As a key input parameter for simulating the moving trail of a rockfall, the magnitude of the normal coefficient of restitution (Rn) directly affects the prediction accuracy. However, few comprehensive and accurate calculation models are available for reference, owing to the fact that Rn 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 Rn, the combined effects of the seven influencing factors on Rn 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 Rn 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 (η) > Schmidt hardness of the block (SHV1) > impact angle (θ) > rotational speed (ω) > Schmidt hardness of the slope surface (SHV2) > incident velocity (V) > block size (d). However, for angular blocks, the sequence is θ > SHV1 > ω > η > V > SHV2 > d. There are also many interaction parameters that had significant effects on the Rn of the test blocks (for non-angular blocks: η–θ > d–η > η–ω > V–d > SHV1–η > SHV1–θ; for angular blocks, d–θ > SHV1–d > V–η > SHV1–ω > d–η > η–ω > SHV1–η), 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 Rn) and the previous single-factor experiments, the SPSS19.0 software was used to perform multivariate non-linear regression on the test results. Consequently, two Rn 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 Rn 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.

中文翻译：

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基于多因素交互作用实验的正态恢复系数计算模型

作为模拟落石运动轨迹的关键输入参数，法向恢复系数（Rn）的大小直接影响预测精度。然而，由于Rn受多种因素共同控制，影响机制复杂，可供参考的全面准确的计算模型很少。考虑到影响因素的交互作用以及部分影响因素与Rn的非线性关系，本研究首先采用响应面法-中心复合设计（RSM-CCD）研究了7个影响因素对Rn的综合影响方法。7个主要因素对Rn的影响均显着；回归和方差分析的结果表明，对于非角块，这些因素的影响程度由以下顺序给出：形状系数（η）> 砌块施密特硬度（SHV1）> 冲击角（θ）> 转速（ω）> 坡面施密特硬度（SHV2） > 入射速度 (V) > 块大小 (d)。然而，对于角块，序列是 θ > SHV1 > ω > η > V > SHV2 > d。还有许多交互参数对测试块的 Rn 有显着影响（对于非角块：η–θ > d–η > η–ω > V–d > SHV1–η > SHV1–θ；对于有角的块：η–θ > d–η > η–ω > V–d > SHV1–η > SHV1–θ块，d–θ > SHV1–d > V–η > SHV1–ω > d–η > η–ω > SHV1–η)，通过等高线和三维曲面图检查其影响。根据这些实验的结论（确定Rn的显着影响参数）和前面的单因素实验，利用SPSS19.0软件对测试结果进行多元非线性回归。因此，建立了非角块和角块两种Rn值计算模型。通过现场试验实测值与各模型预测值对比分析，两类区块的模型“a”预测能力与实测值接近，平均偏差仅为3.4%和9.8%；因此，这些模型基本上可以用于在各种条件下实现对 Rn 值的准确预测。本研究得到的模型考虑了各种因素的综合影响，其中不仅包括所有主要控制因素的影响，还包括它们之间相互作用的影响。因此，这些模型能够更准确地反映落石冲击过程中的能量损失，有助于提高落石运动路径的预测精度，能够为落石灾害的防治提供更可靠的参考。