# Terzaghi Unsaturated Soil Mechanics (2007)

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Unsaturated Soil Mechanics in EngineeringProfessor Delwyn G. Fredlund University of Saskatchewan Saskatoon, SK, Canada

GeoFrontiers 2005, Austin, Texas

Geo-Institute, ASCEJanuary 23-26, 2005

Karl Terzaghi elevated SoilMechanics 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)

John Wiley & Sons, 1943

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:

?

Local vertical zones of unsaturated soils

Regional distribution of unsaturated soilsSATURATED SOIL

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

Zones of Unsaturation Defined by a Soil-Water Characteristic Curve, SWCC (%)35 30 25 20 15 10 5 0 0.1

Gravimetric water content, w

Transition zone Air entry value Boundary effect zone Residual condition1.0 10. 100. 1000. 10,000 100,000 1000,000

Inflection point Residual zone

Soil suction (kPa)

Unsaturated Soil REV as a Four Phase SystemREV = Representative Elemental Volume Air Contractile skin Soil particles -Two Phases that deform and come to rest under a stress gradient (SOLIDS) -Soil structure -Contractile skin Water -Two phases that continuously flow under a stress gradient (FLUIDS) -Water -Air

Structure and Stresses in the Contractile Skin Airthickness of the contractile skin

t90/10

WaterLiquid water density B PN

Hyperbolic Tangent Function

Water vapor density

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

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

(ua - uw) yx

(y - ua) yz xz xy zy (ua - uw) (x - ua)

(ua - uw) zx (z - ua)

Definition of stress state at a point in an unsaturated soil (ua - uw) (y - ua) Defines the stress state at a point in a continuum State variables are independent of soil properties yx yz xz xy zy (ua - uw) (x - ua)

(ua - uw) zx (z - ua)

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 TensorX - direction Y - direction Z - direction

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

(x ua) xy xz (ua uw) 0 0

yz (zua ) 0 0 (ua uw) 0 (ua uw) 0

(yua)

yx

zx zy

Matric Suction Stress Tensor

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

In Situ Matric Suction measurements using Thermal Conductivity sensorsVersus1.0 -to m to 1.3mDepth Range roadway Matric Suction at Time 1.0 1.3 m below200.0T 1-3 T 2-8 T 3-11 T 4-14

Matric suction (kPa) Matric Suction (kPa)

175.0 150.0 125.0 100.0 75.0 50.0

Frost

T 4-14 T 5-16 T 5-16 T 1-3

T 2-8

25.0 0.0 15-Sep-00

Equalization5-Oct-00 25-Oct-00 14-Nov-00 Time (Days)

T 3-11

4-Dec-00

24-Dec-00

Time (Days)

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 Top cap O - ring Coarse corundum disk Filter paper Silicone rubber grommet Rubber membrane Latex rubber, to seal the rubber membrane and grommet Mini suction probe

Specimen

O - ring 5 bar high air-entry ceramic disk

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 behaviorVoid ratio e am at

Solution #3:- Constitutive relations for saturated soils needed to be extended to embrace the effect of changing degrees of saturation

tr al s rm no - u a) t ( Ne

ess

Matric suction (ua - uw)

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!

Water Seepage Constitutive Relations

uw h = +Y wg

Driving potential for water flow is hydraulic head, h

dh vx = k wx dx dh v y = k wy dy dh vz = k wz dz

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

Shape of the water permeability function for glass beads tested by Mualem (1976 )Coefficient of permeability (m/s)1.E-01 1.E-02 1.E-03 1.E-04 1.E-05 1.E-060.1 1 10

Drying

Wetting

Drying Drying

Wetting Wetting

Soil suction (kPa) Soil suction (kPa)

The SWCC for the glass beads showing hystere

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