中文摘要：

基于应力-应变关系中包含三阶非线性项的岩石介质和非线性法向变形节理模型，结合波动方程特征线法，得到在非线性岩石介质中纵波法向入射单节理时透射波的半数值解，并编写计算程序。对波源参数、节理参数和岩石非线性、节理位置等进行一系列参数研究，探讨节理岩石双重非线性弹性介质对透射波波形、透射系数和频谱分布的影响。研究结果表明，岩石的非线性系数会对节理的高频滤波作用以及节理面质点位移的恢复路径产生影响。双重非线性作用下的透射波除了和线性岩石中一样受节理参数、波源参数的影响外，还与节理位置和岩石的非线性系数有关。在纵波受岩石非线性作用较大的情况下，频率相同振幅较小的纵波的透射系数较大。大振幅波在双重非线性的影响下，透射波中会产生一系列高谐波，该高谐波是应力波受岩石和节理综合作用的结果。

英文摘要：

Based on the nonlinear rock mechanics with third order nonlinearity and nonlinear normal deformation behaviour joint model, by using wave equation characteristic method, the semi-numerical solutions of P-wave across single joint in dual nonlinear elastic medium are obtained. Computational programs are compiled. Studies of parameters of joint and wave source, nonlinear coefficient of soft rock, position of joint are conducted to get an insight into transmitted waveform, transmission coefficient and frequency spectra distribution under the influence of dual nonlinear elasticity. The results show that the nonlinear coefficient of rock affects the high-frequency filter of joint and displacement recovery path of particle on joint surface. The wave propagation is not only affected by the same factors in linear wave, but also by the nonlinear coefficient and joint position. When P-wave with the same frequency is influenced greatly by the nonlinear behaviour of rock; the transmission coefficient of P-wave with smaller amplitude is bigger. When P-wave with large amplitude is influenced by dual nonlinearity; a series of higher harmonics are produced in transmitted wave; and this higher harmonics is affected by the combined effect of rock and joint.