Unraveling rate-strengthening and fracture-weakening effects in fractured rock masses: A hybrid bonded particle model-discrete fracture network and physics-inspired machine learning framework

Understanding the dynamic behavior of fractured rock masses is crucial for ensuring safety and stability in mining, tunneling, and underground construction, particularly where structures are subjected to seismic events or blast-induced vibrations. While previous studies have examined either rate effects or fracture-related influences separately, the coupled impact of loading rate and fracture network characteristics remains poorly understood, especially given the stochastic nature of geological discontinuities. This study introduces a novel hybrid framework that combines the bonded particle model (BPM), the discrete fracture network (DFN) and physics-inspired machine learning (PIML) to investigate these complex interactions. The framework uniquely integrates stochastic fracture generation, dynamic numerical simulation, and machine learning to capture both deterministic and probabilistic aspects of rock mass behavior. Results reveal distinct competing mechanisms between rate-strengthening and fracture-weakening effects. Dynamic strength exhibits a positive correlation with loading rate while weakening as fracture intensity increases, with a critical fracture intensity range (5-10 m/m 2 ) where strength variability peaks. A significant finding is the transition in failure modes from predominantly shear failure along pre-existing fractures to mixed tensile-shear failure as fracture intensity and loading rate increase. The developed PIML-based model achieves 97.43% accuracy in predicting dynamic uniaxial compressive strength, while uncertainty quantification demonstrates that loading rate and fracture intensity independently contribute 31.17% and 34.71% to strength variation, respectively. These findings provide quantitative guidance for engineering design, enabling more accurate assessment of rock mass stability under dynamic loading conditions and the optimal design of support system based on fracture characteristics.