Unsaturated Soil Mechanics in Soil Mechanics Problems Described in “Theoretical...

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Transcript of Unsaturated Soil Mechanics in Soil Mechanics Problems Described in “Theoretical...

  • 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)

    JMVANoteUnmarked set by JMVA

  • Unsaturated Soil Mechanics Problems Described in Theoretical Soil

    Mechanics by K. Terzaghi (1943)

  • 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

  • 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

  • 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

  • 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:

    ?

  • 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:

    ?

  • 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:

    ?

  • 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: ?

  • 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:

    ?

  • 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:

    ?

  • Regional distribution of unsaturated soils

    Local vertical zones of

    unsaturated soils

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

    SATU

    RA

    TED

    SO

    IL

  • 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

    Gra

    vim

    etric

    wat

    er c

    onte

    nt,w

    (%)

    Soil suction (kPa)

    Air entry value

    Boundary effect zone

    Transition zone

    Residual zone

    Residualcondition

    Inflection point

  • 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

  • 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)

  • 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)

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

    (z - ua)

    (y - ua)(ua - uw)

    (ua - uw)

    zx

    zy

    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

  • Variations in Stress State Description

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

    *ij = ij [S uw + (1 S) ua ] ij

    ij = 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

  • 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

  • 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

  • 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.

  • Monitoring of Matric Suction

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

  • 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)

    Mat

    ric

    Suct

    ion

    (kPa

    )

    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)

    Mat

    ricsu

    ctio

    n (k

    Pa)

  • 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

  • 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

  • Fundamental Constitutive Relations for Unsaturated Soils

    Constitutive Behaviors in Class