A calculation model to assess the crack propagation length of rock block in clastic flow

The primary cracks in the rock block undergo series of steps and finally disintegrate,during this procession,the radius affects the impact force of rock block in clastic flow.Therefore,it is essential to figure out the evolution mechanism of crack propagation for the design of engineering protection.In this study,based on fracture mechanics and Hertz contact theory,collision happened between rock block and slope surface is assumed to be elastic contact.Based on the above assumption,the critical impact force of crack propagation is obtained,and a model used to calculate the crack propagation length in a single collision is established.Besides,a rock fall site in Jiuzhai Valley was used to verify the calculation model.According to the model,several key factors were identified to influence crack propagation length including falling height,initial equivalent radius,and recovery coefficient of slope surface.Moreover,as a result of the orthogonal experiment,the influence of those factors on the crack propagation length was ranked,normal recovery coefficient>initial radius>initial falling height.In addition,the kinetic energy of the rock block in the compression stage is transformed into elastic deformation energy,angular kinetic energy,and dissipated energy of crack propagation.Due to the increase of collisions,the kinetic energy is gradually transformed into angular kinetic energy,and the dissipated energy of crack propagation weights is reduced.In conclusion,the crack propagation in rock block is a complicated progress,which is affected by multiple factors,especially falling height,initial equivalent radius,and recovery coefficient of slope surface.Our study may provide guidance for the design of protective structure of clastic flows.