Abstract The processes of deformation and fracture of porous sandstones are studied by a 3D finite-difference analysis coupled with a continuous damage mechanics approach. The statistics of more than 100 samples is analyzed. The structure of the pore space is considered explicitly with an assumption of spherical pores distributed in the computational domain. The sample represents a dual-phase material while other structural features are disregarded. In contrast to numerous works, the piecewise linear function based on the Drucker-Prager criterion is used as the yield/damage envelope. The modification is related to different slopes for positive and negative semispaces of a stress space similar to the two-dimensional Haigh-Westergaard space. This allows for a more flexible validation of the model parameters against the experimental data. The method applied is based on an explicit dynamic formulation. Coupled with MPI algorithm, it allows using more than 20 million mesh elements and yields a sufficiently more smooth description of phase boundaries. The scalar damage parameter, which controls the features of damage accumulation and degradation of strength, is also modified. Special attention is paid to the stages of deformation of the samples, which are matched with the points of the complete stress-strain curve. Based on the results of numerical modelling, the threshold stresses of crack initiation σ c i , damage σ c d , and peak σ p are evaluated for samples with different porosities. The resulting values of the threshold stresses at different sample porosities and their failure patterns are in a satisfactory agreement with the experimental data and complement them.

中文翻译：

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弱多孔砂岩单轴压缩变形破坏三维有限差分分析

摘要 通过三维有限差分分析结合连续损伤力学方法研究了多孔砂岩的变形和断裂过程。分析了 100 多个样本的统计数据。孔隙空间的结构被明确考虑，假设球形孔隙分布在计算域中。样品代表双相材料，而忽略其他结构特征。与众多作品相比，基于 Drucker-Prager 准则的分段线性函数被用作屈服/损伤包络。该修改与类似于二维 Haigh-Westergaard 空间的应力空间的正负半空间的不同斜率有关。这允许根据实验数据更灵活地验证模型参数。所应用的方法基于显式动态公式。结合 MPI 算法，它允许使用超过 2000 万个网格元素，并产生足够平滑的相边界描述。控制损伤累积和强度退化特征的标量损伤参数也被修改。特别注意样品的变形阶段，这些阶段与完整的应力-应变曲线的点相匹配。根据数值模拟结果，对不同孔隙率的样品评估了裂纹萌生阈值应力σ ci 、损伤σ cd 和峰值σ p 。不同样品孔隙率下的阈值应力及其失效模式的结果值与实验数据一致，并对其进行了补充。