Effect Of Particle Gradation On The Repose Angle Of Ballast Based On Hopper Flow Test And Discrete Element Simulation

The interaction of ballast particles happens during train passage,which results in the rearrangement,abrasion,breakage,densification,reduction of large particles,increase of small particles,and the consequent deterioration of ballast gradation as well as the settlement of the trackbed.Repose angle is an important physical indicator in reflecting the mechanical properties of granular materials,which reflects the frictional properties of granular materials.The repose angle of ballast particles equals the internal friction angle,which serves as an indicator for evaluating the shear strength of a trackbed.To further study the effect of gradation of the ballast particles on repose angle,self-developed apparatus for the measurement of the repose angle of coarse grain was used for hopper flow tests with different gradations of ballast particles.The gradation parameters,including median particle size D₅₀,non-uniform coefficient Cu,curvature coefficient Cc,particle size distribution and maximum particle size D₁₀₀,were utilized to investigate their effect on repose angle.The gradation range of super ballast particles,as stipulated in the specification,was subdivided on the basis of its repose angle to further investigate the optimal gradation range.The hopper flow tests ballast particles with different gradations were simulated using the discrete element method.Moreover,the accumulation process and the distribution law of the size group,as well as the stress chain of ballast particles were analyzed from a mesoscopic view.The relationship between the gradation parameters and the repose angle was established based on k NN algorithm to predict the range of repose angle,whereby a method of evaluating the deterioration of ballast particles with gradation parameters was proposed.The results are as follows:（1）With the increase in median size D₅₀ from 36.8mm to 45mm,there is the optimal gradation within the super gradation range of ballast particles defined in the specification.And the repose angle reaches its maximum as D₅₀=40 mm,suggesting that the optimal median size is 40mm.When the median particle size D₅₀ remains unchanged,the repose angle of ballast piles reaches its maximum when the ballast contains 13%small size particles（below 31.5mm）and 15.5%large size particles（above 50mm）.（2）In the outside the super gradation range of ballast particles,the repose angle of ballasts pile decreases with the increase in maximum particle size D₁₀₀ as the median particle size D₅₀ remains unchanged.When the non-uniformity coefficient Cu falls between 1.06～4.25,the repose angle has a maximum value as D₅₀=40 mm with the increase in the median particle size D₅₀ from 36.8mm to 45mm.This suggests that40mm is the optimum median particle size,which remains the case outside the super gradation range.Under the same median particle size D₅₀,the repose angle of the ballast pile in the super gradation range is larger than that outside the range,which suggests the deterioration of the trackbed combines with the reduction of small particles in proportion and the decrease in the repose angle and the shear strength of ballast particles.（3）The accumulation process of ballast particles can be simplified as"stacking stage","pile peak stage"and“peak clipping stage”.The“stacking stage”refers to the early stacking process of ballast particles,gradually forming a stable layer of ballast particles on the platform.The second stage is the"pile peak stage",in which the falling particles gradually accumulate on the building platform of ballast particles.The third stage is termed the“peak clipping stage”.As ballast particles continue falling,the top of the pile was clipped due to the impact of falling ballast particles.From the distribution image of the stress chain,it was also shown that the pile top is almost flat and even sunken at the time.The growth trend of the repose angle from numerical results is consistent with that from the hopper flow tests.The repose angle increases with the increase in non-uniformity coefficient Cu.In the stacking process,the large particles mainly play the supporting role,while the fine particles mainly play the role of filling pores.（4）k NN model was established based on 150 data samples with different gradation parameters obtained from the experiment,and the remaining 8 gradation data samples were used to predict repose angle.It was shown that:the average prediction accuracy of the k NN model is 84.21%and fluctuates between 81.6%and 86.8%as k=3.It is feasible to use k NN algorithm to predict the value of repose angle.Based on the assumption that the angle is normally distributed,it is found that the deviation between the predicted and the actual value of the repose angle is no more than 1°for the correctly classified samples.