非线性变形节理中纵波传播特性的理论研究

基于波前动量守恒理论和位移不连续方法所提出的时域分析新方法,引入岩石非线性法向本构关系,对弹性纵波在岩石非线性节理中的传播特性进行了理论分析。采用节理变形的双曲线模型(BB模型),获得纵波P波斜入射非线性节理的传播波动方程,并通过参数研究分析了在岩石节理中节理非线性系数、节理初始刚度、应力波入射角和入射波幅值等因素对纵波传播规律的影响。结果表明:所推导的应力波传播方程在考虑多种非线性问题时,通过迭代计算即可方便求出透射波和反射波的数值解,避免了复杂的数学运算;当波斜入射节理面时,产生了波型转换,节理变形的非线性对透射波和反射波有较大影响,透射系数和反射系数并非随着非线性参数的变化而单调变化。时域内所推导的波传播方程更有益于波斜入射时非线性参数的广泛研究,为开展该方面的理论研究工作提供了借鉴。

Theoretical research into the wave propagation of P-wave across rock joint with nonlinear deformation

Based on an optimization method combined with the conservation of momentum and the displacement discontinuity method,theoretical study is presented on elastic P-wave obliquely impinging the nonlinear rock joint for normal deformation.The hyperbolic elastic model(BB model) is introduced,afterwards the wave propagation equations of incident P-wave across the nonlinear rock joint are deduced.Based on the equations,Parameter studies are carried out,in terms of the nonlinear coefficient of rock joint,the initial normal stiffness of rock joint,the incident angle of stress wave and the amplitude of incident wave.The results indicate that the wave propagation equations derived in the present study have the virtue of convenience to considering the nonlinear problems without complicated mathematical methods.When the stress wave obliquely impinges on the rock joint,nonlinear deformation of rock joint has great influence on the transmitted wave and reflected wave;moreover,the coefficients of the transmitted wave and reflected wave vary non-monotonically with the nonlinear parameter.The wave propagation equations derived bring great facility to further research for considering the nonlinear factors,when the P-wave obliquely propagates in rock mass.