A Frequency-Domain Method for Determining Joint Stiffness in a Rock Mass Using Stress Wave Response

Abstract

Abstract Accurate determination of joint stiffness is crucial for evaluating the deformation and stability of rock mass in geotechnical engineering. This study proposes a novel method for determining joint stiffness by analyzing the frequency characteristics of the stress wave. Pendulum impact tests were conducted to generate and capture incident and reflected waves. The frequency spectra of these waves were then obtained using the discrete Fourier transform. The joint stiffness was subsequently determined by comparing the frequency-domain characteristics of the incident and reflected waves. To validate the accuracy and robustness of the determined stiffness, a series of reflected waves at different incident amplitudes and frequencies were predicted based on the derived stiffness parameter and compared with experimental measurements. The results demonstrate that the predicted reflected waveforms show excellent agreement with experimental records, with correlation coefficients exceeding 0.98 and amplitude relative errors of up to 4.35% across varying loading conditions. These findings confirm that the frequency-domain method can determine joint stiffness with high accuracy and robustness, and the influence of incident wave frequency is negligible (relative deviation <3.20%). Compared with traditional static methods or complex full-waveform inversion techniques, this method offers a simpler, effective, and practical approach. It shows significant potential for predicting wave reflection behavior in rock mass with unknown joints, providing a promising tool for nondestructive site characterization and stability assessment in rock engineering.