中文摘要：

将传统的BB模型与经典指数模型统一起来，提出的准静态条件下改进的节理弹性非线性法向变形本构关系可定量化描述节理变形的这类差异。在不考虑加载速率对节理变形行为影响的情况下，将该本构关系推广至动态条件，建立了法向入射纵波在弹性半无限空间中干性单节理处传播的位移不连续模型，基于Lemaitre假设获得了节理透、反射系数｜TIMP｜和｜RIMP｜的近似解析解；同时结合一维波动方程特征线法推导了节理透、反射波质点速度时域数值差分格式并自编了计算程序，进而得到｜TIMP｜、｜RIMP｜透、反射波能量etra和eref、延迟时间Tdel的半数值解，依此研究弹性纵波在单节理处的传播过程及特征。在针对节理法向初始切线刚度Kn,i、节理闭合量与最大允许闭合量比值y=dn/dmax、入射波频率厂等因素对｜TIMP｜、｜RIMP｜的影响进行探讨的同时，着重分析模型非线性程度掌及入射波最大振幅｜Vinc｜的变化对透射波振幅及能量衰减、波形及频谱畸变、时间延迟所产生的影响，并解释了一种“超越”现象。

英文摘要：

The improved elastic nonlinear normal deformation constitutive model under the quasi-static condition which generalizes the BB model and the classical exponential model can describe the extent of nonlinearity quantitatively. Without the loading-rate effect considered, the improved constitutive relationship is extended to be under the dynamic condition, and then a nonlinear displacement discontinuity model for normally incident P-wave propagation across a dry fracture is established in an elastic half-space. By introducing the Lemaltre hypothesis, the approximate analytical solutions of transmission and reflection coefficients ｜TIMP｜ and ｜RIMP｜ are obtained. Furthermore, using one-dimensional wave equation characteristic method, the time-domain numerical difference scheme of reflected and transmitted particle velocities is proposed, and computational programs are compiled to obtain semi-numerical solutions of ｜TIMP｜ and ｜RIMP｜, transmission and reflection energy etra and eref and delay time Tdel. Parameter studies are conducted to get an insight into the effects of the extent of nonlinearity ξ and the incident wave maximum amplitude ｜Vinc｜ on transmitted wave amplitude and energy attenuation, waveform and spectral aberration, and time delays, in terms of fracture initial stiffness Kn,i, the ratio of given closure to the maximum allowable closure γ=dn/dmax, and frequency f. In addition, the phenomenon of exceeding is explained.