Data-driven hierarchical multiscale FDEM for simulating rock meso-macro mechanical behavior

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.