1

Plaxis Workshop for POPP & ASOCIATII – Inginerie Geotehnică S.R.L.

Hardening Soil ModelParameters

1

Parameter Explanation γ [kN/m³] Unit weight (unsaturated)

γr [kN/m³] Unit weight (saturated) ϕ′ [°] Friction angle (Mohr-Coulomb) c′ [kPa] Cohesion (Mohr-Coulomb) ψ [°] Angle of dilatancy

νur [-] Poisson’s ratio unloading-reloading E50 ref [kPa] Secant modulus for primary triaxial loading Eoed ref [kPa] Tangent modulus for oedometric loading Eur ref [kPa] Secant modulus for un- and reloading m [-] Exponent of the Ohde/Janbu law pref [kPa] Reference stress for the stiffness parameters K0 nc [-] Coefficient of earth pressure at rest (NC)

Rf [-] Failure ratio σTension [kPa] Tensile strength Rint friction reduction factor

Plaxis Workshop for POPP & ASOCIATII – Inginerie Geotehnică S.R.L.

Hardening Soil ModelParameters

2

Fig. 1: Different ways of visualizing the Mohr-Coulomb criterion

Fig. 2: Determination of ψ in a drained, triaxial test

2

Plaxis Workshop for POPP & ASOCIATII – Inginerie Geotehnică S.R.L.

Hardening Soil ModelParameters

3

Stress dependent stiffness (OHDE, 1930)

With:

Esref = Eoed

ref = ve * σat σat = pref

we = m extended for the Hardening Soil model to:

Plaxis Workshop for POPP & ASOCIATII – Inginerie Geotehnică S.R.L.

Hardening Soil ModelParameters

4

3

Plaxis Workshop for POPP & ASOCIATII – Inginerie Geotehnică S.R.L.

Hardening Soil ModelParameters

5

Plaxis Workshop for POPP & ASOCIATII – Inginerie Geotehnică S.R.L.

Hardening Soil ModelParameters

6

4

Plaxis Workshop for POPP & ASOCIATII – Inginerie Geotehnică S.R.L.

Hardening Soil ModelParameters

7

Fig. 3: Determination of Eur and E50 in a drained triaxial test with a deviatoric failure stress qf

Plaxis Workshop for POPP & ASOCIATII – Inginerie Geotehnică S.R.L.

Hardening Soil ModelParameters

8

Fig. 4: Definition of Eoed

ref in Oedometer test result

5

Plaxis Workshop for POPP & ASOCIATII – Inginerie Geotehnică S.R.L.

Hardening Soil ModelParameters from geotechnical report versus HS parameters

9

Plaxis Workshop for POPP & ASOCIATII – Inginerie Geotehnică S.R.L.

Hardening Soil ModelParameters

Hardening Soil Model Parameters

surface level = -1,50 mG.W. level = -3,90 m

Soil ProfileSoil type Top level Bottom level Layer C. L level γsat [kN/m³]

Fill -1,50 -2,80 -2,15 17Sandy Silt -2,80 -5,80 -4,30 18soft clay -5,80 -9,80 -7,80 18sand 1 -9,80 -18,00 -13,90 18sand 2 -18,00 -30,00 -24,00 18

Soil Strength

Soil typeν (Poisson`s

ratio) c' [kN/m²] ϕ' [°] ψ [°]

fill 0,30 0 28,0 0,0silty sand 0,30 0 32,0 2,0soft clay 0,35 5 26,0 0,0sand 1 0,30 0 34,0 4,0sand 2 0,30 0 36,0 6,0

Soil deformation modulus and constantsSoil type E50% [kN/m²] Eur / E50% m (power)

fill 5000 3 0,5silty sand 9500 3 0,5soft clay 4500 8 1,0sand 1 15000 3 0,5sand 2 23500 3 0,5

Calculated Stresses

Soil type σtot [kN/m²] u [kN/m²]vertical stress

σy [kN/m²] Ko at restσ3 Horizontal

pressure [kN/m²]

fill -11,1 0,0 -11,1 0,53 -5,86silty sand -49,1 -4,0 -45,1 0,47 -21,20soft clay -112,1 -39,0 -73,1 0,56 -41,06sand 1 -221,9 -100,0 -121,9 0,44 -53,73sand 2 -403,7 -201,0 -202,7 0,41 -83,56

10

Calculating HSM Parameters

Where:

E50ref =

pref = 100 stress units m 0,5 For sand and silts (accordinbg to Janbu 1963)

Where:E50 =

ν = Poisson's ratio

Calculated Stiffness ParametersSoil type E50

ref [kN/m²] Eoed [kN/m²] Eoedref [kN/m²] Eur

ref [kN/m²]

fill 20651 6731 20248 61952silty sand 20632 12788 19043 61897soft clay 9670 7222 9553 77360sand 1 20463 20192 18289 61388sand 2 25709 31635 22220 77126

Reference stiffness modulus corresponding to reference confining pressure pref

Young's modulus

6

Plaxis Workshop for POPP & ASOCIATII – Inginerie Geotehnică S.R.L.

Hardening Soil ModelParameters

11

• The interface factor Rint reduces the the strength of the soil in contact to the piles/walls.

• Rint = 0,5 for Diaphragm walls (ϕ/2)

• Rint = 0,67 for sheet pile walls and pile walls (2ϕ/3)

• Rint = 1,0 for bored piles

Plaxis Workshop for POPP & ASOCIATII – Inginerie Geotehnică S.R.L.

Hardening Soil ModelCorrelations - CPT

10 20

qc = 15

7

Plaxis Workshop for POPP & ASOCIATII – Inginerie Geotehnică S.R.L.

Hardening Soil ModelCorrelations DIN 4094 - CPT

qc = 15

SE

v = 300

Eoedref = v * 100kN/m² = 30000kN/m²

Plaxis Workshop for POPP & ASOCIATII – Inginerie Geotehnică S.R.L.

Hardening Soil ModelCorrelations - CPT

8

Plaxis Workshop for POPP & ASOCIATII – Inginerie Geotehnică S.R.L.

Hardening Soil ModelCorrelations - DPH, DPL

Plaxis Workshop for POPP & ASOCIATII – Inginerie Geotehnică S.R.L.

Hardening Soil ModelCorrelations - DPH, DPL

9

Plaxis Workshop for POPP & ASOCIATII – Inginerie Geotehnică S.R.L.

Hardening Soil ModelCorrelations - DPH, DPL

Plaxis Workshop for POPP & ASOCIATII – Inginerie Geotehnică S.R.L.

New Model: HS smallHardening Soil with small strain overlay model

• Same parameters for loading (E50ref, Eoed

ref) and unloading/reloading (Eurref) as in HS-model but with

increased stiffness for small strains (Eo)• lab tests: γ > 10-3 (larger strains, triaxial test oedometer test)• small strains: 10-6 to 10-3 (investigated in dynamic tests), range for retaining walls• additional model parameters: G0 ("dynamic" shear modulus and γ0,7 (value of shear strain, where the Gs

is reduced to 70% of Go)• following parameters are recommended:

1·10-510 2)rock

>1·10-44 - 8clay

1·10-42 - 3sand, loose

1·10-4 - 2·10-43 - 4sand, dense

γ0,7G-factor(=Go/Gur) 1)

1) Go/Gur = Eo/Eur2) factor 10 is the limit in the model

10

Plaxis Workshop for POPP & ASOCIATII – Inginerie Geotehnică S.R.L.

New Model: HS smallHardening Soil with small strain overlay model

Plaxis Workshop for POPP & ASOCIATII – Inginerie Geotehnică S.R.L.

New Model: HS smallHardening Soil with small strain overlay model

11

Plaxis Workshop for POPP & ASOCIATII – Inginerie Geotehnică S.R.L.

New Model: HS smallHardening Soil with small strain overlay model

Plaxis Workshop for POPP & ASOCIATII – Inginerie Geotehnică S.R.L.

New Model: HS smallHardening Soil with small strain overlay model

12

Plaxis Workshop for POPP & ASOCIATII – Inginerie Geotehnică S.R.L.

New Model: HS smallHardening Soil with small strain overlay model

Plaxis Workshop for POPP & ASOCIATII – Inginerie Geotehnică S.R.L.

New Model: HS smallHardening Soil with small strain overlay model

13

Plaxis Workshop for POPP & ASOCIATII – Inginerie Geotehnică S.R.L.

New Model: HS smallHardening Soil with small strain overlay model

Plaxis Workshop for POPP & ASOCIATII – Inginerie Geotehnică S.R.L.

New Model: HS smallExample for additional parameters

sand, dense:

→ E50ref = Eoed

ref = 50.000 kN/m²→ Eur

ref = 3 x Eoedref = 3 x 50.000 kN/m² = 150.000 kN/m², νur = 0,2

→ Eur= (1 + 2νur) x Gur → Gur= Eur / (1 + 2νur) = 150.000 / (1 + 2 x 0,2) = 107.000 kN/m²

→ Go / Gur = 3 (acc. to last page) → Go = 3 x Gur = 3 x 107.000 = 321.000 kN/m²→ γ0,7 = 1·10-4 (acc. to last page)

fortune of the model:

→ location of boundaries gets less important - radius of settlements behind a rataining wall is smaller→ heave of excavation bottom has less value→ better results for deflection of walls (with HS our expiriences show too high values)

14

Plaxis Workshop for POPP & ASOCIATII – Inginerie Geotehnică S.R.L.

New Model: HS smallExample for additional parameters

Plaxis Workshop for POPP & ASOCIATII – Inginerie Geotehnică S.R.L.

New Model: HS smallExcavation in Limburg, two anchor layers

15

Plaxis Workshop for POPP & ASOCIATII – Inginerie Geotehnică S.R.L.

New Model: HS smallExcavation in Limburg, two anchor layers

Hardening-Soil Model - Non-linear constitutive law

In lots of analyses almost all layers are modeled with the Hardening-Soil Model which is a double hardening model. By introducing two more yield surfaces next to the MOHR-COULOMB failure criterion both, irreversible plastic shear strains due to primary deviatoric loading as well as irreversible volumetric strains due to primary isotropic loading, can be described by the model. Further model features are stress dependent stiffness and the distinction between primary loading and unloading or reloading. In the following the meaning and determination of these parameters from laboratory tests is explained in more detail.

Meaning of the parameters:

a) Strength parameters & dilatancy angle ( ϕ′, c′, σTension, ψ, Rint)

The parameters ϕ′ und c′ correspond to the shear strength parameters according to MOHR-COULOMB (see Figure 1). They can be determined from triaxial or shear test data. In absence of laboratory test data, they can be correlated to in-situ test data. Material softening often observed in dense soils is not accounted for in the Hardening-Soil model.

Tab. 1: Required parameters of the Hardening-Soil model

Parameter Explanation γ [kN/m³] Unit weight (unsaturated)

γr [kN/m³] Unit weight (saturated) ϕ′ [°] Friction angle (Mohr-Coulomb) c′ [kPa] Cohesion (Mohr-Coulomb) ψ [°] Angle of dilatancy

νur [-] Poisson’s ratio unloading-reloading E50 ref [kPa] Secant modulus for primary triaxial loading Eoed ref [kPa] Tangent modulus for oedometric loading Eur ref [kPa] Secant modulus for un- and reloading m [-] Exponent of the Ohde/Janbu law pref [kPa] Reference stress for the stiffness parameters K0 nc [-] Coefficient of earth pressure at rest (NC)

Rf [-] Failure ratio

σTension [kPa] Tensile strength Rint friction reduction factor

Fig. 1: Different ways of visualizing the Mohr-Coulomb criterion

Fig. 2: Determination of ψ in a drained, triaxial test

The parameter σTension describes the maximum tensile strength of the material.

The dilatancy angle ψ describes the volumetric behaviour of the soil under deviatoric loading. In simple shear ψ corresponds to the angle of the deviation of the grain movement to the direction of shearing. In a triaxial test the dilatancy angle can be determined as shown in Figure 2.

The interface factor Rint reduces the the strength of the soil in contact to the piles/walls.

b) Stiffness parameters ( νur, Eurref, E50

ref, Eoedref , m, pref, Rf)

The elastic stiffness matrix of the Hardening-Soil model is quantified using the parameters νur and Eur

ref. If no plastic straining occurs (stresses inside the yield surfaces) these elastic parameters identify in combination with the parameter m the stress strain behaviour of the model. The elastic Poisson’s ratio νur and the elastic stiffness Eur

ref can be determined in a triaxial test. The secant stiffness Eur

ref is determined in an un-/reloading loop (see Figure 3).

The index „ref“ indicates, that the elasticity modulus Eurref as well as the stiffness

parameters E50ref and Eoed

ref introduced below, relate to a reference stress pref. According to the assumption of OHDE these parameters are converted to the

present stress as follows:

Fig. 3: Determination of Eur and E50 in a drained triaxial test with a deviatoric failure stress qf

E50ref

indicates the secant modulus in primary triaxial loading when reaching half the ultimate deviatoric stress qf (see Figure 3) and Eoed

ref

the tangent modulus in an Oedometer test for an axial load of σ1 = p

ref

, (refer to Fig. 4).

Fig. 4: Definition of Eoed

ref in Oedometer test result

The ratio of qf and qa is given by the failure ratio Rf, where the ultimate deviatoric stress qf is defined by the shear strength parameters ϕ′ and c′. When assuming Rf = 1.0 an asymptotic approach of the stress strain curve to the ultimate deviatoric stress (qf = qa) is given. Smaller values of Rf yield non-asymptotic stress strain curves, similar to the one shown in Figure 3. However, Rf < 1.0 often produces more accurate model predictions, i.a. better agreement with test data.

c) Miscellaneous ( γ, γr, Konc)

The unit weights γ and γr define the unsaturated and the saturated weight of the material, respectively. The coefficient of earth pressure at rest K0

nc identifies the horizontal stress for normally consolidated soils. The rate of plastic-deviatoric strains in a compression test (steepness of the cap) in the Hardening-Soil model is calculated based on K0

nc.