An NZGS 1 day short course

Unsaturated soils

Antonio GensTechnical University of Catalonia, Barcelona, Spain

Unsaturated soils Session 1 Problems involving unsaturated

soils Suction and suction-controlled

laboratory tests Stress variables Mechanical behaviour: strength

Session 2 Mechanical behaviour: volume

change BBM: a conceptual framework Flow and consolidation in

unsaturated soils Case histories

An NZGS 1-day short course: outline

Ground movement control Session 3: Tunnelling Generation of ground movements by

tunnelling Tunnelling procedures: TBMs Screen (curtain) walls Structural jacking Compensation grouting

Session 4: Deep excavations Generation of ground movements by

deep excavations Estimation of ground movements Procedures for control and reduction

of ground movements Case history Excavations with large deformations

Introduction: characteristic problems in unsaturated soils

Suction and suction-controlled laboratory tests

Stress variables

Mechanical behaviour of unsaturated soils Shear strength Volume change

A (basic) model for unsaturated soils

Flow and consolidation in unsaturated soils Continuity equation Retention curve Darcy’s law and relative permeability

Case histories

Unsaturated soils: outline

Unsaturated soils

pores liquid gas

total total

V V Vn

V V

Porosity Degree of saturation

1liquid liquidr g

pores liquid gas

V VS S

V V V

Solid

GasLiquid

Unsaturated soils: failure

Shum Wan Road landslide, Hong Kong Island on August 13th,1995Photographs from Geotechnical Engineering Office, Hong Kong

Fig. 4Collapse in Via Luigi Settembrini, Naples (15-09-2001)

Engineering problems involving unsaturated soils: collapse

Fig. 5Collapse in Via Luigi Settembrini, Naples (15-09-2001)

Engineering problems involving unsaturated soils: collapse

Underground cistern before the rainstorm

Underground cistern about two months after the rainstorm

Collapse in Via Luigi Settembrini, Naples (15-09-2001)

Engineering problems involving unsaturated soils: collapse

At the beginning of 1972 important settlements were detected. The situationworsened with time and generalized collapses were measured with settlementsin excess of 1.5m

The canal went into service in 1969. Canal de Terreu (in collapsible soils) (Huesca Province)

Engineering problems involving unsaturated soils: collapse

Terreu Canal, Spain (ca. 1960)

Engineering problems involving unsaturated soils: collapse

Ascó Nuclear Power Station, Spain

Engineering problems involving unsaturated soils: deformations

Ascó Nuclear Power Station, Spain

Heave contours (1982-1992) Heave evolution (1982-2002)

Engineering problems involving unsaturated soils: deformations

Engineering problems involving unsaturated soils: generalised behaviour

Disposal in vertical boreholes Disposal in horizontal drifts

Engineering problems involving unsaturated soils: generalised behaviour

Introduction: characteristic problems in unsaturated soils

Suction and suction-controlled laboratory tests

Stress variables

Mechanical behaviour of unsaturated soils Shear strength Volume change

A (basic) model for unsaturated soils

Flow and consolidation in unsaturated soils Continuity equation Retention curve Darcy’s law and relative permeability

Case histories

Unsaturated soils: outline

New additional variable: suction

Water potential, : work required to transport a unit mass from a reference pool of pure water to the soil water under consideration

zgoc Matric Osmotic Gas Gravitational

Suction in unsaturated soils

Matric (capillary) potential

Osmotic potential:RTcmo :)( awc uu

:)( atmag uu Gas pressure potential

:zwz Gravitational potential

Review panel (1965)

Suction in unsaturated soils

Matric potential

Gas pressure potential

Gravitational potential

Suction in unsaturated soils

Osmotic potential

RTV

nsos

SEMIPERMEABLE MEMBRANE

SOLUTEPURE

WATER

New additional variable: suction

Water potential, : work required to transport a unit mass from a reference pool of pure water to the soil water under consideration

zgoc

Total water potential controls water flow Water potential affects mechanical behaviour. Not all potential

components have, however, the same effect

(Review panel, 1965)

Matric Osmotic Gas Gravitational

:w cs Matric suction Osmotic suction:w o Total suction:ts s

Total suction is directly related to relative humidity (psychrometric law)

Suction in unsaturated soils

Matric suction is often associated with capillary phenomena

a ws p p

Suction in unsaturated soils

EFFECT OF SURFACE TENSION. LAPLACE’S LAW

The surface tension is ableto maintain different pressuresof liquid and gas in the interface

This effect is evident in the capillary ascension of water in small diameter tubes

FORCE EQULIBRIUM IN AN INTERFACE ELEMENT

Differential pressure Vertical force

s applied in 2dl1 Vertical force

s applied in 2dl2 Vertical force

v l g 1 2

v1 1 s 2

v2 2 s 1

F p p dl dl

F 2dl senF 2dl sen

and 1 1 1 2 2 2senβ dl /2R y senβ dl /2R

Equilibrium:

(Laplace)

Mean radius, r

(Laplace)

Example:

s = pg-pl is called capillary suction

2v1vv FFF

1 2 1 2g l 1 2 s s

2 1

dl dl dl dlp p dl dlR R

g l s2 1

1 1p pR R

21 R1

R1

r2

sg l

2p pr

g l

g l

Si p p 0.1 MPa a T 20ºC ; r 1.45 mSi r 1 mm ; T 20ºC ; p p 0.145 kPa

HEIGHT OF CAPILLARY RISE

Example:

The capillary rise height is therefore equal to the value of suction expressed in length units. Capillary suction depends essentially on pore geometry

cosr2hr stw2t

Waster column equilibrium between A and C

Weight = Force exerted by the surface tension

g ls s

w t w w w

p p2 cos 2 s0º ; hr r

mm14.8h;kPa0.073s;mm1rm10h;MPa0.1s;μm0.73r

HEIGHT OF CAPILLARY RISE

Suction in unsaturated soils

Matric suction is often associated with capillary phenomena

a ws p p

Intergranular capillary forces

Suction in unsaturated soils

Suction in unsaturated soils

0 1000 2000 3000 4000

s (kPa)

1

1.1

1.2

1.3

1.4

1.5

f(s)

(Fisher, 1926)

Intergranular capillary forces

Sand Clay

Suction in unsaturated soils

Matric suction contains a capillary component and an adsorptive component

Matric suction should be viewed as the result of the general interaction between solid surface, liquid and associated interfaces

However we keep expressing it as pa: air pressure, pw: water pressure

wa pps

Suction in unsaturated soils

Vapour pressure (no solutes, no curvature)

ov

5239.7p T 136075 exp273.15 T

ovp : MPa

T :ºC

Temperature (ºC)

Vapo

ur p

ress

ure

(MPa

)

AIR + VAPOUR

WATER

Suction in unsaturated soils

Concentration of water vapour (psychrometric law)

gw: vapour density in the gaseous phase

water potentialT: temperature

(gw)0: vapour density in the gaseous phase

(Pg – Pl=0)

Mw: molecular mass of water (0.018 kg/mol)R: the gas constant (8.314 J/mol/oK)

Concentration of water vapour depends on: Temperature (water viscosity) (Thermal) Suction (Hydraulic)

Vapour concentration with no capillary effects

(depends on temperature and concentration)

Modification of vapour concentration due to

capillary effects (depends on suction and temperature)

l

wwg

wg TR

M15.273

exp0

Suction in unsaturated soils

Psychrometric law

Temperature = 20ºC 0 relative humidtywg v

owvg

pp

Suction in unsaturated soils

Controlled-suction oedometer cell

diffu

sed

air f

lush

ing

syst

em

water volumechange indicatorwithDPT

uw

vapour trap (hr > 98%)

diaphragm pressure: v

1

2

3

1: soil sample 2: HAEV ceramic disc3: coarse porous stone

ua= constant

LVDT or load cell

SUCTION-CONTOLEED OEDOMETER

OSMOTIC TECHNIQUE(polietilenglicol-PEG solution) (Tarantino & Mongiovi, 2000)

Suction in unsaturated soils

Osmotic technique for suction control

(polietilenglicol-PEG solution)

0.05 0.10 0.15 0.20 0.25 0.30 0.35

Concentración, kg PEG/kg agua

0

500

1000

1500

Pres

ión

osm

ótic

a,

(kPa

)

PEG20000-psicrómetroWilliams & Shaykewich (1969)PEG6000-adaptado deHeyer, Cass & Mauro (1969)PEG20000-Spectrum-tensiómetroTarantino & Mongiovi (2000)PEG20000-Visking-tensiómetroDineen (1997)PEG35000-Spectrum(Por5)-tensiómetroUPC-GEOLAB: Ávila, en prep.

promedio para PEG condiferentes MWCOTensiómetro Imperial College

Agitador

Solución PEG

Juntastóricas

Membrana de acetatoSpectrum/ Por 5

Imán

Calibration of PEG-35000 With IC tensiometer

Suction in unsaturated soils

Forced convection transport of vapour• Through sample (Sr<0.85)

Ac, Bc, Cc, Do• Series configuration

Ac, Bo, Cc, Do• Parallel configuration

Ao, Bo, Co, Dc

A

D C

B

air pump

desiccator

salt/base or acid solutions

flow meter

hygrometer

thermocouplepsychrometeror hygrometer

sample

coarse porousstoneprecision balance

(uv / uvo)T

(v- ua)

densimeter

Suction in unsaturated soils

CONSTANT COLUME CELLS. SUCTION CONTROLLED BY RELATIVE HUMIDITY OF AIR

(UPC, 2000)

Suction in unsaturated soils

TRIAXIAL CELL WITH SUCTION CONTROLLED BY RELATIVE

HUMIDITY OF AIR(Romero & García, 2002)

Air pump

Controlled realtivehumidity

Scales to measure water exchange

Suction in unsaturated soils

Introduction: characteristic problems in unsaturated soils

Suction and suction-controlled laboratory tests

Stress variables

Mechanical behaviour of unsaturated soils Shear strength Volume change

A (basic) model for unsaturated soils

Flow and consolidation in unsaturated soils Continuity equation Retention curve Darcy’s law and relative permeability

Case histories

Unsaturated soils: outline

Presence of water and air in pores

Three phases: Solid Liquid Gas

Solid

Air

Water

Stress variables

Which stress variables should we use?

1950’s, 1960’s Relevance of suction recognized Interpretation in terms of single ‘effective stress’

Late1960’s, 1970’s Unsaturated soils as ‘difficult soils’, `special soils’, ‘regional soils’

Late1970’s, 1980’s Recognition of need for two stress variables State surface approach

Late 1980’s onwards Large expansion of research Suction control and measurement Elastoplastic models Incorporation into mainstream Soil Mechanics

Unsaturated soils: a bit of history

Bishop´s (1959) expression for effective stress

' ( )a a wu u u

Stress variables

Sr

Bishop´s (1959) expression for effective stress

' ( )a a wu u u

Stress variables

Jennings & Burland (1962)

• Collapse behaviour upon wetting

2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 90.1 1.0 10.0

Vertical stress (MPa)

-1.0

1.0

3.0

5.0

7.0

9.0

11.0

13.0

15.0

Vert

ical

str

ain

(%)

Series D-D

(a)

Barcelona silt

Stress variables

Lixhe chalk

(De Gennaro et al., 2004)

Stress variables

oil-water system

Effect of intergranular forces due to external stresses and suction

Stress variables

(Coleman, 1962; Bishop & Blight, 1963; Matyas & Radhakrishna, 1968; Fredlund & Morgenstern, 1977)

Two sets of stress variables are required

:au Net stress

:)( wa uus Matric suction

Stress variables

: Wetting at constant (net) stress : Loading a saturated soil : Drying at constant (net) stress : Loading at constant suction : Stress path during a swelling pressure test

Stress variables

Isotropic plane

Introduction: characteristic problems in unsaturated soils

Suction and suction-controlled laboratory tests

Stress variables

Mechanical behaviour of unsaturated soils Shear strength Volume change

A (basic) model for unsaturated soils

Flow and consolidation in unsaturated soils Continuity equation Retention curve Darcy’s law and relative permeability

Case histories

Unsaturated soils: outline

First suction control direct shear cell described by Escario and Sáez, 1980.

Shear strengthUnsaturated soils: features of behaviour

Suction control direct shear cell

Shear strengthUnsaturated soils: features of behaviour

Suction control direct shear cell

Shear strengthUnsaturated soils: features of behaviour

Behaviour of unsaturated soils: shear strength

Escario & Sáez (1986)

Moderate suctions

Shear strength increases with suction

Shear strength increases with suction: a bilinear relationship

Behaviour of unsaturated soils: shear strength

Fredlund & Rahardjo(1985)

Variation ofapparent cohesionand friction withsuction

banf tans'tanp'c

Satija, 1978Consolidated drainedtriaxial12.629.020.3

Dhanauri clayw = 22.2%

pd = 1478 kg/m3

Satija, 1978Constant water contenttriaxial22.628.515.5

Dhanauri clayw = 22.2%

pd = 1580 kg/m3

Satija, 1978Constant water contenttriaxial16.529.011.3

Dhanauri clayw = 22.2%

pd = 1478 kg/m3

Satija, 1978Consolidated drainedtriaxial16.228.537.3

Dhanauri clayw = 22.2%

pd = 1580 kg/m3

Constant water contenttriaxial

Constant water contenttriaxial

TEST PROCEDURE

Bishop et al., 196021.727.39.6Boulder clayw = 11.6%

Bishop et al., 196018.124.615.8Compacted shale

w = 18.6%

REFERENCEb

(º)’(º)

c’(kPa)

SOIL TYPE

Reported shear strength parameters for partially saturated soils

bwaanf tanpp'tanp'c

Close to saturation: f n wc ' p tan '

b'

(df/ds) = (df /d’) btan tan '=

Consistency conditions in the vicinity of saturation

For a change in suction:

Failure envelope and variation of b with suction from suction controlled directshear tests on a glacial till

Gan et al., 1988

Behaviour of unsaturated soils: shear strength

The bilinear relationship is not valid and must be modified The rate of increase of strength close to saturation must be tan’ The increase of strength is not linear but it becomes asymptotic at high

suctions A single stress variable may account for the strength increase with suction

' ( ) ; ( )l g l lp p p S

Escario & Jucá(1990)

Shear strength

MATRIC SUCTION, s (kg/cm2)

s

ss

Introduction: characteristic problems in unsaturated soils

Suction and suction-controlled laboratory tests

Stress variables

Mechanical behaviour of unsaturated soils Shear strength Volume change

A (basic) model for unsaturated soils

Flow and consolidation in unsaturated soils Continuity equation Retention curve Darcy’s law and relative permeability

Case histories

Unsaturated soils: outline

Fig. 5

Behaviour of unsaturated soils: consolidation lines

Suction increases the apparent preconsolidation stress The soil can sustain a higher void ratio at the same stress value

(Oedometer tests on a Brazilianresidual soil; Lemos, 1998)

Behaviour of unsaturated soils: volume change

Jennings & Burland (1962)

Collapse

Two stress variables are required to describe collapse

e

Behaviour of unsaturated soils: volume change

Volume change behaviour on saturation depends on applied stress level

Behaviour of unsaturated soils: volume change

Triaxial wetting tests on Ko-consolidated samples of Lower Cromer Till (Maswoswe, 1985)

After collapse, the saturated void ratio is recovered

Collapse (compression) is observed on wetting at high stresses, but a (small) swelling is observed upon wetting at low stresses

swelling collapse

Behaviour of unsaturated soils: volume change

Specimens of compacted clay at 90% of Normal Proctor energy and two different water contents (Escario & Sáez, 1973)

During collapse, volume strain may change sign (it can only be observed in suction controlled tests)

Sample A

Sample B

STATICALLY COMPACTED KAOLINITE (dry of optimum)Change of specific volume during equalization phase. Several specimens

of compacted kaolinite are taken to zero suction under an isotropic stress of 40 kPa (Wheeler and Sivakumar, 1993)

21.1ecm/g20.1 o3

d

During collapse, volume strain may change sign(it can only be observed in suction controlled tests)

Unsaturated soils: features of behaviour

Sometimes, collapse reaches a maximum for a given confining stress and decreases for higher stresses (generally very loose soils)

Oedometer tests on compactedspecimens of red clayey silt from

Barcelona

Collapse during saturation of a low density fill. Interpreted behaviour on the basis of

extensometer readings

Unsaturated soils: features of behaviour

Barden et al, 1969 tests on low plasticity clays (wl = 20%; wp = 10%). Samples compacted to half of Normal Proctor energy. Slightly dry of optimum

Stress path dependency (wetting)

Unsaturated soils: features of behaviour

Barden et al, 1969 tests on low plasticity clays (wl = 20%; wp = 10%). Samples compacted to half of Normal Proctor energy. Slightly dry of optimum

Stress path dependency (drying)

Unsaturated soils: features of behaviour

Application of a suction cycle to two different clays of low initial consistency (Yong et al, 1970)

Suction changes may lead to irreversible deformationsUnsaturated soils: features of behaviour

COMPACTED SAMPLES (“Kneading”). KAOLINITESuction cycles in a suction controlled triaxial cell

(Alonso et al., 1990)

Paths Observed changes in v=1+e

875.0S;915.0e

ML%9.26w;%7.38w

roo

pL

Suction changes may lead to irreversible deformationsUnsaturated soils: features of behaviour

FEATURES OF VOLUME CHANGE BEHAVIOUR

Suction increases the apparent preconsolidation pressure (yield stress) and (often) soil stiffness

Volume change behaviour depends on stress level. Swelling or compression (“collapse”) may occur depending on applied load

Collapse behaviour

After collapse soil lies on saturated consolidation line Volume change reversal may occur during collapse In loose soils, collapse strains reach a maximum at a

certain intermediate stress level Volume change behaviour is path independent only for a certain

class of stress paths Suction changes may lead to irreversible deformations

Unsaturated soils

Introduction: characteristic problems in unsaturated soils

Suction and suction-controlled laboratory tests

Stress variables

Mechanical behaviour of unsaturated soils Shear strength Volume change

A (basic) model for unsaturated soils

Flow and consolidation in unsaturated soils Continuity equation Retention curve Darcy’s law and relative permeability

Case histories

Unsaturated soils: outline

Elasto plastic model for unsaturated soils

The Barcelona Basic Model (BBM)

S1

S = 0 Yield

S = 0

S2

S3

MEAN NET STRESS, p

VOID

RA

TIO

, e

MEAN NET STRESS, p

SUC

TIO

N, s

S1

S3

S2

Yield curve LC

Elastic domain

( )ap Suction: ( )a ws p p Net stress:Isotropic plane

Elasto plastic model for unsaturated soils

The Barcelona Basic Model (BBM)

Yield curve LC1

Elastic domain

Yield curve LC2

C

LS1

*

1op

1op

*

2op MEAN NET STRESS, p

SUC

TIO

N, s

Isotropic plane

Loading

Collapse

Elasto plastic model for unsaturated soils

The Barcelona Basic Model (BBM)

Isotropic plane

volSU

CTI

ON

, scompression swelling

elastic swelling

ABC

plastic compression

A B C

Yield curve LC

Elastic domain

LCC

*op *

o Bp

MEAN NET STRESS, p

SUC

TIO

N, s

LCB

*o C

p

MODEL PARAMETERS

r = 0.75;

pc = 0.1MPa; s= 0.08

s = 0.008

Soil “profile”:

-Moderate compressibility

-Compressibility when dry=75% of saturated compressibility

Wetting and Loading paths

Elasto plastic model for unsaturated soils

MODEL PARAMETERS

r = 0.75;

pc = 0.1MPa; s= 0.08

s = 0.008

v0 = 1.9

Drying and Loading paths

Elasto plastic model for unsaturated soils

*op op

q

CSL (s)

CSL (s=0)

ss=0

Elasto plastic model for unsaturated soils

The Barcelona Basic Model (BBM)

Deviatoric planeIsotropic plane

Elastic domain

*op op

s

MEAN NET STRESS, p

SUC

TIO

N,s

LC

MEAN NET STRESS, p

FEATURES OF BEHAVIOUR

Suction increases the apparent preconsolidation pressure (yield stress) and (often) soil stiffness

Volume change behaviour depends on stress level. Swelling or compression (“collapse”) may occur depending on applied load

Collapse behaviour After collapse soil lies on saturated consolidation line Volume change reversal may occur during collapse

Volume change behaviour is path independent only for a certain class of stress paths

Suction changes may lead to irreversible deformations Shear strength increases with suction

Unsaturated soils

Elasto plastic model for unsaturated soils

The Barcelona Basic Model (BBM)

Capable of reproducing main features of unsaturated soil behaviour

Provides a consistent framework for an integrated understanding of unsaturated soil behaviour

Complete/consistent but based on drastically simplified assumptions

Compatible with classical models of saturated soils

Other forms of stress variables can (and have) been usedDevelopments of constitutive models for unsaturated soils

Class IJosa, Balmaceda, Gens & Alonso (1992); Wheeler & Sivakumar (1995); Cui, Delage & Sultan (1995), Sheng et al. (2008)

Class IIKohgo, Nakano & Miyazaki (1993); Modaressi & AbouBekr (1994); Pakzad (1995); Geiser, Laloui & Vulliet(2000); Loret & Khalili (2002); Russell & Khalili (2006)

Class IIIJommi & di Prisco (1994); Bolzon, Schrefler & Zienkiewicz (1996); Jommi (2000); Wheeler, Sharma & Buisson (2003); Gallipoli, Gens, Sharma & Vaunat (2003); Sheng, Sloan & Gens(2004); Tamagnini (2004)

1( , )a ru s S 2( , )rs S(Gens,1995)

1 ( 0)au

1( )au s

1( , )a ru s S

Class I

1( , )a ru s S

2 ( , )rs S

1 ( 0)au

Easy representation of conventional stress paths

Difficulties in the transition saturated-unsaturated

Hysteresis and hydraulic effects difficult to incorporate

Independent function required to model the increase of strength with suction

Josa, Balmaceda, Gens & Alonso (1992); Wheeler & Sivakumar (1995); Cui, Delage & Sultan (1995), Sheng et al. (2008)

Stress variables for unsaturated soils

Class II

Stress variables for unsaturated soils

1( , )a ru s S

2 ( , )rs S Representation of conventional stress paths not straightforward

Difficulties in the transition saturated-unsaturated (even when incorporating desaturation suction)

Hysteresis and hydraulic effects difficult to incorporate

The increase of strength with suction results from stress variable definition

1( )au s Kohgo, Nakano & Miyazaki (1993); Modaressi & AbouBekr (1994); Pakzad (1995); Geiser, Laloui & Vulliet(2000); Loret & Khalili (2002); Russell & Khalili (2006)

Class III

Stress variables for unsaturated soils

1( , )a ru s S

2 ( , )rs S Representation of conventional stress paths not straightforward, sometimes impossible

No difficulties in the transition saturated-unsaturated

Hysteresis and hydraulic effects can be naturally incorporated

The increase of strength with suction results from stress variable definition

1( , )a ru s S Jommi & di Prisco (1994); Bolzon, Schrefler & Zienkiewicz (1996); Jommi (2000); Wheeler, Sharma & Buisson (2003); Gallipoli, Gens, Sharma & Vaunat (2003); Sheng, Sloan & Gens(2004); Tamagnini (2004)

' ( ) (1 )a r a w r a r wu S u u S u S u Includes average skeleton (or Bishop’s) stress:

Most elastoplastic models share the following features:Use of two stress variables Incorporate a LC yield curve or equivalent concept Adopt a saturated model as reference

* ( , ) ( ) ( , )d D ds sh ds

Stress variables for unsaturated soils

“in fact, no single stress variable has ever been found which, substituted for effective stress, allows for a description of all the aspects of the mechanical behaviour of a given soil in the unsaturated range”.

(Jommi, 2000)

Stress variables for unsaturated soils

Class III

Class II

Class I

Category 2 effective

stress

Category 1 effective

stress

Independent stress

variables

Category

+++-

+-+?-

---+

Direct accounting of increase in strength

Hysteresis and

hydraulic effects

Sat-unsattransition

Represen-tation

(Nuth & Laloui, 2008)

1 ( 0)au

1( )au s

1( , )a ru s S

Independent stress variable:

Category 1 effective stress:

Category 2 effective stress:

At present there are no compelling (theoretical) reasons to choose a stress variable in preference to another. It is largely a matter of convenience

It can be argued that the use of the term “effective stress model”for unsaturated soils may be misleading or confusing given the conventional concept of effective stress in mainstream geotechnical engineering. If the name “effective stress model” is to be used, the term should be carefully defined

Final remarks on stress variables for unsaturated soils

Introduction: characteristic problems in unsaturated soils

Suction and suction-controlled laboratory tests

Stress variables

Mechanical behaviour of unsaturated soils Shear strength Volume change

A (basic) model for unsaturated soils

Flow and consolidation in unsaturated soils Continuity equation Retention curve Darcy’s law and relative permeability

Case histories

Unsaturated soils: outline

Saturated soils: equation of continuity (with soil deformation)

0

yq

xq

tn yx

tn

Unsaturated soils: flow and consolidation

Unsaturated soils: equation of continuity (with soil deformation)

0)(

yq

xq

tSn yxr

tSn r

)(

Unsaturated soils: flow and consolidation

Unsaturated soils: equation of continuity (with soil deformation)

0)(

yq

xq

tSn yxr

tSn r

)(

0),(),(

yq

xqn

tsSS

tsn yxr

r

Constitutive law

Retention curve

Darcy’s law

Unsaturated soils: flow and consolidation

Unsaturated soils: retention curve(also called soil water characteristic curve, SWCC)

=r a wS f p p f s

Retention curve

Drying case

Wetting case

Unsaturated soils: flow and consolidation

UNSATURATED

SATURATED

SATURATED

Unsaturated soils: flow and consolidation

Unsaturated soils: retention curve

1. Retention curves exhibit hysteresis effects2. This value of negative water pressure is called the air entry value

for that soil3. Negative pore pressures can exist in saturated soils

(Brooks and Corey, 1964)

UNIFORM

WELL GRADED

Unsaturated soils: flow and consolidation

Unsaturated soils: retention curve

Unsaturated soils: flow and consolidation

Retention curve: analytical expressions the Van Genuchten expression frequently used

n

nn g

gg

paresidusatresidup gSSSS1

1)()(

min )( wap pps

286.2 m 24.2

027.0 0.11

na

residusat

gg

SS

Unsaturated soils: flow and consolidation

Unsaturated soils: Darcy’s law

dyk

dyhkq

w

wpyh

satrrel kSkk )(

Relative permeability

Fredlund & Rahardjo (1993)

Unsaturated soils: flow and consolidation

Relative permeability: analytical expressions the Van Genuchten expression

0.0286.2 m 24.2

027.0 0.11

l

na

residusat

ggg

SS

21

111)()(

n

n

n

nl

gg

gg

eg

errel SSSkresidusat

residure SS

SSS

Introduction: characteristic problems in unsaturated soils

Suction and suction-controlled laboratory tests

Stress variables

Mechanical behaviour of unsaturated soils Shear strength Volume change

A (basic) model for unsaturated soils

Flow and consolidation in unsaturated soils Continuity equation Retention curve Darcy’s law and relative permeability

Case histories

Unsaturated soils: outline

Paraná river

PB town

Tietê riverDam

Collapse of a colluvium formation induced by water table rise, Vilar et al.

1/5 – INTRODUCTION

Collapse of a colluvium formation induced by water table rise, Vilar et al.

1/5 – INTRODUCTION

Reservoir level

Collapse of a colluvium formation induced by water table rise, Vilar et al.

1/5 – INTRODUCTION

Edificaciones

monitoreadas

Pruebas de Carga

Edificación

Monitoreada (PB_5)

Collapse of a colluvium formation induced by water table rise, Vilar et al.

1/5 – INTRODUCTION

1/5 – INTRODUCTION

Collapse of a colluvium formation induced by water table rise, Vilar et al.

1/5 – INTRODUCTION

Collapse of a colluvium formation induced by water table rise, Vilar et al.

Collapse of a colluvium formation induced by water table rise, Vilar et al.

1/5 – INTRODUCTION

0

20

40

60

80

100

120

08/03/90 24/09/90 12/04/91 29/10/91 16/05/92 02/12/92 20/06/93

Date

Settl

emen

t (m

m)

314

316

318

320

322

324

326

328

330

Gro

undw

ater

leve

l (m

)

S-3 settlement gage S-5 settlement gage Groundwater level

PB-1

PB-3

0

10

20

30

40

50

60

7008/03/90 25/11/90 14/08/91 02/05/92 19/01/93 08/10/93

Date

Settl

emen

t (m

m)

314

316

318

320

322

324

326

328

330

Gro

undw

ater

leve

l (m

)

Collapse of a colluvium formation induced by water table rise, Vilar et al.

1/5 – INTRODUCTION

S-3 settlement gage S-5 settlement gage Groundwater level

S-7 settlement gage S-9 settlement gage Groundwater level

Collapse of a colluvium formation induced by water table rise, Vilar et al.

2/5 – FIELD CHARACTERIZATION

Collapse of a colluvium formation induced by water table rise, Vilar et al.

2/5 – FIELD CHARACTERIZATION

Collapse of a colluvium formation induced by water table rise, Vilar et al.

2/5 – FIELD CHARACTERIZATION

Collapse of a colluvium formation induced by water table rise, Vilar et al.

2/5 – FIELD CHARACTERIZATION

0

10

20

30

40

50

60

70

801/

1/20

05

1/2/

2005

1/3/

2005

1/4/

2005

1/5/

2005

1/6/

2005

1/7/

2005

1/8/

2005

1/9/

2005

1/10

/200

5

1/11

/200

5

1/12

/200

5

Tiempo [días]

Prec

ipita

ción

[mm

]

0

10

20

30

40

50

60

70

80

90

100

Succ

ión

[kPa

]

lluvia (2004) succión 1.2m (2004) succión 1.2m (2004) succión 0.9m (2004) succión 0.6m (2004)

Collapse of a colluvium formation induced by water table rise, Vilar et al.

3/5 – LABORATORY TESTS

Retention curve

Collapse of a colluvium formation induced by water table rise, Vilar et al.

3/5 – LABORATORY TESTS

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

1,00

0,1 1 10 100 1000 10000

Pg - Pl [kPa]

Sl

0

5

10

15

20

25

301 10 100 1000 10000

v - ua (kPa)

H /

H (%

)

flooding at 50 kPa flooding at 100 kPaflooding at 200 kPa flooding at 400 kPa

s = 0 kPa s = 25 kPa s = 50 kPas = 75 kPa s = 100 kPa s = 200 kPas = 400 kPa

0

5

10

15

20

25

301 10 100 1000 10000

v - ua (kPa)

H

/H (%

)Suction controlled oedometer tests

Collapse of a colluvium formation induced by water table rise, Vilar et al.

3/5 – LABORATORY TESTS

S = 60 kPa

S = 200 kPa

Max. in situ stress

Max. in situ stress

Application of the BBM model

050

100150200250300350400

0 50 100 150 200

p - pa (kPa)

Suct

ion

(kPa

)

LC curve Experimental data

Collapse of a colluvium formation induced by water table rise, Vilar et al.

3/5 – LABORATORY TESTS

Collapse of a colluvium formation induced by water table rise, Vilar et al.

4/5 – MODELLING

Colluvium

Gravel

Residual soil

F

qw = 0qw = 0

Pw (t)

0

20

40

60

80

100

120

08/03/90 24/09/90 12/04/91 29/10/91 16/05/92 02/12/92 20/06/93

Date

Settl

emen

t (m

m)

314

316

318

320

322

324

326

328

330

Gro

undw

ater

leve

l (m

)

S-3 settlement gage S-5 settlement gageModel Groundwater level

0.6 m

1.17 m76 kPaColluvium

Residual soil

Gravel

Colluvium

Residual soil

Gravel

Colluvium

Residual soil

Gravel

Site PB-1

Collapse of a colluvium formation induced by water table rise, Vilar et al.

4/5 – MODELLING

0.6 m

1.17 m76 kPaColluvium

Residual soil

Gravel

Colluvium

Residual soil

Gravel

Colluvium

Residual soil

Gravel

Site PB-1

Collapse of a colluvium formation induced by water table rise, Vilar et al.

4/5 – MODELLING

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15-100 -75 -50 -25 0 25 50 75 100

Pl [kPa]

Pl (30/07/91) Pl (11/03/92)Pl (14/07/92) Pl (13/09/93)

COLLAPSIBLE SOIL

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15-10 10 30 50 70 90 110

u [mm]

z [m

]

u (30/07/91) u (11/03/92)u (14/07/92) u (13/09/93)

COLLAPSIBLE SOIL

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15-10 10 30 50 70 90

du/dz [mm/m]

z [m

]

u (30/07/91) u (11/03/92)u (14/07/92) u (13/09/93)

COLLAPSIBLE SOIL

Colluvium

Colluvium Colluvium

0.9 m

0.7 m21 kPa

0

10

20

30

40

50

60

7008/03/90 25/11/90 14/08/91 02/05/92 19/01/93 08/10/93

Date

Settl

emen

t (m

m)

314

316

318

320

322

324

326

328

330

Gro

undw

ater

leve

l (m

)

S-7 settlement gage S-9 settlement gageModel Groundwater level

Colluvium

Residual soil

Gravel

Colluvium

Residual soil

Gravel

Colluvium

Residual soil

Gravel

Site PB-3

Collapse of a colluvium formation induced by water table rise, Vilar et al.

4/5 – MODELLING

0.9 m

0.7 m21 kPaColluvium

Residual soil

Gravel

Colluvium

Residual soil

Gravel

Colluvium

Residual soil

Gravel

Site PB-3

Collapse of a colluvium formation induced by water table rise, Vilar et al.

4/5 – MODELLING

0123456789

101112131415161718

-10 0 10 20 30 40 50

u [mm]

z [m

]

u (03/06/92) u (16/03/93) u (14/09/93)

COLLAPSIBLE SOIL

0123456789101112131415161718

-100 -75 -50 -25 0 25 50 75 100

Pl [kPa]

Pl (03/06/92) Pl (16/03/93) Pl (14/09/93)

COLLAPSIBLE SOIL

0123456789

101112131415161718

-10 0 10 20 30 40 50

du/dz [mm/m]

z [m

]u (03/06/92) u (16/03/93) u (14/09/93)

COLLAPSIBLE SOILColluvium Colluvium Colluvium

-10

10

30

50

70

90

110

130

15008/03/90 25/11/90 14/08/91 02/05/92 19/01/93 08/10/93

Time [date]

Settl

emen

t [m

m]

314

316

318

320

322

324

326

328

330

Gro

undw

ater

tabl

e [m

]

0 kPa 25 kPa 50 kPa load in situ: 76 kPa 100 kPa 125 kPa 150 kPa Groundwater table

Effect of load

Collapse of a colluvium formation induced by water table rise, Vilar et al.

4/5 – MODELLING

Effect of load

Collapse of a colluvium formation induced by water table rise, Vilar et al.

4/5 – MODELLING

-10

0

10

20

30

40

50

60

7008/03/90 25/11/90 14/08/91 02/05/92 19/01/93 08/10/93

Time [date]

Settl

emen

t [m

m]

314

316

318

320

322

324

326

328

330

Gro

undw

ater

tabl

e [m

]

load in situ: 21 kPa 0 kPa 50 kPa 75 kPa 100 kPa 125 kPa Groundwater table

Effect of the thickness of the collapsible layer

Collapse of a colluvium formation induced by water table rise, Vilar et al.

4/5 – MODELLING

-10

10

30

50

70

90

110

13008/03/90 25/11/90 14/08/91 02/05/92 19/01/93 08/10/93

Time [date]

Settl

emen

t [m

m]

layer 3m layer 4m layer 5m layer 6m layer 7m layer 8m

Effect of the thickness of the collapsible layer

Collapse of a colluvium formation induced by water table rise, Vilar et al.

4/5 – MODELLING

-10

0

10

20

30

40

50

60

7008/03/90 25/11/90 14/08/91 02/05/92 19/01/93 08/10/93

Time [date]

Settl

emen

t [m

m]

layer 6m layer 7m layer 8m layer 9m layer 10m

Collapse of a colluvium formation induced by water table rise, Vilar et al.

5/5 – CONCLUSIONS

Case history

Unique set of data: collapse controlled by phreatic level (monitored with time) suction measured in the zone influenced by atmospheric conditions monitoring of vertical displacements at the ground level complete field survey including pressure plate tests complete series of laboratory tests

Numerical modelling

very good reproduction of field collapse measurements using BBM model

evidence a “deep-seated” collapse with low influence of the load and high influence of the thickness of the collapsible layer

CASE DESCRIPTION

020406080

100120140

1-Sep

11-Sep

21-Sep

1-Oct

11-Oct

21-Oct

31-Oct

Inte

nsid

ad d

e llu

via

(mm

/día

)

Septiembre Octubre

Rainfall distribution

Accumulated rainfall in 38 days: 374 l/m2

Maximum daily rainfall: 123 l/m2

BRIDGE ABUTMENT

Erosion of slopes

Gaps opened between transition slab and fill

Collapsed fill around a bridge abutment

Collapsed fill around a bridge abutment

Soil: Low plasticity sandy clay (Granitic residual soil)

Position of soil before heavy rainfalls

Collapsed fill around a bridge abutment

Combined effect of collapse settlement and slope instability on bridge abutments

transiciónLosa de

RellenoA'

A

b)

Puente

Relleno

Losa detransición

Hueco

A-A’ Cross Section

Lateral Abutment Wing

EmbankmentVoid(20 cm)

Transition slab

Transition slab

Bridge beam

Identify the causes for the damage suffered by the recently built road.

Determine if future rainfalls of similar or higher intensity would induce additional damage.

Questions asked by the Road Authority:

ROAD EMBANKMENT (Lérida-Gerona, Cataluña)

SOIL CHARACTERISTICS:

Residual soil from granite wL = 30-40%IP = 10-16%

Normal Proctor (original design) d opt = 1.75 Mg/m3

wopt = 14.7%

Field control (nuclear probe) d opt = 1.85 Mg/m3

(1.76-1.99 Mg/m3)wopt = 9.4%(6.5-12.4%)

Samples recovered in borings after the heavy rainsd opt = 1.76 Mg/m3

(1.67-1.95 g/cm3)wopt = 13.2%(8-17.8%)

Soil Properties

< 74 m 45%

0

10

20

30

10 20 30 40 50

Liquid Limit

Plas

ticity

Inde

x

Tested specimensMean value

CL

MLCL-ML

1.5

1.7

1.9

2.1

5 10 15 20 25Water Content (%)

Dry

Den

sity

(g/c

m3 )

Construction averageConstruction pointsOptimum Normal Proctor

Sr=0.6 Sr=0.8

Sr= 1.0

Residual granitic soil

Average; samples

from borings

Range; samples

from boringsField

control; nuclear probe

- All specimens satisfied d > 95% d OPT PN . However embakments collapsed (vertical andhorizontal displacements)- Displacements in excess of 30 cm were measured in embankments 6-7 m high

Saturationline

Effect on Compaction Conditions on Collapse

Soil: Low Plasticity red clay UPC Campus, Barcelona (Gens et al, 1995)

1.5

1.6

1.7

1.8

1.9

5 10 15 20 25Water Content(%)

Dry

Den

sity

(g/c

m3 ) P4 (95)

P1(96)

P3(62)

P2 (75)

Sr=100NormalProctor

Static Compaction(v=0.6 MPa)

0.01

0.1

1

10

0.0 0.4 0.8 1.2 1.6Vertical Stress (MPa)

Col

laps

e D

efor

mat

ion

(%)

P1P4

P3

P2

Wetting under load tests

Degree of saturation after the rainfall period 0.01 0.1 1Effective vertical stress (v-uw) MPa

0.40

0.50

0.60

0.70

,e

wf=19.8%

wn=15.7%

Saturation

n= 1.89 g/cm3

eo=0.681 ; Sro=63.2%

.

Voi

d ra

tio

0

2

4

640 50 60 70 80 90 100

Degree of saturation (%)

Dep

th (m

)

Shoulders Road axis

Mean initialvalue

diffu

sed

air f

lush

ing

syst

eman

d vo

lum

e in

dica

tor

water volumechange indicator

waterpressure

vapor trap

diaphragm pressure

1

2

3

ram pump

air pressure and vaporpressure control

1: soil sample2: HAEV ceramic disc3: coarse porous stone

Suction controlled oedometer

Wetting under load tests on recovered specimensRemaining collapse potential

-2

0

2

4

0 0.05 0.1 0.15Vertical Stress (MPa)

Col

laps

eD

efor

mat

ion

(%)

= 1.7 g/cm =1.9 g/cm 3d3

d

Water retention curve (under wetting) of a recovered specimen of the compacted fill

Slope Stability: Suction Effects on Soil Strength

f = c’+ (ua-uw) tan b + (-ua) tan ’= cap+ (-ua) tan ’

0.00 0.05 0.10 0.15 0.20 0.25Net Vertical Stress, ( v-ua) MPa

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Tens

ión

deco

r te,

(MPa

)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.00 0.10 0.20 0.30 0.40 0.50Suction, (ua-uw) MPa

' = 29.0º(ua-uw) = 0.40 MPa

wn=15.7%

(ua-uw)=0 (wf21.6%)

'=21.0º

(ua-uw)=0.05 MPa

wf 21.6%

b'(Sr>0.95)

b=14.1º

(v-ua):0.20 MPa0.07 MPa

wn=15.7%

.

.

Shea

r stre

ss

Girona road embankment

Sketch of the collapsed embankment. The coupled flow-deformation problem will be solved in a central column

nat (1 ) s r wn nS

00

1 1 2 (1 ) d3

z

s r wp K n nS z z

Srmax = 1, Srmin = 0, = 0.09 and P0 = 0.05 MPa1

0

0

0.133 0.054log log 0.8 0.07c

v v

e eC

= Cc/ln10 = 0.024

The rain is simulated by imposing suction zero in the top of the embankment. At the base, suction is imposed also zero because it is in contact with a saturated natural soil (phreatic level)

The Problem

Weight

Stress (oedometric conditions)

Water Retention Curve

Sr = 0.6 (s = 8 MPa)

Compressibility (plastic)

Initial conditions

n0 = 0.35

Boundary conditions

Girona road embankment

0 0

vol vol vol 00

0 vol vol 0

d 1ln1 1

1 (1 )exp

t t

t t

n nd t tn n

n n t t

Numerical integration by backward finite differences2

2

1 1 0vol volr rr r

w w r

S Ss p k s s k sn S Ss s t p t z S s zz

Notation

2

2

1 1 0,w w

s p k s s sf g ht t z zz

, , .i i

i

z t t z t

z

y yyt t

1 1, , ,i iz t z t

t

y yyz z

1 1

2, , ,

2 2

2.i i iz t z t z t

t

y y yyz z

, ,i iz t z t tp ppt t

vol vol r

r

S kp s s S

Functions of s(t) and p(t)

1 1 1 1

2, , , , , , , , , ,

, , , ,2,

2 1 .i i i i i i i i i i

i i i i

i

z t z t z t z t z t z t t z t z t z t z tz t t z t z t z t

z t w w

k s s s p p s s s sts g h hf t z zz

Soved by Fortran Program (Excel, Matlab…)

Results

Calculated evolution of crest settlement of an 8 m high embankment under a

top and bottom infiltration

Calculated suction isochrones

First wetting

Calculated suction evolution of two points within the

embankment at different depths.

Calculated evolution of collapse strains for two points within the

embankment

First wetting

Calculated evolution of crest settlement of an 8 m high embankment under a top and bottom infiltration, after an initial stage of wetting

lasting three days.

Second wetting

Calculated suction evolution of two points within the embankment after an initial stage of wetting lasting three

days

Second wetting

Numerical Simulation of Embankment Behavior

0 2 4 6 8 10 12 14x (m)

0

2

4

6

8

y (m

)

LLUVIA

P

.

uw=0

Water Flow

Kw(Sr)=Kws((Sr-0.25)/0.75)3

Sr (ua-uw)

Deformation

v= f ((ua-uw),(-ua))

0.00

0.01

0.10

1.00

Succ

i ón

mat

r ici a

l ,(u

a-uw

)MP a

(v-ua)= 0.07 MPa

76 80 84 88 92 96 100Degree of saturation Sr (%)

.

.

.

Rainfall

Modelling Water Infiltration

Kws= 5· 10-9 m/s

0 5 10 15x (m)

0

2

4

6

y (m

)

0.860.9

2

0.96

0.84

Sr (t=92 days)

Depth=1m

P

P

-0.6

-0.4

-0.2

0.0

0.1 1.0 10.0 100.0Time (days)

Wat

er P

ress

ure

(MPa

)

Numerical Simulation of Embankment Behaviour

Residual Settlement

(lab) Kws= 5· 10-9 m/sH= 7 m

t1= 21 days

1E-5 1E-4 1E-3 1E-2 0.1T · K / H

0.0

0.2

0.4

0.6

0.8

1.0

Asien

t o/ a

sient

ofin

al

ws

1

2

3

t

t

t

.

0 2 4 6 8 10 12 14 16x (m)

0

2

4

6

8

y(m

)

ttt1

32

Displacements(10 cm)

.

.

Lessons learned

Compaction on the dry sideSoils compacted dry of optimum may experience significant compressive volumetric strains when wetted under load. An additional condition required to experience collapse is to compact the soil to a relatively low density.

Suction and stress variablesBecause of the difficulty in finding a single effective stress, unsaturated soil behaviour is defined in terms of two independent stress variables which combine total stress and suction.

The nature of collapseCollapse strains are essentially volumetric and irreversible. In the limit, if collapse is induced by a full wetting, the soil will not experience further collapse deformations if it is later dried and wetted again.

Capillary riseCapillary rise from shallow water tables may also lead to wetting. This is an additional reason for the accelerated wetting of embankments because under these circumstances, they are subjected to surface as well as to base infiltration.

Coupled flow-deformationColapse modelling involves the hidro-mechanical coupling. Suction provides the link between flow and mechanical behaviour because suction gradients control flow and suction changes control volumetric deformations.

Predicting the future behaviour of embankmentsThe coupled model developed is useful to investigate the future behaviour of embankments under weather action.

Lessons learned