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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 : SLOPE STABILITY

LATERAL EARTH PRESSURES FOR A TOTAL STRESS ANALYSIS


Figure  shows a smooth, vertical wall supporting a homogeneous soil mass under undrained condition. Using the limit equilibrium method, we will assume, for the active state, that a slip plane is formed at an angle u to the horizontal. The forces on the soil wedge are shown in Figure 15.11. Using static equilibrium, we obtain the sum of the forces along the slip plane:

Equation  then yields

We are using P rather than Pa because Pa is the limiting value. To fi nd the maximum active lateral earth force, we differentiate P with respect to u and set the result equal to zero, giving

The solution is u =ua = 450 .
By substituting u = 450 into the above equation for P, we get the maximum active lateral earth force as

If we assume a uniform distribution of stresses on the slip plane, then the active lateral stress is

Let us examine Equation. If (sx)a = 0, for example, when you make an excavation, then solving for z from Equation  gives

 

 

Depth zcr is the depth at which tension cracks would extend into the soil (Figure). If the tension crack is fi lled with water, the critical depth can extend to

In addition, the soil in the vicinity of the crack is softened and a hydrostatic pressure, gwz9cr, is imposed on the wall. Often, the critical depth of water-fi lled tension cracks in overconsolidated clays is greater than the wall height. For example, if su 5 80 kPa, and g 5 gsat 5 18 kN/m3, then z'cr 5 19.5 m. A wall height
equivalent to the depth of the tension crack of 19.5 m is substantial. This is substantially more than the average height of the Great Wall of China, which is about 7.6 m. When tension cracks occur, they modify the slip plane, as shown in Figure 15.12; no shearing resistance is available over the length of the slip plane above the depth of the tension cracks. For an unsupported excavation, the active lateral force is also zero. From Equation, we get

 

and, solving for Ho, we obtain

If the excavation is fi lled with water, then

We have two possible unsupported depths, as given by Equations. The correct solution lies somewhere between these critical depths. In design practice, a value of

is used for unsupported excavation in fi ne-grained soils. If the excavation is filled with water

The passive lateral earth force for a total stress analysis, following a procedure similar to that for the active state above, can be written as

and the passive lateral pressure is

We can write Equations  using apparent active and passive lateral earth pressures for the undrained condition as

 

where Kau and Kpu are the undrained active and passive lateral earth pressure coeffi cients. In our case, for a smooth wall supporting a soil mass with a horizontal surface, Kau 5 Kpu 5 2. Walls that are embedded in fi ne-grained soils may be subjected to an adhesive stress (sw) at the wall face. The adhesive stress is analogous to a wall–soil interface friction for an effective stress analysis. The undrained lateral earth pressure coeffi cients are modifi ed to account for adhesive stress as

Questions of this topic


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