ZSoilDay2018 Constitiutive models for geotechnical ... · from classical soil mechanics ... Darcy’s law coefficients Soil water retention curve constants (van Genuchten’s model)

Constitutive models for geotechnical practice

in ZSoil v2018

BASICS

Rafal OBRZUD

ZSoil® August 2018

1

Constitutive models for geotechnical practice, 22-23.08.2018, Lausanne, Switzerland

Introduction

Initial stress state and definition of effective stresses

Saturated and partially-saturated two-phase continuum

Introduction to the Hardening Soil model (HSM)

Contents

2


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


Continuum models available in ZSoil v2018

Basic laws

Advanced laws(more or less complex)

1

2

3

4

0


Better approximation of soil behavior for simulations of practical cases

Plasticity (yielding) before reaching the ultimate state

Why do we need advanced constitutive models?

q = σ1−σ3

σ3

5

Stress path

32' 31 σσ ⋅+=p

qTriaxial stress conditions

(e.g. under footing)

3

1


Tunneling

Standard Mohr-Coulomb Hardening Soil Model

Practical applications of the Hardening Soil model

6

Unique and constant stiffnessmodulus

Soil stiffness depending on stress path

Different moduli also varying on stress current stress level


Standard Mohr-Coulomb Hardening-Soil

Excavation


7

Standard Mohr-Coulomb Hardening Soil Model

Unrealistic kinematics



8

Spread footing boundary value problem


Introduction




Contents

9


Setting parameters: Initial state setup

10


Setting unit weight

DEFORMATIONANALYSIS

DEFORMATION + FLOWANALYSIS

GWTPartially saturated

Unsaturated

Fully saturated

Total stress

analysis

Effective stress

analysis Effective stress analysis

Material 1

Material 2

Material 1

11


Setting unit weight

12

Parameters given in geotechnical reports


Bishop’s effective stress principle

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, ν′, ν′ur

o Effective strength parameters φ′, c′

Definition of effective stresses

13

totalstress

effectivestress

Bishop’sparameter

pore pressure


Setting initial Ko state

14

1. K0 = K0NC only for normally-

consolidated soil

2. Automatic Ko setting only for Hardening Soil model

= ′′

= ⋅ OCRbut ≤


Introduction




Contents

15


From fully saturated to partially saturated state

16

from Nuth (2009)

S - saturation degree

pw – pressure in liquid phase

NB. fluid = liquid + gas

Interstitial pressureSaturation degree

+

-

p>0

p<0


Effective stress in ZSoil

17

Bishop’s effective stress in single-phase model for fluid

Fluid is considered as a mixture of air and water (single-phase model of fluid)

p – pore water pressure

S = S(p) – degree of saturation depending on pore water pressure

suction stressif p > 0 (above GWT)


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)

18


Suction pressure effect in ZSoil

19

0 S·p

c’=0 kPa

Apparent cohesion effectin unsaturated, unstructured clay

p

p<0

p>0 σij'= σij – p+·δij

Let’s consider stress sign conventionfrom classical soil mechanics

σij'= σij – p– ·S·δij

= 2 sin ′1 − sin ′ ′ + ′ ⋅ cot ′Soil resistance:


Setting flow parameters

Darcy’s lawcoefficients

Soil water retention curve constants(van Genuchten’s model)

Setup for Driven Load (Undrained)analysis type

20



from Nuth (2009)

Flow parameters from Yang & al. (2004)

Soil type α [1/m] Sr [-]

Gravely Sand

100 0

Medium Sand

10 0

Fine Sand 8 0

Clayey Sand

1-1.7 0.09-0.23

Fines content , constant α

21

α can be taken as an inverse of height of the capillary rise



22

Saturation constant taken as the inverse of the capillary rise

Soil type α [1/m]

Silt 0.2 – 0.5

Clay: low plasticity (lean clay) 0.2 – 0.5

Clay: medium plasticity 0.083 – 0.25

Clay: high plasticity (fat clay) 0.05 - 0.125

Clay: very high plasticity 0.033 – 0.067


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 Sr = 0.0 and p → ∞αγ FpS →⋅

Suction(apparent cohesion)

Positive pore pressure above GWT

23



Reproducing an apparent cohesion

o For Sr > 0.0 and p → ∞ S·p (for p → ∞)

Suction(apparentcohesion)

Positive pore pressure above GWT

NB.To avoid too much apparent cohesion above the GWT set Sr = 0.0 and an appropriate α value(e.g. if α = 1.0, the apparentcohesion will not exceed 10 kPa)

24



25

Max suction S·p = 13 kPa

Single phase (Deformation): Instability at initial state analysis

Two-phase (Deformation+Flow): Stability at initial state analysis

φ =30°c = 0 kPa

α=45°



26

Max suction S·p = 8 kPa

Heavy rain bydistributed fluxes

Instability



27

Excavation

Steady-state analysis Consolidation


Suction profiling with Virtual Lab

28


Introduction




Contents

29


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

30


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 reacheda strong stiffness degradation is observed

On exceeding the domain of non-linear elasticity, plastic (irreversible) strains develop

31


HSM – Dialog windows

32


HSM – Geotechnical parameters as model parameters

33

Initial state Shear resistance

Deformation Deformation in small strains

.OCR /

and

Most influential parameters on numerical analysis

Intercorrelated parameters reduce number of unknowns

OCR /

Soil type .

Preconsolidationstate


Hardening Soil model framework

34


Standard Mohr-Coulomb

HS SmallStrain

HS standard vs small strain

settlements

lifting

Reduced zone of influence due to E0

True zone of influence

Accumulation of spurious strains

HS without E0

extended zone of influence

Vertical displacements at soil surface

NB. HS SmallStrain makes it possible to reduce FE mesh extension

35


Hyperbolic Hardin-Drnevich relation to describe S-shaped stiffness

HS-SmallStrain: Elasticity for very small strains

( = ε1 − ε3 )

36


Determination of G0 from geophysical tests, SCPT, SDMT and others

with ρ denoting density of soil and Vs 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)

• 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

HS-SmallStrain: Estimation of E0

37



38

Approximate relation between "static" Es and "dynamic“ modulus Ed

corresponding to E0 proposed by Alpan (1970)


after Robertson and Campanella (1983)

Determination of G0 for sands from CPT


Rix & Stokoe (1992)

Typical ratios

granular soils G0/Gur= 2 ÷ 3.5clays G0/Gur = 2.5 ÷ 7

NB.

39


Relation between E0 and E50


Natural clays E0 / E50 = 5 ÷ 30higher values for the ratio are suggested for aged, cemented and structured clays, whereas the lower ones for insensitive, unstructured andremoulded clays

Granular soils E0 / E50 = 4 ÷ 18higher values are suggested fornormally-consolidated soils

See HS Report

40



41

Reducing uncertainty:

1. Compute E0 from Vs measurements

2. Compute E0 from typical values of Vs

3. Compute E0 from typical ratios

4. Compute E0 from typical ratios

Best estimate

• Soil type • Preconsolidation state• Triaxial tests


HS-SmallStrain: Influence of E0 on numerical predictions

42

where:

with :

Spread footing boundary value problem


after Wichtmann & Triantafyllidis (2004)

Granular soils γ0.7 mainly depends on magnitude of mean eff. stress p’

Typically for clean sands and pref = 100kPa:

8⋅10-5 < γ0.7 < 2 ⋅ 10-4

HS-SmallStrain: Non-linear elasticity at small strains

For more correlations see report on HS model in Zsoil Help

43


Cohesive soils

Influence of soil plasticity

after Vucetic & Dobry (1991)

Stokoe et al. 2004

γ0.7 depends on soil plasticity PI, wL, , wP

HS-SmallStrain: Non-linear elasticity for small strains

For more correlations see report on HS model in Zsoil Help

44


HS-SmallStrain: Influence of E0 and γ0.7 on numerical predictions

45

γ0.7 = 2⋅10-4

γ0.7 = 6⋅10-4


Hardening Soil: Double hardening – shear hardening

Pure deviatoric shear in overconsolidated material with HS Standard model

σ0 Initial stress stateσ0 −σp Linear elastic

σp −σf Elasto-plasticσf On failure surface

σf −σu Linear elastic

q = σ1−σ3

46


E50 – secant stiffness modulus corresponding to 50% of the ultimate deviatoric stress qf described by Mohr-Coulomb criterion

Eur – unloading/reloading modulus

Hardening Soil: Hyperbolic approximation of the stress-strain

47

Typically for most soils:Eur / E50 = 2 ÷ 6

depending on:

• soil type

• relative density

• preconsolidation state

Must be satisfied:

Eur / E50 > 2


Hardening Soil: Stiffness moduli

loose sands:

Eur / E50 = 3 ÷ 5

Secant vs unloading-reloading modulus in drained test on sand

dense sands:

Eur / E50 = 2 ÷ 3

In the case of cohesive soils

the analogy to Cs/Cc can be considered

typical Cs/Cc ratios are 3 ÷ 6

48

Claysoverconsolidated :Eur / E50 = 2 ÷ 3

lightly overconsolidated :Eur / E50 = 3 ÷ 4

normally-overconsolidated :Eur / E50 = 4 ÷ 6


0

200

400

600

800

1000

1200

0.00% 5.00% 10.00% 15.00%

Devi

ator

ic st

ress

[kP

a]

q=

σ 1-σ

3

Axial Strain ε1

Triaxial drained compression test - Texas sand

SIG3 = 34.5kPa

SIG3 = 138kPa

SIG3 = 345kPa

E(1)

E(2)

E(3)

Hardening Soil: Stress dependent stiffness

σ3(1) < σ3

(2) < σ3(3)

E(1) < E(2) < E(3)

49


E0ref , E50

ref, , Eurref correspond to reference minor stress σref

in Sigma-3 formulation minor eff. stress

NB.Setting m=0 -> constant stiffness like in the standard M-C model


50

in conditions where K0 < 1

′ = ′



51

Let’s assume that the geotechnical report suggests assuming the stiffnessmodulus E for a given layer which is located at given depth but …

1. Define what is given E with respect to E50 and Eur

2. Evaluate reference stress σref


Hardening Soil: Stiffness exponent m

after Viggiani&Atkinson (1995) , and Hicher (1996)

Cohesive soilsCoarse-grained soils

Typically m > 0.5 Typically m = 0.4 to 0.6

52


A typical value for the elastic unloading/reloading Poisson’s ratio of νur = 0.2 can be adopted for most soils.

Hardening Soil: Unloading/reloading Poisson’s ratio νur

53


Experimental measurements from local strain gauges show that the initial values ofPoisson’s ratio in terms of small mobilized stress levels q/qmax varies between 0.1 and 0.2 for clays, sands.

0.0

0.1

0.2

0.3

0.4

0.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

−ε3

/ ε1

[-]

Mobilized stress level q / qmax

Toyoura Sand (Dr=56%) Ticino Sand (Dr=77%)Pisa Clay (Drained Triaxial) Sagamihara soft rock

Typically elastic domain

results after Mayne et al. (2009)

Hardening Soil: Unloading/reloading Poisson’s ratio νur

54


Dilatancy

Initial configuration

Configuration at failure

δγδε

δδψ v

hv ==tan

Dilatancy mainly occurs in coarse materials and overconsolidatedcohesive soils


Dilatancy


Typical dilatancy angles

Fine soils

Coarse soils

General well-working approximation


Typical stress path in the oedometric test

M and H is automatically optimised to fulfil two conditions:

1. K0NC produced by the model in oedometric

conditions is the same as K0NC specified by

the user

2. Eoed generated by the model is the sameEoed

ref specified by the user

Hardening Soil: Parameters M and H

58


Eoedref E50

ref

σrefσoedref = σref / K0

NC

Hardening Soil: selection of oedometric modulus Eoed

In case of lack of oedometric test data the oedometricmodulus can approximately be taken as:

Eoedref ≈E50

ref

if so σoedref should be matched to the reference minor stress

σref since the latter typically corresponds to the confining (horizontal) pressure

On the other hand, when defining σoed

ref =σref in the model, the following relationship should be taken:

Eoedref ≈E50

ref (K0NC)m

59


where Cc is the compression index

Since we look for tangent Eoed, Δσ’0, and

σ*=2.303σoedref

Hardening Soil: Tangent oedometric modulus Eoed

60


0

0.02

0.04

0.06

0.08

0.1

0.121 10 100 1000

Volu

met

ric st

rain

ε v

[-]

Vertical stress σv' [ kPa]

Simulation

Experiment

Vertical preconsolidationpressure σ‘vc

Overconsolidation ratio: Typical oedometer test

σ‘v0 – current in situ stress

σ‘vc – equivalent past vertical preconsolidation pressure

NB. In natural soils, overconsolidationmay stem from mechanical unloading such as erosion, excavation, changes in ground water level, seasonal changes, or due to other phenomena such as desiccation, melting of ice cover, compression and cementation.

Initial state variables - OCR

σv

61

OCR =


A – past stress σ’SR

B – current in situ stress σ’0

Horizontal effective stress

Vertical effective stress

σ’vσ’h

A B

σ’v

σ’h

A

B

p’

q

Excavation

Initial state variables – K0 and K0NC

K0NC

σ’h0

σ’v0

σ’cK0

SR ≡ K0NC

K0

νur

1−νur

qPOP

62


Laboratory:

- Oedometer test (Casagrande’s method, Pacheco Silva method (1970), cf. report on HS model)

Field tests:

- Static piezocone penetration (CPTU) (for correlations see Mayne’s publications or 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)

Estimation of preconsolidation pressure and OCR

σv

63


Profiles for Bothkennar clay

Deposits with varying OCR over the depth (typically superficial soil layers)

64


1. through OCR (gives constant OCR profile)

At the beginning of FE analysis, Zsoil sets the stress reversal point (SR) with:

2. through qPOP (gives variable OCR profile)

Initial state variables – preconsolidation effect

65


0

2

4

6

8

10

12

14

16

18

1 3 5 7 9 11 13

Dept

h [m

]

OCR [-]

0

2

4

6

8

10

12

14

16

18

0 500 1000 1500

Dept

h [m

]

Effective stress [kPa]

SigEff verticalSigEff preconsolidation

0

2

4

6

8

10

12

14

16

18

0.00 0.50 1.00 1.50

Dept

h [m

]

Ko [-]

Deposits with constant OCR over the depth (typically deeply bedded soil layers)

Stress history through OCR

66

= ⋅


Overconsolidation in superficial layers

67

Wetting/drying scenario

Dry freshly-deposited

sand

Clayey silt

Sand

= 16 /= 19.75 /

= 10kPa

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

1 6 11 16

OCR

= 0 = 1 t= 2

Soils below saturated sand

soil are normally-consolidated now

Soils below drysand soil are

normally-consolidated now

Soils below drysand soil are

overconsolidatednow


0

2

4

6

8

10

12

14

16

18

0 0.5 1 1.5

Dept

h [m

]

Ko [-]

0

2

4

6

8

10

12

14

16

18

1 3 5 7 9 11 13

Dept

h [m

]

OCR [-]

0

2

4

6

8

10

12

14

16

18

0 200 400 600

Dept

h [m

]

Effective stress [kPa]

SigEff verticalSigEff preconsolidation

qPOP

Variable K0 can be automatically calculated for HSM

Deposits with varying OCR over the depth (typically superficial soil layers)

Stress history through qPOP

68

+= ⋅ OCR


qPOP fitting based on OCR profiles

1. Plot OCR profile derived from in situ test (CPTU, DMT, …)

2. Compute OCR profile for a given qPOP

3. Apply fitting (visual, curve-fitting)

Stress history through qPOP - estimation

69

OCR( ) = ( ) +( )


OCR profiling with Virtual Lab

70


HS-SmallStrain: Influence of OCR and qPOP on predictions

71


HSM – Parameter determination

72

,

Program of laboratory experiments should be carefully established accounting for dominant stress paths


Hardening Soil Model - Report

73

Updated with every release of the new version

List of modifications at the beginning of the document


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

The HS model – a practical guidebook

74

Documents

ZSoilDay2018 Constitiutive models for geotechnical ... · from classical soil mechanics ... Darcy’s law coefficients Soil water retention curve constants (van Genuchten’s model)