Attenuation of elastic wave across single fracture with finite shear strength

When a wave propagates the wave is greatly attenuated due to the presence of fractures. This paper presents a study on S-wave attenuation across single fracture with the Coulomb slip behaviour. In the 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 numerically solved. To compare with the theoretical study, numerical modelling using Universal Distinct Element Code (UDEC) is conducted. A general agreement between UDEC modelling and theoretical analyses is achieved. The magnitude of transmission coefficient is calculated as a function of shear stress ratio and normalized shear stiffness. The study shows that the shear stress ratio is the important factor influencing wave transmission. The influence of normalized shear stiffness becomes obvious, when shear stress ratio is small.