Dynamic Analysis

Dynamic analysis is required for the following types of geomechanical problems:

1. seismic (i.e., earthquake) loading;

2. explosive or impulsive loading;

3. mining problems involving seismic release of energy (i.e., rockbursts); and

4. flow of particles (angular or rounded) under gravity.

The fundamental assumption in all cases is that time is relevant. In almost all cases, the time of interest is less than one minute; in the case of explosive or impulsive loading, it is less than one second.

• Damping
  • Rayleigh Damping
    • Example of Different Damping Techniques
    • Guidelines for Selecting Rayleigh Damping Parameters for Dynamic Analysis
  • Maxwell Damping
    • Formulation
      • Standard Linear Solid
      • Full Maxwell Damping Scheme
      • User Inputs and Maxwell Component Properties
    • Implementation
      • Explicit Algorithm
      • Implicit Algorithm
    • Verification Problem
      • Verification problem: Maxwell damping in 3DEC
        • Rigid Blocks
        • Deformable Block
        • Deformable Blocks with Joints
      • Site Response using Maxwell Damping
• Natural Modes of Oscillation
  • Example Problems (from Cundall et al. (1979), pp. 71-73)
• Wave Transmission
• Partial Density Scaling for Dynamic Analysis
  • Example of Partial Density Scaling
• Boundary Conditions
  • Nonreflecting Boundaries
  • Free-Field Boundaries
    • Example Using Dynamic Free Field
• Application of Dynamic Input
  • Baseline Correction of Input Histories
• Calculation of Natural Frequencies and Modes of Vibration
  • Rigid Block Example
  • Deformable Block Example
• Verification Examples
  • Slip on a Joint Induced by a Propagating Harmonic Shear Wave
    • Problem Statement
    • Analytic Solution
    • Material Properties
    • Dynamic Loading
    • Results
  • Line Source in an Infinite Elastic Medium with a Discontinuity
    • Problem Statement
    • Analytic Solution
    • Model Setup
    • Properties of Joints and Continuous Medium
    • Dynamic Loading
    • Results
  • References