Accurate determination of the representative elementary volume (REV) size plays a pivotal role in analysing the mechanical properties and failure processes of heterogeneous rocks in complex engineering environments. In this study, a novel microstructure modelling strategy (NMMS) for determining the REV size is proposed by combining deep learning and an improved phase-field method (PFM). Micro- and macroscale experiments are systematically conducted to determine the real microstructural characteristics and mechanical properties of heterogeneous rocks with different grain sizes. On the basis of this experimental evidence, geometric models of different sizes were reconstructed through deep learning to avoid the limitations of human-based methods, and an improved PFM was used for numerical calculations. These models were then employed to perform numerical tests under uniaxial loading conditions, and the coefficient of variation was introduced to determine the REV size of heterogeneous rocks with different grain sizes. The research findings indicate that the final REV size is the maximum value of the REVs defined by the evaluation properties within an acceptable coefficient of variation. At a criterion of 5% for the coefficient of variation, the REV sizes are 60 mm×60 mm, 70 mm×70 mm, and 90 mm×90 mm for fine-medium-grained (FMG), medium-grained (MG), and coarse-grained (CG) rocks, respectively. Furthermore, the REV determined by the NMMS was applied to investigate the effects of microstructure on macromechanical properties and damage evolution under triaxial loading conditions. The numerical results show that the NMMS can accurately predict the macromechanical properties and microcracking patterns of heterogeneous rocks, especially the intracrystalline cracks in feldspar, the interfacial cracks in gravel, and the “voids” of cracks in biotite. This research can provide some basic references for the optimal choice of the REV size of heterogeneous rocks.

中文翻译：

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确定不同晶粒尺寸的非均质岩石的 REV 尺寸：深度学习和数值方法


在分析复杂工程环境中非均质岩石的机械性能和失效过程时，准确测定代表性基本体积 （REV） 大小起着关键作用。在这项研究中，通过将深度学习和改进的相场法 （PFM） 相结合，提出了一种用于确定 REV 大小的新型微观结构建模策略 （NMMS）。系统地进行微观和宏观实验，以确定不同粒度的非均质岩石的真实微观结构特征和力学性能。基于这一实验证据，通过深度学习重建了不同大小的几何模型，以避免了基于人类方法的局限性，并使用改进的 PFM 进行数值计算。然后利用这些模型在单轴加载条件下进行数值测试，并引入变异系数来确定不同粒度的非均质岩石的 REV 尺寸。研究结果表明，最终的 REV 大小是由评估属性在可接受的变异系数内定义的 REV 的最大值。在变异系数为 5% 的标准下，细粒×粒 （FMG）、中粒 （MG） 和粗粒 （CG） 岩石的 REV 尺寸分别为 60 mm60 mm、70 mm×70 mm 和 90 mm×90 mm。此外，将 NMMS 确定的 REV 应用于研究微观结构对三轴加载条件下宏观机械性能和损伤演变的影响。 数值结果表明，NMMS能够准确预测非均质岩的宏观力学性质和微裂纹模式，特别是长石中的晶内裂纹、砾石中的界面裂纹和黑云母中裂纹的“空隙”。该研究可为非均质岩 REV 尺寸的优化选择提供一些基础参考。