02 mountain-risks laloui soil mechanics part02(1)

8/13/2019 02 Mountain-Risks Laloui Soil Mechanics Part02(1)

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When the soil pores are filled by more than one fluid, e.g. water and air,

the porous material is termed unsaturated with respect to the wetting

fluid:

Solid

grains

Gas, ua

Water, uw

Solid

grains

Saturated Unsaturated

Water, uw

The matric suctions is defined as: ( )a w

s u u=

Unsaturated soils: definitions and notations


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Ln s

Sr

se

Sr(res)

1

Water retention curve

Funicular Pendular

Hydric

hysteresis

Sr(res) :Residual

degree of saturation

se : Air entry suction,

below which Sr=1

1 2 3 4 1 2

3 4

The water retention curve plots the evolution of the degree of saturation,

Sr, as a function of the matric suction.


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Volumetric response

to drained isotropic consolidationunder three levels of applied

suction, p = exterior load

Ln(p)

v

Ln(p)

s

A1

A1

A2

A2

A3

A3

B1

B1B2

B2 B3

B3

C1

C1

C2

C2

C3

C3

Points A2, B2 and C2 delimit theelastic domain for each path

They define a yield locus

in (p-s) plane calledLoading Collapse (LC)yield curve

(Alonso et al., 1990 BBM)

Isotropic mechanical loading path


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s

p

v

s

Wetting collapse

For given soils, a decrease in suction

can induce a collapse.

A necessary condition to obtain plastic

compression on wetting is a preliminary

mechanical consolidation.

AB: drying (p=const.)

BC: mechanical consolidation

(s=const.)

CC: wetting elastic swelling

CD: wetting plastic collapse

A

A

B

B

C

C

C

C

D

D

CollapseCollapseLC curve Elastic domain

SwellingSwelling


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Effective stress for a multiphase material

Extending Terzaghis proposal to unsaturated soils:

Gas, ua

Water, uw

Solid

Continuum

solid

Multi-phase descriptionSingle-phase

description

Effective stress

2

1

'ij ij ijd d u

=

=

Bishop (1959) thus proposed writing the effective stress as:

( ) ( )ij ij a ij a w ij

u u u = +


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In Bishops equation, the effective stress parameter is

expressed as a function of Sr(involving volume ratios)

rS=

Effective stress for a multiphase material

A possible approximation is:

( )rf S=

Experimental

determination

The relation is

not unique for

all materials

(Schrefler 1984)

(adapted from

Jennings and

Burland 1962)


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Advanced hydro-mechanical coupling

Both the Bishops effective stress concept and the

independent stress framework allow the description of

the effect of suction on the mechanical behaviour For a complete description of the hydro-mechanical

coupling the Bishops effective stress is not sufficent.

Mechanical

behaviour

MechanicalMechanical

behaviourbehaviourHydraulic

behaviour

HydraulicHydraulic

behaviourbehaviour

Advanced feature:

2-sided coupling

1

2


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Mechanical behaviour

Stress and strain variables

stress strain rate

Modifications to the constitutive model:

( )ij ij a ij rp Ss = + ij&

Mechanical

behaviour



behaviour

HydraulicHydraulic

behaviourbehaviour

- Use of a complete elasto-

plastic framework-The influence of suction on the

mechanical behaviour must be

taken into account

(e.g suction-induced hardening)

1

1

3. Advanced hydro-mechanical coupling


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Hydraulic behaviour

The mechanical model needs to be completed:

Evolution of Srand s need to be known to obtain the effective stress

A full description of the state of the material must include the hydric

behaviour :

( )ij ij a ij ru Ss = +

Mechanicalbehaviour

MechanicalMechanicalbehaviourbehaviour

HydraulicbehaviourHydraulicHydraulicbehaviourbehaviour

The hydraulic part undergoesthe influence of the mechanical

state (coupling )

2

2



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The work input rate study leads to work conjugate stress

variables and strain rates:

stresses strain rates

( )ij ij a ij r

p Ss = + ij&

a ws p p= rS&

In this combination, if Bishops generalised effective stress ischoosed for the mechanical part, the stress variable for the hydric part

is the matric suction

Mechanical

behaviour



behaviour

HydraulicHydraulic

behaviourbehaviour



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A constitutive model for unsaturated soils

Referring to previous discussion, the following stress framework is

adopted:

Stresses work conjugate strain rates

(Bishops generalised effective stress) (soil skeleton strain)

(matric suction) (degree of saturation)

The model is formulated within the framework of hardening plasticity

The strain rate is decomposed into an elastic and a plastic part:

( )ij ij a ij ru Ss = + ij&

srS

&

e p

ij ij ij

= +& & &

ACMEG - S


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Isotropic stress paths

Under this type of loading, i.e. mechanical load at constant level of

suction, the strain rate is elastic-plastic:

The parallel representation of experimental results in

and planes lets appear the existence of a yield curve.

p'

A1

vm

se

Ln p'

s

A2 A3

C1 C2

C3

D3D1 D2

E

p'c0

(s)

LC yield curve

A1 A2

A3 C3

D1D2

D3

C1C2

(a) (b)

m/(1+e0)m/(1+e0)

( ln ')v p ( ')s p

m m e m p

v v v = +& & &

ACMEG - S


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Isotropic stress paths : LC yield curve

Comparison between numerical and experimental results

0

0

( ) 0

( ) 1 log

c c e

c c s e

e

p s p s s

sp s p s ss

= <

for

for

(Sharma 1998)

Bentonite/kaolin mix

0

50

100

150

200

250

300

350

400

0 100 200 300 400

P' (kPa)

s

(kPa)

EXP

model

(Kane 1973)

loess

0

10

20

30

40

50

60

70

80

90

100

0 50 100 150

P' (kPa)

s

(kPa)

EXP

model

ACMEG - S


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p' vh

Ln s

p'c0

sese

Ln s

PathAB : ( 0


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Ln(p')

s

se

v

Ln(p')

sA

sBsC

LC curve: swelling collapse mechanisms

PathAB : The stress state

remains inside the elastic domain.

.if s , then , so .

net s = +

A

A

B

B

C

C

Path BC: The yield limit is reached

on point B. Further wetting provokesa yielding on the LC curve. The only

possible straining is a plastic

compression to reach point C.

The path followed is a wetting on a

initially consolidated material.

LC curve Elastic zone

sAsBsC

ACMEG - S


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Deviatoric stress paths

The modif ied Cam-clay model (Schofield and Wroth, 1968; Roscoe

and Burland, 1968) is extended to unsaturated states by substituting

Terzaghis effective stress by Bishops generalised effective stress.

The deviatoric yield surface is simply expressed as follows:

which includes the effects of suction such as the increasepc with s

The critical state line is assumed unique in (p-q) plane and obeysthe relation:

The elastic part of the deviatoric strain increment is simply written:

with G being the elastic shear coefficient

(assumed independent on suction)

2 2( ( ) ) 0

cf q M p p s p = =

q Mp=

3

e

d

q

G

= &

&


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Graphical representation of the yield surface

Deviatoric stress pathsACMEG - S


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Modelling the hydraulic behaviour :

A constitutive model for unsaturated soils

Mechanical

behaviour



behaviour

HydraulicHydraulic

behaviourbehaviour

2

The aim of the second part of the model is the description of the evolution

of the hydraulic stress and strain variables, respectivelys and Sr.

Model for the soil water retention curve (SWRC)

The mechanical influence on the hydric state is introduced by the HM

coupling

( ), ), rs S

ACMEG - S


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Modelling the soil water retention curve

Ln s

Sr

se

Sr(res)

1

Hydraulic behaviour Hydric hysteresis

Ln s

Sr

se

Sr(res)

MODEL

A B C

DE

AB: Saturated part, 0


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Mass and momentum balances

( ) 0pKkv

t

p

s

S

S

n

t

p

p

n

s

S

S

n

ww

w

rws

w

w

w

w

w

w

w

w

=

+

+

+

g

g

( ) 0pKkv

t

p

s

S

S1

n

t

p

p

n

s

S

S1

n

ras

ww

w

w

w

=

+

+

+

gggg

g

g

g

g

Water/solid mass balance

Air/solid mass balance

[' - Sw pwI - ( 1 - Sw) pg I] + g = 0Momentum balanceof the three-phasemixture

neglected for two-

phase modeling

Content


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Content

Introduction to Geomechanics

Introduction standard approach

Effective stress concept Soil constitutive behaviour

Seepage

Advanced Geomechanics for Landslides

Hydro-Mechanical coupling Unsaturated soils

Finite elements simulations


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Predicting time-dependent

(Trisenberg) landslide

Location


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Location

4 km

Principality of Liechtenstein

Slope in the Rhine valley : 5 km2

The infratructures of Triesen andTriesenberg are subject to

signif icant damage induced by

the movements during cri tical

periods

The major difficulties in

modelling the Triesenberg

landslide are related to the huge

area of instabil ity, theunsaturated conditions of the

slope and the relatively low

velocity of the movements.

Location


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24

3 km

1.5 km

Location

Deeper-seated slope movement : 1.7 km2 - 74 Mio m3

Active slide : 3.1 km2 37 Mio m3

Mean inclination : 24

Mean depth : 10 to 20 m

Two main parts :


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Hydrogeology


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The upper part : Buntsandstein sandstone, schists and limestones

The lower part : Austroalpine Triesen Flysh (clayey schists)

Toe : Rhine river alluvia

Hydraulic input from ValnaValley

Direct infiltration

Double feeding system inpiezometric observations

Water table is about 20 m to 30 m below the soil surface at the top of

the landslide, whereas at the bottom, it almost reaches the surface

The landslide takes place in unsaturated conditions for a large part of its profile

Tacher et al.

Hydrogeology

2D modelling : [2000 crisis modelling] 2 main actives zones


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0

2

4

6

8

Nov/15/1999

Jan/15/2000

Mar/15/2000

May/15/2000

Jul/15/2000

Sep/15/2000

Continuous inclinometer B5Inclinometer KL1A

Inclinometer KL1A (Trend)Numerical modelling

Displacements[cm]

Date

Initial time1st January 2000

Zone clearly observable on the map of the

average annual displacements

Good agreement with the

general trend

The measured values are

higher than the simulated ones

3D modelling : [2000 crisis modelling]


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g

-1

0

1

2

3

4

5

6

7

20

30

40

50

60

70

80

90

100

0 50 100 150 200 250 300

Displacements

Pore wa ter pressure

Displacements[mm

]

Porewaterpressure[k

Pa]

Time [days]

0

3

6

9

12

15

10

20

30

40

50

60

0 50 100 150 200 250 300

Displacements

Pore w ater pressure

Displacements[mm]

Porewaterpressure[kPa]

Time [days]

0

10

20

30

40

50

-60

-40

-20

0

20

40

0 50 100 150 200 250 300

Displacements

Pore wa ter pressure

Displacements[mm

]

Porewaterpressure

[kPa]

Time [days]

Elastic reversible behaviour Elasto-plastic (irreversible) behaviour

April August Qualitatively, the simulated distribution of the movements is fairly similar to themeasured values (by survey and GPS) of annual displacement

The modelling results exhibit one main active zone within each slide, which is fairly

small in size

St bili i L F l d lid


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Stabilizing La Frasse landslide

Characteristics of the landslide


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Instabilities induced by :

Hydraulic pore pressures (crises)

Viscosity of the materials (between crises)

Characteristics of the landslide

Background


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Background

Evolution of the observed displacements of three points A, B, C on La

Frasse Landslide and of rainfall (monthly and 6-month running mean

values). The shaded triangular bands represent the range of long-term

average velocity characterizing the zones in which points A, B and C are

located.

Hydro-Mechanical Modelling


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Hydro Mechanical Modelling

1890 m

433m

406.3 kN/m

600.0 kN/m

Main assumptions:

Hydro-mechanical coupled formulation

Darcys law for the fluid phase + saturated media + K = f(porosity) Cyclic elasto-plastic + viscoplastic constitutive laws (Mohr-Coulomb,

Cap, Hujeux)

2D Mesh: 1694 nodes, 1530 elements

Six layers with different mechanicalcharacteristics

Comparison between two constitutive laws: cyclic elasto-

plastic model (Hujeux) and elasto-perfectly plastic model


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Horizontal displacement Vertical displacement

12 Crisis 94 300 days

Displacement point 1

plastic model (Hujeux) and elasto-perfectly plastic model

(Mohr-Coulomb)

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0 50 100 150 200 250 300

-0.05

0

0.05

0.1

0.15

0.2

0.25

0 50 100 150 200 250 300

Time [Days]Time [Days]

Hujeux EP

M-C

Verticaldis

placement[m

]

Horizontald

isplacement

[m]

Point 1Point 1 Hujeux EP

M-C

Influence of drainage pumping


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-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0 50 100 150 200 250 300

12

0

1

2

3

4

5

0 50 100 150 200 250 300


Verticald

isplacement[m

]

Horizontaldisplacement[m]

Without pumping

With pumping

With pumping

Without pumpingPoint 1 Point 1


Crisis 94 300 days





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-0.1

-0.05

0

0.05

0.1

0 50 100 150 200 250 300-0.1

0

0.1

0.2

0.3

0.4

0 50 100 150 200 250 300

12



Verticaldisplacement[m

]

Horizontald

isplacement[

m]

Without pumpingWithout pumping

With pumpingWith pumping

Point 2Point 2

Crisis 94 300 days



Conclusion Conclusions


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Natural slopes represent complex phenomena

to model, both in space and time

Strong need for numerical analysis Multiphase coupled formulation and

unsaturated soil mechanics may significantly

improve the modelling

Advanced 3D FEM analysis is confirmed to be

a useful tool for the design and selection ofrisk mitigation strategies

Conclusions

ConclusionRecent publications


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Franois B., L. Tacher, C. Bonnard, L Laloui, V. Triguero. Numerical modelling ofthe hydrogeological and geomechanical behaviour of a large slope movement: TheTriesenberg landslide (Liechtenstein) . Canadian Geotechnical Journal, vol. 44,pp. 840-857, 2007.

Nuth M., Laloui L. Effective Stress Concept in Unsaturated Soils: Clarification andValidation of a Unified Framework . International Journal of Numerical andAnalytical Methods in Geomechanics (in press), 2007.

Charlier R, L. Laloui, F. Collin Numerical modelling of coupled poromechanicsprocesses . REGC (European Journal of Civil Engineering), Volume 10, N6-7, pp.

669-702, 2006.

Laloui L., M. Nuth. An introduction to the constitutive modelling of unsaturatedsoils . REGC (European Journal of Civi l Engineering), Volume 9, N5-6, pp. 651-670, 2005.

Tacher L., C. Bonnard, L. Laloui, A. Parriaux. "Modelling the behaviour of a largelandslide with respect to hydrogeological and geomechanical parameterheterogeneity" . Landslides journal. Vol. 2, N1, pp. 3-14, 2005.

Recent publications

Conclusion Course Notes


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Laloui L. "Mechanics of Porous Media" . Course notes -Doctoral programme of Mechanics - EPFL, 2006. 122pages.

Laloui L. "Ecoulements souterrains" . Course notes for

students of the Civil Engineering Section of the EPFL,2002 (new edition in 2007). 114 pages.

Laloui L. "Seepage and Consolidation in Tunnelling" .Course notes Master of Advanced Studies in

Tunnelling - EPFL, 2007 (95 pages). Laloui L. "Groundwater Flows Interacting with

Structures" . Course notes for the Advanced-levelcourses in hydraulic schemes, EPFL 2001.

Course NotesCould be obtained at : www.lelivre.ch

02 mountain-risks laloui soil mechanics part02(1)

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