Seismic response of a single and a set of filled joints of viscoelastic deformational behaviour

Abstract

S U M M A R YRock joints are often filled with weak medium, for example, saturated clay or sand, of viscoelastic nature. Their effects on wave propagation can be modelled as displacement and stress discontinuity conditions. The viscoelastic behaviour of the filled joint can be described by either the Kelvin or the Maxwell models. The analytical solutions for wave propagation across a single joint are derived in this paper by accounting for the incident angle, the nondimensional joint stiffness, the non-dimensional joint viscosity and the acoustic impedance ratio of the filled joint. It is shown that the viscoelastic behaviour results in dissipation of wave energy and frequency dependence of the reflection and transmission coefficients. Based on curve fitting of the experimental data of P-wave propagation across a single joint filled with saturated sand, both the Kelvin and Maxwell models are found to reproduce the behaviour of the filled joint, in terms of the amplitude and frequency contents. Then, wave transmission across a filled joint set is studied with the virtual wave source method and the scattering matrix method, where multiple wave reflections among joints are taken into account. It is shown that the non-dimensional joint spacing and the number of joints have significant effects on the transmission coefficients.

Dynamic response of a rock fracture filled with viscoelastic materials

“…In the DSDM (Zhu et al, 2011), for a rock fracture filled with dry sand, the Kelvin model, consisting of one spring and one dashpot in parallel, can be adopted to describe the dynamic response of the filled fracture. The specific viscosity is set to zero for a fracture filled with dry sand.…”

“…Meanwhile, the thickness of filling materials may not be overlooked compared with the wavelength. A newer and more precise model to describe the boundary conditions of a filled fracture, the displacement and stress discontinuity model (DSDM), has been developed by Zhu et al (2011). It proposes that the stress discontinuity across a filled fracture is caused by the specific initial mass of filling materials and the displacement discontinuity is determined by the transmitted stress and the specific fracture stiffness.…”

A thin-layer interface model for wave propagation through filled rock joints

“…By modeling the interface between two solids as a thin viscoelastic layer with stiffness and inertia term, wave propagation was addressed by Rokhlin and Wang (1991). Later, the thin viscoelastic layer interface concept was extended by Zhu et al (2011) to study wave propagation across filled joints. The results from Rokhlin and Wang (1991), Li et al (2010) and Zhu et al (2011) showed that the thickness of a filled joint influences wave propagation in a rock mass.…”

“…Later, the thin viscoelastic layer interface concept was extended by Zhu et al (2011) to study wave propagation across filled joints. The results from Rokhlin and Wang (1991), Li et al (2010) and Zhu et al (2011) showed that the thickness of a filled joint influences wave propagation in a rock mass. In practical situation, when a stress wave propagates across a filled joint with one thin thickness, i.e.…”

Loading Rate Dependency of Dynamic Responses of Rock Joints at Low Loading Rate

“…Stress wave propagation across rock joints has been investigated theoretically (e.g., Pyrak-Nolte et al 1990;Cai and Zhao 2000;Li et al 2010a;Zhu et al 2011) and experimentally (e.g., Leucci and Giorgi 2006;Zhao et al 2006Zhao et al , 2008Li et al 2010b). Many studies focus on the interaction between the stress wave and the rock joints (e.g., Li et al 2011;Ma et al 2011).…”