【摘要】 对正向入射弹性纵波穿越岩石节理的过程及特性进行理论研究。所研究的岩石节理具有非线性法向变形本构关系。在没有剪切波的情况下,探讨节理的非线性法向变形行为对弹性纵波传播的影响。传统的有关应力波在节理处传播的线性位移不连续理论模型,发展为非线性模型——双曲模型(BB模型)。依据此模型,获得了节理透射和反射系数的数值解。该数值解用来进行一系列的参数研究,包括节理初始刚度、节理闭合量相对于最大允许闭合量的比率以及入射波的振幅和频率对节理透射系数的影响等参数研究。也对线性和非线性位移不连续理论模型作了比较。结果表明,线性模型得到的透射和反射系数解是非线性解的一种特例,即当入射波的振幅很弱以至于在波传播中产生的最大节理闭合量相对于最大允许闭合量足够小的条件下,非线性与线性解等同。此外,还发现当波在节理处传播时,节理的非线性变形行为会引起一种高谐波现象。更多还原

【Abstract】 A theoretical study is presented on normally incident elastic P-wave transmission across single dry fracture with nonlinear normal deformation behavior. The effects of nonlinear normal deformation on P-wave normal incidence are studied without the shear deformation considered. The linear displacement discontinuity model for wave propagation across fracture is extended to nonlinear model, the hyperbolic elastic model(BB model). Numeric solutions of transmission and reflecton coefficients for normally incident P-wave transmission across the nonlinear deformable fracture are obtained and related to the closure behavior of fracture. Parameter studies are conducted to get an insight into the effects of the nonlinear normal deformation of fracture on P-wave transmission, in terms of initial normal stiffness and the ratio of given closure to maximum allowable closure of the fracture, as well as the incident wave amplitude and frequency. Comparisons between the linear and nonlinear models are presented. It is shown that, the transmission and reflecton coefficients for the linear model are special solutions of those for the nonlinear model, when the incident wave amplitude is so low that the maximum closure of fracture incurred during the wave transmission is much smaller relative to the maximum allowable closure. In addition, the nonlinear behavior of fracture gives rise to the phenomenon of higher harmonics during the wave transmission across the fracture.更多还原