Analytical investigation of wave propagation across jointed rock mass with single-joint and multiple parallel joints

Document Type : Original Article

Authors

faculty

Abstract

Wave propagation across the rock masses is one of the most topics in rock dynamics, which is used in various petroleum, mining, civil military industries. Since rock mass includes rock material and various forms of discontinuities, the nature of rock mass discontinuities significantly affects mechanical properties and engineering behavior. Therefore, adequate knowledge and understanding of how the wave propagates in rock mass, especially for projects that are more important and more sensitive, is necessary. In the present paper, the analytical method for wave propagation across rock mass based on the method developed by Huang et al. (2014) is presented for elastic state and wave propagation in single-joint and multiple parallel joints is studied. Then, a parametric study was performed on parameters including normalized joint stiffness, joint dip, normalized spacing and number of joints on wave propagation in single joint and multiple parallel joints and the obtained results have been compared with the results of other proposed methods.

Keywords


Cai, J.G and Zhao, J., 2000. Effects of multiple parallel fractures on apparent attenuation of stress waves in rock masses. International Journal of Rock Mechanics and Mining Sciences, 37(4), pp.661-682.
Carcione, J.M. and Picotti, S., 2012. Reflection and transmission coefficients of a fracture in transversely isotropic media. Studia Geophysica et Geodaetica, 56(2), pp.307-322.
Gu, B., Suárez‐Rivera, R., Nihei, K.T. and Myer, L.R., 1996. Incidence of plane waves upon a fracture. Journal of Geophysical Research: Solid Earth, 101(B11), pp.25337-25346.
Huang, X., Qi, S., Liu, Y. and Zhan, Z., 2014. Stress wave propagation through viscous-elastic jointed rock masses using propagator matrix method (PMM). Geophysical Journal International, 200(1), pp.452-470.
Li, J. and Ma, G., 2010. Analysis of blast wave interaction with a rock joint. Rock Mechanics and Rock Engineering, 43(6), pp.777-787.
Li, J., Ma, G. and Zhao, J., 2010. An equivalent viscoelastic model for rock mass with parallel joints. Journal of Geophysical Research: Solid Earth, 115(B3).
Ma, G.W., Fan, L.F. and Li, J.C., 2013. Evaluation of equivalent medium methods for stress wave propagation in jointed rock mass. International Journal for Numerical and Analytical Methods in Geomechanics, 37(7), pp.701-715.                                                                                                                                                                                                                                                                                                            Perino, A., Barla, G. and Orta, R., 2010, June. Wave propagation in discontinuous media. In ISRM International Symposium-EUROCK 2010. International Society for Rock Mechanics
Perino, A., Orta, R. and Barla, G., 2012. Wave propagation in discontinuous media by the scattering matrix method. Rock mechanics and rock engineering, 45(5), pp.901-918.
Pyrak‐Nolte, L.J., Myer, L.R. and Cook, N.G., 1990. Transmission of seismic waves across single natural fractures. Journal of Geophysical Research: Solid Earth, 95(B6), pp.8617-8638.
Pyrak‐ Nolte, L.J., Myer, L.R. and Cook, N.G., 1990. Anisotropy in seismic velocities and amplitudes from multiple parallel fractures. Journal of Geophysical Research: Solid Earth, 95(B7), pp.11345-11358.
Schoenberg, M. and Douma, J., 1988. Elastic wave propagation in media with parallel fractures and aligned cracks. Geophysical Prospecting, 36(6), pp.571-590.
Zhao, J. and Cai, J.G., 2001. Transmission of elastic P-waves across single fractures with a nonlinear normal deformational behavior. Rock Mechanics and Rock Engineering, 34(1), pp.3-22.
Zhao, J., Zhao, X.B. and Cai, J.G., 2006. A further study of P-wave attenuation across parallel fractures with linear deformational behaviour. International Journal of Rock Mechanics and Mining Sciences, 43(5), pp.776-788.
Zhao, X. B, Zhao, J and Cai, J. G, 2006. P‐wave transmission across fractures with nonlinear deformational behaviour. International journal for numerical and analytical methods in geomechanics, 30(11), pp.1097-1112.
Zhao, X.B., Zhao, J., Hefny, A.M. and Cai, J.G., 2006. Normal transmission of S-wave across parallel fractures with Coulomb slip behavior. Journal of engineering mechanics, 132(6), pp.641-650.
Zhu, J., 2011. Theoretical and numerical analyses of wave propagation in jointed rock masses.
Zhu, J.B. and Zhao, J., 2013. Obliquely incident wave propagation across rock joints with virtual wave source method. Journal of Applied Geophysics, 88, pp.23-30.