Abstract

Longitudinal stress wave propagation through rock mass with parallel joints is analytically studied. A viscoelastic model (Burgers model) is used to simulate the jointed rock mass and the time-dependent property of the rock material is taken into account. The joints are assumed to deform linear elastically. A displacement discontinuity method is adopted to analyze the longitudinal stress wave transmission and reflection in the rock mass. To verify the analytical results, a numerical study of stress wave propagation through jointed rock mass with single and multiple joints was also carried out. Comparisons of the transmitted and reflected waves with the results derived from the conventional displacement discontinuity method are performed. It shows that the viscosity of the rock material should be considered when analyzing stress wave propagation in jointed rock mass,

Introduction

Modeling the dynamic behavior of jointed rock mass is of great interest to geophysics, mining, and underground constructions. It is also significant to assess the stability and damage of rock structures under stress wave. Currently, there are two different approaches to investigate stress wave propagation in discontinuous rock system. One is called equivalent medium method [1–3], which predicts the aggregate effects of the discontinuous system by using an equivalent material. The effective moduli within a representative elementary volume were derived and they are extended to the discontinuous rock mass system. The effective moduli of the discontinuous rock system can be obtained by using the static method, which is based on the measurement of the deformation induced in a material by the application of a known static force, or by the dynamic method, which measures the ultrasonic body wave velocities. This approach is effective only if the frequency dependence and multiple reflections among the discontinuities are negligible [4]. The other approach is called displacement discontinuity methods [4–6], which assume the stresses across the joint are continuous, whereas the displacements across the joint are discontinuous. This approach has been successfully used to predict the transmission of seismic waves in a discontinuous rock system. The joint can be considered to be linear or nonlinear elastic, but the rock at the two sides of the discontinuity is always intact and linear elastic [6]. However, rocks may not behave entirely elastic when a seismic wave propagating in them. In his investigation, both axial and lateral deformations of marble specimens were measured under a constant loading and a power function was used to simulate creep curves of the marble specimens. Laboratory investigations were performed by Lin et al. [9] to obtain the time-dependent strength degradation of granite by application of a constant loading after an initial loading. Typical creep curves of granite include three stages were obtained. However, the current logarithmic or power creep model of rock can only be used to form integral constitution of rock, which is not as convenient as differential constitution in the analysis of wave propagation in rock mass. Therefore, an explicit and effective model which can be used to form differential constitution are necessary.

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