samplers as well, could be improved with larger diameter in order to reduce effects from friction and influence of small stones and shells etc (Lanzky & Palmquist, 2015). In Figure 3.20, two examples of the difference between block sampling and piston sampling can be seen. 34 3. Theoretical Background Results from Karlsson et al. (2015) have shown that the largest disturbance due to sampling technique will occur at small strains, approximately around 0-2% axial strain, which can be distinguished in Figure 3.20. Figure 3.20: Example of comparison of block and piston sampling (Karlsson et al., 2015). a) CRS b) CADC Even though the sampling technique is an important factor for the quality, it is also important to consider the influence of the remaining disturbance chain, also known as secondary disturbance (T. Wood, 2016). For instance the humidity, temperature and storage time could affect the structure of the clay and hence the laboratory tests will produce unreliable stress-strain responses. Furthermore, depending on which test type or under which conditions the test is performed, the response will be different. In Figure 3.21, the effect of different strain rates and temperatures is illustrated. Figure 3.21: Effect of different test conditions (Leroueil, 2006). a) Strain rate, b) Temperature 35 3. Theoretical Background In order to decrease the influence of sample disturbance, and hence increase the accuracy of the predictions, there exist several methods to classify how disturbed a sample is. One method, introduced by Andresen and Kolstad (1979), is based on evaluating volumetric strain, εp, from laboratory tests. For the Oedometer test and the triaxial compression test, the volumetric strain is evaluated for the assumed σ′v0 (also σ′h0 for triaxial) (Terzaghi et al., 1996). The classification system is called Specimen quality designation, SQD, and the different classes/intervals can be seen in Table 3.3. Another method, introduced by Lunne et al. (1997), is based on estimating the volume change from a relative void ratio. The relative void ratio, ∆e/e0, is calcu- lated by dividing the void ratio change by the in-situ void ratio. The void ratio change, ∆e, is determined from the change in void ratio during consolidation/com- pression until σ′v0 is reached, while e0 is determined from the natural water content in the sample. The rating for the relative void ratios can be found in Table 3.3. Table 3.3: Assessment of sample quality using volumetric strain and void ratio change (Lunne et al., 1997; Terzaghi et al., 1996). Sample quality assessment with volumetric strain Sample quality assessment with normalized void ratio change εp [%] SQD ∆e/e0 for OCR = 1-2 Rating < 1 A < 0.04 Very good to excellent 1 - 2 B 0.04 - 0.07 Good to fair 2 - 4 C 0.07 - 0.14 Poor 4 - 8 D > 0.14 Very poor 36 3. Theoretical Background Further, there is another method introduced by Larsson et al. (2007) based on the work done by Lunne et al. (1997). This method uses the value of volumetric strain, εp, together with the natural water content, wN . The sample quality is retrieved according to Figure 3.22. Figure 3.22: Assessment of sample quality using volumetric strain change and natural water content (Larsson et al., 2007). 37 3. Theoretical Background 38 4 Technical Specifications In this chapter, more specific information concerning the excavation, soil conditions, retaining structure and the used numerical model design are presented. In Figure 4.1 the geometry of the excavation and the analyzed section is shown. In total, the excavation occupies an area of around 1000 m2 and is as deepest 7 m in the south part and as shallowest 2 m in the northern part. The studied section is appropriate for analysis in Plaxis 2D since plane strain can be used for approximation. Figure 4.1 also shows the main boreholes used for the parameter extraction, presented in Section 4.1. Figure 4.1: Overview of the studied section and main boreholes. As stated before, the excavation is located in an urban area which means that the existing structures and the excavation could affect each other. The surrounding structures which are in close connection to the excavation are road embankments on both sides of the excavation and wooden piles beneath the road embankment which 39 4. Technical Specifications is used for trams and buses, see Figure 4.1. Due to the closeness of these structures they are included in the numerical model. For clarity, the analyzed section with these structures together with the finalized excavation and ramp can be seen in Figure 4.2. Figure 4.2: The studied section showing the finished construction as well as a road embankment with existing wooden piles beneath. The piles beneath the embankment (to the right in Figure 4.2) are approximately 15 m long, starting from level +0 or -1 m. Further, the embankment consists of gravel and there are no indications of load distributing layers in connection to the piles. 40 4. Technical Specifications 4.1 Soil Profile and Properties Since the input data is crucial in order to get reliable results, a lot of effort was put into retrieving the soil profile and the soil properties. In this section this iterative process is described. Figure 4.3 presents the methodology for obtaining the soil profile and the soil properties which are used as input to the numerical model. Figure 4.3: Methodology for retrieving soil profile and parameters. The data about the site properties (thickness of clay deposit, depth to bedrock, ground level and level of water table) was retrieved from site investigations for the Hisings bridge project, provided by Skanska Teknik. As mentioned before, the Hisings bridge project is the project which includes the studied excavation. Data related to the properties of the soil was also retrieved from borehole data for the Hisings bridge project. In order to get a wider perspective and to retrieve values for the deeper parts of the soil deposit, borehole data from the West Link project and Regionens hus project were also used. In total 25 boreholes were used for analysis. The data compiled was cu, ρ, wN , wP , wL, St, k and σ′c. The compiled data was then compared in order to determine the soil layering and then parameters for every layer were determined. The data from boreholes closer to the excavation were weighted higher. As the OCR is a very important input parameter for the Creep-SCLAY1S 41 4. Technical Specifications model it was also considered when creating the soil layering. The parameters which were most influential when creating the soil profile were cu, ρ, wN and σ′c, while wP , wL, St and k were used to verify the position of the assumed soil layers. The plots for all these parameters, including test type, can be found in Figure B.1-B.7 in Appendix B. The chosen soil profile along with the selected parameters is presented in Figure 4.4. Figure 4.4: Soil profile with properties. After determining the layering, the "model-specific" parameters κ*, λi*, µi* and φ′cv were determined for each layer. The parameters κ*, λi* were determined by evalu- ating 15 CRS and 6 IL Oedometer tests. The CRS tests used were retrieved from 6-20 m depth while the IL Oedometer tests were retrieved from 7-20 m depth. The parameter µi* was determined solely from the IL Oedometer tests. The methodol- ogy used for retrieval of κ*, λi*, µi* is presented in Section 3.3.1. The parameter φ′cv was determined from the triaxial tests, both for compression (4 tests) and extension (3 tests). All tests used for determination of κ*, λi*, µi* and φ′cv were performed by Skanska in the laboratory at Chalmers. Further, all tests were executed on clay from borehole SKC18-1, which is located in the studied section. Before assigning each layer these "model-specific" parameters, an estimation of the sample quality was done. The assessment was done according to the methods presented in Section 3.5. For the CRS tests the methods according to Andresen and Kolstad (1979) and Larsson et al. (2007) were used and for the IL Oedometer tests, the method according to Lunne et al. (1997) was used. The sample quality assessment for the IL Oedometer tests and CRS tests can be seen in Table C.2-C.3 in Appendix C. The sample quality assessment shows that the IL Oedometer tests are of better 42 4. Technical Specifications quality than the CRS tests. The IL Oedometer tests were therefore weighted higher when choosing parameters for the layers. The triaxial tests were, based on measured axial strain during consolidation stage, assumed to be of good enough quality as well. When all parameters from laboratory tests were assigned to each layer, the rest of the parameters needed for using the Creep-SCLAY1S model were calculated ac- cording to the equations presented in Section 3.3. The first setup of input parameters can be seen in Table C.1 in Appendix C. This setup was then used as input in the soil test function in Plaxis 2D. The calibration was done with triaxial compression and extension tests (level -5.2, -8.2 and -16.1 m), IL Oedometer tests (level -4.1, -7.1 and -17 m) and CRS tests (level -4.1, -7.1 and -16 m). When changing parameters to match the behaviour in the real laboratory tests, certain parameters were changed more than others. One of the most significant changes from the initial parameter setup is the increase of κ*, which is motivated by the effect of sample disturbance (discussed in Section 3.5). With other words, κ* is usually underestimated as small strain stiffness is difficult to estimate due to sample disturbance. λi* was also increased for all layers and set to the same value, as the clay is assumed to have the same mineralogy. It might be contradictory to change the intrinsic parameters since sample disturbance does not have much impact on remoulded tests, although it was evident that the λi* needed to be increased. However, µi* was not changed. Parameters dependent on φ′cv (KNC 0 , ωd, Me andMc) were not altered or just altered slightly. Also, χ0 and the OCR were not changed when calibrating. Other parameters which were changed are ω, ξ and ξd. ω is stated to only be an estimate which might need calibration while ξ and ξd are parameters that are supposed to be calibrated to fit the laboratory tests as good as possible, and are therefore expected to be changed. All final results from soil tests can be seen in Figure D.1-D.9 in Appendix D. The parameter calibration against laboratory tests was only done for depths in Clay 2 - Clay 4. Therefore, Clay 1 is assumed to have similar properties as Clay 2 based on the borehole data, except γ, OCR, k and St. In the same way Clay 5 and Clay 6, have similar properties as Clay 4, except γ, OCR and k. The final chosen input parameters can be seen in Table 4.1. 43 4. Technical Specifications Table 4.1: Chosen parameters. Parameter Unit Clay 1 Clay 2 Clay 3 Clay 4 Clay 5 Clay 6 γ kN/m3 15.4 16.2 15.2 16 16 16.9 k m/s 1.2E-9 0.7E-9 2.1E-9 1.2E-9 0.8E-9 0.5E-9 φ′c ° 35 35 34.3 34.5 34.5 34.5 K0 - 0.5 0.5 0.5 0.5 0.5 0.5 KNC 0 - 0.43 0.43 0.44 0.44 0.44 0.44 OCR - 1 1.05 1.1 1.15 1.2 1.3 ν ′ - 0.15 0.15 0.15 0.15 0.15 0.15 κ* - 0.019 0.019 0.014 0.014 0.014 0.014 λi* - 0.072 0.072 0.072 0.072 0.072 0.072 Mc - 1.42 1.42 1.39 1.4 1.4 1.4 Me - 1.1 1.1 0.96 1.06 1.06 1.06 α0 - 0.55 0.55 0.53 0.53 0.53 0.53 ω - 55 55 55 60 60 60 ωd - 0.96 0.96 0.94 0.94 0.94 0.94 χ0 - 9 14 24 14 14 14 ξ - 12 12 11 11.5 11.5 11.5 ξd - 0.25 0.25 0.3 0.35 0.35 0.35 µi∗ - 1.9E-3 1.9E-3 2E-3 1.5E-3 1.5E-3 1.5E-3 τ days 1 1 1 1 1 1 It should also be mentioned that K0 was taken from the automatic calculation in Plaxis 2D based on the input of KNC 0 into the software, and automatically no K0 value beneath 0.5 was used. However these values (which are estimated with Jaky’s formula) seem to be a bit low for Gothenburg clay. Therefore, the sensitivity of changes in K0 has been investigated through comparison with values obtained with the method presented by Larsson et al. (2007), see Section 3.3.1.1. For the results from the sensitivity analysis, see Section 5.3. 4.2 Numerical Modelling of Excavation The numerical modelling of the excavation is done with Plaxis 2D (FEM analysis) assuming plane strain conditions. In this section the model design properties are presented. Since the model design using Creep-SCLAY1S is based on the NGI-ADP model design created by Skanska Teknik, both model set-ups are presented here. 4.2.1 Existing Contractor Design with NGI-ADP Originally, the NGI-ADP model design created by Skanska Teknik was 100 m wide and 45 m thick. As the NGI-ADP model does not incorporate consolidation nor rate- effects, the full thickness of the clay deposit was not necessary to include. However, in order to make comparisons with the predictions from the Creep-SCLAY1S model (which includes consolidation and rate-effects) the original geometry of the NGI- 44 4. Technical Specifications ADP model design was altered. The whole model was therefore expanded to be 180 m wide and 95 m thick (before the construction of the existing embankment), to include the entire clay deposit. Figure 4.5 shows the geometry and included elements of the modified contractor’s NGI-ADP model design. Further, the soil profile in this model consists of three clay layers. The first ranging from level 0 m to -3 m, the second from level -3 m to -25 m, and the third from level -25 m down to the friction material (-90 m). More specific information about the properties of the clay layers can be found in Table C.4 in Appendix C. On top of the clay deposit, there is filling material ranging from level +3.7 m to 0 m. The embankment lies on the filling material and has a maximum height at level +4.8 m. Both the filling material and the embankment are modelled as Mohr-Coulomb materials. For more information about the filling material and the embankment, see Table C.5 in Appendix C. Figure 4.5: Section of NGI-ADP model design in Plaxis 2D. The wooden piles are modelled as embedded piles, and are approximately 15m long, while the sheet pile walls, SPW, are modelled as elasto-plastic. The SPW on the east side of the excavation has a PU12 profile and is 14 m long. As deformations were crucial to minimize, considering the embankment, the SPW on the west side has an AU23 profile and is 16 m long. The struts are modelled as an elastic material and have circular hollow section, CHS, profiles on both levels (y=+3 m and y=-0.3 m, respectively). For more detailed information about the structural entities, see Table C.6-C.7 in Appendix C. More specific details about the design can be retrieved from Skanska Teknik (2018a). The slightly modified construction sequence with the NGI-ADP model, which matches the Creep-SCLAY1S model, is presented in Table E.1 in Appendix E. 45 4. Technical Specifications 4.2.2 Modified Design with Creep-SCLAY1S To be able to use Creep-SCLAY1S for modelling the excavation, some additional modifications were done to the existing NGI-ADP model design. The changes (ex- cept changing constitutive model for the soil) were to divide the soil into new layers, which is described in Section 4.1, and to change the interface of the SPWs to facili- tate the calculations. The interfaces were modelled with the Soft Soil model, where the used parameters can be found in Table C.8 in Appendix C. The filling material, embankment, pile