Constitutive models for geotechnical practice

Transcription

1 Constitutive models for geotechnical practice in ZSoil v2016 Rafal OBRZUD ZSoil August

2 Contents Introduction Initial stress state and definition of effective stresses Saturated and partially-saturated two-phase continuum Introduction to the Hardening Soil model (HSM) Undrained behavior analysis using HSM Practical applications of HSM Assistance in parameter identification 2

3 Constitutive laws for finite element analysis Goal of FE analysis: reproduce as precisely as possible stress-strain response of a system subject to different or complex stress paths 3

4 Continuum models available in ZSoil v Basic laws Advanced laws (more or less complex) 4

5 Why do we need advanced constitutive models? Better approximation of soil behavior for simulations of practical cases q = s 1 -s 3 Plasticity (yielding) before reaching the ultimate state s 3 q Triaxial stress conditions (e.g. under footing) Stress path p s s 3 ' 5

6 Why do we need advanced constitutive models? Accounting for stress history and volumetric plastic straining s v Odometer test conditions (e.g. very wide foundation) error q p' 6

7 Why do we need advanced constitutive models? ENGINEERING CALCULATIONS ULTIMATE STATE ANALYSIS DEFORMATION ANALYSIS Bearing capacity Slope stability Pile, retaining wall deflection Supported deep excavations Tunnel excavations Consolidation problems Basic models e.g. Mohr-Coulomb Advanced soil models 7

8 Basic differences between implemented soil models Mohr-Coulomb q yield surface K 0 -line q q Linear elastic domain p K 0 - unloading p E E ur E = E ur e 1 8

9 Practical applications of the Hardening Soil model Tunneling Standard Mohr-Coulomb Hardening-Soil 9

10 Basic differences between implemented soil models Mohr-Coulomb Volumetric cap models q yield surface K 0 -line q isotropic hardening mechanism q Linear elastic domain p Linear elastic domain p s 1 constant q q Stiffness degradation p E E ur E E ur E=E ur e 1 E < E ur e 1 10

11 Practical applications of the Hardening Soil model Berlin sand excavation Standard Mohr-Coulomb Hardening-Soil 11

12 Basic differences between implemented soil models Mohr-Coulomb Volumetric cap models Hardening Soil models q yield surface K 0 -line q isotropic hardening mechanism q + shear hardening mechanism Linear elastic domain p Linear elastic domain p NON-LINEAR elastic domain p q q Stiffness degradation q Stiffness degradation E E ur E E ur E E ur E 0 E=E ur E ur E<E ur E 0 e 1 e 1 e 1 12

13 Contents Introduction Initial stress state and definition of effective stresses Saturated and partially-saturated two-phase continuum Introduction to the Hardening Soil model (HSM) Undrained behavior analysis using HSM Practical applications of HSM Assistance in parameter identification 13

14 Defining type of analysis 14

15 Setting parameters: Initial state setup 15

16 Material 1 Setting unit weight DEFORMATION ANALYSIS DEFORMATION + FLOW ANALYSIS Total stress analysis Effective stress analysis Always effective stress analysis Material 1 Unsaturated GWT Partially saturated Material 2 Fully saturated 16

17 Imposing initial stresses using superelements Below GWT sat - F Below GWT s' YY h D F n 0-1 s' XX s' ZZ K 0 s' YY s' XX NB. Effective initial stresses setup is mandatory for Modified Cam-clay 17

18 Contents Introduction Initial stress state and definition of effective stresses Saturated and partially-saturated two-phase continuum Introduction to the Hardening Soil model (HSM) Undrained behavior analysis using HSM Practical applications of HSM Assistance in parameter identification 18

19 Od nienasyconego do pełnego stanu nasycenia gruntu Saturation degree Interstitial pressure S - saturation degree + p w pressure in liquid phase p>0 p<0 - NB. fluid = liquid + gas from Nuth (2009) 19

20 Effective stress in ZSoil Fluid is considered as a mixture of air and water (single-phase model of fluid) Bishop s effective stress in single-phase model for fluid suction stress if p > 0 (above GWT) p pore water pressure S = S(p) degree of saturation depending on pore water pressure 20

21 Deformation + flow analysis (soil water retention curve) Effect of an apparent cohesion can be easily reproduced by coupling: o constitutive model described by effective parameters o Darcy s flow in consolidation analysis o Soil water retention curve model (van Genuchten s model) from Nuth (2009) 21

22 Deformation + flow analysis (uncoupled or coupled) Effective stress principle Bishop stress All constitutive models are formulated in terms of effective stresses Therefore effective stress parameters should be used o Effective stiffness parameters E, E 0, E ur, E 50, n, n ur o Effective strength parameters f, c 22

23 Suction pressure effect in ZSoil Let s consider stress sign convention from classical soil mechanics p Apparent cohesion effect in unsaturated, unstructured clay 0 S p p<0 s ij '= s ij p S d ij c =0 kpa p>0 s ij '= s ij p + d ij Soil resistance: q f = 2 sin φ 1 sin φ σ 1 + c cot φ 23

24 Setting flow parameters Darcy s law coefficients Soil water retention curve constants Setup for Driven Load (Undrained) analysis type 24

25 Setting flow parameters Flow parameters from Yang & al. (2004) Soil type a [1/m] S r [-] Gravely Sand Medium Sand Fine Sand 8 0 Clayey Sand Fines content, constant a from Nuth (2009) a can be taken as an inverse of height of the capillary rise 25

26 Setting flow parameters Saturation constant taken as the inverse of the capillary rise Soil type a [1/m] Silt Clay: low plasticity (lean clay) Clay: medium plasticity Clay: high plasticity (fat clay) Clay: very high plasticity

27 Effect of SWRC constants on soil strength Reproducing an apparent cohesion o Effective stress principle (Bishop) o Find a limit for S p (for p ) using van Genuchten s model o For S r = 0.0 and p Suction (apparent cohesion) S p F a Positive pore pressure above GWT 27

28 Effect of SWRC constants on soil strength Reproducing an apparent cohesion o For S r > 0.0 and p S p (for p ) Suction (apparent cohesion) NB. To avoid too much apparent cohesion above the GWT set S r = 0.0 and an appropriate a value (e.g. if a 1.0, the apparent cohesion will not exceed 10 kpa) Positive pore pressure above GWT 28

29 Effect of SWRC constants on soil strength Single phase (Deformation): Instability at initial state analysis Two-phase (Deformation+Flow): Stability at initial state analysis a=45 f =30 c = 0 kpa Max suction S p = 13 kpa 29

30 Effect of SWRC constants on soil strength Heavy rain by distributed fluxes Max suction S p = 8 kpa Instability 30

31 Effect of SWRC constants on soil strength Excavation Steady-state analysis Consolidation 31

32 Exercise 1 Determining the initial state Open file: Ex_1_InitialState.inp Medium sand Clayey sand Clay D ( SAT )[kn/m 3 ] 16.5 (20.3) 17.6 (21.4) 16.5 (20.9) e 0 [-] a [1/m]

33 Exercise 1 Determining the initial state Defining physical properties and hydraulic constants 33

34 Exercise 1 Determining the initial state Problem type: Deformation+Flow Analysis type: Initial State 34

35 Exercise 1 Determining the initial state Profiles of saturation degree Import sections Ex_1_Sections.sec 35

36 Exercise 1 Determining the initial state S*p profiles 36

37 Contents Introduction Initial stress state and definition of effective stresses Saturated and partially-saturated two-phase continuum Introduction to the Hardening Soil model (HSM) Undrained behavior analysis using HSM Practical applications of HSM Assistance in parameter identification 37

38 List of soil models and description of the most versatile one Mohr-Coulomb Drucker-Prager Cap (+DP) Modified Cam-Clay Hardening Soil SmallStrain Main features non-linear elasticity including hysteretic behavior strong stiffness variation for very small strains stress dependent stiffness (power law) volumetric hardening (accounting for preconsolidation effects) deviatoric hardening (prefailure nonlinearities before reaching ultimate state) failure: Mohr-Coulomb Rowe s dilatancy flow rule non-associated for deviatoric mechanism associated for isotropic mechanism 38

39 HSM Dialog windows 39

40 Small strain stiffness in geotechnical practice Strain range in which soils can be considered truly elastic is very small Once a certain shear strain threshold is reached a strong stiffness degradation is observed On exceeding the domain of non-linear elasticity, plastic (irreversible) strains develop 40

41 Hardening Soil model framework 41

42 HS-SmallStrain: Non-linear elasticity for very small strains Hyperbolic Hardin-Drnevich relation to describe S-shaped stiffness e 1 - e 3 ) 42

43 HS-SmallStrain: Non-linear elasticity estimation of E 0 Determination of G 0 from geophysical tests, SCPT, SDMT and others with r denoting density of soil and V s shear wave velocity. (n= for small strains) In situ tests with seismic sensors: seismic piezocone testing (SCPTU) (Campanella et al. 1986) seismic flat dilatometer test (SDMT) (Mlynarek et al. 2006, Marchetti et al. 2008) cross hole, down hole seismic tests Geophysical tests: (see review by Long 2008) continuous surface waves (CSW) spectral analysis of surface waves (SASW) multi channel analysis of surface waves (MASW) frequency wave number (f-k) spectrum method 43

44 HS-SmallStrain: Non-linear elasticity estimation of V s from SPT G 0 = ρ V s 2 V s measured at given depth at s v0 G 0 = G 0 (σ 3) where: σ 3 = min (σ v0 K 0, σ v0) then G 0 can be scaled to σ ref : (correlations for all types of soil) For correlations see report on HS model in Zsoil Help G 0 ref (σ ref ) = G 0(σ 3) σ 3 + a σ ref + a with : a = c cot φ m 44

45 HS-SmallStrain: Non-linear elasticity estimation of E 0 Approximative relation between "static" E s and "dynamic modulus E d corresponding to E 0 proposed by Alpan (1970) 45

46 HS-SmallStrain: Non-linear elasticity estimation of E 0 Determination of G 0 for sands from CPT NB. after Robertson and Campanella (1983) Rix & Stokoe (1992) Typically for soils G 0 /G ur = 2 10 Average ratios granular soils (G 0 /G ur ) avg = 3 4 clays (G 0 /G ur ) avg = 6 46

47 HS-SmallStrain: Non-linear elasticity estimation of E 0 Natural clays E 0 / E 50 = 5 30 higher values for the ratio are suggested for aged, cemented and structured clays, whereas the lower ones for insensitive, unstructured and remoulded clays Relation between E 0 and E 50 Granular soils E 0 / E 50 = 4 18 higher values are suggested for normally-consolidated soils See HS Report 47

48 HS-SmallStrain: Non-linear elasticity at small strains Granular soils 0.7 mainly depends on magnitude of mean eff. stress p after Wichtmann & Triantafyllidis (2004) Typically for clean sands and p ref = 100kPa: < 0.7 < Constitutive models for geotechnical For practice more correlations see report on HS model in Zsoil Help 48

49 HS-SmallStrain: Non-linear elasticity for small strains Cohesive soils 0.7 depends on soil plasticity PI, w L,, w P Influence of soil plasticity after Vucetic&Dobry (1991) Stokoe et al For more correlations see report on HS model in Zsoil Help 49

50 Hardening Soil: Double hardening model Why do we need two hardening mechanisms? 1. Volumetric plastic strains are often dominant in normally consolidated clays and loose sands 2. Deviatoric (shear) plastic strains are dominant in overconsolidated and dense sands 3. In practice, all depends on stress paths 50

51 Hardening Soil: Double hardening shear hardening Pure deviatoric shear in overconsolidated material with HS Standard model q = s 1 -s 3 s 0 Initial stress state s 0 -s p Linear elastic s p -s f Elasto-plastic s f On failure surface s f -s u Linear elastic 51

52 Hardening Soil: Hyperbolic approximation of the stress-strain E 50 secant stiffness modulus corresponding to 50% of the ultimate deviatoric stress q f described by Mohr-Coulomb criterion E ur unloading/reloading modulus hardening parameter which tracks the evolution of the deviatoric mechanism that evolves with the deviatoric plastic strains For most soils R f falls between 0.75 and 1 52

53 Hardening Soil: Stiffness moduli Typically for most soils: E ur / E 50 = 2 6 Must be satisfied: E ur / E 50 >2 53

54 Hardening Soil: Stiffness moduli Secant vs unloading-reloading modulus in drained test on sand In the case of cohesive soils the analogy to C s /C c can be considered loose sands: E ur / E 50 = 3 5 dense sands: E ur / E 50 = 2 3 typical C s /C c ratios are

55 HSM: Parameter identification based on drained triaxial test Stiffness characteristics E 50 < E s (e 1 =0.1%) < E ur 0.1% being resolution of a standard triaxial apparatus

56 HSM: Identifying E 50 from drained triaxial test Identification of E 50 and R f

57 HSM: Identifying E 50 based on known E s Classical, geotechnical modulus so-called «static» modulus E s corresponds to e 1 =0.1% E 50 < E s < E ur Shear strain-shear stress hyperbolic relation in HSM Assumption e 1 =0.1% E s = q E R q f f

58 E s / E 50 for s 3 = 100kPa HSM: Identifying E 50 based on known E s E s R 2E50 q f ( f, c) f Friction angle [deg]

59 Hardening Soil: Stress dependent stiffness 1200 Triaxial drained compression test - Texas sand Deviatoric stress [kpa] q= s 1 -s E (3) E (1) E (2) SIG3 = 34.5kPa SIG3 = 138kPa SIG3 = 345kPa s (1) 3 < s (2) 3 < s (3) 3 E (1) < E (2) < E (3) % 5.00% 10.00% 15.00% Axial Strain e 1 59

60 Hardening Soil: Stress dependent stiffness E 0 ref, E 50 ref,, E ur ref correspond to reference minor stress s ref where i.e. stiffness degrades with decreasing s 3 up to the limit minor stress s L NB.Setting m=0 -> constant stiffness like in the standard M-C model 60

61 HSM: Identyfikacja parametru m II identification method for E 50 q = s 1 -s 3 s 3 1. Find three values of E 50 (i) corresponding s 3 (i) to respectively 2. Find a trend line y = ax + b by assigning variables y = x = 3. Then the determined slope of the trendline a is the parameter m - HS Standard

62 Hardening Soil: Stress dependent stiffness Setting s ref Let s assume that the geotechnical report suggests assuming the stiffness modulus E for a given layer which is located at given depth 1. Define what is given E with respect to E 50 and E ur 2. Evaluate reference stress s ref s ref -reference minor stress so if K 0 < 1 then s 3 s h 62

63 Hardening Soil: Stiffness exponent m Coarse-grained soils Cohesive soils after Viggiani&Atkinson (1995), and Hicher (1996) Typically m = 0.4 to 0.6 Typically m >

64 z [m] z [m] z [m] Hardening Soil: Stress dependent stiffness at initial state E [kpa] E [kpa] E [kpa] m = 0.4 m = 0.6 m = phi = 20 phi = 30 phi = c = 0 c = 15 c = Level of reference stress During computation, stiffness moduli will evolve according to actual stress magnitudes 64

65 Hardening Soil: Unloading/reloading Poisson s ratio n ur A typical value for the elastic unloading/reloading Poisson s ratio of n ur = 0.2 can be adopted for most soils. 65

66 Dilatancy Initial configuration Configuration at failure dv de tan v dh d - HS Standard

67 Dilatancy - HS Standard

68 Dilatancy in HS model Non-associated flow for deviatoric mechanism Mobilized dilatancy m increases from 0 up to the input dilatancy angle once M-C line is reached Associated flow for volumetric mechanism Contractancy increases from zero to maximum value at M-C failure only when cap is mobilized

69 Typical dilatancy angles Coarse soils Cohesive soils

70 -e 3 / e 1 [-] Hardening Soil: Unloading/reloading Poisson s ratio n ur Experimental measurements from local strain gauges show that the initial values of Poisson s ratio in terms of small mobilized stress levels q/q max varies between 0.1 and 0.2 for clays, sands Typically elastic domain results after Mayne et al. (2009) Mobilized stress level q / q max Toyoura Sand (Dr=56%) Ticino Sand (Dr=77%) Pisa Clay (Drained Triaxial) Sagamihara soft rock 70

71 Hardening Soil: Parameters M and H Evolution of the hardening parameter p c : dε v p H controls the rate of volumetric plastic strains 71

72 Hardening Soil: Parameters M and H M and H must fulfil two conditions: 1. K 0 NC produced by the model in oedometric conditions is the same as K 0 NC specified by the user 2. E oed generated by the model is the same E oed ref specified by the user Typical stress path in the oedometric test 72

73 Hardening Soil: selection of oedometric modulus E oed In case of lack of oedometric test data for granular material the oedometric modulus can approximately be taken as: E oed ref E 50 ref if so s ref oed should be matched to the reference minor stress s ref since the latter typically corresponds to the confining (horizontal) pressure E oed ref E 50 ref s oed ref = s ref / K 0 NC s ref On the other hand, when defining s ref oed s ref in the model, the following relationship should be taken: E oed ref E 50 ref (K 0 NC ) m 73

74 Hardening Soil: Tangent oedometric modulus E oed where C c is the compression index Since we look for tangent E oed, Ds 0, and s * =2.303s oed ref 74

75 Volumetric strain e v [-] Initial state variables - OCR Notion of overconsolidation ratio: 0 Typical oedometer test Vertical preconsolidation pressure s vc OCR = σ vc σ v s v0 current in situ stress s vc past vertical preconsolidation pressure NB. In natural soils, overconsolidation may stem from mechanical unloading such as erosion, excavation, changes in ground water level, or due to other phenomena such as desiccation, melting of ice cover, compression and cementation s v Simulation Experiment Vertical stress s v ' [ kpa] 75

76 Estimation of preconsolidation pressure and OCR Laboratory: - Oedometer test (Casagrande s method, Pacheco Silva method (1970), cf. report on HS model) s v Field tests: - Static piezocone penetration (CPTU) (for correlations see report on HS model in Zsoil Help) - Marchetti flat dilatometer (DMT) (correlations by Marchetti (1980), Lacasse and Lunne, 1988), see report on HS model in Zsoil Help) 76

77 Initial state variables OCR and K 0 K 0 NC consolidation most cases of natural soils; the value is automatically copied from Isotropic consolidation for running triaxial compression test after isotropic consolidation Anisotropic consolidation for running triaxial compression test after anisotropic consolidation 77

78 Initial state variables K 0 and K 0 NC A B Excavation s v s v Vertical effective stress s h s h s c A past stress s SR K SR 0 K NC 0 q q POP s v0 n ur 1-n ur B current in situ stress s 0 K 0 A K 0 NC B s h0 Horizontal effective stress p 78

79 Initial state variables K 0 and K 0 NC s SR s 0 Preconsolidation stress configuration corresponding to K 0 NC Current in situ stress configuration corresponding to K 0 (at the beginning of numerical simulation) 79

80 Initial state variables K 0 vs. OCR Estimation of earth pressure at rest Normally-consolidated soils sin(phi') Brooker&Ireland(1965) 0.8 Simpson(1992) Overconsolidated soils K 0 NC f' [deg] K OCR [-] phi=20deg phi=30deg phi=40deg so-called (Jaky s formula) 80

81 Setting initial effective stresses 1. Through K 0 (Materials) s y = depth s x = s x K 0 (x) 2. Through Initial Stress (PrePro->FE->Initial conditions) 81

82 Setting initial state variables - troubleshooting What to do if a model does not converge at Initial State even though for a specified K 0 1. try to start Initial State analysis from a small Initial loading Fact. and Increment 2. otherwise, define initial conditions through Initial Stresses option Numerics, like engineers, they like regularity and elegancy. Privilege regular meshes to avoid spourious oscillations and lack of convergence. embanking troubleshooting by means of Initial stresses 82

83 Initial state variables preconsolidation effect 1. through OCR (gives constant OCR profile) At the beginning of FE analysis, Zsoil sets the stress reversal point (SR) with: 2. through q POP (gives variable OCR profile) 83

84 Depth [m] Depth [m] Depth [m] Stress history through OCR Deposits with constant OCR over the depth (typically deeply bedded soil layers) OCR [-] Effective stress [kpa] Ko [-] SigEff vertical SigEff preconsolidation 18 84

85 Deposits with varying OCR over the depth (typically superficial soil layers) Profiles for Bothkennar clay 85

86 Depth [m] Depth [m] Depth [m] Stress history through q POP Deposits with varying OCR over the depth (typically superficial soil layers) Effective stress [kpa] OCR [-] Ko [-] q POP SigEff vertical SigEff preconsolidation Variable K 0 can be introduced merely through Initial Stress option K 0 OC = K 0 NC OCR K 0 OC = K 0 NC OCR sin(f) (Mayne&Kulhawy 1982) 86

87 Versatility of Hardening Soil model Good approximation of stress-strain relation for different and complex stress paths that can be encountered in geotechnical engineering 87

88 Hardening Soil Model - Report 88

89 The HS model a practical guidebook Report contents Short introduction to the HS models (theory) Parameter determination Experimental testing requirements for direct parameter identification Alternative parameter estimation for granular materials Alternative parameter estimation for cohesive materials Benchmarks Case studies including parameter determination retaining wall excavation tunnel excavation shallow footing 89

90 Contents Introduction Initial stress state and definition of effective stresses Saturated and partially-saturated two-phase continuum Introduction to the Hardening Soil model (HSM) Undrained behavior analysis using HSM Practical applications of HSM 90

91 Undrained behavior analysis (1 st approach) Hardening Soil model is formulated in effective stresses (s 1, s 2, s 3 and p ) and therefore it requires: o Effective stiffness parameters E 0, E ur, E 50, n ur o Effective strength parameters f, c Undrained or Partially drained conditions can be obtained by in Deformation+Flow, Consolidation type analysis depending on action time and adequate permeability coefficients Advantages: 1. Partial saturation effects included 2. Possibility of running any analysis type after consolidation analysis 91

92 Undrained behavior analysis Schematic representation of shear strength for normallyconsolidated material in drained and undrained conditions 92

93 Undrained behavior analysis (2 nd approach) Undrained behavior can be simulated in effective stress analysis Deformation+Flow, Driven Load (Undrained) It follows any other like Driven load+steady state, Driven load+transient or Consolidation then the condition for the suction pressure is verified for pressure p = S(p 0 ) p 0 + Dp (Dp is produced exclusively by the undrained driver.). In order to trace the evolution of the pore pressure values stored at the element integration point must be used so: Disadvantages 1. Undrained driver cannot be followed by any other driver Advantages: 1. Fully undrained behavior (no volume change) with effective stress parameters 2. Useful for dynamics 93

94 Setting undrained behaviour for Driven Load(Undrained) Mixed drainage conditions Sand Clay 94

95 Undrained behavior analysis (3 rd approach - simplified) Undrained behavior in total stress analysis can also be performed for the HS model using total stress strength parameters, i.e. f 0, c = S u, 0 ) E 0, E ur, E 50 ud, n=0.499 (undrained conditions) Set high OCR, e.g to disable cap mechanism (no plastic volumetric deformations) however o o o sequence of parameter setup should be followed (given below) appropriate analysis type should be selected (Deformation) Limitations 95

96 Undrained behavior analysis single phase analysis using HS Parameter setup for undrained simulation with single phase analysis: 1. Insert effective parameters E 0, E ur in Elastic menu. 2. Disable Automatic evaluation of H and M parameters (to avoid autoeval. while closing the dialog and errors due to null friction angle) 3. Set high OCR, e.g.1000, to disable cap mechanism (no plastic volumetric deformations should be produced due to assumed undrained conditions) 4. Change f and c into undrained parameters f = 0 and c = S u. In order to ensure stability of numerical computing, specify = 0 5. Considering that the undrained conditions imply s 1 = s 3, change n ur into n ur = (the undrained stiffness behavior will be obtained in the analysis by recomputing the stiffness tensor with n ur =

97 Undrained behavior analysis single phase analysis using HS Parameter setup for undrained simulation with single phase analysis: 6. Set input E 50 as undrained E 50 ud (but not E ur and E 0 which should remain as effective ones) shear modulus is not affected by the drainage condition so one can write: where n u is the Poisson's coffecient in undrained conditions equalk to So the above equation can be rewritten for E 50 as: E u 50 3E' 50 2(1 ) where n should be considered as that corresponding to E 50, i.e. n 0.3 (plastic deformations) 97

98 Post-processing Undrained pressure only for Driven Load (Undrained) Pore pressure (p) only for Deformation+Flow Suction pressure (S*p) 98

99 Contents Introduction Initial stress state and definition of effective stresses Saturated and partially-saturated two-phase continuum Introduction to the Hardening Soil model (HSM) Undrained behavior analysis using HSM Practical applications of HSM Assistance in parameter identification 99

100 Practical applications Shallow footing on an overconsolidated sand Input files: HS-small-Footing-Texas-Sand-2phase.inp (Help/Reports/Hardening Soil small -> Benchmarks/Spread footing on overconsolidated sand) 100

101 Practical applications Shallow footing on an overconsolidated sand 5. Interpreting and Setting K 0 Variable K 0 can be introduced merely through Initial Stress option 101

102 Practical applications Shallow footing on an overconsolidated sand 4. Selecting q POP 5. OCR based on q POP Variable OCR profile 102

103 Practical applications Shallow footing on an overconsolidated sand Comparison of models: HS-SmallStrain, HS-Std vs Mohr-Coulomb 103

104 Practical applications Excavation in Berlin sand Engineering draft and the sequence of excavation Input files: HS-small-Exc-Berlin-Sand-2phase.inp HS-std-Exc-Berlin-Sand-2phase.inp MC-Exc-Berlin-Sand-2phase.inp 104

105 Practical applications Excavation in Berlin sand Berlin sand excavation Standard Mohr-Coulomb Hardening-Soil Absolute displacements 105

106 Practical applications Excavation in Berlin sand lifting Accumulation of spurious strains Vertical displacements at soil surface Standard Mohr-Coulomb extended zone of influence HS without E 0 True zone of influence settlements «Stiff» zone of G max NB. HS SmallStrain makes it possible to reduce the extension of the FE mesh HS SmallStrain 106

107 Practical applications Excavation in Berlin sand Meaning of stress level in HS model Displayed stress levels are computed as: SL = q / q f q current deviatoric stress at given p q f failure stress corresponding to p 107

108 Contents Introduction Initial stress state and definition of effective stresses Saturated and partially-saturated two-phase continuum Introduction to the Hardening Soil model (HSM) Undrained behavior analysis using HSM Practical applications of HS Assistance in parameter identification 108

109 Virtual Lab a highly-interactive tool for assistance in parameter selection for constitutive models for soils first-guess for model parameters for any incomplete or complete material data automatic or interactive knowledge extraction parameter identification from laboratory curves provides parameter ranges (parametric studies) testing constitutive models 109

110 Virtual Lab Access Help Reports Toolbox available for: Hardening-Soil Mohr-Coulomb Cap Cam-Clay 110

111 Exercise 2 Parameter identification from laboratory curves 1 1. Select the determination method: Identification 111

112 Exercise 2 Import experimental test data In order to define a new laboratory test: 1. Preselect the type of test and press Add 2. Give a label to the test and define initial state variables 3. Import test results from an ASCII file by pressing Import experimental data, selecting the file, and assigning variables to corresponding columns 3 112

113 Exercise 2 Import experimental test data 1B Import prepared data files: SandMedium-txcd-sig25kPa.pit SandMedium-txcd-sig50kPa.pit SandMedium-txcd-sig75kPa.pit 1A. In order to import prepared in advance and saved experimental data for three triaxial tests, click right button and select Load test(s) 1B. Select files and open them 2. Browse imported resuts by seleacting each test separately in Assembly of tests 1A Load test(s) 113

114 Exercise 2 Data interpretation Move to Data Interpretation in order to interpret three selected laboratory tests (only checked tests are interpreted) 2. Run parameter identification algorithm by pressing Interpret Selected 2 3. Configure identification algorithm; in this case, define the identification of stiffness power law exponent m based on the values of modulus E ur derived from unloading-reloading cycle 114

115 Exercise 2 Post-processing of results 1 1. Browse values of parameters identified for the chosen constitutive law, i.e. HS model, and other identified variables 2. Leave the identification tool by clicking OK 2 115

116 Exercise 2 Post-processing of results 116

117 Exercise 2 Reproducing laboratory tests using identified parameters 1 1. Select : Lab Test Simulation 117

118 Exercise 2 - Reproducing laboratory tests with identified parameters Select drained test in the test preselection (TX-CD) and enable Use real test data to simulate the tests used for parameter identification (notice that the initial state variables and loading program have been already defined). 2. Select one of tests 3. Import parameters identified with TX-CD 4. Press Simulate selected test 5. Compare model responses with laboratory curves 118