The paper is devoted to simulation of the effective elastic properties of rock materials containing two substantially different types of defects simultaneously: random sets of ellipsoidal pores (cavities) and elliptical cracks. For solution of the homogenization problem and calculation of the effective elastic properties of such materials, the self-consistent effective field method is used. For composites with one type of heterogeneities, the method coincides with the Mori–Tanaka method. The method allows deriving analytical expressions for the effective elastic stiffness tensors of the materials containing pores and cracks of various scales. These tensors have correct symmetry with respect to tensor indices and provide physically reasonable values of the effective elastic constants in wide regions of porosity and crack density. The materials with pores and cracks of substantially different sizes and of close sizes are considered. The method predicts substantially different effective elastic constants of the materials with these microstructures. Comparison of the components of the effective elastic stiffness tensors for the materials with various values of porosity and crack density are presented. Wave surfaces of acoustical waves in the materials containing pores and cracks are constructed. It is shown that for materials with spherical pores and circular cracks, the shapes of these surfaces are close to ellipsoidal. The results of the paper can be used for determination of fracture level in damaged rock materials by acoustical methods.

该论文致力于模拟同时包含两种基本不同类型缺陷的岩石材料的有效弹性特性：随机组的椭圆形孔（空腔）和椭圆形裂缝。为了解决均匀化问题和计算此类材料的有效弹性性能，使用自洽有效场法。对于具有一种异质性的复合材料，该方法与 Mori-Tanaka 方法一致。该方法允许导出包含各种尺度孔隙和裂缝的材料的有效弹性刚度张量的解析表达式。这些张量相对于张量指数具有正确的对称性，并在广泛的孔隙率和裂纹密度区域中提供有效弹性常数的物理合理值。考虑了具有不同尺寸和接近尺寸的孔隙和裂缝的材料。该方法预测具有这些微结构的材料的有效弹性常数大不相同。比较了具有不同孔隙率和裂纹密度值的材料的有效弹性刚度张量的分量。在含有孔隙和裂纹的材料中构造声波的波面。结果表明，对于具有球形孔和圆形裂纹的材料，这些表面的形状接近椭圆形。该论文的结果可用于通过声学方法确定受损岩石材料的断裂水平。该方法预测具有这些微结构的材料的有效弹性常数大不相同。比较了具有不同孔隙率和裂纹密度值的材料的有效弹性刚度张量的分量。在含有孔隙和裂纹的材料中构造声波的波面。结果表明，对于具有球形孔和圆形裂纹的材料，这些表面的形状接近椭圆形。该论文的结果可用于通过声学方法确定受损岩石材料的断裂水平。该方法预测具有这些微结构的材料的有效弹性常数大不相同。比较了具有不同孔隙率和裂纹密度值的材料的有效弹性刚度张量的分量。在含有孔隙和裂纹的材料中构造声波的波面。结果表明，对于具有球形孔和圆形裂纹的材料，这些表面的形状接近椭圆形。该论文的结果可用于通过声学方法确定受损岩石材料的断裂水平。在含有孔隙和裂纹的材料中构造声波的波面。结果表明，对于具有球形孔和圆形裂纹的材料，这些表面的形状接近椭圆形。该论文的结果可用于通过声学方法确定受损岩石材料的断裂水平。在含有孔隙和裂纹的材料中构造声波的波面。结果表明，对于具有球形孔和圆形裂纹的材料，这些表面的形状接近椭圆形。该论文的结果可用于通过声学方法确定受损岩石材料的断裂水平。