Research on Damage Model of Rock Under Freeze-Thaw Cycles Based on Maximum Tensile Strain Criterion
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摘要:
为反映寒区遭受冻融的岩石在外力作用下的应力-应变全过程，基于统计损伤力学理论，假设岩石微元体强度服从Weibull分布，结合最大拉应变破坏准则，建立了考虑冻融和荷载耦合作用的寒区冻融岩石损伤模型；推导了模型参数的理论解，利用已有的试验结果和已有损伤本构对模型进行了验证，探讨了不同冻融次数下岩石的总损伤曲线演化规律，并对模型参数进行了分析；采用数值模拟方法计算了冻融循环对隧道工程稳定性的影响. 结果表明：本文所建立的模型可较好地重现岩石的应力-应变全过程，并能反映岩石的峰后强度；不同冻融次数下岩石的总损伤演变曲线呈“S”形，总损伤演变曲线可分为3个阶段，即初始损伤阶段、加速阶段和完全损伤阶段；Weibull分布参数$ m $和$ {f}_{0} $分别代表岩石的脆性特征和塑性特征；随着冻融次数的增加，隧道围岩的垂直位移、最大主应力及衬砌最大主应力均逐渐增加，但隧道围岩的应力增幅较小，经历10次冻融循环后，隧道拱顶的围岩下沉量和底部的围岩隆起量分别增加17.87%和19.24%，隧道围岩最大拉应力和压应力极值分别增加了2.70%和2.01%，隧道衬砌最大拉应力和压应力极值分别增加了21.52%和17.87%.
Abstract:In order to reflect the whole process of stress-strain of rock subjected to freeze thawing in the cold region under external force, this paper uses the theory of statistical damage mechanics and assumes that the strength of rock microelements obeys Weibull distribution. Then, according to the maximum tensile strain failure criterion, a damage model of rock subjected to freeze thawing in the cold region is established by considering the coupling effect of freeze thawing and load. The theoretical solution of the model parameters is deduced, and the damage model is verified by the test results and damage constitutive model of the predecessors. The evolution law of the total damage curve of the rock under different freeze-thaw cycles is discussed, and the model parameters are analyzed. Finally, the influence of the freeze-thaw cycle on the stability of tunnel engineering is calculated by the numerical simulation method. The results show that the model established in this paper can well reproduce the stress-strain curve of the rock and reflect the post-peak strength of the rock. The total damage evolution curve of the rock under different freeze-thaw cycles is S-shaped, and it can be divided into three stages: initial damage stage, accelerated stage, and complete damage stage. Weibull distribution parameters
m and $ {f}_{0} $ represent the brittle and plastic characteristics of rock, respectively. Additionally, with the increase in freeze-thaw cycles, the vertical displacement and the maximum principal stress of the tunnel surrounding rock increase. Meanwhile, the maximum principal stress of tunnel lining also increases. However, the stress of the tunnel surrounding rock increases slightly. After 10 freeze-thaw cycles, the settlement of surrounding rock at the top of the tunnel arch and the uplift of surrounding rock at the bottom increase by 17.87% and 19.24%, respectively; the maximum tensile stress and compressive stress extremes of the tunnel surrounding rock increase by 2.70% and 2.01%, respectively, while those of the tunnel lining increase by 21.52% and 17.87%, respectively.-
Key words:
- rock /
- freeze-thaw cycle /
- failure criteria /
- damage model /
- parameter analysis
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图 1 低孔隙率硬质花岗岩试验与理论曲线对比（${\sigma }_{3} $ = 10 MPa）
Figure 1. Comparison of experimental and theoretical curves of hard granite with low-porosity (${\sigma }_{3} $ = 10 MPa)
图 2 高孔隙率软质红砂岩试验与理论曲线对比
Figure 2. Comparison of experimental and theoretical curves of soft red sandstone with high porosity
图 3 低孔隙率硬质花岗岩总损伤演变曲线
Figure 3. Total damage evolution curves of hard granite with low-porosity
图 4 高孔隙率软质红砂岩总损伤演变曲线
Figure 4. Total damage evolution curves of soft red sandstone with high porosity
图 5 冻融受荷岩石总损伤演变规律
Figure 5. The evolution of total damage of rock under loading and freeze-thaw action
图 7 参数$ {f}_{0} $对应力-应变曲线的影响
Figure 7. Influence of parameter $ {f}_{0} $ on the stress-strain curve
图 9 参数$ {f}_{0} $对总损伤量的影响
Figure 9. Influence of parameter $ {f}_{0} $ on the total damage
图 10 隧道工程算例计算模型（单位：m）
Figure 10. Calculation model of tunnel engineering example （unit: m）
图 12 不同冻融次数下隧道围岩最大主应力矢量场
Figure 12. Maximum principal stress vector field of surrounding rock for tunnel under different freeze-thaw cycles
图 11 不同冻融次数下隧道围岩竖向位移
Figure 11. Vertical displacement of surrounding rock for tunnel under different freeze-thaw cycles
图 13 不同冻融次数下隧道衬砌最大主应力
Figure 13. Maximum principal stress in tunnel lining under different freeze-thaw cycles
表 1 低孔隙率硬质花岗岩力学参数
Table 1. Mechanical parameters of hard granite with low porosity
N/次 围压/
MPa峰值应力/
MPa峰值点
应变残余强度/
MPa弹性模量/
GPa0 10 185.14 0.0052 40 36.71 50 160.02 0.0068 140 26.67 100 123.29 0.0058 90 22.99 150 106.24 0.0064 40 21.12 
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表 2 高孔隙率软质红砂岩力学参数
Table 2. Mechanical parameters of soft red sandstone with high porosity
N/次 围压/MPa 峰值应力/MPa 峰值点应变 残余强度/MPa 弹性模量/GPa 泊松比 0 6 24.866 0.016 22.408 1.649 0.254 5 4 19.132 0.013 14.822 1.452 0.257 10 2 12.701 0.011 7.020 1.156 0.262
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表 3 不同冻融次数下隧道围岩力学参数
Table 3. Mechanical parameters of surrounding rock for tunnel under different freeze-thaw cycles
N/次 弹性模量/GPa 黏聚力/MPa 泊松比 容重/（kN·m−3） 内摩擦角/（°） 0 1.387 1.91 0.258 22 30 5 1.295 1.62 0.259 10 1.156 1.41 0.262
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