Fundamentals of Rock Mechanics

Understanding the engineering properties and behavior of rocks under various conditions

Engineering Properties of Rocks

Classification Systems

Rocks are classified based on their engineering properties using systems like:

  • Rock Quality Designation (RQD)
  • Rock Mass Rating (RMR)
  • Q-system
  • Geological Strength Index (GSI)

Index Properties

Key index properties include:

  • Density and specific gravity
  • Porosity and permeability
  • Water content and absorption
  • Durability and weathering characteristics
  • Hardness and abrasiveness

Rock Strength Characteristics

Compressive Strength

The maximum axial compressive stress that a rock specimen can withstand before failure. Typically measured through uniaxial or triaxial compression tests.

Compressive strength diagram

Tensile Strength

The resistance of rock to failure in tension. Typically much lower than compressive strength. Measured through Brazilian test or direct tension tests.

Tensile strength diagram

Shear Strength

The resistance to failure along internal surfaces. Governed by Mohr-Coulomb criterion: τ = c + σ·tanφ, where c is cohesion and φ is friction angle.

Shear strength diagram

Compression and Shear Tests

Uniaxial Compression Test

The most common test for determining rock strength. Cylindrical rock specimens are subjected to axial load until failure.

Procedure:

  1. Prepare specimen (typically L/D ratio of 2.5-3.0)
  2. Measure dimensions and weight
  3. Apply load at constant strain rate (0.5-1.0 MPa/s)
  4. Record stress-strain data until failure
  5. Calculate uniaxial compressive strength (UCS)
Uniaxial compression test setup

Triaxial Compression Test

Conducted under confined pressure to simulate in-situ conditions. Provides more comprehensive strength parameters.

Key Parameters:

  • Confining pressure (σ₃)
  • Peak strength (σ₁)
  • Cohesion (c)
  • Angle of internal friction (φ)
  • Dilatancy angle
Triaxial test setup

Shear Test Methods

Direct Shear Test

Rock specimen is sheared along a predetermined plane under constant normal stress.

Brazilian Test

Indirect tensile strength test where disk-shaped specimen fails in tension when compressed diametrically.

Point Load Test

Index test for estimating UCS by applying concentrated load to rock specimen.

Rock Deformation and Elastic Properties

Elastic Parameters

Young's Modulus (E)

Ratio of axial stress to axial strain in the elastic range. Typically 1-100 GPa for rocks.

Poisson's Ratio (ν)

Ratio of lateral strain to axial strain. Typically 0.1-0.4 for most rocks.

Bulk Modulus (K)

Resistance to uniform compression. Related to E and ν by K = E/[3(1-2ν)].

Shear Modulus (G)

Resistance to shear deformation. G = E/[2(1+ν)].

Stress-Strain Behavior

Stress-strain curve

Typical stages in rock deformation:

  1. Elastic deformation (reversible)
  2. Crack initiation and stable crack growth
  3. Unstable crack propagation (damage accumulation)
  4. Peak strength and post-peak behavior
  5. Residual strength

Significance in Engineering

Tunnel Design

Deformation characteristics determine support requirements and excavation methods.

Slope Stability

Understanding deformation helps predict failure mechanisms in rock slopes.

Foundation Design

Elastic properties affect settlement calculations for structures on rock.

Rock Failure Mechanisms

Coulomb's Failure Criterion

The simplest and most widely used failure criterion for rocks:

τ = c + σ·tanφ

Where:

  • τ = shear strength
  • c = cohesion
  • σ = normal stress
  • φ = angle of internal friction

Mohr-Coulomb failure envelope

Factors Affecting Rock Strength

Water Content

Water reduces rock strength through pore pressure effects and chemical weathering. Strength reduction up to 50% possible when saturated.

Temperature

High temperatures generally reduce strength, while freezing can increase strength temporarily.

Loading Rate

Higher loading rates typically show higher apparent strength (strain rate effect).

Scale Effects

Strength generally decreases with increasing specimen size due to greater probability of defects.

Advanced Failure Criteria

Hoek-Brown Criterion

Empirical criterion considering intact rock properties and rock mass conditions.

Griffith Theory

Based on crack propagation in brittle materials under tensile stress.

Drucker-Prager

Smooth approximation of Mohr-Coulomb in principal stress space.