Pre-failure Deformability of Geomaterials

Hsin-yu ShanDept. of Civil Engineering

National Chiao Tung University

Strain Levels

Strain at failureSandClayRock

Distribution of strain of soil in the field when a structure/soil fails

Strain Distribution in the Field

Shallow foundationDeep foundationRetaining structureSlope

Strain under Working Load

Less than 1%Axial strain under footing

0.01 – 1.0 %Shear strain along pile

Less than 0.1% near the top of the pile

Variation of Deformation Parameters

Small strain modulus?Equivalent Elastic Parameters

Ei = Initial tangent modulus (initial linear section)Ef = Secant modulus (0 to strain at failure)E50 = Modulus from (0 to 50% strength)

Variation of undrained Young’s modulus Eu with mean normal effective stress derived from various sites on London Clay (St. John, 1975)

Stress-Strain Relationship

Under small strainSoil behaves like elastic materialLinear stress-strain relationship

Under large strainNonlinear stress-strain relationshipTransition from elastic to plastic behavior

Unconcolidated undrained triaxial compression tests on London Clay using local strain transducers (Costa-Filhoand Vaughan, 1980)

Obtaining Stress-Strain Relationship

Laboratory testsTraditionally determine the deformation of the whole specimenAverage strain

In-situ testsNeed to use model to back calculate

Source of Errors in Conventional Deformation Measurement

Seating errors caused by gaps closing between:

Ram or internal load cell and top platenPlatens and porous stones

(after Baldi et al. 1988)

Sources of errors in external axial deformation measurements (Baldi et al., 1988)

Alignment errors resulting from equipment and specimen nonconformity, specially:

Nonverticality and eccentricity of loading ramNonhorizontality of platen surfaceTilt of specimen

Bedding errors caused by surface irregularities and poor fit at the interface between the specimen and porous stone

Compliance errors which may occur because:The tie bars extend and cause relative displacement of the top of the cell with respect to the pistonThe internal load cell deflectsThe lubricant is compressed in systems using lubricated endsThe porous paper is compressed

Strain Distribution

How does the failure plane/zone in a specimen develop?Different stages of loadingAxial strain? Shear Strain?

Improvement over Traditional Techniques

Higher resolutionMore relevant to shear zoneReduction of boundary effects

E.g. friction, inclination, off-center loading

Internal strain measuring systems

Whole body (imaging) Local (electrical)

X-ray Video tracking Contacting Noncontacting

Cylindrical capacitance device (R)

Proximity transducer (A, R)

Hall effect gage (A, R)

Local deformation transducer (A)

Flexible strip radial strain caliper (R)

Inclinometer gage (A)

LVDT (A, R)

Pendulum gageElectrolevel

A: axialR: radial

Small Strain Measurement Instrument

Internal proximeter

External proximeter

External LVDT

Local LVDT

Radial proximeterLocal LVDT

Stress-strain response during consolidation

Stress-strain response during shearing

Requirements of Small Strain Measurement

Strains must be measured to an accuracy of at least 10-3%Measuring systems must be able to accommodate coupled axial and radial deformation without loss of accuracyInstrumentation must not interfere with the soil behavior

Axial strain measurement must ideally be made locally, over the central one third of the specimens so that end-restraint stress pathsInstruments must be capable of operating under different stress pathInstruments must be submersible and capable of operating under typical range of triaxial cell pressuresInstruments must be capable of operating on triaxialspecimens of any dimension typically used throughout the world

10105External – measured differential movements between piston and top cap

Inductive displacement transducer

2.510.3ExternalNoncontactingproximity transducer

2.510.3Internal – between top cap and base pedestal

Noncontactingproximity transducer

210.3Internal – central portion of specimen

Submersible LVDTs

Range (mm)

Accuracy (µm)

Resolution (µm)

LocationInstrument

Circular split-spring collar LVDT mounting mechanism for axial deformation measurement (Brown and Snaith, 1974)

Fixed LVDT support system (Costa-Filho, 1985)

Operating principle of inclinometer level (electrolevel) (Jardine et al., 1984)

Pendulum inclinometer (Ackerly et al., 1987)

Hall effect gage for axial strain measurement (Clayton and Khatrush, 1986)

Hall effect gage for radial strain measurement (Clayton et al, 1989)

Local deformation transducer (Tastuoka, 1988)

Radial deformation monitoring using proximity transducers mounted in cell wall (Cole, 1978)

Arrangement of proximity transducers for deformation measurement (Hird and Yung, 1989)

Lateral Deformation and Poisson’s Ratio

Do we need to know the Poisson’s ratio?How to obtain Poisson’s ratio?How to measure lateral deformation?

Circumference displacement - extensometerCalculate from volume change

∆V ∆V

Modulus Determined from Geophysical Tests

Relationship between wave velocity and elastic modulusLevel of strain induced by seismic wavesRelevance of the obtained elastic modulus and shear modulus

What will happen when approaching failure?

Degree of stress concentration decreasesExpansion of highly-stressed zoneExpansion of plastic zone

From local to overall specimenOverall strain increases at a higher rate than local strain?

Overall deformation is the sum of local deformationOverall strain is the average of local strains

What about shear stress?

Do we need to know the stress distribution?Are we not using the average stress and the local strain to make the stress-strain curve?What is the effect of stress concentration?

Importance of Small Strain Parameters

Deformation in the fieldWhen?Where?How much?Did we take it into account?Level of accuracy?Numerical simulation?

How Do We Make Use of the Parameters?

Conventional analysisNumerical simulation