Progressive failure and quantitative stability analysis of rock slope with cross-type discrete fracture network using spring-based smoothed particle hydrodynamics method

Abstract

The propagation and coalescence of discontinuous cross-type joints are often the primary drivers of rock slope failures. Due to the inherent randomness of these joints, identifying suitable methods to accurately characterize progressive failure and quantitatively assess the stability of slopes with cross-type joints is particularly challenging. To address this, a Discrete Fracture Network-Spring Based-Smoothed Particle Hydrodynamics (DFN-SB-SPH) method is proposed, which considers cross-type DFN generation, rock matrix heterogeneity, cracking, block contact, and deposition within a unified SPH framework. In this approach, damage and contact of blocks are achieved by introducing a fracture sign to enhance the kernel function and applying Newton's law to the damaged particles to realize the point to point contact. A uniaxial compression test on rock samples with double fissures is carried out to verify the accuracy of the proposed method. The influence of joint density, geometric parameters (i.e., trace length, dominate dip angle) of cross joints, and rock mass heterogeneity on the failure characteristics of RSCD are investigated. The results revealed that the DFN-SB-SPH model possesses robust capabilities for crack tracking, mass movement, and contact slipping along fracture surfaces. Moreover, DFN generation, heterogeneous characterization, shear and tensile fractures within a single SPH framework without mesh distortion are realized. Five typical failure modes calculated by DFN-SB-SPH are primarily determined by the combination of joint dip angles and trace lengths. Furthermore, the dip angle, trace length, joint density, and rock mass heterogeneity significantly alter the stability of RSCD with sensitivity coefficients for factor safety of 27.7 %, 44.6 %, 72.9 % and 35.0 %, respectively. Higher dominant dip angles (above 60°) lead to significantly longer run-out distances for RSCD compared to lower angles (below 30°) once instability occurs. The sudden rise in major principal stress at the slope's top and toe, along with the shift of tensile stress concentration towards the middle, predicts the stages of crack propagation and sliding in slope failure.