Coupled wave propagation in meso-scale heterogeneous medium

Heterogeneous media are very common in nature. Due to the complex internal structure, the heterogeneous compressive shear coupled stress field is inside heterogeneous media, which leads to a mutual influence of compression and shear waves. The study of wave mechanics behavior and description of heterogeneity in heterogeneous media is of great significance and full of challenges. This article establishes a general constitutive relationship that reflects the compression shear coupling characteristics of heterogeneous materials, proposes coupling coefficients to describe material heterogeneity, combines momentum conservation law to establish a generalized wave equation, and provides a general method for solving the generalized wave equation. As an example, expressions for the three characteristic wave velocities of compression shear coupling under the first-order compression shear coupling constitutive relationship are provided, and the finite difference method is employed to obtain the propagation process of coupled compression and shear waves. The effects of four heterogeneous coupling coefficients on stress state, coupled wave velocity, and wave propagation process are studied. The positive and negative values of coupling parameters and their combinations reflect the structural characteristics of heterogeneous media and also determine the properties of compression shear coupling waves. For heterogeneous media with high-pressure effects, shear dilation effects, and shear weakening effects, the coupled compression wave velocity is lower than the elastic compression wave velocity corresponding to uniform media, and the coupled shear wave velocity is higher than the elastic shear wave velocity. The effect of shear on compression delays the propagation of compressive stress, while compression promotes the propagation of shear. Coupled compression wave velocity is the result of the competition between the coupling effect of shear on compression and the volume compaction effect. Coupled shear wave velocity is the result of the competition between the coupling effect of compression on shear and the shear weakening effect caused by continuous distortion of the medium. These mechanisms could be achieved through different combinations of compression shear coupling parameters. A true triaxial experimental testing system was used to measure the longitudinal wave velocity of granite, model materials made of mortar, and materials made of cement mortar with coarse aggregates under different compressive and shear stresses. The results indicate that for heterogeneous media, the longitudinal wave velocity decreases with the increase of static water pressure and equivalent shear stress, and the shear expansion and shear weakening effects dominate. The experimental results and theoretical results have the same trend. The conclusion of this study is expected to provide a physical mechanism explanation for the phenomenon of the variation of wave velocity with stress state in heterogeneous materials. © 2024 Explosion and Shock Waves. All rights reserved.