One of the current problems in studying the mechanical properties and behavior of structurally inhomogeneous media with cracks is the characterization of acoustic wave propagation. This is especially important in Geomechanics and prognosis of earthquakes. In this work, the authors propose an approach that could simplify characterization of wave propagation in medium with cracks. It is based on homogenization procedure performed at a set of equations characterizing acoustic wave propagation in media weakened by fractures under condition of external distributed loading. Such kind of loading in most cases is close to the real one in case of consideration of Geomechanics problems. On the basis of the proposed homogenization technique, we performed characterization of elastic properties and plane acoustic waves propagation in a pre-loaded linear elastic medium weakened by a large amount of cracks. We have investigated two special cases of loading: uniaxial compression and complex compression. We have also studied how the wavespeeds depend on averaged concentration and distribution of craks. Effective elastic properties were theoretically characterized for fractured media under external loading. The results revealed high dependency of the longitudinal wave propagation speed on the relation between stresses reasoned by an external loading.

中文翻译：

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周期性压缩下裂隙岩中的弹性波

研究具有裂纹的结构不均匀介质的力学性能和行为的当前问题之一是声波传播的表征。这在地质力学和地震预后中尤其重要。在这项工作中，作者提出了一种可以简化波在具有裂纹的介质中的传播特性的方法。它基于均质化程序，该均质化程序以一组方程式为特征，这些方程式表征了在外部分布载荷条件下声波在被裂缝削弱的介质中的传播。在考虑地质力学问题的情况下，这种载荷在大多数情况下接近实际载荷。在提出的均质技术的基础上，我们对被大量裂缝削弱的预加载线性弹性介质中的弹性特性和平面声波传播进行了表征。我们研究了两种特殊的加载情况：单轴压缩和复杂压缩。我们还研究了波速如何取决于裂缝的平均浓度和分布。理论上表征了外部载荷下压裂介质的有效弹性。结果表明，纵向波传播速度高度依赖于外部载荷引起的应力之间的关系。理论上表征了外部载荷下压裂介质的有效弹性。结果表明，纵向波传播速度高度依赖于外部载荷引起的应力之间的关系。理论上表征了外部载荷下压裂介质的有效弹性。结果表明，纵向波传播速度高度依赖于外部载荷引起的应力之间的关系。