Revealing Size Effect and Associated Variability of Rocks Based on BPM–μDFN Modelling: Significance of Internal Microstructure and Strain Rate

Accurate determination of rock strength is always a crucial problem to ensure the stability of rock engineering, which can be estimated from experimental data at a small scale through size effect models. Previous studies examined the scaling behaviors of rocks from a deterministic perspective, ignoring the strength variabilities around the mean values. In this study, the bonded particle model–μdiscrete fracture network (BPM–μDFN) modelling has been utilized to analyze size effect and associated strength variability for rocks considering microstructure and strain rate. The numerical results demonstrate that the size effect is more significant for rocks with increasing micro-crack intensity, while it becomes less obvious with increasing micro-crack size or increasing strain rate. In addition, the strength variability of rocks is largely influenced by the internal microstructure and strain rate. Finally, a modified empirical size effect model incorporating model parameters of internal microstructure and strain rate is proposed to predict the scaling behaviors of rock considering internal microstructure and strain rate, which can capture the numerical results soundly. The findings of this study could enhance our understanding of rock strength determination from a small scale and provide a guide to design rules for rock engineering.