10-Nordal_ICG Nov 2012 Instab in Stain Softening Soils

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Hans Petter Jostad NGI/NTNU Anders Samstad Gylland NTNU Steinar Nordal NTNU With special thanks to: Gustav Grimstad (HIOA), Vikas Thakur (NPRA), Francesco Bonadies (Univ. Salerno)

Numerical Modelling of Instability in Strain-Softening Soils

ICG Symposium Geohazards and Society November 2012

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Strain-Softening Soils

Displacement

Load

Strain softening

Load Reduction in resistance for increasing deformation

Sensitive clay

Peak

Residual


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Kaare Höeg 1972

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Strain-Softening Soils • Smårød, 20.12.06


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Strain-Softening Soils • Kattmarkveien 13.03.09


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Strain-Softening Soils • Esp 01.01.12

Photo:Ned Alley/Scanpix


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Strain-Softening Soils • Esp 01.01.12

Photo: KRISTOFFER FURBERG


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Sensitive clay

• Deposited in salt water • Landrise • Fresh water infiltration

– House-of-cards without glue

• Liquefies when remoulded – Quick clay: sr < 0.5 kPa

ww

w.ng

u.no

www.forskning.no


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Sensitive clay • CIUc triaxial tests, block samples Tiller quick clay


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Sensitive clay • CIUc triaxial tests, block samples Tiller quick clay


(ICSMFE Mexico, 1969)


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Stig Bernander: Surte slide 1950, Tuve slide 1977 PhD 2011


T

F

F

Δ

Δ

T

δ δ

T T

δ

T

δ1-δ2

N N

F

F

Δ

Δ

T

δ1 δ2

T T

δ3

1 2 3

δ2-δ3

RIGID SPRINGS COMPRESSIBLE SPRINGS


τ0 > cR


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EA

Force

Weak layer

Downward progressive failure

Long natural slope

Bar on weak layer


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EA Force

Weak layer A B


δA δB

δA ≠ δB x


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EA Force

Weak layer A B


δA δB

δA ≠ δB x

δ

τ τ

Strain softening

A B

δ


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EA Force

Weak layer A B


δA δB

δA ≠ δB x τ τ

Strain softening

A B

x

Initial shear stress τ0

τ δ δ


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EA Force

Weak layer A B


δA δB

δA ≠ δB x τ τ

Strain softening

A B

x

Initial shear stress τ0

δ δ


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• Slope resistance depends on:

• Higher resistance for: – Higher stiffness – Higher peak strength – Lower rate of strain softening (perfect plastic = zero strain softening) – Lower initial stress level


x

τ0

Peak strength Stiffness Softening behaviour

Initial shear stress level


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• Initial shear stress level – Highly sensitive – 10% change of the initial

shear stress level gives a 40-50% change of the capacity

• Stiffness – Sensitive for low values

• Softening – Sensitive for low values – Uncertain parameter


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Example calculations with Bifurc Example Bernander App. I

0

20

40

60

80

100

120

140

0 20 40 60 80 100

Distance along slope (m)

Nor

mal

forc

e ab

ove

slip

su

rfac

e (K

N/m

) Bernander

Bifurc

Example Bernander App. I

0

5

10

15

20

25

30

35

0 20 40 60 80 100


Shea

r str

ess

(kPa

)

Bernander

Bifurc

Example Bernander App. I

0.00

0.05

0.10

0.15

0.20

0.25

0 20 40 60 80 100


Dis

plac

emen

t (m

)

Bernander

Bifurc

Dr. Hans Petter Jostad and Dr. Lars Andresen at NGI/ICG

Load-displacement curve Example Appendix I

0

20

40

60

80

100

120

140

0 0.05 0.1 0.15 0.2 0.25

Displacement at x = 100 m (m)

Forc

e at

x=1

00 m

(kN/

m)

BernanderBifurc


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Strain-Softening Soils

Displacement

Load

Strain softening

Load Reduction in resistance for increasing deformation

Sensitive clay

Peak

Residual


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Localized failure - shear bands


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Softening gives mesh dependency δ

t1

L

γ1

δ

L

t2 γ2

Τ Τ

W1 > W2

τ

γ

τ1

τ2

γ2 γ1

W1 W2

Τ 1

2 δ


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Regularisation technique in order to obtain mesh independent solution

0 0.01 0.02 0.03 00 D i s p l a c e m e n t δ m a x

0

1

2

3

4

L o a d

p /

s u C

tsb = 150 cm tsb = 50 cm tsb = 1 cm

Shear band thickness:

Need a procedure that gives a capacity or safety factor that is mesh independent. This means that the solution should converge upon mesh refinements and the shear band thickness should be larger than given by the element size.


(Andresen /Jostad)

Regularization – non-local strain

( )* ( ) ( ) ( ) ( ) ( )p p p p

i i i w dVV

αα∆ = ∆ − ⋅ ∆ + ⋅ ∆∫ε x ε x ε x x ε x

γp

δh

tsb

τ

γ Control of the shear band thickness

1D shear column

0

20

40

60

80

100

0 10 20 30

Nor

mai

lzed

pos

ition

(x/L

) [%

]

Normalized displacement (δ/L) [%]

1 el

0

20

40

60

80

100

0 10 20 30

Nor

mai

lzed

pos

ition

(x/L

) [%

]


10 el

0

20

40

60

80

100

0 10 20 30

Nor

mai

lzed

pos

ition

(x/L

) [%

]


20 el

0

20

40

60

80

100

0 10 20 30

Nor

mai

lzed

pos

ition

(x/L

) [%

]


50 el

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0

Nor

mal

ized

shea

r stre

ss (τ

/su)

Normalized displacement δ/L [%]

1 el

10 el

20 el

50 el

L

δ τ

γ tsb

Mesh independent solution when the element size is smaller than the shear band thickness!

α = 1.58, l/L = 0.1 => t/L =π/10

The shear band thickness is defined by the softening zone!

Slope stability problem

“Almost” mesh independent results!

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Problem: The shear band is mm scale, elements are m scale Trick for FEM simulations: Increasing the internal length by reducing the softening strain, ∆γsoft

∗

Shear strain, γ

Shear stress, τ

Peak

Residual

∆γsoft∗∙linternal* = ∆γsoft ∙ linternal

Only really OK for 1D problems

∆γsoft

∗

Material model – NGI-ADPSoft

γ

4 5 o

9 0 o

α = 0 o

τ

α

z

σ1 σzz

τxz

σxx

),(),( pu

p sf γατγ −=σ

oτ

suC

suDSS

suE

surC

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Smårød, 20.12.06

Volume [m3] 750.000

Length [m] 200

Width [m]

Slip surface [m]

500

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Three main phases: - area A first - area B next, - area C final

A fill of about 7 meters is the triggering agent ?

Slides by Francesco Bonadies, Univ. Salerno

Simulated by NGI-ADPSoft as part of the SVV-NVE project : Effekt of progressive failure on physical development of areas with quick clay

• dry crust • soft clay layer • firm bottom

1

2

3

3

2 1


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Smårød

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Smårød


Principal total strains directions

Triggering embankment

Old embankment River

190 m


Input


Gylland, A. & Jostad, H.P (2010) NUMGE

Effect of updated geometry in analyses of progressive failure Updated geometry is important for capturing the final slide configuration


Masterthesis Magne Mehli, vår 2010

Initial stresses are difficult to evaluate:


How important is strain softening for evaluating the stability of a slope? Key project: Effekt of progressive failure on physical development of areas with quick clay Thanks to:

Effect of softening:

Handbook 016 standard psamples?

Karlsrud/NGI

Preliminary results from NGI project: Effekt of progressive failure on physical development of areas with quick clay

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Modified triaxial cell • Moving, low friction base sled • Instrumented • Planar shear bands • Why triax?

– Optimal sample handling and quality – Maintain relevance of tested material


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Excess pore pressure • Strain softening by excess pore pressure • Characteristic consolidation time ≈ lab test time • Internal pore pressure gradients

Plastic shearing Generation of excess

pore pressure

Elastic unloading Reciever of excess

pore pressure


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Micro CT, PhD work A. Gylland


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Concluding remarks

• Numerical Modeling of Instability in Strain-Softening Soils is still difficult, but may now be done in a consistent manner

• The NGI – ADPSoft with non-local strain is a powerful tool • A pragmatic «effect of softening factor» is studied, 10% ? • Old message repeated: Prevent the initial slide! • More research needed:

– Understanding material behaviour – Scaling the softening curve only exact for 1D – Initial stresses are hard to determine, but has high influence – Effective stress based simulations wanted Geofuture

• Design codes and guidelines


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Thank you ICG !


10-Nordal_ICG Nov 2012 Instab in Stain Softening Soils

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