The effects of roughness and offset on fracture compliance ratio

Fractures are a source of extra compliance in the rock mass. The mechanical properties of the rock matrix as well as the propagation of seismic waves inside the rock medium are dependent on the magnitude of roughness and offset between the imperfect fracture interfaces. Fracture compliance can estimate the degree of contact between fracture faces, type of fluid filling the fracture and the fracture roughness. To characterize these fracture properties, compliance ratio, known by the ratio of normal-to-shear compliance, can be a potential tool in the subsurface studies to improve the well layout design. The focus of this study is to illustrate how the compliance ratio of a rough fracture, with or without the offset between the fracture faces, can diverge from the compliance ratio of a fracture with smooth interface. Quasi-static and dynamic methods are two common ways to calculate the compliance. The former calculates the compliance by measuring the change in the displacement with the applied stress, while the latter estimates the compliance through monitoring the changes in propagation of seismic waves. To compare the compliance ratios of fractures with imperfect and smooth interfaces in an infinite medium, a numerical finite-element model is built in commercial finite-element software. The imperfect interface of the fracture is modeled with saw-tooth-like structures where they can be partially or fully in contact. The defined saw-tooth-like structures of contact asperities impose an in-plane asymmetry in the shear direction. This asymmetry causes two different values for the compliance in shear direction, known as the soft and stiff shear compliance. Our numerical simulations suggest the increase in the degree of contact between the fracture faces increases the compliance ratio in the stiff direction more than the soft direction. The compliance ratio of the fracture with the imperfect interface is larger than the compliance ratio of the smooth fracture. We suggest that the interlocking and riding up effects at the fracture interface may explain our findings in this study.