The Hardening Soil model with small strain stiffness - Zace Services ...

The Hardening Soil model
with small strain stiffness
in Zsoil v2011
Rafal OBRZUD
GeoMod Ing. SA, Lausanne
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, 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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne

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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Introduction

Basic differences between implemented soil models
Mohr-Coulomb
q
yield
surface
K 0 -line
q
q
E
Linear
elastic
domain
p’
K 0 -
unloading
p’
E ur
E = E ur
ε 1
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Introduction

Practical applications of the Hardening Soil model
Tunneling
Standard Mohr-Coulomb
Hardening-Soil
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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
E=E ur
q
Stiffness
degradation
E E ur
ε 1
E
p’
E ur
E < E ur
ε 1
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Introduction

Practical applications of the Hardening Soil model
Berlin sand excavation
Standard Mohr-Coulomb
Hardening-Soil
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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
q
Linear
elastic
domain
E=E ur
p’
q
elastic
domain
Stiffness
degradation
E E ur
ε 1
Linear
E
E ur
E

Small strain stiffness in geotechnical practice
e.g. Atkinson, Jardine and many others
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Introduction

Perceived application of ZSoil models
ULS - Ulitmate Limit State analysis
SLS - Serviceability Limit State analysis
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Introduction

Content
Introduction
Hardening Soil model framework
Hardening Soil SmallStrain
Hardening Soil Standard
Model parameters
Parameter Identification
Assistance in Parameter Selection
Practical applications
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne

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)
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Framework of HS model

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)
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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Framework of HS model

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.
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Framework of HS model

Hardening Soil model in ZSoil
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Framework of HS model

Hardening Soil model framework
Activation of G 0 degradation
in the small strain range
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Framework of HS model

Hardening Soil model framework
Triaxial test simulation
Secant stiffness in small strains
zoom
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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 [-]
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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)
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Framework of HS model

Content
Introduction
Hardening Soil model framework
Hardening Soil SmallStrain
Hardening Soil Standard
Model parameters
Parameter Identification
Assistance in Parameter Selection
Practical applications
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne

Non-linear elasticity for very small strains
Hyperbolic Hardin-Drnevich relation
to describe S-shaped stiffness
a = 0.385
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- HS SmallStrain

Content
Introduction
Hardening Soil model framework
Hardening Soil SmallStrain
Hardening Soil Standard
Model parameters
Parameter Identification
Assistance in Parameter Selection
Practical applications
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne

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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- HS Standard

Hyperbolic approximation of the stress-strain curve
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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)
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- HS Standard

Stiffness stress dependency parameter m
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- HS Standard

Stiffness exponent m
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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.
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- HS Standard

160,0
140,0
120,0
Asymptote q a =1/b
E 50 = 2a
Failure ratio R f
0,0
q = σ 1 -σ 3
100,0
80,0
60,0
1
40,0
20,0
1,8E-03
1,6E-03
1,4E-03
0 0,05 0,1 0,15 0,2
Identification of R f
R f = q f / q a = b·q f
1,2E-03
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
ε 1 /q
- HS Standard
1,0E-03
8,0E-04
6,0E-04
4,0E-04
2,0E-04
0,0E+00
1
a =1/2E 50
0 0,05 0,1 0,15 0,2
ε 1 [-]
b=1/q a

Double hardening model
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- HS Standard

Dilatancy
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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.
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- HS Standard

Parameters M and H
Evolution of the hardening
parameter p c :
H controls the rate of volumetric
plastic strains
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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]
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- HS Standard

Initial state variables – K 0 and K 0
NC
A
B
Excavation
σ’ v
σ’ v
σ’ h
Vertical effective stress
B
A
σ’ h
A
q
B
Horizontal effective stress
p’
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- HS Standard

Initial state variables – K 0 and K 0
NC
σ’ SR
Preconsolidation stress configuration corresponding to K 0
NC
σ’ 0
- HS Standard
Current in situ stress configuration corresponding to K 0
(at the beginning of numerical simulation)
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne

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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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’
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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)
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- HS Standard

Deposits with varying OCR over the depth (typically superficial soil layers)
Profiles for Bothkennar clay
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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)
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- HS Standard

Content
Introduction
Hardening Soil - SmallStrain
Hardening Soil – Standard
Model Parameters
Parameter Identification
Assistance in Parameter Selection
Practical applications
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne

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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Model parameters

Content
Introduction
Hardening Soil - SmallStrain
Hardening Soil – Standard
Model Parameters
Parameter Identification
Assistance in Parameter Selection
Practical applications
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne

Parameter identification
Report
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Parameter identification

The HS model – a practical guidebook
Contents:
Theory
Parameter identification
Parameter estimation
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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)
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
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)
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Parameter identification

Parameter identification
Stiffness parameters Estimation of E 0 from E 50
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Parameter identification

Parameter identification
Stiffness parameters Estimation of E 0 from E 50
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Parameter identification

Parameter identification
Stiffness parameters
Estimation of E 0 from E ur
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Parameter identification

HS-SmallStrain
Non-linear elasticity for small strains
Cohesionless soils
Influence of voids ratio Influence of confining stress p’
after Wichtmann & Triantafyllidis
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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.
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Parameter identification

Parameter identification
Stiffness parameters
Determination of E 50 for sands from CPT
after Robertson and Campanella (1983)
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Parameter identification

Parameter selection
Stiffness parameters
Undrained vs drained moduli – theoretical relationship
Since the shear modulus is not affected by the drainage conditions
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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) )
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Parameter identification

Parameter identification
Preconsolidation pressure and OCR
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
(from Lunne et al. 1997)
- Parameter identification

Parameter identification
Preconsolidation pressure and OCR
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Parameter identification

Parameter identification
Other information from DMT
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Parameter identification

Parameter identification
Strength parameters
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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)
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Parameter identification

Content
Introduction
Hardening Soil - SmallStrain
Hardening Soil – Standard
Model Parameters
Parameter Identification
Assistance in Parameter Selection
Practical applications
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne

The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Assistance in parameter selection

Non-cohesive soil setup
Initialization menu
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Assistance in parameter selection

Initialization menu
Cohesive soil setup
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Assistance in parameter selection

Initialization menu
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Assistance in parameter selection

HS Menu
Scroll
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Assistance in parameter selection

The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Assistance in parameter selection

Parameter selection – secant modulus E 50
In most practical cases:
In toolbox - ranges: = 2 to 4
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Assistance in parameter selection

Content
Introduction
Hardening Soil - SmallStrain
Hardening Soil – Standard
Model Parameters
Parameter Identification
Assistance in Parameter Selection
Practical applications
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne

Practical applications – Excavation in Berlin sand
Engineering draft and the sequence of excavation
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Practical applications

Practical applications – Excavation in Berlin sand
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Practical applications

Practical applications – Excavation in Berlin sand
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Practical applications

Practical applications – Excavation in Berlin sand
Berlin sand excavation
Standard Mohr-Coulomb
Hardening-Soil
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Practical applications

Practical applications – Shallow footing
Texas sand benchmark
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Practical applications

Practical applications – Shallow footing
Texas sand benchmark
0
Vertical stress[kPa]
0 200 400 600 800
0
OCR [-]
0 10 20 30 40 50
1
1
2
q POP
2
DMT-1
DMT-2
FE Model
3
3
4
4
Depth [m]
5
Depth [m]
5
3. Selecting q POP 4. OCR based on q POP Variable
profile
6
6
7
7
8
8
9
10
vertical effectivve stress
preconsolidation pressure
9
10
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- 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.
The Hardening Soil model with small strian stiffness
Rafal Obrzud, GeoMod SA
30.08.2011, Lausanne
- Practical applications