Calibration of discrete element model parameters for cohesive soil considering the cohesion between particles
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摘要:目的
实现黏性土壤离散元模型的接触参数与接触模型参数标定。
方法基于土壤堆积角物理试验结果,采用考虑颗粒间黏结力的“Hertz-Mindlin with JKR”接触模型进行土壤堆积角仿真试验,借助GEMM（Generic EDEM material model database）数据库获得离散元模型关键参数(包括JKR表面能、恢复系数、静摩擦系数与动摩擦系数),进一步运用Box-Behnken试验方法进行堆积角仿真试验。
结果通过对试验结果进行多元回归拟合分析获得了堆积角回归模型,回归模型的方差分析表明该模型极显著,试验因素对堆积角的影响为二次多项式,且存在复杂的一次与二次交互作用。以堆积角40.45°为目标对回归模型进行寻优,得到了优化解：JKR表面能7.91 J·m-2;恢复系数0.66;静摩擦系数0.83;动摩擦系数0.25。以此优化解进行仿真试验获得的堆积角为39.73°。堆积角仿真试验与物理试验在堆积角度和形状上具有较高的相似性。
结论可利用该优化参数对样品土壤进行进一步的黏性土壤与触土部件间的离散元仿真,从而揭示黏性土壤在触土部件作用下的运动规律。
Abstract:ObjectiveTo calibrate contact parameters and contact model parameters for the cohesive soil discrete element model.
MethodThe Hertz-Mindlin with JKR contact model which consider the cohesion between particles was employed for the repose angle simulation test. The simulation test was based on the results of physical test for angle of repose. The key parameters including JKR surface energy, coefficient of restitution, coefficient of static friction and coefficient of rolling friction were obtained from the GEMM (Generic EDEM material model) database. A Box-Behnken design was then used to perform the simulation test for repose angle in above value ranges.
ResultThe regression model for repose angle was acquired from the test results by multiple regression analysis. Analysis of variance showed that the model was extremely significant, and the relationship between experimental factors and repose angle was fitted to a quadratic polynomial with complex liner and quadratic interactions. The optimized solution was acquired by using 40.45° as the target of repose angle. The optimized solution was as follow, JKR surface energy was 7.91 J·m-2, coefficient of restitution was 0.66, coefficient of static friction was 0.83, and coefficient of rolling friction was 0.25. The optimized solution was then used for simulation test and the obtained repose angle was 39.73°. The simulation test was highly matched with physical test on both angle and shape of repose.
ConclusionFor the soil sample used in this research, the optimized parameters can be used for further simulation of kinematics and dynamics between cohesive soil and soil contact components, and for providing the motion characteristics of cohesive soil under the actions of soil contact components.
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图 4 优化解下的堆积角仿真试验与物理试验结果
Figure 4. Results of the physical test and simulation test under the optimal solution
表 1 堆积角仿真试验因素及水平
Table 1 Factors and levels of simulation test for repose angle
变量 试验因素 低水平 中心水平 高水平 x1 JKR表面能 3.50 7.00 10.50 x2 恢复系数 0.15 0.45 0.75 x3 静摩擦系数 0.44 0.80 1.16 x4 滚动摩擦系数 0.05 0.15 0.25 
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表 2 堆积角仿真试验设计及结果
Table 2 Results and arrangement of simulation test for repose angle
试验序号 JKR表面能/（J·m-2） 碰撞恢复系数 静摩擦系数 动摩擦系数 堆积角/（°） 1 10.5 0.45 0.80 0.05 42.19 2 7.0 0.45 0.44 0.05 36.44 3 3.5 0.45 1.16 0.15 37.00 4 10.5 0.45 0.44 0.15 39.03 5 7.0 0.45 0.44 0.25 37.16 6 7.0 0.15 0.44 0.15 36.50 7 7.0 0.75 1.16 0.15 36.40 8 7.0 0.45 0.80 0.15 37.90 9 10.5 0.45 1.16 0.15 36.86 10 7.0 0.75 0.80 0.05 28.85 11 3.5 0.45 0.44 0.15 37.33 12 10.5 0.15 0.80 0.15 33.02 13 3.5 0.15 0.80 0.15 32.76 14 10.5 0.75 0.80 0.15 38.54 15 3.5 0.45 0.80 0.25 39.92 16 10.5 0.45 0.80 0.25 38.52 17 7.0 0.45 0.80 0.15 37.98 18 7.0 0.15 0.80 0.05 40.07 19 7.0 0.15 0.80 0.25 35.62 20 7.0 0.45 1.16 0.05 37.71 21 3.5 0.45 0.80 0.05 30.69 22 3.5 0.75 0.80 0.15 33.03 23 7.0 0.45 0.80 0.15 37.28 24 7.0 0.75 0.80 0.25 39.60 25 7.0 0.75 0.44 0.15 34.29 26 7.0 0.45 1.16 0.25 37.78 27 7.0 0.15 1.16 0.15 31.09 28 7.0 0.45 0.80 0.15 37.39 29 7.0 0.45 0.80 0.15 37.46
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表 3 堆积角回归模型的方差分析
Table 3 ANOVA of regression model of repose angle
方差源 平方和 自由度 均方 F P 模型 257.11 24 10.71 107.00 0.000 2 x1 25.50 1 25.50 254.72 <0.000 1 x2 13.10 1 13.10 130.89 0.000 3 x3 0.89 1 0.89 8.92 0.040 5 x4 0.16 1 0.16 1.56 0.280 0 x1x2 6.89 1 6.89 68.82 0.001 2 x1x3 0.85 1 0.85 8.45 0.043 8 x1x4 41.60 1 41.60 415.53 <0.000 1 x2x3 14.14 1 14.14 141.21 0.000 3 x2x4 57.76 1 57.76 576.91 <0.000 1 x3x4 0.11 1 0.11 1.05 0.362 4 x12 0.24 1 0.24 2.36 0.198 9 x22 19.19 1 19.19 191.65 0.000 2 x32 3.39 1 3.39 33.86 0.004 3 x42 1.36 1 1.36 13.56 0.021 2 x12x2 21.22 1 21.22 211.97 0.000 1 x12x3 2.41 1 2.41 24.06 0.008 0 x12x4 2.84 1 2.84 28.41 0.006 0 x1x22 2.34 1 2.34 23.41 0.008 4 x1x32 9.12 1 9.12 91.06 0.000 7 x22x3 3.37 1 3.37 33.63 0.004 4 x22x4 3.80 1 3.80 37.90 0.003 5 x2x32 13.36 1 13.36 133.48 0.000 3 x12x22 0.62 1 0.62 6.23 0.067 0 x12x32 1.42 1 1.42 14.14 0.019 8 纯误差 0.40 4 0.10 总和 257.51 28
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