低幅值应力波在岩石三维节理面的折反射规律理论研究

Reflection and refraction laws of low amplitude stress wave on a 3D rock joint surface

岩土动力问题中,岩石节理对应力波的传播与能量的传递极大的影响,进而对岩土工程的动力响应特性造成影响。在以往应力波在非连续面传播规律的研究中,较少能够从理论上研究三维节理的复杂表面形态所导致的复杂力学性质对应力波传播规律的影响。为此,基于细观接触理论分析了岩石三维节理的应力-变形本构方程一般形式,分析了平面谐波与三维节理面上的变形与应力之间的变化规律,并基于DDM方法给出P波、SV波与SH波在三维节理面上折反射解析解。在模型研究和理论求解基础上通过参数分析研究了应力波的入射角、节理的交叉耦合变形刚度系数对折反射应力波的影响规律。研究发现,对于三维岩石节理,当本构方程中刚度系数矩阵中的交叉耦合刚度系数非零时,三种简谐波(P、SV、SH波)之间皆可已相互转化,且增大三维节理的交叉耦合刚度系数能够显著的增大转换波的幅值系数,使得同型波反射系数增大,同型波透射系数减小。

In dynamic rock engineering,the existence of rock joint has a large influence on stress wave propagation and energy transmission in rock,and it affects dynamic response characteristics of geotechnical engineering. In the past studies,effects of complex surface morphology of 3 D rock joint on stress wave ＇s propagation were rarely investigated theoretically. Here,the general form of a 3 D rock joint surface＇s stress-deformation constitutive equation was analyzed based on the microscopic contact theory. The relationship between planar harmonic wave propagation and stressdeformation on a 3 D rock joint surface was analyzed. Analytical solutions to P-wave,SV-one and SH-one＇reflection and refraction laws on a 3 D rock joint surface were derived using the displacement discontinue method（ DDM）. Based on the theoretical analysis and derivation,the parametric analysis was performed to analyze effects of stress wave＇s incident angle and rock joint＇s cross-coupled stiffness coefficients on stress wave＇s reflection and refraction. The study showed that on a3 D rock joint surface,P-wave,SV-one and SH-one can be transformed into each other when cross-coupled stiffness terms in rock joint surface＇s constitutive equation are nonzero; increasing cross-coupled stiffness terms can increase amplitude coefficients of transformed waves and isomorphic reflected ones,and decrease those of isomorphic refracted ones.