A Modified Thin-Layer Interface Model for Wave Propagation Across a Rock Fracture with Viscoelastic Filling

Abstract

A modified thin-layer interface model (MTLIM) is established to investigate stress wave propagation across a fracture filled with viscoelastic materials in a rock mass. First, this MTLIM treats the viscoelastic filling material as a composite of elastic thin layers and viscoelastic bonds. The displacement discontinuity at the bond is described by the Zener model, and the wave propagation equation through the fracture is derived in the time domain. Then, this MTLIM is degenerated to the thin-layer interface model (TLIM) for the extreme case and verified by the transmitted wave in a dynamic experiment. Its performance is compared with those of the TLIM and a zero-thickness interface model (ZTIM). Finally, the waveform evolution, transmission and reflection coefficients, and the energy dissipation ratio for stress wave incidence are investigated for viscoelastic filled fractures at different thicknesses. Results indicate that the MTLIM has better performance than the TLIM, Maxwell model, and Kelvin model in accurately reproducing the dynamic response of stress waves through viscoelastic filled fractures. Significant differences are observed between thin and thick filled fractures in the variation of the waveform and the velocity transmission and reflection coefficients with filling thickness. A thin filled fracture can cause more total energy dissipation than a thick one in some cases. The MTLIM can describe the effects of repeated reflections and the viscoelastic effects of filled fractures on the frequency and amplitude of seismic responses.