CELE Geotechnical Engineering — Shear Strength of SoilsConcept Map

Concept

Mohr-Coulomb Failure Criterion

Sub Concepts

• Total Stress Analysis (τf = c + σ tan φ)
• Effective Stress Analysis (τf = c' + σ' tan φ')
• Cohesion Component
• Friction Component
• Principal Stress Relationships

Relationship To Central

Fundamental theory defining when soil fails

Concept

Soil Types and Behavior

Sub Concepts

• Sands (c ≈ 0, frictional)
• Clays (c > 0, cohesive)
• Saturated Clay Undrained (φ = 0)
• Granular Soils (always drained)

Relationship To Central

Different soils exhibit different shear strength characteristics

Concept

Laboratory Testing Methods

Sub Concepts

• Direct Shear Test
• Triaxial Compression Test
• Unconfined Compression Test
• Test Interpretation and Parameter Extraction

Relationship To Central

Experimental procedures to measure shear strength parameters

Concept

Triaxial Test Variants

Sub Concepts

• UU (Unconsolidated-Undrained)
• CU (Consolidated-Undrained with pore pressure measurement)
• CD (Consolidated-Drained)
• Pore Pressure Development
• Effective Stress Path

Relationship To Central

Different drainage conditions during triaxial testing

Concept

Drained vs Undrained Conditions

Sub Concepts

• Undrained Analysis (Short-term stability)
• Drained Analysis (Long-term stability)
• Pore Pressure Dissipation
• Loading Rate Effects
• Time-Dependent Consolidation

Relationship To Central

Controls time-dependent shear strength behavior

Concept

Field Applications

Sub Concepts

• Foundation Design (bearing capacity)
• Slope Stability Analysis
• Retaining Wall Design
• Embankment Construction
• Safety Factor Calculation

Relationship To Central

Practical use of shear strength in engineering design

Concept

Key Formulas and Relationships

Sub Concepts

• Mohr-Coulomb equation
• Unconfined strength cu = qu/2
• Principal stress relation
• Friction angle determination
• Deviator stress calculations

Relationship To Central

Mathematical expressions for shear strength calculations

Concept

Stress States and Failure

Sub Concepts

• Normal Effective Stress (σ')
• Shear Stress (τ)
• Mohr Circle Construction
• Failure Plane Orientation
• Maximum Principal Stress

Relationship To Central

Understanding normal and shear stress at failure

To

Soil Types and Behavior

From

Mohr-Coulomb Failure Criterion

Strength

strong

Relationship

Different soil types exhibit different parameters (c and φ) in the same fundamental failure equation

To

Mohr-Coulomb Failure Criterion

From

Laboratory Testing Methods

Strength

strong

Relationship

Tests provide the experimental data needed to determine c and φ parameters for the failure criterion

To

Drained vs Undrained Conditions

From

Triaxial Test Variants

Strength

strong

Relationship

The choice of triaxial test (UU, CU, CD) directly determines whether drained or undrained conditions are simulated

To

Field Applications

From

Drained vs Undrained Conditions

Strength

strong

Relationship

Design approach and timing (short-term vs long-term) depend on whether conditions are drained or undrained

To

Mohr-Coulomb Failure Criterion

From

Key Formulas and Relationships

Strength

strong

Relationship

Formulas mathematically express the failure criterion and related calculations

To

Key Formulas and Relationships

From

Stress States and Failure

Strength

strong

Relationship

Understanding principal stresses and Mohr circles enables calculation of friction angle and cohesion

To

Key Formulas and Relationships

From

Unconfined Compression Test

Strength

moderate

Relationship

UC test uses the specific formula cu = qu/2 derived from Mohr-Coulomb principles

To

Mohr-Coulomb Failure Criterion

From

Direct Shear Test

Strength

strong

Relationship

Test directly plots τf vs σ to extract c and φ following the failure criterion equation

To

Mohr-Coulomb Failure Criterion

From

Triaxial Compression Test

Strength

strong

Relationship

Triaxial test provides principal stresses at failure used in failure criterion analysis

To

Drained vs Undrained Conditions

From

Soil Types and Behavior

Strength

strong

Relationship

Sands are always drained; clays behave as undrained under rapid loading and drained long-term

To

Laboratory Testing Methods

From

Field Applications

Strength

moderate

Relationship

Specific field applications require appropriate lab tests to obtain valid design parameters

To

Mohr-Coulomb Failure Criterion

From

Stress States and Failure

Strength

strong

Relationship

Mohr circle construction visualizes stress states and determines failure orientation using the failure criterion

To

Drained vs Undrained Conditions

From

CU Test

Strength

strong

Relationship

CU test bridges undrained and drained analysis by measuring pore pressures during consolidation-undrained shearing

To

Key Formulas and Relationships

From

Principal Stress Relationships

Strength

strong

Relationship

sin φ = (σ1 - σ3)/(σ1 + σ3) provides direct calculation of friction angle from principal stresses

To

Drained vs Undrained Conditions

From

Field Applications

Strength

strong

Relationship

Foundation bearing capacity uses undrained cu for short-term; slopes use drained c' and φ' for long-term