颗粒离散元岩石模型的颗粒尺寸效应研究

颗粒尺寸是影响颗粒离散元模型宏观力学性质与计算效率的一个重要因素。为充分考虑由模型随机性导致的模拟结果的不确定性，利用统计学方法对模型的颗粒尺寸效应进行研究。整体检验结果表明：特征长度比L/R的改变对模型力学参数（峰值强度、弹性模量、泊松比及峰值应变）与破坏特征参数（黏结破裂率）的总体分布位置均有显著性影响，且各参数的变异系数会随着L/R的减小而增大。进一步的多重比较结果表明：当L/R≥125时，L/R对峰值强度、弹性模量、泊松比及峰值应变的总体分布位置均无显著影响；当L/R≥79时，相邻3个粒径水平的黏结破坏率总体分布位置无显著性差异；随着L/R的减小，模型损伤程度增加，破坏模式由整体剪切破坏转向局部损伤引起的失稳破坏，最终失去模拟岩石材料的效力。最后，综合各项力学参数的统计学检验结果、模型破坏模式及计算效率，岩石模型颗粒的特征长度比取L/R=200较为合适。

Study of particle size effect of rock model based on particle discrete element method

Particle size is an important factor affecting macroscopic mechanical properties and computational efficiency of particle discrete element model. To account for the uncertainty of numerical results caused by the stochastic model, we study the effect of particle size using statistical methods. The result of the global test shows that the distribution position of mechanical parameters (i.e. peak strength, elastic modulus, Poisson's ratio and peak strain) and the failure characteristic parameter (bond failure rate) is significantly affected by the characteristic length ratio L/R. The coefficient of variation (CV) of these parameters increases as L/R decreases. The further multiple comparisons show that L/R has no significant effect on the distribution of these parameters as L/R≥125. When L/R≥79, the L/R has no significant effect on the distribution position of bond failure rate within the range of three adjacent ball radius levels. With the decrease of L/R, the damage degree of the model increases gradually, and the failure mode is changed from the whole shear failure to the unstable failure caused by the local damage, which makes the model lose the simulation effectiveness to rock materials. Finally, by combining the statistical results of mechanical parameters, the failure mode of the model and the computational efficiency, the L/R=200 should be suitable for the simulation of rock materials.