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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γ=dn/dmax、入射波频率f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ξ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。
By combining the traditional BB model with the classical index model, the improved nonlinear elastic normal deformation constitutive relation proposed by quasi-static condition can quantitatively describe this kind of difference of joint deformation. Without considering the effect of loading rate on the deformation behavior of joints, this constitutive relation is generalized to dynamic conditions, and a discontinuous discontinuity model is established for the propagation of normal incident longitudinal waves in the dry single joints in a semi-infinite elastic semi-infinite space. Based on Lemaitre The approximate analytical solutions of joint penetration, reflection coefficients TIMP and RIMP are obtained. In the meantime, the finite difference time domain method of joint penetration and reflection particle velocity is deduced by combining with the characteristic line method of one-dimensional wave equation. RIMP, the transmitted and reflected wave energy etra and eref, and the delay time Tdel. Based on this, we study the propagation and characteristics of the elastic longitudinal wave at a single joint. The effects of factors such as initial knuckle stiffness Kn, i, joint closing ratio and maximum allowable closure ratio γ = dn / dmax and incident wave frequency f on TIMP and RIMP are discussed. At the same time, the nonlinearity of the model ξ and the maximum amplitude of the incident wave vinc on the amplitude and attenuation of transmitted waves, waveforms and spectral distortion, the impact of time delay, and explained a “transcendence ” phenomenon.