1、 第146页英文原文Study on the transmission and reflection of stress waves across jointsYexue Li a,b, Zheming Zhuc,n , Bixiong Lic, Jianhui Denga , Heping Xiec a College of Water Resource & Hydropower, Sichuan University, Chengdu 610065, Chinab Department of Civil Engineering, Xiangfan University, Xiangfan,
2、 Hubei 441053, Chinac College of Architecture and Environment, Sichuan University, Chengdu 61005, ChinaAbstract：In order to investigate the transmission and reflection of stress waves across joints, a fractal damage joint model is developed based on fractal damage theory, and the analytical solution
3、 for the coefficients of transmission and reflection of stress waves across joints is derived from the fractal damage joint model.The fractal geometrical characteristics of joint surfaces are investigated by using laser profilometer to scan the joint surfaces. The dynamic experiments by using Split
4、Hopkinson Pressure Bar (SHPB) for rock specimens with single joint are conducted to confirm the analytical solution of the coefficients of transmission and reflection. The SHPB experimental results of the coefficients agree well with the analytical solution.Keywords: Stress wave Transmission and ref
5、lection Joint Fractal dimension Damage SHPB1. IntroductionAs is well known, rocks usually contain defects or discontinuities, such as joints, cracks, pores and faults. These discontinuities weaken rock material strength and stability as they are subjected to dynamic loads, such as blasts and earthqu
6、akes, therefore, the stability of geotechnical structures, such as tunnels, subways, dams, etc., would be controlled by these discontinuities. The designers of such geotechnical structures are required to have the knowledge of wave propagation across joints, and therefore, the corresponding study on
7、 transmission and reflection of waves across joints is significant. Currently, a large number of theoretical, empirical and numerical models concerning the geometrical and mechanical properties of joints have been established to study the joint effects on wave propagation and attenuation 18.However,
8、 our understanding of the process of transmission and reflection of stress waves crossing joints is far from complete, as joints are still complex for us.When stress waves encounter joints, they will suffer partial reflection and transmission. The characteristics of reflection and transmission depen
9、d on many factors, such as, joint spacing, joint orientation 9, joint width, joint roughness, joint stiffness, filling material inside joints 10,11, liquid saturation, etc. For the issue of wave propagation across joints, Cai and Zhao 4 have investigated the effects of multiple parallel fractures on
10、 apparent attenuation of stress wave in rock masses. Fan et al. 6 have presented the study on wave propagation and wave attenuation in jointed rock masses by using discrete element method (DEM). Gulyayev and Ivanchenko 8 have investigated the problem about dynamic interaction of discontinuous waves
11、with interfaces between anisotropic elastic media. Perak-Nolte 12 and Zhao and Cai 13 have investigated stress wave propagation across linear deformation joints, and obtained the coefficients of stress wave transmission and reflection. Wang et al. 14 have derived the coefficients of transmission and
12、 reflection of stress wave crossing non-linearly deformational joints by using the rock damage mechanics theory 15 and strain equivalent hypothesis, and the result of the coefficients agreed well with the numerical results presented by Zhao and Cai 13.Kahraman 16 has simulated joint surface roughnes
13、s and investigated the relation between the roughness of joint surfaces and the particle velocity of stress waves.The surfaces of natural joints developed during a long time of geological digenesis are not smooth, and actually they are very rough. A coefficient of joint roughness JRC (joint roughnes
14、s coefficient), proposed by Bam ford 17 in 1978, somehow can express the effect of joint roughness on stress wave propagation. However, JRC is an empirical parameter, and it can only express the roughness of one-dimensional curve and cannot be employed to describe the natural joint roughness precise
15、ly because the natural joints contain three-dimensional rough surfaces, in which the dimension should be greater than 2 and less than 3. As stress waves cross joints, it is very difficult to determine the incident angle because the joint surfaces usually consist of various sub surfaces with differen
16、t normal directions. Under this scenario, it is necessary to use another parameter, fractal dimension, to describe the joint roughness. Fractal dimensions can be applied to describing the joint roughness 1820 and it will be employed in this study.In this paper, an attempt is made to obtain the analytical solution for the coefficients of transmission and reflection of stress waves across joints. The fractal theory
