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The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
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
0
50
100
150
200
250
300
350
400
450
0,00% 2,00% 4,00% 6,00% 8,00% 10,00% 12,00% 14,00%
Dev
iato
ric
stre
ss [
kPa]
q
= σ
1-σ
3
Axial Strain ε1
Triaxial drained compression test
Experiment: Texas sand
Simulation: Hardening Soil
Why do we need advanced constitutive models? Approximation of soil behaviour for reliable simulations of practical cases
- Introduction
Simulation: Mohr-Coulomb
Plasticity (yielding) before reaching the ultimate state
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Why do we need advanced constitutive models?
ENGINEERING CALCULATIONS
LIMIT STATE ANALYSIS
Bearing capacity
Slope stability
DEFORMATION ANALYSIS
Pile, retaining wall deflection
Supported deep excavations
Tunnel excavations
Consolidation problems
Basic models e.g. Mohr-Coulomb Advanced soil models
- Introduction
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Basic differences between implemented soil models
Mohr-Coulomb
p’
q
K0-line
yield surface
Linear elastic domain
ε1
q
E Eur
E = Eur
p’
q
K0-unloading
- Introduction
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Tunneling
Standard Mohr-Coulomb Hardening-Soil
Practical applications of the Hardening Soil model
- Introduction
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Basic differences between implemented soil models
Mohr-Coulomb Volumetric cap models
p’
q
K0-line
yield surface
p’
q
ε1
q
E Eur
ε1
q
Eur
E=Eur
Stiffness degradation
isotropic hardening
mechanism
E
E < Eur
p’
q
σ1’ constant
Linear elastic domain
Linear elastic domain
- Introduction
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Standard Mohr-Coulomb Hardening-Soil
Practical applications of the Hardening Soil model
Berlin sand excavation
- Introduction
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Basic differences between implemented soil models
Mohr-Coulomb Volumetric cap models
Hardening Soil models
p’
q
K0-line
yield surface
Linear elastic domain
p’
q
p’
q
ε1
q
E Eur
ε1
q
Eur
ε1
q
Eur
E0
E=Eur
Stiffness degradation
Stiffness degradation
isotropic hardening
mechanism + shear
hardening mechanism
E
E<Eur Eur
Linear elastic domain
E0
E
NON-LINEAR elastic domain
- Introduction
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Small strain stiffness in geotechnical practice
e.g. Atkinson, Jardine and many others
- Introduction
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Stiffness in different models
0
20
40
60
80
100
120
140
160
-3,61E-16 0,05 0,1 0,15 0,2
Dev
iato
ric
Stre
ss q
[kPa
]
Axial Strain ε1 [-]
Mohr-Coulomb
Modified Cam Clay
Cap model
HS-Standard
HS-Small A
B
0
0,2
0,4
0,6
0,8
1
1E-06 1E-05 0,0001 0,001 0,01 0,1 N
orm
aliz
ed s
oil s
tiff
ness
G/G
0 [-]
Axial Strain ε1 [-]
Linear elasticity at very small strains
Linear elasticity at small strains
Non-linear elasticity at very small strains
- Introduction
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Perceived application of ZSoil models
ULS - Ulitmate Limit State analysis SLS - Serviceability Limit State analysis
- Introduction
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
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
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)
HS-Standard
- Framework of HS model
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
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)
HS-Standard
- Framework of HS model
0
200
400
600
800
1000
1200
0.00% 5.00% 10.00% 15.00%
Dev
iato
ric
stre
ss [
kPa]
q=
σ1-
σ3
Axial Strain ε1
Triaxial drained compression test - Texas sand
SIG3 = 34.5kPa
SIG3 = 138kPa
SIG3 = 345kPa
E(1)
E(2)
E(3)
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
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)
Stiffness variation (degradation of G0 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-Standard
+ HS-SmallStrain for handling stiffness in a small strain range
* 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
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Hardening Soil model in ZSoil
- Framework of HS model
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Hardening Soil model framework
Activation of G0 degradation in the small strain range
- Framework of HS model
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Hardening Soil model framework
Secant stiffness in small strains
Triaxial test simulation
zoom
- Framework of HS model
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
0
100
200
300
400
500
600
700
800
900
1000
0,019 0,02 0,021 0,022 0,023 0,024 D
evia
tori
c st
ress
q
[kPa
]
Axial strain ε1 [-]
HS-SmallStrain
HS-Standard
0
100
200
300
400
500
600
700
800
900
1000
0 0,01 0,02 0,03 0,04 0,05
Dev
iato
ric
stre
ss
q [k
Pa]
Axial strain ε1 [-]
HS-SmallStrain
HS-Standard
Hardening Soil model framework
Triaxial test simulation with the unloading/reloading cycle
zoom
- Framework of HS model
Eur Eur E0
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Main mechanical features of HS model
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
Nonlinear elasticity which includes hysteretic effects (Hardin-Drnevich concept)
HS-Standard
+ HS-SmallStrain
- Framework of HS model
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
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 Hardin-Drnevich relation to describe S-shaped stiffness
Non-linear elasticity for very small strains
a = 0.385
- HS SmallStrain
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
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
E0 – tangent initial stiffness modulus E50 – secant stiffness modulus corresponding to 50% of the ultimate deviatoric stress qf described by Mohr-Coulomb criterion Eur – unloading/reloading modulus (parameter corresponding to in Modified Cam Clay)
For most soils Rf falls between 0.75 and 1
- HS Standard
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Hyperbolic approximation of the stress-strain curve
- HS Standard
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Stress stiffness dependency
0
200
400
600
800
1000
1200
0,00% 5,00% 10,00% 15,00%
Dev
iato
ric
stre
ss [
kPa]
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)
- HS Standard
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Stress stiffness dependency
E0ref , E50
ref, , Eurref correspond to reference minor stress σref
where i.e. stiffness degrades with decreasing σ3 up to the limit minor stress σL which can be assumed by default σL =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
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Stiffness stress dependency parameter m
1. Find three values of E50(i) corresponding σ3
(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
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Stress stiffness dependency at initial state
0,0
2,0
4,0
6,0
8,0
10,0
12,0
14,0
16,0
18,0
20,0
0 50000 100000 150000 200000
z [m
]
E [kPa]
m = 0.4
m = 0.6
m = 0.8
0,0
2,0
4,0
6,0
8,0
10,0
12,0
14,0
16,0
18,0
20,0
0 50000 100000 150000 200000
z [m
]
E [kPa]
phi = 20
phi = 30
phi = 40
0,0
2,0
4,0
6,0
8,0
10,0
12,0
14,0
16,0
18,0
20,0
0 50000 100000 150000 200000
z [m
]
E [kPa]
c = 0
c = 15
c = 30
Level of reference stress
- HS Standard
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Stiffness exponent m
- HS Standard
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Unloading/reloading Poisson’s ratio νur
Experimental measurements from local strain gauges show that the initial values of Poisson’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
Pois
son'
s ra
tio ν
[-]
Mobilized stress level q / qmax
Toyoura Sand (Dr=56%) Ticino Sand (Dr=77%) Pisa Clay (Drained Triaxial) Sagamihara soft rock
Typically elastic domain
after Mayne et al. (2009)
- HS Standard
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Unloading/reloading Poisson’s ratio νur
Therefore, the characteristic value for the elastic unloading/reloading Poisson’s ratio of νur = 0.2 can be adopted for most soils.
- HS Standard
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Failure ratio Rf
0,0
20,0
40,0
60,0
80,0
100,0
120,0
140,0
160,0
0 0,05 0,1 0,15 0,2
q =
σ 1-σ
3
Asymptote qa=1/b
E50 = 2a
1
0,0E+00
2,0E-04
4,0E-04
6,0E-04
8,0E-04
1,0E-03
1,2E-03
1,4E-03
1,6E-03
1,8E-03
0 0,05 0,1 0,15 0,2
ε 1/q
ε1 [-]
a =1/2E50
1
b=1/qa
Identification of Rf
Rf = qf / qa = b·q f
- HS Standard
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
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
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Double hardening model
p’-q section through shear and cap yield surfaces
σ1
σ2
σ3
p’
cap yield surfaces described with van Ekelen’s formula
Mohr-Coulomb failure surface
- HS Standard
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Dilatancy
-0,4
-0,3
-0,2
-0,1
0,0
0,1
0,2
0,3
0,4
0,5
0 10 20 30 40
sinϕ
m [
-]
φm [deg]
Dilatancy domain
Contractancy domain
Contractancy cut-off for
φm < φcs
Rowe's dilatancy for
φm≥ φcs
Rowe's dilatancy
- HS Standard
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Dilatancy
- HS Standard
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Dilatancy in HS-SmallStrain
Since the cut-off for the contractancy domain could yield too small volumetric strain, the scaling parameter D is introduced.
Contractancy domain
Dilatancy domain
- HS Standard
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Parameters M and H
H controls the rate of volumetric plastic strains
Evolution of the hardening parameter pc :
- HS Standard
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Typical stress path in the oedometric test
M and H must fulfil two conditions: 1. K0
NC produced by the model in oedometric conditions is the same as K0
NC specified by the user
2. Eoed generated by the model is the same Eoed
ref specified by the user
Parameters M and H
- HS Standard
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
ASSUMPTIONS: 1. At given σoed
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 Eoed
= δσ/δε ≅ ∆σ/∆ε
4. Optimisation of M and H must fulfil two conditions: K0
NC produced by the model in oedometric conditions = K0NC specified by the user
Eoed generated by the model = Eoed ref specified by the user
Parameters M and H
- HS Standard
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Initial state variables - OCR
0
0,02
0,04
0,06
0,08
0,1
0,12 1 10 100 1000
Vol
umet
ric
stra
in
ε v [-
]
Vertical stress σv' [ kPa]
Simulation
Experiment
Vertical preconsolidation pressure σ‘vc
Notion of overconsolidation ratio:
Typical oedometer test σ‘vc OCR =
σ‘v0
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.
- HS Standard
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Initial state variables – OCR and K0
Normally-conslidated soil (OCR=1) Overconslidated soil (OCR>1)
Why does it appear and what should be inserted?
- HS Standard
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Initial state variables – K0 and K0NC
A
B
Horizontal effective stress
Verti
cal e
ffect
ive
stre
ss
σ’v
σ’h
A B
σ’v
σ’h
A
B
p’
q
Excavation
- HS Standard
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Preconsolidation stress configuration corresponding to K0NC
Current in situ stress configuration corresponding to K0 (at the beginning of numerical simulation)
Initial state variables – K0 and K0NC
σ’ SR
σ’0
- HS Standard
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Estimation of earth pressure at rest
Normally-consolidated soils
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
0 20 40 60
K 0NC
φ' [deg]
1-sin(phi')
Brooker&Ireland(1965)
Simpson(1992)
Overconsolidated soils
0,0
0,5
1,0
1,5
2,0
2,5
0 5 10 15 20
K 0
OCR [-]
phi=20deg phi=30deg phi=40deg
Initial state variables – K0 vs. OCR
- HS Standard
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Initial state variables – K0 and K0NC
K0NC K0
For most cases when soil was subject to “natural” consolidation before unloading
K0SR = K0
NC
- HS Standard
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Initial state variables – K0 and K0NC
A B
q
In the case of simulating the triaxial compression test after isotropic loading/unloading: K0
SR ≠ K0NC
but
K0SR =1
p’
C
isotropic loading/unloading
- HS Standard
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
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 pc0 is computed
- HS Standard
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Setting initial state variables
1. Through K0
2. Through Initial Stress
σy = γ “depth” σx = σxK0(x)
- HS Standard
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Setting initial state variables
If the model does not converge at Initial State for the specified K0
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
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
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 qPOP (gives variable OCR profile)
- HS Standard
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
0
2
4
6
8
10
12
14
16
18
1 3 5 7 9 11 13
Dep
th [m
]
OCR [-]
0
2
4
6
8
10
12
14
16
18
0 500 1000 1500
Dep
th [m
]
Effective stress [kPa]
SigEff vertical SigEff preconsolidation
0
2
4
6
8
10
12
14
16
18
0,00 0,50 1,00 1,50
Dep
th [m
]
Ko [-]
Stress history through OCR Deposits with constant OCR over the depth (typically deeply bedded soil layers)
- HS Standard
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Deposits with varying OCR over the depth (typically superficial soil layers)
Profiles for Bothkennar clay
- HS Standard
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
0
2
4
6
8
10
12
14
16
18
0 0,5 1 1,5
Dep
th [m
]
Ko [-]
0
2
4
6
8
10
12
14
16
18
1 3 5 7 9 11 13
Dep
th [m
]
OCR [-]
0
2
4
6
8
10
12
14
16
18
0 200 400 600
Dep
th [m
]
Effective stress [kPa]
SigEff vertical SigEff preconsolidation
qPOP
Stress history through qPOP
K0OC = K0
NC √OCR
K0OC = K0
NC OCRsin(φ) (Mayne&Kulhawy 1982)
Variable K0 can be introduced merely through Initial Stress option
Deposits with varying OCR over the depth (typically superficial soil layers)
- HS Standard
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
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. E0ref kPa SCPT, SDMT, geophysical methods
2. γ0.7 - Triaxial test with local gauges, geotechnical evidence
Elastic constants
3. E50ref kPa Triaxial test
4. Eurref kPa Triaxial test
5. νur - Triaxial test
6. m - Triaxial test
Auxiliary variable
7. σ3ref kPa Triaxial test
- Model parameters
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 2)
Shear mechanism
8. c kPa Triaxial test, in situ test
9. φ ˚ Triaxial test, in situ test
10. (Rf) - Triaxial test or the default value 0.9
11. ψ ˚ Triaxial test
12. emax ˚ Triaxial test on dense granular or overconsildated cohesive soil
Volumetric (cap) mechanism
13. Eoedref kPa Oedometric test
14. σoedref kPa Oedometric test
Initial state variable
15. OCR / qPOP
- / kPa
Oedometric test or in situ tests
16. K0SR - K0
SR = 1-sin φ (or Ko-consolidation triaxial test)
17. σ0 kPa Init. stress conditions accounting for K0 = K0
SR (for normally-consolidated soil), K0 = K0
OC (for overconsolidated soil)
- Model parameters
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Hardening Soil model Comparison of corresponding soil parameters for selected ZSoil models
Corresponding soil parameters
Hardening-Soil
Cap Mohr-Coulomb
Small strain stiffness E0 and γ0.7
none none
Elastic constants Eur and νur E50 and m
E and ν E and ν
Failure criterion φ and c
φ and c φ and c
Dilatancy ψ and emax ψ ψ and emax
Cap surface parameters
Eoed(can be determined from λ) OCR , K0 and K0
SR
λ
OCR , K0
None
K0
- Model parameters
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
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
- Parameter identification
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
The HS model – a practical guidebook
Contents:
Theory Parameter identification Parameter estimation
- Parameter identification
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Parameter identification Stiffness parameters Determination of G0 from geophysical tests SCPT, SDMT and others with ρ denoting density of sol 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)
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
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Parameter identification Stiffness parameters Determination of G0 for sands from CPT
after Robertson and Campanella (1983)
- Parameter identification
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Parameter identification Stiffness parameters Estimation of E0 from E50
- Parameter identification
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Parameter identification Stiffness parameters Estimation of E0 from E50
- Parameter identification
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Parameter identification Stiffness parameters Estimation of E0 from Eur
- Parameter identification
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
HS-SmallStrain Non-linear elasticity for small strains
Cohesionless soils Influence of voids ratio Influence of confining stress p’
after Wichtmann & Triantafyllidis
- Parameter identification
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
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
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Parameter identification Stiffness parameters Determination of E50 for sands from CPT
after Robertson and Campanella (1983)
- Parameter identification
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Parameter selection Stiffness parameters
Undrained vs drained moduli – theoretical relationship Since the shear modulus is not affected by the drainage conditions
- Parameter identification
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Parameter identification Oedometric modulus Eoed
where Cc is the compression index
Since we look for tangent Eoed, ∆σ’0, and σ*=2.303σoed
ref
If λ is known
- Parameter identification
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Parameter selection - oedometric modulus Eoed
Eoedref
≈ E50ref
but
Eoedref
E50
ref
σref σoedref = σref / K0
NC
- Parameter identification
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
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
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Parameter identification Preconsolidation pressure and OCR
(from Lunne et al. 1997)
- Parameter identification
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Parameter identification Preconsolidation pressure and OCR
- Parameter identification
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Parameter identification
Other information from DMT
- Parameter identification
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Parameter identification Strength parameters
- Parameter identification
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
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
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
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
- Assistance in parameter selection
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
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
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Initialization menu
Non-cohesive soil setup
- Assistance in parameter selection
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Initialization menu
Cohesive soil setup
- Assistance in parameter selection
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Initialization menu
- Assistance in parameter selection
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
HS Menu
Scr
oll
- Assistance in parameter selection
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
Parameter selection – secant modulus Eur
Typical values of the stiffness modulus which are provided in most textbooks are referred to as the "static" stiffness modulus Es It can be assumed that they represent the values of the unloading/reloading modulus Eur In the basic parameter selection, typical Eur is taken as Es and the reference pressure is assumed σref=100kPa
- Assistance in parameter selection
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Parameter selection – secant modulus E50
In most practical cases:
In toolbox - ranges: = 2 to 4
- Assistance in parameter selection
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Parameter selection - oedometric modulus Eoed
Eoedref
≈ E50ref
but
Eoedref
E50
ref
σref σoedref = σref / K0
NC
- Assistance in parameter selection
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
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
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
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
- Practical applications
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Practical applications – Excavation in Berlin sand
- Practical applications
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Practical applications – Excavation in Berlin sand
- Practical applications
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Standard Mohr-Coulomb Hardening-Soil
Practical applications – Excavation in Berlin sand
Berlin sand excavation
- Practical applications
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Practical applications – Excavation in Berlin sand
Berlin sand excavation
-35
-30
-25
-20
-15
-10
-5
0
-0.04 -0.03 -0.02 -0.01 0
Dis
tanc
e fr
om s
urfa
ce
Y [m
]
Horizontal displacement Ux [m]
HS-smallHS-StdMCMeasurements
- Practical applications
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Texas sand benchmark
Practical applications – Shallow footing
- Practical applications
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Texas sand benchmark Practical applications – Shallow footing
0
1
2
3
4
5
6
7
8
9
10
0 5 10 15 20D
epth
[m]
KD [-]
DMT-1
DMT-2
1. DMT data 2. OCR interpreted form DMT data
0
1
2
3
4
5
6
7
8
9
10
0 10 20 30 40 50
Dep
th [m
]
OCR [-]
DMT-1
DMT-2
Variable profile
- Practical applications
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
0
1
2
3
4
5
6
7
8
9
10
0 10 20 30 40 50
Dep
th [m
]
OCR [-]
DMT-1
DMT-2
FE Model
0
1
2
3
4
5
6
7
8
9
10
0 200 400 600 800D
epth
[m]
Vertical stress[kPa]
vertical effectivve stress
preconsolidation pressure
Texas sand benchmark Practical applications – Shallow footing 3. Selecting qPOP 4. OCR based on qPOP
Variable profile
qPOP
- Practical applications
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Texas sand benchmark Practical applications – Shallow footing 5. Interpreting and Setting K0
0
1
2
3
4
5
6
7
8
9
10
0 0.5 1 1.5 2 2.5
Dep
th [m
]
K0 [-]
DMT-1
DMT-2
FE Model
Variable K0 can be introduced merely through Initial Stress option
- Practical applications
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
Texas sand benchmark
Practical applications – Shallow footing
-0.14
-0.13
-0.12
-0.11
-0.1
-0.09
-0.08
-0.07
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0
0 2000 4000 6000 8000 10000
Sett
lem
ent [
m]
Load [kN]
Experiement
Hardening Soil SmallStrain
Standard Mohr-Coulomb
- Practical applications
The Hardening Soil model with small strian stiffness Rafal Obrzud, GeoMod SA 30.08.2011, Lausanne
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
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