Elastic Wave Propagation and Evaluation of Low Strain Dynamic Properties in Jointed Rocks

Abstract

When the point under consideration is not near to the source of vibration, the strains developed in the rock mass due to the passage of waves are usually of small magnitude, and within the elastic range. However, the rock mass may be subjected to a wide range of strain levels depending on the source of vibration and the wave frequency, even within the elastic limit. The present study is based on the two general conditions existing at field, long wave length propagation of waves and intermediate wavelength propagation of waves. When the wavelength of propagating wave is much longer than the joint spacing, it is referred to as long wavelength condition and is associated with propagation of low frequency waves across closely spaced joints. When wavelength of propagating wave is nearly equal to joint spacing, it is known as intermediate wavelength condition and is associated with propagation of high frequency waves. Long wave length propagation of waves has been studied by conducting laboratory experiments using Resonant Column Apparatus on developed plaster gypsum samples. The influence of joint types, joint spacing and joint orientation on wave propagation has been analyzed at three confining stresses under various strain levels. The wave velocities and damping ratios at various strain levels have been obtained and presented. Shear wave velocities are more dependent on confining stress than compression wave velocities across frictional joints whereas, compression wave velocities are more dependent on confining stress than shear wave velocities across filled joints. Wave velocities are at minimum and wave damping is at maximum across horizontal joints whereas wave velocities are at maximum and wave damping is at minimum across vertical joints. Shear wave velocity and shear wave damping are more dependent on joint orientations than compression wave velocity and compression wave damping. As Resonant Column Apparatus has some limitations in testing stiff samples, a validated numerical model has been developed using Discrete Element Method (DEM) that can provide resonant frequencies under torsional and flexural vibrations. It has been found from numerical simulations, that reduction of normal and shear stiffness of joint with increasing strain levels leads to wave velocity reduction in jointed rock mass. Intermediate wave length propagation of waves has been studied by conducting tests using Bender/ extender elements and the numerical simulations developed using 3DEC (Three Dimensional Distinct Element Code).Parametric study on energy transmission, wave velocities and wave amplitudes of shear and compression waves, has been carried out using the validated numerical model. The propagation of waves across multiple parallel joints was simulated and the phenomenon of multiple reflections of waves between joints could be observed. The transformations of obliquely incident waves on the joint have been successfully modeled by separating the transmitted transformed P and S waves. The frequency dependent behavior of jointed rocks has been studied by developing a numerical model and by applying a wide range of wave frequencies. It has been found that low frequency shear waves may involve slips of rock blocks depending on the strength of rock joint, leading to less transmission of energy; while low frequency compression waves are well transmitted across the joints. High frequency shear and compression waves experience multiple reflections and absorptions at joints.