Reflection and refraction laws of low amplitude stress wave on a 3-D rock joint surface
LIU Chuanzheng1,2, ZHANG Jianjing3, CUI Peng1
1.Key Laboratory of Mountain Hazards and Earth Surface Processes,Institute of Mountain Hazards and Environment,Chinese Academy of Science,Chengdu 610041,China;
2.School of Engineering Science,University of Chinese Academy of Science,Beijing 100049,China;
3.School of Civil Engineering,Southwest Jiaotong University, Chengdu 610031,China
Abstract：In dynamic rock engineering, the existence of rock joint has a large influence on stress wave propagation and energy transmission in rock, and it affects dynamic response characteristics of geotechnical engineering. In the past studies, effects of complex surface morphology of 3-D rock joint on stress wave’s propagation were rarely investigated theoretically. Here, the general form of a 3-D rock joint surface’s stress-deformation constitutive equation was analyzed based on the microscopic contact theory. The relationship between planar harmonic wave propagation and stress-deformation on a 3-D rock joint surface was analyzed. Analytical solutions to P-wave, SV-one and SH-one’ reflection and refraction laws on a 3-D rock joint surface were derived using the displacement discontinue method (DDM). Based on the theoretical analysis and derivation, the parametric analysis was performed to analyze effects of stress wave’s incident angle and rock joint’s cross-coupled stiffness coefficients on stress wave’s reflection and refraction. The study showed that on a 3-D rock joint surface, P-wave, SV-one and SH-one can be transformed into each other when cross-coupled stiffness terms in rock joint surface’s constitutive equation are nonzero; increasing cross-coupled stiffness terms can increase amplitude coefficients of transformed waves and isomorphic reflected ones, and decrease those of isomorphic refracted ones.
刘传正1,2, 张建经3, 崔鹏1. 低幅值应力波在岩石三维节理面的折反射规律理论研究[J]. 振动与冲击, 2018, 37(15): 68-77.
LIU Chuanzheng1,2, ZHANG Jianjing3, CUI Peng1. Reflection and refraction laws of low amplitude stress wave on a 3-D rock joint surface. JOURNAL OF VIBRATION AND SHOCK, 2018, 37(15): 68-77.
[1] Belem T., Homand-Etienne F., Souley M.. Quantitative Parameters for Rock Joint Surface Roughness[J]. Rock Mechanics and Rock Engneering, 2000, 33(4): 217-242.
[2] 孙辅庭, 佘成学, 蒋庆仁. 一种新的岩石节理面三维粗糙度分形描述方法[J]. 岩土力学, 2013, 34(8): 2238-2242.
SUN Futing, SHE Chengxue, JIANG Qingren. A new fractal description method for three-dimensional roughness surface of rock joint[J]. Rock and Soil Mechanics, 2013, 34(8): 2238-2242.
[3] Jing L., Nordlund E., Stephansson O.. An Experimental Study on the Anisotropy and Stress-dependency of the Strengh and Deformability of rock Joint[J]. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 1992, 29(6):535-542.
[4] Jing L., Nordlund E., Stephansson O.. A 3-D Constitutive Model for Rock Joints with Anisotropy Friction and Stress Dependency in Shear Stiffness[J]. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 1994, 31(2):173-178.
[5] 王光纶, 尹显俊. 岩体结构面三维循环加载本构关系[J]. 清华大学学报(自然科学版), 2005, 45(9): 1193-1197.
WANG Guanglun, YIN Xianjun. 3-D constitutive relation for rockjoints during cyclic loading[J]. Tsinghua Univ.(Sci.&Tech.), 2005, 45(9): 1193-1197.
[6] Misra A. Micromechanical model for anisotropic rock joints[J]. Journal of Geophysical Research, 1999, 104(10):23175-23187.
[7] Schoenberg M. Reflection of Elastic Waves from Periodically Stratified Media with Interfacial SLIP[J]. Geophysical Prospecting, 1983, 31(2):265–292.
[8] Myer L.R., Hopkins D., Cook N.G.W.. Effects of contact area of an interface on acoustic wave refraction characteristics[J]. In: Proc., 26th US Rock Mechanics Symposium, Boston, 1985,1, 565-572.
[9] Myer L.R., Pyrak-Nolte L.J., Cook N.G.W. Effects of single fracture on seismic wave propagation[J]. In: Proc., ISRM Symposium on Rock Fractures, Leon, 1990:467-473.
[10] Pyrak-Nolte L.J., Myer L.R., Cook N.G.W.. Refraction of seismic waves across single natural fractures[J]. J. Geophys. Res. 95 1990(a)(B6):8617-8638.
[11] Pyrak-Nolte L.J.. Seismic visibility of fractures[D]. Ph. D. Thesis. University of California 1988, Berkeley, USA.
[12] Pyrak-Nolte L.J.. The seismic response of fractures and the interrelations among fracture properties[J]. Int. J. Rock Mech. Min. Sci. 1996,33(8): 787-802.
[13] Gu B, Suárez‐Rivera R, Nihei K T, et al. Incidence of plane waves upon a fracture[J]. Journal of Geophysical Research Solid Earth, 1996, 101(B11):25337-25346.
[14] Roy S., Pyrak-Nolte L.J.. Interface waves propagating along tensile fracture in dolomite[J]. Geophysical Research Letters, 1995, 22(20):2773-2777.
[15] Roy S., Pyrak-Nolte L.J.. Observation of a distinct compressional mode interface wave on a single fracture[J]. Geophysical Research Letters, 1997,24(2):173-176.
[16] Zhao J., Cai J.G.. Refraction of Elastic P-waves across Single Fractures with a Nonlinear Normal Deformational Behavior[J]. Rock Mech. Rock Engng. 2001,34(1):3-22.
[17] 俞缙, 宋博学, 钱七虎. 节理岩体双重非线性弹性介质中的纵波传播特性[J]. 岩石力学与工程学报, 2011, 30(12): 2463-2473.
YU Jin, SONG Boxue, QIAN Qihu. PROPAGATION OF P-WAVES IN DUAL NONLINEAR ELASTIC MEDIUM FOR JOINTED ROCK MASS[J]. Chinese Journal of Rock Mechanics and Engineering, 2011, 30(12): 2463-2473.
[18] 俞缙, 宋博学, 蔡燕燕, 等. 非线性波在岩石节理处的透射规律研究[J]. 应用基础与工程科学学报, 2012, 20(6): 1088-1098.
YU Jin, SONG Boxue, CAI Yanyan, et al.. Transmission Law of Nonlinear Wave across Jointed Rock[J]. JOURNAL OF BASIC SCIENCE AND ENGINEERING, 2012, 20(6): 1088-1098.
[19] Daehnke A., Rossmanith H.P.. Reflection and refraction of plane stress waves at interfaces modeling various rock joints[J]. International Journal for Blasting and Fragmentation, 1997(a), 1(2):111-231.
[20] Misra A., ASCE M., Marangos O.. Rock-Joint Micromechanics: Relationship of Roughness to Closure and Wave Propagation[J]. INTERNATIONAL JOURNAL OF GEOMECHANICS, 2011, 11(6): 431-439
[21] Jing L.. Numerical Modeling of Jointed Rock Masses by Distinct Element Method for Two, and Three-Dimensinal Problems[D]. Lulea University of Technology, 1990.
