This study presents a data-driven based hierarchical multiscale combined finite-discrete element method (DHM-FDEM) for accurately reproducing rock macro-scale mechanical behavior while ensuring acceptable computational costs. To construct the DHM-FDEM scheme, firstly, upscale finite elements assembly (UFEA) and upscale crack elements assembly (UCEA) are constructed, incorporating meso-scale finite elements and crack elements with mechanical parameters directly derived from meso mechanics test results. Then, a conversion method is proposed to transform the mechanical response of UFEA and UCEA into a strain-stress pair of the macro-scale element, avoiding directly solving the mechanical state of macro-scale elements with mismatched mechanical parameters, thus ensuring the accurate reproduction of rock mechanical properties. Furthermore, UFEA and UCEA subjected to various loading paths are conducted by meso-scale FDEM to generate data sets comprising sequential strain-stress pairs with history dependence and one-to-many mapping relationships. The generated data sets are then applied to train a data-driven method, long short-term memory with mixture density network (LSTM-MDN), which directly maps strain input to stress output, thus replacing tedious and repetitive meso-scale FDEM computation on UFEA and UCEA to significantly save computational costs. Subsequently, UFEA and UCEA driven by LSTM-MDN are equivalent to macro-scale FDEM elements, replacing their phenomenological constitutive relationships and thereby achieving the multiscale numerical computation scheme. After that, the uniaxial compression test and Brazilian disk test are conducted to validate the computational accuracy and efficiency of DHM-FDEM. Finally, the capability of DHM-FDEM to accurately reproduce rock accumulated damage from loading-unloading cycles is verified through uniaxial and biaxial cyclic loading-unloading tests.

中文翻译：

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数据驱动的分层多尺度 FDEM 用于模拟岩石细观宏观力学行为

本研究提出了一种基于数据驱动的分层多尺度组合有限离散元方法（DHM-FDEM），用于准确再现岩石宏观尺度力学行为，同时确保可接受的计算成本。为了构建 DHM-FDEM 方案，首先构建高档有限元组件 (UFEA) 和高档裂纹单元组件 (UCEA)，将细观有限元和裂纹单元与直接从细观力学测试结果导出的力学参数结合起来。然后，提出一种转换方法，将UFEA和UCEA的力学响应转换为宏观单元的应变应力对，避免直接求解力学参数不匹配的宏观单元的力学状态，从而保证了精确再现岩石力学特性。此外，UFEA 和 UCEA 通过细观尺度 FDEM 进行各种加载路径的处理，生成包含具有历史依赖性和一对多映射关系的连续应变-应力对的数据集。然后，生成的数据集用于训练数据驱动的方法，即具有混合密度网络的长短期记忆网络 (LSTM-MDN)，该方法直接将应变输入映射到应力输出，从而取代繁琐且重复的细观尺度 FDEM 计算。 UFEA 和 UCEA 显着节省计算成本。随后，LSTM-MDN驱动的UFEA和UCEA相当于宏观尺度的FDEM元素，取代了它们的唯象本构关系，从而实现了多尺度数值计算方案。之后，进行单轴压缩试验和巴西盘试验，验证DHM-FDEM的计算精度和效率。最后，通过单轴和双轴循环加卸载试验验证了DHM-FDEM准确再现加卸载循环中岩石累积损伤的能力。