Pre-failure Deformability of Geomaterials · Pre-failure Deformability of Geomaterials Hsin-yu Shan...
Transcript of Pre-failure Deformability of Geomaterials · Pre-failure Deformability of Geomaterials Hsin-yu Shan...
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 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)
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
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)
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
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?