A calculation model of the normal coefficient of restitution based on multi-factor interaction experiments

As a key input parameter for simulating the moving trail of a rockfall, the magnitude of the normal coefficient of restitution (R-n) directly affects the prediction accuracy. However, few comprehensive and accurate calculation models are available for reference, owing to the fact that R-n is jointly controlled by multiple factors with the influence mechanisms being complex. Considering the interactive effects of influencing factors and the non-linear relationships between some influencing factors and R-n, the combined effects of the seven influencing factors on R-n were first investigated in this study by the response surface methodology-central composite design (RSM-CCD) method. The effects of the seven main factors on R-n were all significant; the results of the regression and variance analysis indicate that for non-angular blocks, the degree of influence of these factors is given by the following sequence: shape factor (eta) > Schmidt hardness of the block (SHV1) > impact angle (theta) > rotational speed (omega) > Schmidt hardness of the slope surface (SHV2) > incident velocity (V) > block size (d). However, for angular blocks, the sequence is theta > SHV1 > omega > eta > V > SHV2 > d. There are also many interaction parameters that had significant effects on the R-n of the test blocks (for non-angular blocks: eta-theta > d-eta > eta-omega > V-d > SHV1-eta > SHV1-theta; for angular blocks, d-theta > SHV1-d > V-eta > SHV1-omega > d-eta > eta-omega > SHV1-eta), the effects of which were examined via contour and three-dimensional surface plots. Based on the conclusions of these experiments (the determined significant influence parameters of R-n) and the previous single-factor experiments, the SPSS19.0 software was used to perform multivariate non-linear regression on the test results. Consequently, two R-n value calculation models of both non-angular and angular blocks were established. Through a contrastive analysis of the measured values of field tests and the predicted values of various models, the prediction ability of models a of the two types of blocks closely approached the measured values, with average deviations of only 3.4% and 9.8%; thus, these models can basically be used to achieve an accurate prediction of R-n values under various conditions. The models obtained in this study consider the comprehensive influences of various factors, which include not only the effects of all the main controlling factors, but also those of the interactions between them. Thus, these models can more accurately reflect the energy loss in the process of rockfall impact, which is helpful to improve the prediction accuracy of rockfall motion paths and is capable of providing a more reliable reference for the prevention and control of rockfall disasters.

Automated summary

This study investigated the combined effects of seven influencing factors on the normal coefficient of restitution (R-n) in rockfall simulations. Two calculation models for R-n values of non-angular and angular blocks were established, which can accurately predict values under various conditions. The models consider the comprehensive influences of various factors and interactions, providing reliable reference for rockfall prevention and control.