A rapid and nondestructive method to determine normal and shear stiffness of a single rock joint based on 1D wave-propagation theory

Abstract

Determination of joint stiffness, one of the most important mechanical properties of rock joints, is of great significance. However, joint stiffness is often difficult to complete and accurate determine because of the 3D nature of joints and limited budgets and visible exposure. Wave attenuation in a rock mass is mainly attributed to the presence of joints. Based on 1D plane-wave theory, a rapid and nondestructive method, namely, the rapid evaluation method, is proposed to calculate normal and shear stiffness of joints. The joint is viewed as a boundary condition modeled by the displacement discontinuity model. By solving wave equations with reasonable approximation, joint stiffness can be inversely solved, which is dependent on the seismic impedance, transmission or reflection coefficient, and dominant frequency of transmitted waves. Ultrasonic laboratory tests were carried out to record incident, reflected, and transmitted waveforms as input to the rapid evaluation method. It was found that the presence of joints played three major roles on wave propagation, i.e., velocity, amplitude, and dominant frequency decay. Compared with wave slowness, wave attenuation, on which the proposed rapid evaluation method is based, is more sensitive to the presence of joints. Uniaxial compression tests and direct shear tests were also carried out to directly measure the normal and shear stiffness of joints, respectively. A comparison was then made between joint stiffness obtained from the rapid evaluation method and from direct measurements. It was found that joint stiffness acquired from the rapid evaluation method agreed with the direct laboratory measurements. In addition, theoretical predictions of joint stiffness using different ultrasonic transducers are almost the same. Therefore, the applicability and reliability of this proposed method are verified.