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  • INTRODUCTION OF SOIL MECHANICS
    • GEOTECHNICAL LESSONS FROM FAILURES
    • BASIC GEOLOGY
    • INTRODUCTION OF SOILS INVESTIGATION
    • PHASE RELATIONSHIPS
    • Importance of soil compaction
    • HEAD AND PRESSURE VARIATION IN A FLUID AT REST
    • GEOLOGICAL CHARACTERISTICS AND PARTICLE SIZES OF SOILS
    • Composition of the Earth’s Crust
    • PHASES OF A SOILS INVESTIGATION
    • PHYSICAL STATES AND INDEX PROPERTIES OF FINE-GRAINED SOILS
    • INTERPRETATION OF PROCTOR TEST RESULTS
    • DARCY’S LAW
    • COMPOSITION OF SOILS
    • SOILS EXPLORATION PROGRAM
    • DETERMINATION OF THE LIQUID, PLASTIC, AND SHRINKAGE LIMITS
    • SOIL CLASSIFICATION SCHEMES
    • FIELD COMPACTION
    • FLOW PARALLEL TO SOIL LAYERS
    • Surface Forces and Adsorbed Water
    • Soil Identifi cation in the Field
    • DETERMINATION OF THE HYDRAULIC CONDUCTIVITY
    • DETERMINATION OF PARTICLE SIZE OF SOILS
    • Soil Sampling
    • Falling-Head Test
    • Particle Size of Fine-Grained Soils
    • Groundwater Conditions
    • Pumping Test to Determine the Hydraulic Conductivity
    • COMPARISON OF COARSE-GRAINED AND FINE-GRAINED SOILS
    • Types of In Situ or Field Tests
    • GROUNDWATER LOWERING BY WELLPOINTS

  • SOIL WATER AND WATER FLOW
    • STRESSES AND STRAINS
    • STRESS AND STRAIN INVARIANTS
    • IDEALIZED STRESS–STRAIN RESPONSE AND YIELDING
    • Hooke’s Law Using Stress and Strain Invariants
    • PLANE STRAIN AND AXIAL SYMMETRIC CONDITIONS
    • STRESS PATHS
    • Axisymmetric Condition
    • Plotting Stress Paths Using Two-Dimensional Stress Parameters
    • ANISOTROPIC, ELASTIC STATES
    • Mohr’s Circle for Stress States
    • Mohr’s Circle for Strain States
    • The Principle of Effective Stress
    • Effective Stresses Due to Geostatic Stress Fields
    • Effects of Capillarity
    • Effects of Seepage
    • LATERAL EARTH PRESSURE AT REST
    • STRESSES IN SOIL FROM SURFACE LOADS
    • Strip Load
    • Uniformly Loaded Rectangular Area
    • Vertical Stress Below Arbitrarily Shaped Areas

  • STRESS DISTRIBUTIONCOMPRESSIBILITY AND SETTLEMENT
    • BASIC CONCEPTS
    • TYPICAL RESPONSE OF SOILS TO SHEARING FORCES
    • BASIC CONCEPTS
    • Consolidation Under a Constant Load—Primary Consolidation
    • Effects of Increasing the Normal Effective Stress
    • Soil Yielding
    • Void Ratio and Settlement Changes Under a Constant Load
    • Effects of Soil Tension
    • Primary Consolidation Parameters
    • Coulomb’s Failure Criterion
    • CALCULATION OF PRIMARY CONSOLIDATION SETTLEMENT
    • Taylor’s Failure Criterion
    • Procedure to Calculate Primary Consolidation Settlement
    • Mohr–Coulomb Failure Criterion
    • ONE-DIMENSIONAL CONSOLIDATION THEORY
    • PRACTICAL IMPLICATIONS OF THE FAILURE CRITERIA
    • Solution of Governing Consolidation Equation Using Fourier Series
    • INTERPRETATION OF THE SHEAR STRENGTH OF SOILS
    • Finite Difference Solution of the Governing Consolidation Equation
    • LABORATORY TESTS TO DETERMINE SHEAR STRENGTH PARAMETERS
    • SECONDARY COMPRESSION SETTLEMENT
    • Conventional Triaxial Apparatus
    • Oedometer Test
    • Unconfi ned Compression (UC) Test
    • Determination of the Coeffi cient of Consolidation
    • Consolidated Undrained (CU) Compression Test
    • Determination of the Past Maximum Vertical Effective Stress
    • POREWATER PRESSURE UNDER AXISYMMETRIC UNDRAINED LOADING
    • PRECONSOLIDATION OF SOILS USING WICK DRAINS
    • OTHER LABORATORY DEVICES TO MEASURE SHEAR STRENGTH
    • Hollow-Cylinder Apparatus
    • FIELD TESTS

  • SHEAR STRENGTH
    • ALLOWABLE STRESS AND LOAD AND RESISTANCE FACTOR DESIGN
    • COLLAPSE LOAD USING THE LIMIT EQUILIBRIUM METHOD
    • Prediction of the Behavior of Coarse-Grained Soils Using CSM
    • BEARING CAPACITY EQUATIONS
    • ELEMENTS OF THE CRITICAL STATE MODEL
    • MAT FOUNDATIONS
    • FAILURE STRESSES FROM THE CRITICAL STATE MODEL
    • BEARING CAPACITY OF LAYERED SOILS
    • Undrained Triaxial Test
    • SETTLEMENT CALCULATIONS
    • MODIFICATIONS OF CSM AND THEIR PRACTICAL IMPLICATIONS
    • Primary Consolidation Settlement
    • RELATIONSHIPS FROM CSM THAT ARE OF PRACTICAL SIGNIFICANCE
    • DETERMINATION OF BEARING CAPACITY AND SETTLEMENT OF COARSE-GRAINED SOILS
    • Relationships Among the Tension Cutoff, Mean Effective Stress, and Preconsolidation Stress
    • Cone Penetration Test (CPT)
    • Relationships Among Undrained Shear Strength, Critical State Friction Angle, and Preconsolidation Ratio
    • Plate Load Test (PLT)
    • Relationship Between the Normalized Undrained Shear Strength of One-Dimensionally Consolidated or Ko-Consolidated and Isotropically
    • SHALLOW FOUNDATION ANALYSIS USING CSM
    • Relationship Between the Normalized Undrained Shear Strength at Initial Yield and at Critical State for Overconsolidated Fine-Grained Soils Under Triaxial Test Condition
    • Dense, Coarse-Grained Soils
    • Relationship Between Direct Simple Shear Tests and Triaxial Tests
    • Relationship for the Application of Drained and Undrained
    • Relationship Among Excess Porewater Pressure, Preconsolidation Ratio, and Critical State Friction Angle
    • Undrained Shear Strength, Liquidity Index, and Sensitivity
    • SOIL STIFFNESS
    • STRAINS FROM THE CRITICAL STATE MODEL
    • Shear Strains
    • CALCULATED STRESS–STRAIN RESPONSE
    • APPLICATION OF CSM TO CEMENTED SOILS

  • SLOPE STABILITY
    • TYPES OF PILES AND INSTALLATION
    • TWO-DIMENSIONAL FLOW OF WATER THROUGH POROUS MEDIA
    • BASIC CONCEPTS OF LATERAL EARTH PRESSURES
    • SOME CAUSES OF SLOPE FAILURE
    • Pile Installation
    • FLOWNET SKETCHING
    • COULOMB’S EARTH PRESSURE THEORY
    • Construction Activities
    • LOAD CAPACITY OF SINGLE PILES
    • INTERPRETATION OF FLOWNET
    • RANKINE’S LATERAL EARTH PRESSURE FOR A SLOPING BACKFILL AND A SLOPING WALL FACE
    • INFINITE SLOPES
    • PILE LOAD TEST (ASTM D 1143)
    • FLOW THROUGH EARTH DAMS
    • LATERAL EARTH PRESSURES FOR A TOTAL STRESS ANALYSIS
    • ROTATIONAL SLOPE FAILURES
    • METHODS USING STATICS FOR DRIVEN PILES
    • SOIL FILTRATION
    • APPLICATION OF LATERAL EARTH PRESSURES TO RETAINING WALLS
    • METHOD OF SLICES
    • PILE LOAD CAPACITY OF DRIVEN PILES BASED ON SPT AND CPT RESULTS
    • TYPES OF RETAINING WALLS AND MODES OF FAILURE
    • APPLICATION OF THE METHOD OF SLICES
    • LOAD CAPACITY OF DRILLED SHAFTS
    • STABILITY OF RIGID RETAINING WALLS
    • PROCEDURE FOR THE METHOD OF SLICES
    • PILE GROUPS
    • STABILITY OF FLEXIBLE RETAINING WALLS
    • STABILITY OF SLOPES WITH SIMPLE GEOMETRY
    • ELASTIC SETTLEMENT OF PILES
    • Analysis of Sheet Pile Walls in Mixed Soils
    • CONSOLIDATION SETTLEMENT UNDER A PILE GROUP
    • BRACED EXCAVATION
    • SETTLEMENT OF DRILLED SHAFTS
    • MECHANICAL STABILIZED EARTH WALLS
    • PILE-DRIVING FORMULAS AND WAVE EQUATION
    • OTHER TYPES OF RETAINING WALLS
    • LATERALLY LOADED PILES
    • MICROPILES

Branch : Civil Engineering
Subject : Soil Mechanics
Unit : SHEAR STRENGTH

Shear Strains


Let the yield surface be represented by

To fi nd the shear or deviatoric strains, we will assume that the resultant plastic strain increment, Dεp, for an increment of stress is normal to the yield surface ). Normally, the plastic strain increment should be normal to a plastic potential function, but we are assuming here that the plastic potential function, and the yield surface (yield function, F ) are the same. A plastic potential function is a scalar quantity that defi nes a vector in terms of its location in space. Classical plasticity demands that the surfaces defi ned by the yield and plastic potential coincide.

 

 

If they do not, then basic work restrictions are violated. However, advanced soil mechanics theories often use different surfaces for yield and potential functions to obtain more realistic stress–strain relationships. The resultant plastic strain increment has two components—a deviatoric or shear component, Dεpq , and a volumetric component, Dεpp , as shown in Figure  We already found Dεpp in the previous section. Since we know the equation for the yield surface [Equation], we can fi nd the normal to it by differentiation of the yield function with respect to p9 and q. The tangent or slope of the yield surface is

 

 

 

Rearranging Equation , we obtain the slope as

 

 

The normal to the yield surface is

 

 

From Figure  the normal, in terms of plastic strains, is dεpq /dεpp . Therefore

 

which leads to

 

The elastic shear strains can be obtained from Equation as

 

These equations for strain increments are valid only for small changes in stress. For example, you cannot use these equations to calculate the failure strains by simply substituting the failure stresses for p' and q. You have to calculate the strains for small increments of stresses up to failure and then sum each component of strain separately. We need to do this because the critical state model considers soils as elastoplastic materials and not linearly elastic materials.

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