Normal transmission of S-wave across parallel fractures with Coulomb slip behavior

When an elastic wave propagates through a rock mass, its amplitude is attenuated and velocity is slowed due to the presence of fractures. During wave propagation, if the shear stress at a fracture interface reaches the fracture shear strength, the fracture will experience a large shear displacement. This paper presents a study of the normal transmission of S-waves across parallel fractures with Coulomb slip behavior. In our theoretical formulation, the method of characteristics combined with the Coulomb slip model is used to develop a set of recurrence equations with respect to particle velocities and shear stress. These equations are then solved numerically. In a comparison with the theoretical study, numerical modeling using the universal distinct element code (UDEC) has been conducted. A general agreement between UDEC modeling and theoretical analysis is achieved. The magnitude of the transmission coefficient is calculated as a function of shear stress ratio, nondimensional fracture spacing, normalized shear stiffness, and number of fractures. The study shows that the shear stress ratio is the most important factor influencing wave transmission, and the influence of other factors becomes more apparent when the shear stress ratio is small.