Theoretical Methods for Wave Propagation across Jointed Rock Masses

Abstract

Different methods are presently available for the analysis of wave propagation across jointed rock masses with the consideration of multiple wave reflections between joints. These methods can be divided into two categories. One is based on the displacement discontinuity model for representing rock joints, where the displacements across a joint are discontinuous and the tractions are continuous, and the other is the equivalent medium method. For the first category, there are three methods, i.e., method of characteristics (MC), scattering matrix method (SMM) and virtual wave source method (VWS). MC solves the equation of motion by using the theory of characteristic curves. SMM is based on the definition of the scattering matrix in which the reflection and transmission coefficients of a set of joints are stored. VWS method replaces the joints in the rock mass with a virtual concept. For the second category, equivalent medium model treats the problem in the frame of continuum mechanics and simplifies it from an explicit wave propagation equation. The objective of this paper is to review and compare these theoretical methods. The comparison shows that the four solutions agree very well with each other. Some additional considerations about the advantages and disadvantages of these methods are also given in the paper.

Experimental Study on Viscoelastic Behavior of Sedimentary Rock under Dynamic Loading

“…Although some viscoelastic constitutive models have been introduced in analyzing stress wave amplitude attenuation, waveform dissipation (Pyrak-Nolte et al 1990;Jaeger et al 2007;Li et al 2010), and mechanical energy dissipation (Perino et al 2010) in jointed rock mass, these viscoelastic models were mainly proposed for the consideration of the joint effect in jointed rock mass. There still lacks an effective method to determine the viscosity and parameters in the theoretical models for rocks with micro defects.…”

Fracture-Induced Anisotropic Attenuation

“…Faults in the earth's crust constitute sources of earthquakes (Pyrak-Nolte et al 1990) and hydrocarbon and geothermal reservoirs are mainly composed of fractured rocks (Nakagawa and Myer 2009). Applications in geotechnical engineering, such as analysis of the dynamic stability of rock slopes and tunnels, involve the study of imperfect joints in rock masses (Perino et al 2010;Fan et al 2011). In geophysical prospecting, knowledge of reservoirs' fracture orientations, densities, and sizes is essential, since these factors control hydrocarbon production (Hansen 2002;Hall and Kendall 2003;Barton 2007).…”

Application of the discontinuous deformation analysis method to stress wave propagation through a one-dimensional rock mass

“…46 To compare with the existing theoretical results, the DDA simulations of this paper such as in section 4 use DDM. In the following content, the effects of both the no tension and slipping characteristics of a joint on wave propagation are investigated with the DDA method.…”