Normal characteristic quantity theory of flying gangue motion in steeply dipping seam with stochastic parameters

The shock motion of flying gangue is complicated,dynamic and uncertain in the working face of steep seam mining.Accurate description on the shock motion of flying gangue is the basis of protection design of steeply dipping coal seam.The normal shock motion of spherical flying gangue in the working face of steeply dipping coal seam was taken as the research background,considering the influences of the randomness of the shock motion parameters of flying gangue,based on the Hertz classical elastic collision theory,the normal shock motion model of flying gangue was established by using the random factor method.The mean and the variance of the maximum impact and collision restitution coefficient in normal were derived by using the algebra synthesis method and moment method.In order to verify the accuracy and feasibility of the proposed method,the Monte Carlo method was used to compare the simulation results.Also,the RocFall software was used to simulate the mean of rebound height for flying gangue,and the influence of randomness of parameters on the rebound height of flying gangue was analyzed.The study results show that the results obtained by this method are in good agreement with those obtained by using the Monte Carlo method.The randomness of shock motion parameters of flying gangue has different effects on the randomness of the maximum impact and collision restitution coefficient in normal of flying gangue in steeply dipping seam mining,and the greater the coefficient of variation,the greater the influence of the randomness of the parameters on the maximum impact and collision restitution coefficient in normal of flying gangue.The randomness of collision restitution coefficient in normal of flying gangue affects the rebound speed of flying gangue,and then affects the rebound height of flying gangue after impact.The rebound height is directly related to the height setting of the protective device.Applying the calculation method of the shock motion of flying gangue to the working face can provide a theoretical basis for the prediction of the motion trajectory of flying gangue and the design of the protective device.