The Hardening Soil model with small strian stiffness

The Hardening Soil model with small strain stiffness in Zsoil v2011 Rafal OBRZUD GeoMod Ing. SA, Lausanne

Content Introduction Framework of the Hardening Soil model Hardening Soil SmallStrain Hardening Soil Standard Model parameters Parameter Identification Assistance in Parameter Selection Practical applications

Why do we need advanced constitutive models? Approximation of soil behaviour for reliable simulations of practical cases 450 Triaxial drained compression test Deviatoric stress [kpa] q= σ 1 -σ 3 400 350 300 250 200 150 100 50 Plasticity (yielding) before reaching the ultimate state 0 0,00% 2,00% 4,00% 6,00% 8,00% 10,00% 12,00% 14,00% Axial Strain ε 1 Experiment: Texas sand Simulation: Hardening Soil Simulation: Mohr-Coulomb - Introduction

Why do we need advanced constitutive models? ENGINEERING CALCULATIONS LIMIT 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 - Introduction

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 ε 1 - Introduction

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

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 σ 1 constant q q Stiffness degradation p E E ur E E ur E=E ur ε 1 E < E ur ε 1 - Introduction

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

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 ε 1 ε 1 ε 1 - Introduction

Small strain stiffness in geotechnical practice e.g. Atkinson, Jardine and many others - Introduction

Stiffness in different models Deviatoric Stress q [kpa] 160 140 B 120 100 80 Mohr-Coulomb 60 Modified Cam Clay 40 Cap model 20 A HS-Standard HS-Small 0-3,61E-16 0,05 0,1 0,15 0,2 Axial Strain ε 1 [-] Normalized soil stiffness G/G 0 [-] 1 0,8 0,6 0,4 0,2 Non-linear elasticity at very small strains Linear elasticity at very small strains 0 1E-06 1E-05 0,0001 0,001 0,01 0,1 Axial Strain ε 1 [-] Linear elasticity at small strains - Introduction

Perceived application of ZSoil models ULS - Ulitmate Limit State analysis SLS - Serviceability Limit State analysis - Introduction

Content Introduction Hardening Soil model framework Hardening Soil SmallStrain Hardening Soil Standard Model parameters Parameter Identification Assistance in Parameter Selection Practical applications

Hardening Soil model to describe macroscopic phenomena exhibited by soils HS-Standard Densification (decrease of voids volume in soil due to plastic deformations) Soil stress history (accounting for preconsolidation effects) Plastic yielding (irreversible strains with reaching a yield criterion) Stress dependent stiffness (increasing stiffness moduli with increasing depth or stress level) Dilatation (occurrence of negative volumetric strains during shearing) + HS-SmallStrain for handling stiffness in a small strain range Stiffness variation (degradation of G 0 modulus with increasing shear strain amplitudes between γ 0.0001 0.1%) Hysteretic, non-linear stress-strain relationship applicable in the range of small strains * * HS-SmallStrain can be used to some extent to model hysteretic behavior under cycling loadings with the exception of gradual softening for increasing number of cycles. - Framework of HS model

Hardening Soil model in ZSoil - Framework of HS model

Hardening Soil model framework Activation of G 0 degradation in the small strain range - Framework of HS model

Hardening Soil model framework Triaxial test simulation Secant stiffness in small strains zoom - Framework of HS model

Hardening Soil model framework Triaxial test simulation with the unloading/reloading cycle E 0 E ur E ur 1000 1000 zoom 900 900 800 800 Deviatoric stress q [kpa] 700 600 500 400 300 Deviatoric stress q [kpa] 700 600 500 400 300 200 100 HS-SmallStrain HS-Standard 200 100 HS-SmallStrain HS-Standard 0 0 0,01 0,02 0,03 0,04 0,05 Axial strain ε 1 [-] 0 0,019 0,02 0,021 0,022 0,023 0,024 Axial strain ε 1 [-] - Framework of HS model

Main mechanical features of HS model HS-Standard Smooth hyperbolic approximation of the stress-strain curve of soil (Duncan-Chang concept) Two plastic mechanisms: isotropic (to handle important plastic volumetric strains observed in normally-consolidated soils) deviatoric (to handle domination of plastic shear strains which are observed in coarse materials and heavily consolidated cohesive soils) Ultimate state described by Mohr-Coulomb criterion Rowe s dilatancy + HS-SmallStrain Nonlinear elasticity which includes hysteretic effects (Hardin-Drnevich concept) - Framework of HS model

Non-linear elasticity for very small strains Hyperbolic Hardin-Drnevich relation to describe S-shaped stiffness a = 0.385 - HS SmallStrain

Hyperbolic approximation of the stress-strain curve E 0 tangent initial stiffness modulus 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 (parameter corresponding to in Modified Cam Clay) For most soils R f falls between 0.75 and 1 - HS Standard

Hyperbolic approximation of the stress-strain curve - HS Standard

Stress stiffness dependency 1200 Triaxial drained compression test - Texas sand Deviatoric stress [kpa] q= σ 1 -σ 3 1000 800 600 400 200 E (3) E (1) E (2) SIG3 = 34.5kPa SIG3 = 138kPa SIG3 = 345kPa 0 0,00% 5,00% 10,00% 15,00% Axial Strain ε 1 - HS Standard

Stress stiffness dependency E 0 ref, E 50 ref,, E ur ref correspond to reference minor stress σ ref where i.e. stiffness degrades with decreasing σ 3 up to the limit minor stress σ L which can be assumed by default σ L =10kPa In natural soils: m = 0.3-1.0 e.g. Norwegian Sands and silts 0.5 (Janbu, 1963) Soft clays m=0.38-0.84 (Kempfert, 2006) - HS Standard

Stiffness stress dependency parameter m 1. Find three values of E 50 (i) corresponding σ 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

Stress stiffness dependency at initial state E [kpa] E [kpa] E [kpa] 0,0 0 50000 100000 150000 200000 0,0 0 50000 100000 150000 200000 0,0 0 50000 100000 150000 200000 2,0 4,0 m = 0.4 m = 0.6 m = 0.8 2,0 4,0 phi = 20 phi = 30 phi = 40 2,0 4,0 c = 0 c = 15 c = 30 6,0 6,0 6,0 z [m] 8,0 10,0 12,0 14,0 16,0 18,0 20,0 Level of reference stress z [m] 8,0 10,0 12,0 14,0 16,0 18,0 20,0 z [m] 8,0 10,0 12,0 14,0 16,0 18,0 20,0 - HS Standard

Stiffness exponent m - HS Standard

Unloading/reloading Poisson s ratio ν 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 0,5 Poisson's ratio ν [-] 0,4 0,3 0,2 0,1 0,0 after Mayne et al. (2009) 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 Mobilized stress level q / q max Toyoura Sand (Dr=56%) Ticino Sand (Dr=77%) Pisa Clay (Drained Triaxial) Sagamihara soft rock - HS Standard

Unloading/reloading Poisson s ratio ν ur Therefore, the characteristic value for the elastic unloading/reloading Poisson s ratio of ν ur = 0.2 can be adopted for most soils. - HS Standard

Failure ratio R f q = σ 1 -σ 3 160,0 140,0 120,0 100,0 80,0 60,0 Asymptote q a =1/b E 50 = 2a 1 40,0 20,0 0,0 1,8E-03 1,6E-03 1,4E-03 1,2E-03 0 0,05 0,1 0,15 0,2 Identification of R f R f = q f / q a = b q f ε 1 /q 1,0E-03 8,0E-04 6,0E-04 4,0E-04 2,0E-04 1 b=1/q a - HS Standard 0,0E+00 a =1/2E 50 0 0,05 0,1 0,15 0,2 ε 1 [-]

Double hardening model r(θ) follows van Ekelen s formula in order to assure a smooth and convex yield surface (cf. Modified Cam clay model) - HS Standard

Double hardening model σ 1 p σ 2 cap yield surfaces described with van Ekelen s formula Mohr-Coulomb failure surface p -q section through shear and cap yield surfaces σ 3 - HS Standard

Dilatancy sinϕ m [-] 0,5 0,4 0,3 0,2 0,1 0,0-0,1-0,2 Contractancy cut-off for φ m < φ cs Rowe's dilatancy for φ m φ cs Rowe's dilatancy -0,3-0,4 Contractancy domain 0 10 20 30 40 φ m [deg] Dilatancy domain - HS Standard

Dilatancy - HS Standard

Dilatancy in HS-SmallStrain Contractancy domain Dilatancy domain Since the cut-off for the contractancy domain could yield too small volumetric strain, the scaling parameter D is introduced. - HS Standard

Parameters M and H Evolution of the hardening parameter p c : H controls the rate of volumetric plastic strains - HS Standard

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 - HS Standard

Parameters M and H ASSUMPTIONS: 1. At given σ oed ref which is located at post-yield plastic curve, both shear an volumetric mechanism are active 2. Initial stress point 3. A strain driven oedometer test is run with vertical strain amplitude ε=10-5 and the tangent oedometric modulus is computed as E oed = δσ/δε σ/ ε 4. Optimisation of M and H must fulfil two conditions: K 0 NC produced by the model in oedometric conditions = K 0 NC specified by the user E oed generated by the model = E oed ref specified by the user - HS Standard

Initial state variables - OCR Notion of overconsolidation ratio: σ vc OCR = σ v0 Typical oedometer test 0 Vertical preconsolidation pressure σ vc σ v0 current in situ stress σ 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. Volumetric strain ε v [-] 0,02 0,04 0,06 0,08 0,1 0,12 Simulation Experiment 1 10 100 1000 Vertical stress σ v ' [ kpa] - HS Standard

Initial state variables OCR and K 0 Normally-conslidated soil (OCR=1) Overconslidated soil (OCR>1) Why does it appear and what should be inserted? - HS Standard

Initial state variables K 0 and K 0 NC A B Excavation σ v σ v σ h σ h Vertical effective stress B A q A B Horizontal effective stress p - HS Standard

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

Initial state variables K 0 vs. OCR Estimation of earth pressure at rest Normally-consolidated soils 0,9 1-sin(phi') Brooker&Ireland(1965) 0,8 Simpson(1992) Overconsolidated soils 2,5 2,0 K 0 NC 0,7 0,6 0,5 0,4 0,3 0,2 0 20 40 60 φ' [deg] K 0 1,5 1,0 0,5 0,0 0 5 10 15 20 OCR [-] phi=20deg phi=30deg phi=40deg - HS Standard

Initial state variables K 0 and K 0 NC For most cases when soil was subject to natural consolidation before unloading K 0 NC K 0 K 0 SR = K 0 NC - HS Standard

Initial state variables K 0 and K 0 NC In the case of simulating the triaxial compression test after isotropic loading/unloading: K 0 SR K 0 NC q but K 0 SR =1 C B isotropic loading/unloading A p - HS Standard

Initial state variables 1. User specifies initial stress conditions σ 0 2. Zsoil at the beginning of a FE analysis calculates σ SR with and the horizontal stress components 3. Then the hardening parameter p c0 is computed - HS Standard

Setting initial state variables 1. Through K 0 σ y = γ depth σ x = σ x K 0 (x) 2. Through Initial Stress - HS Standard

Setting initial state variables If the model does not converge at Initial State for the 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 Stress - HS Standard

Initial state variables - preconsolidation 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) - HS Standard

Stress history through OCR Deposits with constant OCR over the depth (typically deeply bedded soil layers) OCR [-] Effective stress [kpa] Ko [-] 0 1 3 5 7 9 11 13 0 0 500 1000 1500 0,00 0,50 1,00 1,50 0 2 2 2 4 4 4 6 6 6 Depth [m] 8 10 Depth [m] 8 10 Depth [m] 8 10 12 12 12 14 14 14 16 16 16 18 18 18 SigEff vertical SigEff preconsolidation - HS Standard

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

Stress history through q POP Deposits with varying OCR over the depth (typically superficial soil layers) 0 Effective stress [kpa] 0 200 400 600 0 OCR [-] 1 3 5 7 9 11 13 0 Ko [-] 0 0,5 1 1,5 2 2 2 4 4 4 6 q POP 6 6 Depth [m] 8 10 Depth [m] 8 10 Depth [m] 8 10 12 12 12 14 16 18 SigEff vertical SigEff preconsolidation 14 16 18 14 16 18 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(φ) (Mayne&Kulhawy 1982) - HS Standard

Content Introduction Hardening Soil - SmallStrain Hardening Soil Standard Model Parameters Parameter Identification Assistance in Parameter Selection Practical applications

Hardening Soil model List of parameters to be provided by the user (page 1) Small stiffness (HS-SmallStrain only) 1. E 0 ref kpa SCPT, SDMT, geophysical methods 2. γ 0.7 - Triaxial test with local gauges, geotechnical evidence 3. E ref 50 kpa Triaxial test 4. E ref ur kpa Triaxial test 5. ν ur - Triaxial test 6. m - Triaxial test 7. σ ref 3 kpa Triaxial test Elastic constants Auxiliary variable - Model parameters

Hardening Soil model List of parameters to be provided by the user (page 2) Shear mechanism 8. c kpa Triaxial test, in situ test 9. φ Triaxial test, in situ test 10. (R f ) - Triaxial test or the default value 0.9 11. ψ Triaxial test 12. e max Triaxial test on dense granular or overconsildated cohesive soil 13. E oed ref kpa Oedometric test 14. σ oed ref kpa Oedometric test 15. OCR / q POP - / kpa Volumetric (cap) mechanism Initial state variable Oedometric test or in situ tests 16. K 0 SR - K 0 SR = 1-sin φ (or Ko-consolidation triaxial test) 17. σ 0 kpa Init. stress conditions accounting for K 0 = K SR 0 (for normallyconsolidated soil), K 0 = K OC 0 (for overconsolidated soil) - Model parameters

Hardening Soil model Comparison of corresponding soil parameters for selected ZSoil models Corresponding soil parameters Hardening-Soil Cap Mohr-Coulomb Small strain stiffness E 0 and γ 0.7 none none Elastic constants E ur and ν ur E 50 and m E and ν E and ν Failure criterion φ and c φ and c φ and c Dilatancy ψ and e max ψ ψ and e max Cap surface parameters E oed (can be determined from λ) OCR, K 0 and K 0 SR λ OCR, K 0 None K 0 - Model parameters

Content Introduction Hardening Soil - SmallStrain Hardening Soil Standard Model Parameters Parameter Identification Assistance in Parameter Selection Practical applications

Parameter identification Report - Parameter identification

The HS model a practical guidebook Contents: Theory Parameter identification Parameter estimation - Parameter identification

Parameter identification Stiffness parameters Determination of G 0 from geophysical tests SCPT, SDMT and others with ρ denoting density of sol and V s shear wave velocity. (ν=0.15..0.25 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) 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 - Parameter identification

Parameter identification Stiffness parameters Determination of G 0 for sands from CPT after Robertson and Campanella (1983) - Parameter identification

Parameter identification Stiffness parameters Estimation of E 0 from E 50 - Parameter identification

Parameter identification Stiffness parameters Estimation of E 0 from E ur - Parameter identification

HS-SmallStrain Non-linear elasticity for small strains Cohesionless soils Influence of voids ratio Influence of confining stress p after Wichtmann & Triantafyllidis - Parameter identification

HS-SmallStrain Non-linear elasticity for small strains Cohesive soils Influence of soil plasticity after Vucetic and Dobry (from Benz, 2007) approximation proposed by Stokoe et al. - Parameter identification

Parameter identification Stiffness parameters Determination of E 50 for sands from CPT after Robertson and Campanella (1983) - Parameter identification

Parameter selection Stiffness parameters Undrained vs drained moduli theoretical relationship Since the shear modulus is not affected by the drainage conditions - Parameter identification

Parameter identification Oedometric modulus E oed where C c is the compression index Since we look for tangent E oed, σ 0, and σ * =2.303σ oed ref If λ is known - Parameter identification

Parameter selection - oedometric modulus E oed E oed ref E 50 ref but E oed ref E 50 ref σ oed ref = σ ref / K 0 NC σ ref - Parameter identification

Parameter identification Preconsolidation pressure and OCR Laboratory: - Oedometer test (Casagrande s method, Pacheco Silva method (1970)) Field tests: - Static piezocone penetration (CPTU) (see reports by Mayne) - Marchetti flat dilatometer (DMT) (correlations by Marchetti (1980), Lacasse and Lunne, 1988) ) - Parameter identification

Parameter identification Preconsolidation pressure and OCR (from Lunne et al. 1997) - Parameter identification

Parameter identification Preconsolidation pressure and OCR - Parameter identification

Parameter identification Other information from DMT - Parameter identification

Parameter identification Strength parameters - Parameter identification

Parameter identification Strength parameters Friction angle φ for granular soils from in situ tests SPT CPTU (Robertson & Campanella, 1983) DMT Upper bound Lower bound (Totani et al., 1999) - Parameter identification

Content Introduction Hardening Soil - SmallStrain Hardening Soil Standard Model Parameters Parameter Identification Assistance in Parameter Selection Practical applications

- Assistance in parameter selection

Initialization menu Empty field reserved for numeric data (basic soil properties, specific soil properties, in situ test data) in Zsoil v2012 - Assistance in parameter selection

Non-cohesive soil setup Initialization menu - Assistance in parameter selection

Initialization menu Cohesive soil setup - Assistance in parameter selection

Initialization menu - Assistance in parameter selection

HS Menu Scroll - Assistance in parameter selection

- Assistance in parameter selection

Parameter selection secant modulus E ur Typical values of the stiffness modulus which are provided in most textbooks are referred to as the "static" stiffness modulus E s It can be assumed that they represent the values of the unloading/reloading modulus E ur In the basic parameter selection, typical E ur is taken as E s and the reference pressure is assumed σ ref =100kPa - Assistance in parameter selection

Parameter selection secant modulus E 50 In most practical cases: In toolbox - ranges: = 2 to 4 - Assistance in parameter selection

Parameter selection - oedometric modulus E oed E oed ref E 50 ref but E oed ref E 50 ref σ oed ref = σ ref / K 0 NC σ ref - Assistance in parameter selection

Parameter selection friction angle φ Multi-criterion selection depending on quantity of provided input data ( soil keywords ) Keyword: Density Keyword: Soil type, Density, Gradation - Assistance in parameter selection

Content Introduction Hardening Soil - SmallStrain Hardening Soil Standard Model Parameters Parameter Identification Assistance in Parameter Selection Practical applications

Practical applications Excavation in Berlin sand Engineering draft and the sequence of excavation - Practical applications

Practical applications Excavation in Berlin sand - Practical applications

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

Practical applications Excavation in Berlin sand Berlin sand excavation 0-5 -10 Distance from surface Y [m] -15-20 -25 HS-small HS-Std MC Measurements -30-0.04-0.03-0.02-0.01 0 Horizontal displacement Ux [m] -35 - Practical applications

Practical applications Shallow footing Texas sand benchmark - Practical applications

Practical applications Shallow footing Texas sand benchmark 1. DMT data 2. OCR interpreted form DMT data 0 1 K D [-] OCR [-] 0 5 10 15 20 0 10 20 30 40 50 0 DMT-1 DMT-2 1 2 3 2 3 DMT-1 DMT-2 Depth [m] 4 5 Depth [m] 4 5 Variable profile 6 6 7 7 8 8 9 9 10 10 - Practical applications

Practical applications Shallow footing Texas sand benchmark 3. Selecting q POP 4. OCR based on q POP Vertical stress[kpa] OCR [-] 0 200 400 600 800 0 10 20 30 40 50 0 0 1 1 2 q POP 2 DMT-1 DMT-2 FE Model 3 3 Depth [m] 4 5 Depth [m] 4 5 Variable profile 6 6 7 7 8 8 9 10 vertical effectivve stress preconsolidation pressure 9 10 - Practical applications

Practical applications Shallow footing Texas sand benchmark 5. Interpreting and Setting K 0 0 1 K 0 [-] 0 0.5 1 1.5 2 2.5 DMT-1 DMT-2 FE Model 2 3 4 Depth [m] 5 6 7 8 9 Variable K 0 can be introduced merely through Initial Stress option 10 - Practical applications

Practical applications Shallow footing Texas sand benchmark Load [kn] 0-0.01-0.02-0.03-0.04 0 2000 4000 6000 8000 10000 Experiement Hardening Soil SmallStrain Standard Mohr-Coulomb Settlement [m] -0.05-0.06-0.07-0.08-0.09-0.1-0.11-0.12-0.13-0.14 - Practical applications

Summary Hardening Soil-SmallStrain model: correctly reproduces a strong reduction of soil stiffness with increasing shear strain amplitudes is recommended for Serviceability Limit State analyses as it generally predicts soil behavior and field measurements more precisely than basic linear-elasticity models is essential for the engineering problems with unloading/reloading modes such as excavations, tunneling accounts for stress stress history which is crucial for problems such as footing, consolidation, water fluctuation is applicable to most soils as it accounts for pre-failure nonlinearities for both sand and clay type materials regardless of the overconsolidation state The Hardening Soil model is not as difficult in practical use as you may think. When you run a simulation with the M-C model, as an exercise, try to run the Hardening Soil model as well. - Practical applications