Study of wave attenuation across parallel fractures using propagator matrix method

Stress wave attenuation across fractured rock masses is a great concern of underground structure safety. This paper presents an analytical study on wave attenuation across parallel fractures at arbitrary incidence angles, where multiple reflections occurring between fractures are taken into account. Combined with displacement discontinuous model, plane wave analysis and propagator matrix method are applied to develop relations between the first layer and the nth layer with respect to potential amplitudes or displacements and stresses in matrix form. With initial and boundary conditions for different scenarios, potential amplitudes in any layer or displacements and stresses at any point can be obtained by solving corresponding matrixes. After parametric studies, it is found that parameters including incidence angle, normalized fracture stiffness, number of fractures, and fracture spacing have obvious effects on wave attenuation across parallel fractures.