缺陷岩体中弹性波传播的多次散射效应分析

弹性波在岩体中传播时与岩体缺陷相互作用形成复杂的传播图案。为研究缺陷对弹性波多次散射作用的影响，建立了双椭圆缺陷模型，基于Green函数基本解，采用边界积分的计算方法，得到了反映缺陷界面条件的刚度矩阵，分析了弹性波在双椭圆缺陷间的多次散射效应。结果表明：与单椭圆缺陷模型相比，双缺陷的相互作用使得弹性波频散和衰减效应增强，定量给出了缺陷的影响区域，从而明确了多次散射效应的尺度界限。进一步探讨了弹性波传播的多尺度效应，结果表明频散的Rayleigh峰、Mie峰和衰减的峰值频率同椭圆长轴和入射波波长两个尺度密切相关，存在明确的定量关系。相应的数值模拟结果表明，弹性波和缺陷相互作用在缺陷界面上诱发界面波，该界面波也存在频率相关性，影响了弹性波宏观传播的频散和衰减特征。

Multiple scattering analysis of elastic wave propagation in defective rock mass

Multiple scattering effect of elastic waves propagating in rocks with defects is studied theoretically and numerically. First, a double elliptical model is established to describe the multiple scattering paths of elastic wave between two elliptical defects. Second, the wave equations and boundary conditions on the defect interface governing opening displacement generating scattering field are derived based on the basic solution of Green function and the boundary integral method. The opening displacement of the defect boundary induced by the interaction of waves and defects are characterized in terms of a "stiffness matrix" that depends on both the incident harmonic and material properties. The problem of multiple scattering of elastic wave propagation in rocks is then analyzed for the dispersion and attenuation in order to evaluate the multiple scattering effect on the wave speed and amplitude. The calculation results show that compared with the single elliptical defect model, the dispersion and attenuation of the elastic wave are stronger due to the effect of multi-scattering. Moreover, the affected region of a defect is given quantitatively about six times of characteristic scale of the defect, which is basically consistent with the macro porosity limit of multiple scattering. This scale separates the multiple scattering strong interaction from the linear superposition of the single scattering effect. The multi-scale effect of elastic wave propagation is further discussed. It is found that the frequency of Rayleigh peak, Mie peak on the dispersion curve and attenuation peak has a definite quantitative relationship with the ratio of the long axis of the ellipse to the incident wavelength. The corresponding numerical simulation results show that the interaction between elastic wave and defect induces the interface wave at the defect interface, and the frequency dependence of these interface waves affects the dispersion and attenuation characteristics of the macroscopic propagation of elastic wave. Within this double defect model, the multiple scattering for interaction of the elastic waves and the defect can enhance dispersion and attenuation.