Study of wave attenuation across parallel fractures using propagator matrix method

Abstract

SUMMARYStress 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.

Numerical Study on Dynamic Response of a Horizontal Layered-Structure Rock Slope under a Normally Incident Sv Wave

“…In order to verify the capability of FLAC on wave transmission across rock joints, the modeling results are compared with analytical solutions with the propagator matrix method [16], adopting the displacement discontinuity model. In this section, FLAC results of normally incident P and Sv waves transmission across a single joint are compared with analytical solutions, and the effects of joint normal, shear stiffness, and incident wave types (P and Sv waves) on wave transmission in FLAC modeling are verified.…”

“…Analytical solutions and experimental data have proven that the incidence angle of waves, normalized fracture stiffness, number of fractures, and dimensionless fracture spacing have obvious effects on wave attenuation across parallel fractures [16,17].…”

Numerical Modeling of Wave Transmission Across Rock Masses with Nonlinear Joints

“…Based on DDM, the interaction between blast waves and a single rock joint with arbitrary incident angle was effectively analyzed by Li and Ma (2010) and Li et al (2011). In addition, Zhao et al (2012), Li et al (2012), proposed the propagator matrix method, the time-domain recursive method and the virtual wave source method, respectively, and applied them to study wave propagation obliquely across a set of parallel joints. Later, Li (2013) adopted and extended the time-domain recursive method to analyze the effect of nonlinear joints on wave propagation.…”

An improved equivalent viscoelastic medium method for wave propagation across layered rock masses

“…Generally, the DDM treats rock masses as discrete entities to solve the problems in the small-scale. By analyzing stress wave interaction with two surfaces of a joint, this method has been successfully applied for wave propagation across single joint [3,[11][12][13][14] and a set of parallel joints [15][16][17][18][19][20][21]. For joints filled with a viscous fluid, the interaction between the seismic wave and the two fluid-solid boundaries were analyzed [22], when the incidence impinged on the layer with arbitrary incident angle.…”