Modified impact model of large caving rock mass under the composite influence of cushion multi-parameters using Hertz theory
A one-dimensional geometric model is developed for the impact of falling rock mass on a substructure along an inclined orebody.This model simplifies the caving rock mass as a longitudinal cylinder of infinite length along the orebody and considers the rock cushion as an infinitely ideal elastic-plastic body.Drawing on Hertz elastic contact mechanics theory,a modified theoretical calculation model for impact force is established.This model integrates factors such as elastic-plastic effects,cushion thickness,and porosity.The influences of cushion thickness,elastic modulus,porosity,falling rock mass,and impacting velocity on dynamic loading are analyzed using the sensitivity of each factor relative to the others through the new theoretical model.Additionally,by simplifying the pillar under the cushion as a deep beam and integrating bulk stress diffusion theory with classical tensile fracture strength theory from material mechanics,the effective and reasonable cushion thickness protecting goaf pillars from damage under the impact of large falling bodies,using metal mines as a case study,is examined.The results indicate that the cushion thickness has a weak buffering effect,while the porosity and strength of the cushion exhibit strong buffering effects.Specifically,an increase in cushion thickness leads to only a slight reduction in impacting force,whereas higher porosity and lower cushion elastic modulus effectively reduce impacting loading.The buffering effect of cushion thickness is stronger for smaller caving masses,weaker cushion materials,higher impacting velocities,and greater porosity;otherwise,it diminishes gradually.Impacting force increases notably with greater mass and velocity of falling bodies,yet impacting speed imposes a limit on force increase—once exceeded,impacting force stabilizes.Based on simplified pillar models of fixed and simply supported beams,the deduced effective cushion thicknesses are 8.5 m and 17.5 m respectively.Comprehensive analysis suggests that the gravel cushion thickness should not be less than 17.5 m.
万方数据
维普
