NZ course unsaturated soils · BBM: a conceptual framework Flow and consolidation in unsaturated...
Transcript of NZ course unsaturated soils · BBM: a conceptual framework Flow and consolidation in unsaturated...
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