[Terzaghi] Unsaturated Soil Mechanics (2007)

78
Unsaturated Soil Mechanics in Engineering Professor Delwyn G. Fredlund University of Saskatchewan Saskatoon, SK, Canada GeoFrontiers 2005, Austin, Texas Geo-Institute, ASCE January 23-26, 2005

Transcript of [Terzaghi] Unsaturated Soil Mechanics (2007)

  • Unsaturated Soil Mechanics in Engineering

    Professor Delwyn G. FredlundUniversity of Saskatchewan

    Saskatoon, SK, Canada

    GeoFrontiers 2005, Austin, TexasGeo-Institute, ASCE

    January 23-26, 2005

  • John Wiley & Sons, 1943

    Karl Terzaghi elevated Soil Mechanics from an Art to a Science

    Effective Stress, ( uw), for describing mechanical behavior of saturated soils

    Chapter 14 Capillary Forces(Also Chapter 15)

    Biot (1941) addressed consolidation of unsaturated soils

    Concepts from Agriculture (Baver, 1940)

    Chiu Chung Fai1.Terzaghi 2.3.""4. Biot (1941) 5.(Baver, 1940)

  • Unsaturated Soil Mechanics Problems Described in Theoretical Soil

    Mechanics by K. Terzaghi (1943)

    Chiu Chung FaiTerzaghi

  • Unsaturated Soil Mechanics in Engineering

    Introduction Challenges to Implementation Description of the Stress State Fundamental Constitutive Relations Role of the Soil-Water Characteristic Curve Use of SWCC in the Constitutive Relations Solution of a Series of PDEs Modeling Unsaturated Soils Problems

    Chiu Chung Fai1.2.3.4.5.6.7.8.

  • Objectives

    To illustrate the progression from theories and formulations to practical engineering protocols for solving a variety of unsaturated soil mechanics problems (e.g., seepage, shear strength and volume change), through use of direct and indirect characterization of unsaturated soil property functions

    To describe the Challenges Faced and the Solutions Generated in moving towards the Implementation of Unsaturated Soil Mechanics

    Chiu Chung Fai1.2.

  • Gradual Emergence of Unsaturated Soil Mechanics

    1950s: Independent measurement of pore-air and pore-water pressure through use of high air entry ceramic disks

    1960s: Laboratory testing of unsaturated soils 1970s: Constitutive relations proposed and tested

    for uniqueness for unsaturated soils 1980s: Solving formulations for classic Boundary

    Value Problems 1990s: Establishing procedures for determination of

    unsaturated soil property functions 2000+: Implementation into routine engineering

    practice

    Chiu Chung Fai1950s 1960s 1970s 1980s 1990s 2000+

  • Challenges to the Implementation of Unsaturated Soil Mechanics

    Challenge #1: To discover appropriate Stress State

    Variables for describing the physical behavior of unsaturated soils

    Solution #1:

    ?

    Chiu Chung Fai

  • Challenges to the Implementation of Unsaturated Soil Mechanics

    Challenge #2: To develop devices that could measure a wide range of negative pore-water pressures (i.e., high matric suctions)

    Solution #2:

    ?

    Chiu Chung Fai

  • Challenges to the Implementation of Unsaturated Soil Mechanics

    Challenge #3: To develop (and test for uniqueness)

    constitutive relations suitable for describing unsaturated soil behavior

    Solution #3:

    ?

    Chiu Chung Fai

  • Challenges to the Implementation of Unsaturated Soil Mechanics

    Challenge #4: To overcome the excessive costs

    associated with the determination (i.e., measurement) of unsaturated soil properties (i.e., nonlinear functions)

    Solution #4: ?

    Chiu Chung Fai

  • Challenges to the Implementation of Unsaturated Soil Mechanics

    Challenge #5: To solve nonlinear partial differential

    equations for unsaturated soils without having convergence difficulties during the iterative solution process

    Solution #5:

    ?

    Chiu Chung Fai

  • Challenges to the Implementation of Unsaturated Soil Mechanics

    Challenge #6: To promote and teach unsaturated soil

    mechanics at universities and in engineering practice

    Solution #6:

    ?

    Chiu Chung Fai

  • Regional distribution of unsaturated soils

    Local vertical zones of

    unsaturated soils

    GROUNDWATER TABLE- Water filling the voids- Air in a dissolved state

    S

    A

    T

    U

    R

    A

    T

    E

    D

    S

    O

    I

    L

  • Zones of Unsaturation Defined by a Soil-Water Characteristic Curve, SWCC

    0

    5

    10

    15

    20

    25

    30

    35

    0.1 1.0 10. 100. 1000. 10,000 100,000 1000,000

    G

    r

    a

    v

    i

    m

    e

    t

    r

    i

    c

    w

    a

    t

    e

    r

    c

    o

    n

    t

    e

    n

    t

    ,

    w

    (

    %

    )

    Soil suction (kPa)

    Air entry value

    Boundary effect zone

    Transition zone

    Residual zone

    Residualcondition

    Inflection point

    Chiu Chung Fai(SWCC)

  • Unsaturated Soil REV as a Four Phase System

    -Two Phases that deform and come to rest under a stress gradient (SOLIDS)

    -Soil structure

    -Contractile skin

    -Two phases that continuously flowunder a stress gradient (FLUIDS)

    -Water

    -Air

    Soil particlesAir

    Contractile skin

    Water

    REV = Representative Elemental Volume

    Chiu Chung Fai()()

  • Structure and Stresses in the Contractile Skin

    Hyperbolic Tangent Function

    Thickness:1.5 to 2 water molecules or about 5A (Israelachvili, 1991; Townsend and Rice, 1991)

    thickness of thecontractile skin

    Liquid water density

    Water vapor density

    Air Watert90/10

    PBN

    Surface tension = 75 mN/m; Equivalent stress = 140,000 kPa

    Water-molecule distribution across the air-water interface(modified from Kyklema, 2000)

    Chiu Chung Fai-(Kykelma, 2000)

  • Challenges to the Implementation of Unsaturated Soil Mechanics

    Challenge #1: To discover appropriate Stress State

    Variables for describing the physical behavior of unsaturated soils

    Solution #1: Designation of independent Stress State Variables based on multiphase continuum mechanics principles

    (x - ua)

    (z - ua)

    (y - ua)(ua - uw)

    (ua - uw)

    zxzy

    xz

    xy

    yzyx(ua - uw)

    Chiu Chung Fai

  • Definition of stress state at a point in an unsaturated soil

    (z - ua)

    (y - ua)(ua - uw)

    (ua - uw)

    zxzy

    xz

    xy

    yzyx(ua - uw)

    (x - ua)

    Defines the stress state at a point in a continuum

    State variables are independent of soil properties

    Derivation of the Stress State is based on the superposition of equilibrium stress fields for a multiphase continuum

  • State Variable Stage (Unsaturated Soils)

    Net Total Stress Tensor

    ( ) ( ) ( )

    x a yx zx

    xy y a zy

    xz yz z a

    uu

    u

    ( )( ) ( )

    u uu u

    u u

    a w

    a w

    a w

    0 00 00 0

    Matric Suction Stress Tensor

    X - direction

    Y - direction

    Z - direction

    Stress Tensors form the basis for a Sciencebecause we live in a 3-D Cartesian coordinate world

    Chiu Chung Fai

  • Variations in Stress State Description

    = ( ua) + (ua uw) = effective stress = parameter related to saturation

    *ij = ij [S uw + (1 S) ua ] ijij = total stress tensor, ij = Kroneker delta or substitution tensor,

    *ij = Bishops soil skeleton stress (Jommi2000)

    S = degree of saturation

    Above proposed equations are constitutive relations

    Chiu Chung Fai

  • Challenges to the Implementation of Unsaturated Soil Mechanics

    Challenge #2:- To develop devices that can measure a wide range of negative pore-water pressures (i.e., high matric suctions)

    Solution #2:- New instrumentation such as the high suction tensiometersand indirect thermal conductivity suction sensors provide viable techniques for the laboratory and the field

    Chiu Chung Fai

  • Monitoring for Verification Purposes

    Measurements of movement: same as for saturated soils

    Measurement of water content: TDR Technology Measurement of matric suction:

    Direct measurement techniques Low range tensiometers (< 90 kPa) High range direct tensiometers (< 1200 kPa)

    Presently primarily for laboratory use Indirect measurement techniques

    Thermal conductivity sensors

    Chiu Chung Fai1.2.(TDR)3. - (< 90 kPa) (< 1200 kPa) -

  • Monitoring of Water Content

    Measures the dielectric constant for the soil around the rods. Dielectric constant varies with the water content of the soil

    TDR ThetaProbe, ML2x manufactured by AT Delta Devices, U.K.

    Chiu Chung FaiTDR

  • Monitoring of Matric Suction

    Measures the thermal conductivity of a standard ceramic that varies in water content with the applied matric suction

    Chiu Chung Fai

  • Matric Suction Versus Time - 1.0 m to 1.3 m Depth Range

    0.0

    25.0

    50.0

    75.0

    100.0

    125.0

    150.0

    175.0

    200.0

    15-Sep-00 5-Oct-00 25-Oct-00 14-Nov-00 4-Dec-00 24-Dec-00

    Time (Days)

    M

    a

    t

    r

    i

    c

    S

    u

    c

    t

    i

    o

    n

    (

    k

    P

    a

    )

    T 1-3

    T 2-8

    T 3-11

    T 4-14

    T 5-16

    T 4-14

    T 1-3

    T 2-8

    T 3-11

    T 5-16

    In Situ Matric Suction measurements using Thermal Conductivity sensors at 1.0 to 1.3 m below roadway

    Equalization

    Frost

    Time (Days)

    M

    a

    t

    r

    i

    c

    s

    u

    c

    t

    i

    o

    n

    (

    k

    P

    a

    )

    Chiu Chung Fai1 - 1.3 m

  • Silicone rubber grommet

    Rubber membrane

    Latex rubber, to seal the rubbermembrane and grommet

    Mini suction probe

    O - ring5 bar high air-entry ceramic disk

    Direct, high suction sensor used to measure suctions greater than one atmosphere on the side of a triaxial specimen (Meilani, 2004)

    Pore air pressure control

    O - ringCoarse corundum disk

    Filter paper

    Specimen

    Top cap

    Water in the compartment is pre-pressurized to destroy cavitation nuclei

    Chiu Chung Fai100 kPa(Meilani, 2004)

  • Challenges to the Implementation of Unsaturated Soil Mechanics

    Challenge #3: To develop (and test for uniqueness)

    constitutive relations suitable for describing unsaturated soil behavior

    Solution #3:

    Matric suction(ua - uw)

    Voidratio

    e

    Net nor

    mal stre

    ss

    ( - ua)

    amat- Constitutive relations for

    saturated soils needed to be extended to embrace the effect of changing degrees of saturation

    Chiu Chung Fai

  • Fundamental Constitutive Relations for Unsaturated Soils

    Constitutive Behaviors in Classic Soil Mechanics: Seepage Shear strength Volume-mass changes: Void ratio, water content

    changes

    Other topics in soil mechanics: Heat flow (Freeze-Thaw and Evaporation) Air flow Contaminant transport

    Each constitutive relationship requires a nonlinear soil property function; therefore, Unsaturated Soil Mechanics might be referred to as NONLINEAR SOIL MECHANICS!

    Chiu Chung Fai1.2.3.-()4. (-)5.6.

  • Water Seepage Constitutive Relations

    Yg

    uhw

    w += Driving potential for water flow is hydraulic head, h

    x wxdhv kdx

    =

    dydhkv wyy =

    z wzdhv kdz

    =

    Darcys law (1856) for flow in the x-, y-, and z-direction

    Coefficient of permeability, kw is a function of matric suction; therefore, the flow law is nonlinear and subject to hysteresis

    Chiu Chung Fai1.2.Darcy3.(kw)4.5.

  • Shape of the water permeability function for glass beads tested by Mualem (1976 )

    1.E-06

    1.E-05

    1.E-04

    1.E-03

    1.E-02

    1.E-01

    0.1 1 10 Soil suction (kPa)

    Drying

    Wetting

    C

    o

    e

    f

    f

    i

    c

    i

    e

    n

    t

    o

    f

    p

    e

    r

    m

    e

    a

    b

    i

    l

    i

    t

    y

    (

    m

    /

    s

    )

    Wetting

    Drying

    DryingWetting

    Soil suction (kPa)

    Chiu Chung Fai(kw)Mualem (1976)

  • The SWCC for the glass beads showing hysteresis during drying and wetting

    0

    20

    40

    60

    80

    100

    0.1 1 10 Soil suction (kPa)

    D

    e

    g

    r

    e

    e

    o

    f

    s

    a

    t

    u

    r

    a

    t

    i

    o

    n

    ,

    %

    DryingWetting

    Wetting

    Drying

    Soil suction (kPa)Hysteresis in the SWCC produces hysteresis in the Permeability function

    Chiu Chung FaiSWCC

  • Water Storage in an Unsaturated Soil

    0.1 1.0 10 100 1000 10000 100000 1E+6Soil suction, kPa

    W

    a

    t

    e

    r

    c

    o

    n

    t

    e

    n

    t

    ,

    %

    0

    10

    20

    30

    40Soil-Water Characteristic Curve, SWCC

    Also has a hysteretic effect

    Soil suction, kPa

    W

    a

    t

    e

    r

    s

    t

    o

    r

    a

    g

    e

    m

    o

    d

    u

    l

    u

    s

    ,

    k

    P

    a

    -

    1

    0

    2

    4

    8

    0.1 1.0 10 100 1000 10000 100000 1E+6

    Water storage function is the slope of the SWCC; Required for transient seepage analyses

    Chiu Chung Fai1.SWCC2.

  • Air Flow Constitutive Relations

    Driving potential for air flow is Pore-air pressure, uadx

    dukv aaxax =

    dydu

    kv aayay =

    dzdukv aazaz =

    Ficks law for flow in the x-, y-, and z-direction

    Coefficient of permeability, ka is a function of matric suction; therefore, the flow law is nonlinear and subject to hysteresis

    Observation: Soil properties for unsaturated soils become nonlinear functions and are hysteretic in character

    Chiu Chung Fai1.2.Fick3.(ka)4.5.

  • Shear Strength Constitutive Relations

    ' '( ) tan ( ) tan bn a a wc u u u = + + Linear form of the extended Mohr-Coulomb shear strength equation

    Fredlund, Morgenstern and Widger, 1978

    ' '1( ) tan ( )n a a wc u u u f = + +

    f1 = function showing the rate of increase in shear strength with matric suction

    Chiu Chung FaiMohr-Coulomb

  • Extended Mohr-Coulomb failure surface (Fredlund, Morgenstern and Widger, 1978)

    (ua-uw)

    S

    h

    e

    a

    r

    s

    t

    r

    e

    n

    g

    t

    h

    ,

    Net normal stress, ( - ua)

    Shear strength versus suction is nonlinear and affected by hysteresis

    Air entry value

    c

    Chiu Chung Fai Mohr-Coulomb (Fredlund, Morgenstern & Widger, 1978)1.2.

  • Multistage direct shear test results

    on compacted glacial till (Gan et

    al., 1988)

    Soil-Water Characteristic Curve

    for glacial till

    0102030405060708090

    100

    1 10 100 1000 10000 100000 1000000Suction, (kPa)

    D

    e

    g

    r

    e

    e

    o

    f

    S

    a

    t

    u

    r

    a

    t

    i

    o

    n

    ,

    S

    (

    %

    )

    0 kPa, e = 0.517

    25 kPa, e =0.514

    OPTIMUM INITIAL WATER CONTENT

    SPECIMEN

    AEV = 60 kPa

    AEV = 60 kPa

    S

    h

    e

    a

    r

    s

    t

    r

    e

    n

    g

    t

    h

    ,

    ( kP

    a

    )

    200

    250

    150

    100

    50

    00 100 200 300 400 500

    c = 10 kPa(f - ua)f tan = 34.6 kPa

    (f - ua)f = 72.6 kPa = 25.5

    Matric suction, (ua-uw) (kPa)

    Chiu Chung Fai1.SWCC2.(Gan et al., 1988)

  • Reference compression curves for a Saturated Soil

    v

    =

    (

    1

    +

    e

    )

    e

    Log()Ln(p)p0

    Cs

    0Cc

    Effective mean stress Effective vertical stress

    S

    p

    e

    c

    i

    f

    i

    c

    v

    o

    l

    u

    m

    e

    V

    o

    i

    d

    r

    a

    t

    i

    o

    Preconsolidationpressure

    Yield stress

    ss CC 434.0

    )10ln(=

    cc CC 434.0

    )10ln(=

    Effective mean stress Effective vertical stress

    Elasto-plastic form

    Classic soil mechanics form

    Chiu Chung Fai

  • 10000

    1000100

    101 0.1

    0.01

    Log net me

    an stress (k

    Pa)1e+061

    0000010000

    1000100

    1010.

    10.01Log soil suction (kPa)

    0

    0

    0.5

    0.5

    1

    1

    1.5

    1.5

    2

    2

    2.5

    2.5

    V

    o

    i

    d

    r

    a

    t

    i

    o

    V

    o

    i

    d

    r

    a

    t

    i

    o

    VolumeMass Constitutive Surfaces for Regina Clay Preconsolidated at 200 kPa (Pham, 2004)

    Void ratio, e

    Residual value

    YieldYield

    Soil suctionNet tot

    al stress

  • VolumeMass Constitutive Surfaces for Regina Clay Preconsolidated at 200 kPa (Pham, 2004)

    Residual value

    10000

    1000100

    101 0.1

    0.01

    Log net mean

    stress (kPa)

    1e+06100000

    100001000

    10010

    10.10.01Log soil suction (kPa)

    0

    0

    0.1

    0.1

    0.2

    0.2

    0.3

    0.3

    0.4

    0.4

    0.5

    0.5

    0.6

    0.6

    0.7

    0.7

    0.8

    0.8

    G

    r

    a

    v

    i

    m

    e

    t

    r

    i

    c

    w

    a

    t

    e

    r

    c

    o

    n

    t

    e

    n

    t

    G

    r

    a

    v

    i

    m

    e

    t

    r

    i

    c

    w

    a

    t

    e

    r

    c

    o

    n

    t

    e

    n

    t

    Residual value

    Air entry value

    YieldYield

    Water content, w

    Soil suction Net total stres

    s

    SWCC

  • 10000

    1000100

    101 0.1

    0.01

    Log net me

    an stress (k

    Pa)1e+061

    0000010000

    1000100

    1010.

    10.01Log soil suction (kPa)

    0

    0

    0.25

    0.25

    0.5

    0.5

    0.75

    0.75

    1

    1

    1.25

    1.25

    D

    e

    g

    r

    e

    e

    o

    f

    s

    a

    t

    u

    r

    a

    t

    i

    o

    n

    (

    S

    )

    D

    e

    g

    r

    e

    e

    o

    f

    s

    a

    t

    u

    r

    a

    t

    i

    o

    n

    (

    S

    )

    Air entry value

    Residual value

    VolumeMass Constitutive Surfaces for Regina Clay Preconsolidated at 200 kPa (Pham, 2004)

    Degree of saturation, S

    Soil suction Net total stres

    s

  • VolumeMass Constitutive Surfaces for

    Beaver Creek Sand (Pham, 2004)

    10000

    1000100

    101 0.1

    0.01

    Log net mean

    stress (kPa)1e+061

    0000010000

    1000100

    1010.

    10.01Log soil suction (kPa)

    0.3

    0.3

    0.34625

    0.34625

    0.3925

    0.3925

    0.43875

    0.43875

    0.485

    0.485

    0.53125

    0.53125

    0.5775

    0.5775

    0.62375

    0.62375

    0.67

    0.67

    V

    o

    i

    d

    r

    a

    t

    i

    o

    (

    e

    )

    V

    o

    i

    d

    r

    a

    t

    i

    o

    (

    e

    )

    10000

    1000

    10010

    1 0.10.01

    Log net me

    an stress

    (kPa)

    1e+061000

    0010000100

    010010

    10.10.0

    1Log soil suction (kPa)

    0

    0

    0.25

    0.25

    0.5

    0.5

    0.75

    0.75

    1

    1

    1.25

    1.25

    D

    e

    g

    r

    e

    e

    o

    f

    s

    a

    t

    u

    r

    a

    t

    i

    o

    n

    D

    e

    g

    r

    e

    e

    o

    f

    s

    a

    t

    u

    r

    a

    t

    i

    o

    n

    10000

    1000100

    101 0.1

    0.01

    Log net me

    an stress (

    kPa)

    1e+061000

    0010000100

    010010

    10.10.01Log soil suction (kPa)

    0

    0

    0.05

    0.05

    0.1

    0.1

    0.15

    0.15

    0.2

    0.2

    0.25

    0.25

    0.3

    0.3

    G

    r

    a

    v

    i

    m

    e

    t

    r

    i

    c

    w

    a

    t

    e

    r

    c

    o

    n

    t

    e

    n

    t

    G

    r

    a

    v

    i

    m

    e

    t

    r

    i

    c

    w

    a

    t

    e

    r

    c

    o

    n

    t

    e

    n

    t

    Void ratio, e

    Water content, w

    Degree of saturation, S

    SWCC

    AEV

    Basic volume-mass equation S e = w Gs

    Chiu Chung FaiBeaver Creek (Pham, 2004)

  • 10000

    1000100

    101 0.1

    0.01

    Log net me

    an stress (

    kPa)

    1e+061000

    001000010

    0010010

    10.10.0

    1Log soil suction (kPa)

    0

    0

    0.05

    0.05

    0.1

    0.1

    0.15

    0.15

    0.2

    0.2

    0.25

    0.25

    0.3

    0.3

    G

    r

    a

    v

    i

    m

    e

    t

    r

    i

    c

    w

    a

    t

    e

    r

    c

    o

    n

    t

    e

    n

    t

    G

    r

    a

    v

    i

    m

    e

    t

    r

    i

    c

    w

    a

    t

    e

    r

    c

    o

    n

    t

    e

    n

    t

    Residual value

    Air entry value

    VolumeMass Constitutive Surfaces for Beaver Creek Sand (Pham, 2004)

    Water content, w

    Soil suctionNet tot

    al stress

    SWCC

  • Challenges to the Implementation of Unsaturated Soil Mechanics

    Challenge #4: To overcome the excessive costs associated with the

    determination (i.e., measurement) of unsaturated soil properties (i.e., nonlinear functions)

    Solution #4:

    0.0

    10

    20

    30

    40

    1E-1 1E+0 1E+1 1E+2 1E+3 1E+4Suction (kPa)

    Predicted from grain-sizeExperimental

    W

    a

    t

    e

    r

    c

    o

    n

    t

    e

    n

    t

    1E+5 1E+6

    - Indirect, estimation procedures have been developed to obtain unsaturated soil property functions based on Soil-Water Characteristic Curves

    Chiu Chung FaiSWCC

  • Role and Measurement of the Soil-Water Characteristic Curve, SWCC

    -Soil-Water Characteristic Curves, SWCC define the relationship between the amount of water in a soil and soil suction (i.e., matric suction and total suction)

    - SWCC has been successfully used to estimate all unsaturated soil property functions

    * ASTM Standard D6836-02 (2003)

    0

    4

    8

    12

    16

    20

    0.1 1 10 100 1000Soil suction (kPa)

    G

    r

    a

    v

    i

    m

    e

    t

    r

    i

    c

    w

    a

    t

    e

    r

    c

    o

    n

    t

    e

    n

    t

    (

    %

    )

    Specimen 1Specimen 2Specimen 3

    Air Entry Value

    Residual ValueSand

    - Water permeability - Air permeability - Shear strength - Thermal flow - Incremental

    elasticity

    Chiu Chung Fai(SWCC)1.SWCC2.SWCC - - - -

  • Measured drying and wetting curves on processed silt (Pham, 2002)

    0

    5

    10

    15

    20

    25

    0.1 1 10 100 1000Soil suction (kPa)

    G

    r

    a

    v

    i

    m

    e

    t

    r

    i

    c

    w

    a

    t

    e

    r

    c

    o

    n

    t

    e

    n

    t

    (

    %

    )

    Specimen 1Specimen 2Specimen 3

    AEV = 10 kPa

    WEV = 4.5 kPa

    Residual = 120 kPa

    Residual = 62 kPa

    Chiu Chung FaiSWCC (Pham, 2002)

  • Pressure Plate Apparatus to Measure Void Ratio and Water Content While Applying Total Stress and Matric Suction

    Manufactured by GCTS, Tempe, AZ

    Air supply

    High air entry disk

    Chiu Chung Fai

  • Fifteen bar Pressure Plate equipment manufactured by

    GCTS, U.S.A.

    Wide range of applied suctions Applies total stresses Measures water and total

    volume change Measure diffused air Test individual specimens Null-type initial suction Drying and wetting modes

    Chiu Chung Fai15 bar 1.2.3.4.5.6.7.

  • Equations to Best-Fit SWCC Data

    Fredlund and Xing (1994)

    Correction FactorAir entry value

    Rate of desaturation

    Asymmetry Variable

    = Soil suction

    fm

    fn

    f

    s

    ae

    wCw

    ]})({ln[)()( +=

    )1000000(1ln[

    )1ln(1)(

    r

    rC

    ++

    =

    Numerous equations have been proposed:-Brooks & Corey (1964)- van Guenuchten (1980)

    0

    4

    8

    12

    16

    20

    0.1 1 10 100 1000Soil suction (kPa)

    G

    r

    a

    v

    i

    m

    e

    t

    r

    i

    c

    w

    a

    t

    e

    r

    c

    o

    n

    t

    e

    n

    t

    (

    %

    )

    Specimen 1Specimen 2Specimen 3

    Wetting

    Drying

    Chiu Chung FaiSWCC

  • Hysteresis in the Soil-Water Characteristic Curve

    Hysteretic SWCC Models will eventually be available for geotechnical usage

    Presently, the Geotechnical Engineer must decide which curve to use: Select wetting curve or drying curve based on

    process being simulated Hysteresis loop shift at point of inflection:

    Sands: 0.15 to 0.35 Log cycle Average: 0.25 Log cycle

    Loam soils: 0.35 to 0.60 Log cycle Average: 0.50 Log cycle

    Estimation Values

    Chiu Chung FaiSWCC1.SWCC2.

  • Model measurements of water content and matric suction showing the SWCC relationship from water contents and

    matric suctions during wetting and drying simulations (Tami et al, 2004)

    Section MSection B Section T

    1 100.0

    0.1

    0.2

    0.3

    0.4

    I&II-D

    III-WIV&V-D

    IV&V-W

    III-D

    1 10

    I&II-D

    III-WIV&V-D

    IV&V-W

    III-D

    1 10

    I&II-D

    III-WIV&V-D

    IV&V-W

    III-D

    Soil suction (kPa)

    V

    o

    l

    u

    m

    e

    t

    r

    i

    c

    w

    a

    t

    e

    r

    c

    o

    n

    t

    e

    n

    t

    ,

    w

    Suctions with Tensiometers Water content with TDR

    Chiu Chung FaiSWCC (Tami et al., 2004)

  • Approaches that can be used to obtain the SoilWater Characteristic curves

    Determination of Soil-Water Characteristic Curves, SWCC

    Laboratory measurement of

    water content versus suction

    SWCC predictions from grain

    size distribution

    SWCC predictions

    from grain size & Atterberg

    limits

    Dataset mining for

    typical SWCC

    Pressure plate <

    1500 kPa

    Vacuum desiccators > 1500 kPa

    Numerous models

    Parameters for

    numerous models

    Soils with similar grain size or soil

    classification

    Decreasing accuracy

    Chiu Chung FaiSWCC1.2.3.Atterberg4.

  • Soil-Water Characteristic Curve computed from a Grain Size Distribution Curve

    0.0

    10

    20

    30

    40

    0.1 1 10 100 1000 10000Suction (kPa)

    Predicted from grain-sizeExperimental

    W

    a

    t

    e

    r

    c

    o

    n

    t

    e

    n

    t

    1E+5 1E+6

    020

    40

    60

    80

    100

    0.0001 0.001 0.01 0.1 1 10 100Pe

    r

    c

    e

    n

    t

    p

    a

    s

    s

    i

    n

    g

    (

    %

    )

    Particle size (mm)

    ExperimentalFit - curve

    Fredlund et al,1997

    Chiu Chung FaiSWCC

  • Incorporation of SWCC into the Constitutive Relations for Unsaturated Soils

    Unsaturated soil property functions rely on the saturated soil properties PLUS the soil-water characteristic curve, SWCC

    Therefore, MUST have an indication of the SWCC

    Unsaturated soil property functionsrender the solution of a problem nonlinear

    Chiu Chung FaiSWCC1.SWCC2.SWCC3.

  • Seepage Constitutive Relations in Terms of SWCC

    References for the Soil-Water Characteristic CurvePermeability Models

    van Genuchten (1980) Brooks & Cory (1964)

    Mualem (1976)

    Burdine (1953) nnmnn

    rk 22

    ])(1[])(1[)(1)(

    ++=

    5.0

    21

    ])(1[}])(1[)(1{)( n

    mnn

    rk +

    +=

    32)()( =rkn

    m 21 =

    nm 11 =

    kr = kw/ksat

    Chiu Chung FaiSWCC

  • Seepage Constitutive Relations in Terms of SWCC

    References for the Soil-Water Characteristic CurvePermeability Models

    Fedlund and Xing (1994) Campbell (1974)

    Child and Collis George (1950)

    = b

    aev

    yy

    sy

    by

    y

    y

    r

    dyee

    e

    dyee

    e

    k

    )ln(

    '

    )ln(

    '

    )()(

    )()()(

    b

    aevrk

    22

    )(=

    b = Ln (1000000) () = Soil water contenty = Dummy variable of integration representing

    the logarithm of integration

    kr = kw/ksat

  • Usage of several functions to predict permeability functions from the SWCC for a particular soil and a suggested lower limit for the permeability function

    1.E-171.E-161.E-151.E-141.E-131.E-121.E-111.E-101.E-091.E-081.E-071.E-061.E-051.E-04

    0.1 1 10 100 1000 10000 100000 1E+06

    Experimental data

    Overall Kw + Kv

    Fredlund and Xing

    VaporKv

    Campbell

    Brooks and Corey

    Van Genuchten - Mualem

    Van Genuchten- Burdine

    Soil suction (kPa)

    C

    o

    e

    f

    f

    i

    c

    i

    e

    n

    t

    o

    f

    p

    e

    r

    m

    e

    a

    b

    i

    l

    i

    t

    y

    (

    m

    /

    s

    )

    Chiu Chung FaiSWCC

  • Shear Strength Constitutive Equation Written in Terms of SWCC

    Vanapalli et al. (1996)rs

    rn

    =

    'tan'tan)(' nan uc ++=Shear strength

    Net normal stress on the failure plane

    Angle of internal frictionIntercept of the Mohr-

    Coulomb failure envelope on the shear stress axis

    Matric suction

    SWCC

    Chiu Chung FaiSWCC

  • Stress Analysis (for Shear Strength Problems) Constitutive Relations in Terms of SWCC

    sd

    =

    Shear strength

    net normal stress on the failure plane

    Angle of internal frictionIntercept of the Mohr-

    Coulomb failure envelope on the shear stress axis

    'tan)('tan)(' dan uc ++=

    Fitting parameter used for obtaining a best-fit between the measured and predicted value

    Fredlund et al. (1996)

    Matric suction

    SWCC

  • Challenges to the Implementation of Unsaturated Soil Mechanics

    Challenge #5: To solve nonlinear partial differential equations for

    unsaturated soils without having convergence difficulties during the iterative solution process

    Solution #5: Adaptive mesh (grid) generation techniques in

    computer technology facilitates convergence

    0 10 20 30 40 50 60 70 80 90 100 110 120 130 14001020304050

    Chiu Chung Fai

  • Solving a Boundary Value Problem

    Element for which a PartialDifferential Equation, PDE, must be derived

    Boundary Value Must be Supplied

    Boundary

    Boundary

    Boundary

    Typical Boundary Conditions

    Flux Head - for seepageForce Displacement - for stress

    Boundary

    Utilize general purpose PDE Solvers to solve partial differential equations for saturated-unsaturated soil system

    Chiu Chung FaiPDE-

  • Problem Solving Environments, PSEs, for Soil Mechanics Partial Differential Equations, PDEs

    All classic areas of soil mechanics can be viewed in terms of the solution of a Partial Differential Equation

    Water flow through porous soils (Saturated or Unsaturated)

    Air flow through unsaturated soils Stress analysis for slope stability, bearing capacity

    and earth pressure Stress-Deformation volume change and distortion

    Incremental elasticity Elasto-plastic models

    Chiu Chung Fai1.2.()3.4.5.-

  • Partial Differential Equation for Saturated-Unsaturated Water Flow Analysis

    thm

    yh

    yk

    yhk

    xh

    xk

    xhk w

    wwyw

    y

    wxw

    x =

    ++

    +

    22

    2

    2

    2

    Head variable to be solved

    Water coefficient of permeability (function of soil suction)

    Time Water storage (function of soil suction)

    Chiu Chung Fai-

  • Partial Differential Equation for Unsaturated Air Flow Analysis

    Pore-air pressure(primary variable to be solved)

    Air coefficient of permeability (function of soil suction)

    Time Air storage and compressibility

    (function of soil suction)

    tu

    RTgmuS

    ee

    yu

    yk

    xu

    xk

    yuk

    xuk aawaaaaaaaaaa

    +=

    +

    +

    +

    22

    2

    2

    2

    1

    Chiu Chung Fai

  • Partial Differential Equation for Saturated-Unsaturated Stress-Deformation Analysis

    0441211 =

    +

    +

    +

    xv

    yuD

    yyvD

    xuD

    xX

    44 12 11 0tu v u vD D D

    x y x y x y + + + + =

    Y

    D11, D12, D44 = Combination of E and which are function of soil suction and net total stresses

    Stress-deformation analyses have a degrees of freedom in each of the Cartesian coordinate directions

    Chiu Chung Fai-D11, D12D44

  • Convergence of Nonlinear Partial Differential Equations

    Convergence is the single most pressing problem facing modelers

    Most successful solutions have involved Adaptive Grid Refinement methods, AGR (Oden, 1989; Yeh, 2000)

    Mesh is dynamically upgraded during the solution based on error estimates

    AGR becomes extremely important when solving the nonlinear PDEs associated with Unsaturated Soil Mechanics

    Chiu Chung Fai1.2., AGR(Oden,1989;Yen,2000)3.4.PDEsAGR

  • Two-dimensional seepage analysis through an earthfill dam with a clay core.

    Equipotential lines

    Optimized mesh for saturated-unsaturated seepage analysis

    Chiu Chung Fai

  • Problem illustrating the solution of a 3-dimensional, saturated-unsaturated seepage PDEOptimized, automatically generated finite element mesh

    Modeling of a waste tailings pond

    Chiu Chung Fai-

  • Stress analysis PDE combined with the Dynamic Programming procedure to compute the factor of safety

    Distance0 20 40 60 80

    0

    5

    10

    15

    20

    25

    30

    DP Search Bounda ry

    Finite Element S hea r Stre ss

    DP Ge ne ra te dCritica l S lip SurfaceFOS = 1.3 Shape and location of the slip

    surface are a part of the solution

    Chiu Chung FaiPDE

  • Prediction of Heave or Collapse of a Soil

    Requires the solution of a saturated-unsaturated seepage model and a stress-deformation model

    Saturated-Unsaturated Seepage Model

    Saturated-Unsaturated Stress-Deformation

    Model

    Coupled Uncoupled

    Pseudo-coupled

    Computes changes in matric suction Computes deformations

    Chiu Chung Fai1.--2.

  • Scenario of Edge Lift for a Flexible Impervious Cover

    Flexible cover 0

    1

    2

    3

    0 3 6 9 12

    Distance from centre of cover or slab, m

    CL

    Constant suction = 400 kPa

    Flux = 0

    D

    e

    p

    t

    h

    ,

    m

    Flux = 0

    Infiltration, q SVFlux

    Boundary conditions and initial conditions must be specified both seepage and stress-deformation

    Chiu Chung Fai-

  • Concrete slab0

    1

    2

    3

    0 3 6 9 12

    CL

    D

    e

    p

    t

    h

    ,

    m

    Distance from center, m

    SVFluxand

    SVSolid

    Can have one optimized Adaptive Mesh generated for seepage model and another for the stress-deformation model

    Chiu Chung Fai-

  • Matric Suction at Ground Surface after One Day of Infiltration for Various Infiltration Rates

    SVFlux

    0

    100

    200

    400

    0 2 4 6 8 10 12

    Distance from centre of cover, m

    M

    a

    t

    r

    i

    c

    s

    u

    c

    t

    i

    o

    n

    ,

    k

    P

    a

    300

    500

    CL

    Initial

    q = 10 mm/day

    q = 20q = 30

    q = 40q = 50q = 60

    Specifiedzero suction

    Distance under slab

    Chiu Chung Fai

  • Vertical Displacements at Ground Surface after One Day of Infiltration

    Distance under slab

    0

    10

    20

    25

    0 2 4 6 8 10 12

    Distance from centre of cover, m

    H

    e

    a

    v

    e

    ,

    (

    m

    m

    )

    5

    15

    specified zero suction

    q = 10q = 20

    q = 30q = 40

    q = 50

    q = 60 mm/day

    CL

    SVSolid

    Chiu Chung Fai

  • Challenges to the Implementation of Unsaturated Soil Mechanics

    Challenge #6: To promote implementation of unsaturated soil

    mechanics into engineering practice Solution #6:

    - Educational materials and visualization tools have been produced to better teach and understand unsaturated soil mechanics

    Chiu Chung Fai

  • Concluding Remarks

    Unsaturated Soil Mechanics needs to be first understood from the standpoint of the Constitutive equations describing soil behavior

    Constitutive Equations can be written in terms of the SWCC for the soil which are then known as Unsaturated Soil Property Functions, USPF

    Direct and Indirect procedures are available for the assessment of the SWCC

    It is always possible to obtain an estimate of the required Unsaturated Soil Property Functions for geotechnical engineering applications

    Chiu Chung Fai1.2.SWCC(USPF)3.SWCC4.(USPF)

  • Karl Terzaghi deserves credit not only for the

    fundamentals of saturated soil behavior but also for

    the fundamentals of unsaturated soil behavior

    Geo-Institute, Austin, TexasJanuary 23-26, 2005 Thank You

    Unsaturated Soil Mechanics in EngineeringUnsaturated Soil Mechanics Problems Described in Theoretical Soil Mechanics by K. Terzaghi (1943)Unsaturated Soil Mechanics in EngineeringObjectivesGradual Emergence of Unsaturated Soil MechanicsChallenges to the Implementation of Unsaturated Soil MechanicsChallenges to the Implementation of Unsaturated Soil MechanicsChallenges to the Implementation of Unsaturated Soil MechanicsChallenges to the Implementation of Unsaturated Soil MechanicsChallenges to the Implementation of Unsaturated Soil MechanicsChallenges to the Implementation of Unsaturated Soil MechanicsZones of Unsaturation Defined by a Soil-Water Characteristic Curve, SWCCUnsaturated Soil REV as a Four Phase SystemStructure and Stresses in the Contractile SkinChallenges to the Implementation of Unsaturated Soil MechanicsDefinition of stress state at a point in an unsaturated soilVariations in Stress State DescriptionChallenges to the Implementation of Unsaturated Soil MechanicsMonitoring for Verification PurposesTDR ThetaProbe, ML2x manufactured by AT Delta Devices, U.K.In Situ Matric Suction measurements using Thermal Conductivity sensors at 1.0 to 1.3 m below roadwayDirect, high suction sensor used to measure suctions greater than one atmosphere on the side of a triaxial specimen (Meilani,Challenges to the Implementation of Unsaturated Soil MechanicsFundamental Constitutive Relations for Unsaturated SoilsWater Seepage Constitutive RelationsShape of the water permeability function for glass beads tested by Mualem (1976 )The SWCC for the glass beads showing hysteresis during drying and wettingWater Storage in an Unsaturated SoilAir Flow Constitutive RelationsShear Strength Constitutive RelationsExtended Mohr-Coulomb failure surface (Fredlund, Morgenstern and Widger, 1978)Soil-Water Characteristic Curve for glacial tillReference compression curves for a Saturated SoilLimiting or Bounding relationships for Ko loading of a typical clayey silt soilVolumeMass Constitutive Surfaces for Regina Clay Preconsolidated at 200 kPa (Pham, 2004)VolumeMass Constitutive Surfaces for Regina Clay Preconsolidated at 200 kPa (Pham, 2004)VolumeMass Constitutive Surfaces for Regina Clay Preconsolidated at 200 kPa (Pham, 2004)VolumeMass Constitutive Surfaces for Regina Clay Preconsolidated at 200 kPa (Pham, 2004)VolumeMass Constitutive Surfaces for Beaver Creek Sand (Pham, 2004)VolumeMass Constitutive Surfaces for Beaver Creek Sand (Pham, 2004)Challenges to the Implementation of Unsaturated Soil MechanicsRole and Measurement of the Soil-Water Characteristic Curve, SWCCManufactured by GCTS, Tempe, AZFifteen bar Pressure Plate equipment manufactured by GCTS, U.S.A.Equations to Best-Fit SWCC DataHysteresis in the Soil-Water Characteristic CurveModel measurements of water content and matric suction showing the SWCC relationship from water contents and matric suctions dApproaches that can be used to obtain the SoilWater Characteristic curvesSoil-Water Characteristic Curve computed from a Grain Size Distribution CurveIncorporation of SWCC into the Constitutive Relations for Unsaturated SoilsSeepage Constitutive Relations in Terms of SWCCSeepage Constitutive Relations in Terms of SWCCUsage of several functions to predict permeability functions from the SWCC for a particular soil and a suggested lower limit fShear Strength Constitutive Equation Written in Terms of SWCCStress Analysis (for Shear Strength Problems) Constitutive Relations in Terms of SWCCChallenges to the Implementation of Unsaturated Soil MechanicsSolving a Boundary Value ProblemProblem Solving Environments, PSEs, for Soil Mechanics Partial Differential Equations, PDEsPartial Differential Equation for Saturated-Unsaturated Water Flow AnalysisPartial Differential Equation for Unsaturated Air Flow AnalysisPartial Differential Equation for Saturated-Unsaturated Stress-Deformation AnalysisConvergence of Nonlinear Partial Differential EquationsTwo-dimensional seepage analysis through an earthfill dam with a clay core.Problem illustrating the solution of a 3-dimensional, saturated-unsaturated seepage PDEStress analysis PDE combined with the Dynamic Programming procedure to compute the factor of safetyPrediction of Heave or Collapse of a SoilScenario of Edge Lift for a Flexible Impervious CoverMatric Suction at Ground Surface after One Day of Infiltration for Various Infiltration RatesVertical Displacements at Ground Surface after One Day of InfiltrationChallenges to the Implementation of Unsaturated Soil MechanicsConcluding Remarks