A TRUE TRIAXIAL CREEP CONSTITUTIVE MODEL FOR ROCK CONSIDERING HYDROCHEMICAL DAMAGE
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摘要: 为了准确描述岩石在酸性环境下真三轴蠕变行为的各阶段特征, 基于水岩作用的化学动力学理论, 定义了考虑PH值与时间的化学损伤因子, 将弹性体, 非线性Kelvin体, 线性Kelvin体和黏弹塑性体进行串联, 并考虑岩石在真三轴应力作用下的实际情况, 建立岩石酸腐与真三轴应力耦合作用下的损伤蠕变本构模型, 通过已有的蠕变试验数据对该模型进行参数辨识与验证, 并通过数据拟合得到岩石在真三轴应力下的屈服面方程, 探讨中间主应力对蠕变模型的影响. 结果表明, 推导的本构模型能很好地描述岩石在酸腐作用下真三轴蠕变行为的各阶段特性, 验证了其合理性与准确性.Abstract: In order to accurately describe the characteristics of each stage of rock creep behavior under the combined action of acid environment and true triaxial stress, based on the chemical kinetic theory of water-rock interaction, a chemical damage factor considering pH and time is defined. The elastic body, nonlinear Kelvin body, linear Kelvin body, and visco-elastic-plastic body are connected in series, and the actual situation under the action of true triaxial stress is considered at the same time, a damage-creep constitutive model considering the coupling of rock acid corrosion and true triaxial stress is established. The parameters of the deduced model are identified and verified with the existing experimental research results. The yield surface equation of rock under true triaxial stress is obtained by data fitting, and the influence of intermediate principal stress on the creep model is discussed. The results show that the derived constitutive model can well reflect creep properties of the rock under acid corrosion The true triaxial creep characteristics under the action have certain rationality and practicability.
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图 1 非线性黏弹塑性损伤蠕变力学模型
Figure 1. Nonlinear viscoelastic plastic damage creep mechanical model
图 2 溶液pH值拟合结果与实测数据对比
Figure 2. Comparison between the fitting results of solution pH value and the measured data
图 3 考虑化学损伤的岩石蠕变试验曲线和本构曲线对比
Figure 3. Comparison of rock creep experimental curve and constitutive curve considering chemical damage
图 4 八面体剪应力τoct与平均正应力σm,2的线性关系图
Figure 4. Linear relationship between octahedral shear stress τoct and mean normal stress σm,2
图 5 真三轴应力作用下的大理岩实验曲线与模型曲线对比
Figure 5. Comparison between experimental and model curves of marble under true triaxial stress
图 6 不同中间主应力对模型参数的影响
Figure 6. Effects of different intermediate principal stresses on model parameters
表 1 考虑化学损伤的砂岩三轴蠕变模型参数(初始pH = 3)
Table 1. Sandstone triaxial creep model parameters considering chemical damage (initial pH = 3)
$ {\sigma _1} - {\sigma _3} $ K1/
GPaG1/
GPaG2/
GPaη2/
(GPa·h)$ \lambda $ G3/
GPaη3/
(GPa·h)η4/
(GPa·h)tF/h N 11.5 3.21 2.02 5.37 3.37 0.307 17.2 3.21 2.02 2.01 0.14 0.026 22.8 3.21 2.02 2.83 0.17 0.028 17.68 0.326 26.6 3.21 2.02 2.20 0.31 0.01 28.435 0.365 30.4 3.21 2.02 0.042 29.06 0.047 34.654 1.66 23.2 18.4 0.8 
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表 2 真三轴应力下的岩石损伤应力
Table 2. Rock peak stress under true triaxial stress
$ {\sigma _3} $/MPa $ {\sigma _2} $/MPa $ {\sigma _{\text{p}}} $/MPa 0 0 49 0 60 87 5 5 156 5 30 199 5 50 233 5 100 243 10 50 263 15 15 218 15 30 203 20 50 297 30 30 270 30 40 268 30 50 273 30 80 313 30 105 318 30 120 334 30 150 384 40 50 308 40 100 367 40 200 410
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表 3 真三轴应力作用下的大理岩蠕变模型参数
Table 3. Parameters of the marble creep model under true triaxial stress
$ {\sigma _1} $/MPa $ {\sigma _2} $/MPa $ {\sigma _3} $/MPa $ {K_1} $/GPa $ {G_1} $/GPa $ {G_2} $/GPa $ {\eta _2} $/(GPa·h) $ \lambda $ $ {G_3} $/GPa $ {\eta _3} $/(GPa·h) $ {\eta _4} $/(GPa·h) ${t_{\text{F} } }/{\rm{h} }$ $ N $ 225 5 5 132 26 23 0.46 0.02 123 5.01 21 79.4 0.34 225 30 5 132 26 85 0.41 0.28 245 30 5 132 23 86 0.35 0.49 126 4069 265 30 5 132 18 106 3.54 1.41 24 85 35 1.93 0.7 225 50 5 132 25 123 0.31 0.74 245 50 5 138 25 115 0.25 0.12 265 50 5 136 24 108 0.29 0.088 285 50 5 134 24 81 0.25 0.18 306 13542 305 50 5 132 20 24 23 1.01 329 207 42 2.1 2.2 225 80 5 138 28 204 0.35 0.22 245 80 5 143 31 251 0.22 0.05 265 80 5 143 26 446 0.53 0.08 285 80 5 143 31 117 0.17 0.28 647 11954 305 80 5 143 31 129 0.20 0.23 524 13972 325 80 5 143 32 144 0.41 0.36 114 36 23 2.05 3.2
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