Sensitivity Analysis and Determination of Some Parameters of the Rock RHT Model
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摘要: Riedel-Hiermaier-Thoma（RHT）本构模型被广泛应用于爆炸冲击、侵彻等问题的数值模拟和分析，而模拟结果的准确性在很大程度上取决于模型参数取值。为完成不同岩石RHT模型参数的敏感性分析及参数确定，利用LS-DYNA软件开展单一因素变化下弹体侵彻靶体及分离式霍普金森压杆（split Hopkinson pressure bar，SHPB）冲击模拟试验，分析参数取值变化对模拟结果的影响，进而通过正交试验分析，确定参数的交互效应。结果表明：不同工况条件下，模型参数的敏感性排序存在差异，确定了Lode角相关系数、拉伸屈服面参数、参考压缩应变率、参考拉伸应变率、失效压缩应变率及失效拉伸应变率对SHPB冲击曲线弹性阶段、线性强化阶段及损伤软化阶段的影响。利用SHPB冲击正交试验验证了6个参数间无显著交互作用，单因素敏感性分析结果有效，通过量化分析得到了花岗岩、红砂岩及大理岩RHT模型中6个参数的最优取值。研究结果可为岩石类RHT模型参数的敏感性分析及确定提供参考。Abstract: The Riedel-Hiermaier-Thoma (RHT) model is extensively used in the numerical simulation and analysis of phenomena such as explosive impacts and penetration. The accuracy of the simulation results is primarily dependent on the constitutive model and the parameter values used within it. To perform sensitivity analysis and parameter determination for Lode angle correlation coefficient, the tensile yield surface parameter, the reference compressive strain rate, the reference tensile strain rate, the failure compressive strain rate and the failure tensile strain rate in the RHT model for various rock types, LS-DYNA was employed to simulate the projectile penetration into a target and split Hopkinson pressure bar (SHPB) impact tests under single-factor variations. The effects of changes in parameter values on the simulation results were analyzed, followed by an orthogonal test to assess the interaction effects between parameters and determine the optimal parameter values. The results indicate that the sensitivity ranking of the six parameters varies under different operational conditions, and the effects of these parameters on the elastic, linear strengthening, and damage-softening stages of the SHPB impact stress-strain curve were identified. Further orthogonal SHPB impact simulation tests confirm the absence of interaction between these parameters, validating that the single-factor sensitivity analysis results are effective. The optimal values for these parameters in the RHT models of granite, red sandstone, and marble are determined. This finding provides valuable insights for the sensitivity analysis and parameter determination in rock-type RHT models.
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图 3 不同参数变化率下模拟结果的变化
Figure 3. Changes of simulation results under different parameter variation rates
图 5 冲击载荷下数值模拟有效性验证
Figure 5. Verification of the validity of numerical simulations under impact loading
图 6 不同参数取值下3种岩石的动态应力-应变曲线
Figure 6. Dynamic stress-strain curves of three type of rocks with different parameter values
图 7 大理岩SHPB冲击模拟曲线与试验曲线面积差
Figure 7. Difference between the area of simulated SHPB impact curve and test curve of marble
Rock type Target material properties Penetration depth ρ0/(g·cm−3) E/GPa fc/MPa ft/MPa Exp./cm Sim./cm Error/% Red sandstone 2.445 24.826 101.913 5.836 12.134 11.784 −2.884 Marble 2.690 61.212 73.679 5.077 15.059 15.353 −1.952 Granite 2.686 39.874 130.967 7.705 8.410 8.151 −3.080 
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表 2 参数取值
Table 2. Parameter selection
Variation rate/% B $ {g}_{\rm t}^{\mathrm{*}} $ $ {\dot{\varepsilon }}_{0}^{\mathrm{c}} $/s−1 $ {\dot{\varepsilon }}_{0}^{\mathrm{t}} $/s−1 $ {\dot{\varepsilon }}^{\mathrm{c}} $/s−1 $ {\dot{\varepsilon }}^{\mathrm{t}} $/s−1 Red sandstone Marble Granite −80 0.0021 0.1228 0.1344 0.1202 6.00×10−6 6.00×10−7 6.00×1024 6.00×1024 −60 0.0042 0.2456 0.2688 0.2404 1.20×10−5 1.20×10−6 1.20×1025 1.20×1025 −40 0.0063 0.3684 0.4032 0.3606 1.80×10−5 1.80×10−6 1.80×1025 1.80×1025 −20 0.0084 0.4912 0.5376 0.4808 2.40×10−5 2.40×10−6 2.40×1025 2.40×1025 0 0.0105 0.6140 0.6720 0.6010 3.00×10−5 3.00×10−6 3.00×1025 3.00×1025 20 0.0126 0.7368 0.8064 0.7212 3.60×10−5 3.60×10−6 3.60×1025 3.60×1025 40 0.0147 0.8596 0.9408 0.8414 4.20×10−5 4.20×10−6 4.20×1025 4.20×1025 60 0.0168 0.9824 1.0752 0.9616 4.80×10−5 4.80×10−6 4.80×1025 4.80×1025 80 0.0189 1.1052 1.2096 1.0818 5.40×10−5 5.40×10−6 5.40×1025 5.40×1025
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表 3 不同参数的平均敏感度系数
Table 3. Average sensitivity analysis factor of different parameters
Parameter Average SAF Granite Red sandstone Marble B 5.13×10−4 5.35×10−4 3.87×10−4 $ {g}_{\rm t}^{\mathrm{*}} $ 1.09×10−3 1.07×10−3 5.23×10−4 $ {\dot{\varepsilon }}_{0}^{\rm c} $ 1.34×10−3 1.07×10−3 5.72×10−4 $ {\dot{\varepsilon }}_{0}^{\rm t} $ 1.75×10−3 1.44×10−3 6.30×10−4 $ {\dot{\varepsilon }}^{\rm c} $ 9.04×10−4 8.66×10−4 4.56×10−4 $ {\dot{\varepsilon }}^{\rm t} $ 7.98×10−4 8.43×10−4 5.03×10−4
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表 4 SHPB冲击试验参数
Table 4. SHPB impact test parameters
Variation rate/% B $ {g}_{\rm t}^{\mathrm{*}} $ $ {\dot{\varepsilon }}_{0}^{\mathrm{c}} $/s−1 $ {\dot{\varepsilon }}_{0}^{\mathrm{t}} $/s−1 $ {\dot{\varepsilon }}^{\mathrm{c}} $/s−1 $ {\dot{\varepsilon }}^{\mathrm{t}} $/s−1 −40 0.0063 0.42 1.80×10−11 1.80×10−12 1.80×1019 1.80×1019 −20 0.0084 0.56 2.40×10−11 2.40×10−12 2.40×1019 2.40×1019 0 0.0105 0.70 3.00×10−11 3.00×10−12 3.00×1019 3.00×1019 20 0.0126 0.84 3.60×10−11 3.60×10−12 3.60×1019 3.60×1019 40 0.0147 0.98 4.20×10−11 4.20×10−12 4.20×1019 4.20×1019
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表 5 VIF计算结果
Table 5. Results of VIF calculation
Argument VIF Granite Red sandstone Marble B 1.0004 1.0005 1.0002 $ {g}_{\rm t}^{\mathrm{*}} $ 1.0001 1.0002 1.0005 $ {\dot{\varepsilon }}_{0}^{\mathrm{c}} $ 1.0005 1.0004 1.0004 $ {\dot{\varepsilon }}_{0}^{\mathrm{t}} $ 1.0001 1.0003 1.0003 $ {\dot{\varepsilon }}^{\mathrm{c}} $ 1.0003 1.0001 1.0001 $ {\dot{\varepsilon }}^{\mathrm{t}} $ 1.0002 1.0003 1.0002
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