Step-path failure mode and stability calculation of jointed rock slopes

Step-path failure is a kind of typical instability mode in rock slopes. Based on the summary of geological structural features of jointed rock slopes, the step-path failure mode and evolution process are studied by using the discrete element method, particle flow code in two dimensions (PFC^2D). Three rock bridge failure modes in slopes can be summarized: tensile coalescence, shear coalescence and mixed tensile-shear coalescence. Through the evolution analysis of the rock mesoscopic particle bond force vector field, stress state of rock bridges and rock bridge failure, the progressive step-path failure process that rock bridge fractures one by one from the bottom up under the action of gravity is revealed, and the tensile crack development in the trailing edge of slope is due to the traction of lower part of slope. Take the slope with shallow dipping step-path parallel fissures for example (dip angle of rock bridge is 90°, and that of fissure is 30°), the step-path failure process can be distributed into four stages: elastic steady deformation of slope, failure of the lower rock bridges, failure of the upper rock bridges and development of tensile crack in the trailing edge of the slope, and the overall slipping of the slope along the failure surface. It is the critical state of instability at stage No. three that slip band sufficiently extends with micro-cracks expanding dramatically. Based on the understanding of failure modes and evolution process, three slope stability models for the step-path failure by shear coalescence, tensile coalescence and mixed tensile-shear coalescence of rock bridges are established, and the limit equilibrium formulae for the safety factor of slopes considering strength and coalescence coefficient of rock bridges are deduced.