Study on wave propagation across a single rough fracture by the modified thin-layer interface model

• A thin-layer interface model is improved for wave propagation across rough fractures.
• Relation between the normal stress and closure of rough fractures is derived.
• Analytical solutions from the present and existing methods are compared.
• Effects of roughness and weathering of fractures on wave propagation are studied.

Wave propagation across a fracture is dependent on the specific stiffness of the fracture, which is implicitly related to the fracture surface characteristics, such as roughness, matching and wall strength. In this study, a rough fracture with different void spaces and contact areas is modeled by two smooth surfaces separated by square column asperities with different heights, that is, the fracture is modeled as a thin-layer interface. The material properties of the asperities also vary to represent different weathering grades of fracture surfaces. The wave propagation equation is established by analyzing the interaction between a stress wave and the rough fracture. By back analysis, the relation between the normal stress and the closure of the fracture is derived, where the effects of the contact area, the fracture thickness, the frequency of the incidence and the weathering grade of the asperities on wave propagation are studied. The theoretical solutions of the thin-layer interface model (TLIM) are compared with those based on the zero-thickness interface model (ZTIM) which is commonly used currently. The study concludes that the TLIM is able to represent the behavior of fractures with different types of surface roughness and weathering.