Fourier-shape-based reconstruction of rock joint profile with realistic unevenness and waviness features

Rock joint shape characteristics, waviness and unevenness play essential but distinct roles in shear mechanism of rock joints. This study presents a novel method to generate virtual rock joint profiles with realistic waviness and unevenness features. Firstly, joint profiles are obtained by 3D laser scanning device. Secondly, quantification of waviness and unevenness is conducted by traditional method, including digital filtering technique and roughness parameter R_L. Thirdly, the discrete Fourier transform (DFT) method is employed to analyze the joint outlines. Two representative Fourier shape descriptors (D₃, D₈) for characterization of waviness and unevenness are suggested. Then, the inverse discrete Fourier transform (IDFT) is adopted to reconstruct the joint profiles with random values of phase angles but prescribed amplitudes controlled by D₃ and D₈. The traditional method is then applied to the reconstructed joint profiles to examine statistically the relationships between D₃ and D₈ and parameters R_L of waviness and unevenness, respectively. The results show that larger D₈ tends to result in larger waviness while higher D₃ tends to increase unevenness. Reference charts for estimation of waviness and unevenness with different pairs of D₃ and D₈ are also provided to facilitate implementation of random joint reconstruction.