Evaluation of Crack Coalescence and Stability of Jointed Rock Masses for Tunnel Engineering Using a Modified Coalescence Coefficient

Crack coalescence between discontinuities plays a critical role in the progressive failure and stability evolution of jointed rock masses. This study aims to develop a modified coalescence coefficient for quantifying crack coalescence behavior and evaluating its influence on rock mass stability. Uniaxial compression tests and heterogeneous numerical simulations were conducted to investigate the effects of crack dip angle, rock bridge dip angle, crack length, and rock bridge length on crack coalescence. The results revealed cubic polynomial relationships between the coalescence coefficient and crack dip angle, rock bridge dip angle, and crack length, whereas a linear relationship was identified with rock bridge length. Based on an L25(54) orthogonal design and nonlinear regression analysis, a modified coalescence coefficient applicable to jointed rock masses under static loading conditions was proposed. The coefficient was subsequently incorporated into the block theory implemented in GeoSMA-3D and applied to a tunnel excavation case. The results demonstrated that considering structural-plane coalescence significantly alters the geometry and volume of key blocks, leading to a more realistic stability assessment. The proposed coefficient provides an effective tool for improving block identification and stability evaluation in underground rock engineering.