A study of dynamic constitutive model of frozen sandy soil considering confining pressure effect
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摘要: 为描述主动围压作用下冻结砂土的动态力学特性，通过在朱-王-唐模型的非线性体上串联塑性体，建立了能够考虑围压效应的冻结砂土动态损伤本构模型；分析了损伤参数对应力-应变曲线特征、屈服点、峰值应力和峰值应变的影响规律，基于冻结砂土动力学试验数据确定了模型参数；通过将模型和试验数据进行对比，并对不同试验条件下模型的预测误差进行分析，验证了模型的适用性和准确性。结果表明，损伤参数对应力-应变曲线弹性阶段和屈服点无明显影响，而对塑性阶段和破坏阶段的影响较为显著，本构模型预测的应力-应变曲线与试验结果具有较好的一致性。模型能够预测围压引起冻结砂土塑性阶段占比大和屈服点明显的特征，且能够描述围压对冻结砂土动态强度的增强效应；不同负温和主动围压条件下，模型对峰值应力和屈服强度的预测效果优于峰值应变和屈服应变。
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关键词:
- 冻结砂土 /
- 围压效应 /
- 分离式Hopkinson压杆 /
- 动态本构模型 /
- 屈服强度
Abstract: To describe the dynamic mechanical properties of frozen sandy soil under active confining pressure, a dynamic damage constitutive model, which could consider the effect of active confining pressure on the dynamic strength and deformation characteristics of frozen sandy soil, was established by connecting a plastic body to the nonlinear Zhu-Wang-Tang model. The effects of damage parameters on the characteristics of stress-strain curves, yield point, peak stress, and peak strain were analyzed. In addition, the model parameters were determined based on the dynamic test data of frozen sandy soil. The applicability and accuracy of the established model were verified by comparing the model with the test data and analyzing its prediction errors under different test conditions. The results show that the damage parameters have no significant effect on the elastic stage and yield point of the dynamic stress-strain curves. However, it significantly affects the plastic and failure stages. The stress-strain curves predicted by the established constitutive model are in good agreement with the test results. The model is appropriate in predicting the characteristics including large portion of the plastic stage and obvious yield point caused by active confining pressure. Moreover, the model can also describe the enhancement effect of confining pressure on the dynamic compressive strength of frozen sandy soil. The predictions of the model on the peak stress and yield stress are better than those on the peak strain and yield strain under different negative temperatures and active confining pressures. -
图 2 考虑塑性变形的ZWT模型
Figure 2. The ZWT model established in consideration of plastic deformation
图 3 损伤参数μ和η对冻结砂土动态应力-应变曲线的影响
Figure 3. Effects of the damage parameters μ and η on the dynamic stress-strain curves of frozen sandy soil
图 4 不同主动围压下本构模型曲线与试验结果的对比
Figure 4. Comparison of dynamic stress-strain curves by the modified constitutive model with the test results[25] under different active confining pressures
图 5 不同温度和主动围压下冻结砂土应力误差-应变曲线
Figure 5. Stress error-strain curves of frozen sandy soil at different temperatures and active confining pressures
图 6 不同温度和主动围压下本构模型对动态参数的预测结果与试验结果的对比
Figure 6. Comparison of predictions of dynamic parameters by the established constitutive model with the corresponding test results at different temperatures and active confining pressures
表 1 冻结砂土动态本构模型参数
Table 1. Dynamic constitutive model parameters of frozen sandy soil
温度/℃ 围压/MPa E0/MPa E1/MPa E2/MPa α/GPa β/GPa σs/MPa θ2/ms λ φ μ η −5 0.5 1920 45 130 −420 590 3.28 0.1 0.15 7.2 0.036 11.5 −5 1.0 1920 45 130 −420 590 3.49 0.1 0.15 7.2 0.036 11.5 −5 1.5 1920 45 130 −420 590 3.73 0.1 0.15 7.2 0.036 11.5 −5 2.0 1920 45 130 −420 590 4.51 0.1 0.15 7.2 0.036 11.5 −15 0.5 5030 60 210 −740 980 8.12 0.1 0.45 7.2 0.036 11.5 −15 1.0 5030 60 210 −740 980 9.52 0.1 0.45 7.2 0.036 11.5 −15 2.0 5030 60 210 −740 980 12.81 0.1 0.45 7.2 0.036 11.5 
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表 2 不同试验条件下冻结砂土的模型应力与试验应力的平均绝对误差、均方根误差和标准差
Table 2. Mean absolute errors, root mean square errors and standard deviations between the dynamical stresses of frozen sandy soil by the established model and the test ones under different test conditions
温度/℃ 围压/MPa 平均绝对误差/MPa 均方根误差/MPa 标准差/MPa −5 0.5 0.130 0.195 0.174 −5 1.0 0.177 0.279 0.240 −5 1.5 0.677 0.907 0.751 −5 2.0 0.315 0.493 0.356 −15 0.5 0.585 0.701 0.715 −15 1.0 0.615 1.034 0.794 −15 2.0 0.125 0.193 0.158
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