Triaxial creep test and model study of red sandstone based on Weibull distribution
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摘要:
当前，地下工程围岩蠕变问题仍然存在，蠕变理论需要进一步丰富。岩石蠕变实质上是损伤不断积累的过程，针对蠕变条件下岩石损伤演化情况，文章采用TAW-2000多功能三轴伺服试验系统对取自四川乐山依卜隧道的红砂岩进行三轴蠕变试验，分析不同围压下试样蠕变变形规律，同时以西原模型为基础，结合Weibull分布和Perzyna 黏塑性理论，建立一种改进的可以描述岩石蠕变破坏全过程的黏弹塑性蠕变模型。通过划分蠕变阶段来定义临界点损伤变量，从而更为准确地确定加速蠕变启动时间。得出如下结论：（1）模型曲线与试验数据具有良好的一致性，验证了模型的准确性与合理性，说明基于Weibull分布建立的红砂岩黏弹塑性蠕变模型是可行的；（2）基于Perzyna黏塑性理论，建立了可以更加准确的描述加速蠕变的黏塑性应变表达式；（3）文章建立的基于Weibull分布和Perzyna 黏塑性理论的三轴损伤蠕变模型能够较好的描述岩石蠕变全过程，克服了西原模型不能描述加速蠕变的缺点。本研究通过定义不同蠕变阶段的临界点损伤变量更好的反映了岩石蠕变变形与损伤之间关系，丰富了岩石类材料的蠕变本构理论。
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关键词:
- Weibull分布 /
- 红砂岩 /
- 蠕变模型 /
- Perzyna黏塑性理论 /
- 临界阈值
Abstract:At present, the creep problem of underground engineering surrounding rock still exists, and the creep theory needs to be further enriched. In essence, rock creep is a process of constant accumulation of damage. In view of the damage evolution of rock under creep conditions, triaxial creep tests are carried out on red sandstone taken from Yibo Tunnel in Leshan, Sichuan Province by TAW-2000 to analyze the creep deformation rule of specimens under different confining pressures. Based on Weibull distribution and Perzyna viscoplastic theory, an improved viscoelastoplastic creep model is established which can describe the whole process of rock creep failure. The critical point damage variable is defined by dividing the creep stage, so that the acceleration creep start time can be determined more accurately. The following conclusions are drawn: (1) the model curve in this paper is in good agreement with the test data, which verifies the accuracy and rationality of the model in this paper, and indicates that the viscoelastic-plastic creep model of red sandstone established based on Weibull distribution is feasible. (2) Based on Perzyna viscoplastic theory, a more accurate viscoplastic strain expression is established to describe accelerated creep. (3) The triaxial damage creep model established in this paper based on Weibull distribution and Perzyna viscoplastic theory can describe the whole process of rock creep well, overcoming the shortcoming of the Siyuan model which can not describe accelerated creep. The relationship between rock creep deformation and damage can be better reflected by defining the critical point damage variables of different creep stages, which enriches the creep constitutive theory of rock materials.
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Key words:
- Weibull distribution /
- red sandstone /
- creep model /
- Perzyna viscoplastic theory /
- critical threshold
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表 1 红砂岩力学参数
Table 1. Mechanical parameters of red sandstone
参数 围压/MPa 峰值强度/MPa 轴向峰值应变 弹性模量/MPa 泊松比 黏聚力/MPa 内摩擦角/（°） 取值 5 52.51 0.005 4 9.67 0.263 6.27 31.05 10 73.73 0.004 7 15.39 0.257 15 94.19 0.005 0 18.81 0.252 20 110.31 0.004 5 24.41 0.248 
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表 2 红砂岩临界点参数
Table 2. Critical point parameters of red sandstone
参数 围压/MPa 荷载水平/MPa t1/h $\varepsilon _{\rm{vp}}^{{t_1}} $ /%t2/h $\varepsilon _{\rm{vp}}^{{t_2}} $ /%取值 5 31.51 2.54 0.243 — — 36.76 2.21 0.315 — — 42.01 2.02 0.414 — — 47.26 1.33 0.503 5.02 0.527 10 44.24 2.55 0.291 — — 51.61 2.43 0.368 — — 58.98 2.22 0.492 — — 66.36 2.01 0.598 6.66 0.619 15 55.51 1.04 0.323 — — 65.93 1.97 0.401 — — 75.35 1.58 0.502 — — 84.77 1.74 0.658 9.54 0.662 20 66.17 2.61 0.369 — — 77.22 2.56 0.452 — — 88.25 2.35 0.559 — — 99.28 2.11 0.687 9.86 0.703 注：表中“—”表示无数值，下表同。
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表 3 模型参数反演结果
Table 3. Model parameter inversion results
模型
参数荷载水平
/MPaG0
/GPaK
/GPaG1
/GPa$\eta_1^* $
/（GPa·h）$\eta_2^* $
/（GPa·h）F0 m λ0 λ1 $\eta_3^* $
/（GPa·h）$F'_0 $ $m' $ $\lambda'_0 $ $\lambda'_1$ λ2 A R2 反演
结果66.17 105.34 161.58 241.98 142.66 359.63 — — — — — — — — — — — 0.95 77.22 114.29 186.76 435.97 298.66 688.54 5.43 1.79 6.32 12.31 — — — — — — — 0.97 88.25 124.58 246.87 985.64 178.92 1231.55 5.02 2.86 3.05 7.54 — — — — — — — 0.96 99.28 66.48 188.93 92.45 98.33 1112.30 4.62 4.31 1.14 3.88 2041.69 1.96 2.03 1.13 −0.37 –5.01 2.88 0.95
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模型
参数含水率/% G0
/GPaK
/GPaG1
/GPa$\eta_1^* $
/（GPa·h）$\eta_2^* $
/（GPa·h）F0 m λ0 λ1 $\eta_3^* $
/（GPa·h）$F'_0 $ $m' $ $\lambda'_0 $ $\lambda'_1 $ λ2 A R2 反演
结果0 89.75 255.06 124.81 132.75 1 501.61 6.24 5.82 6.99 1.85 2 756.28 5.64 4.35 0.08 –2.31 –4.55 3.44 0.95 4.56 86.42 245.61 120.19 127.83 1 445.99 6.01 5.60 0.87 5.22 2 654.20 2.24 1.37 0.83 –1.55 –2.09 7.48 0.97 8.47 73.13 207.82 101.70 108.16 1 223.53 5.08 4.74 1.25 3.11 2 245.86 2.16 2.23 1.05 –2.54 –10.87 15.21 0.96 12.38 66.48 188.93 92.45 98.33 1 112.30 4.62 4.31 1.14 3.88 2 041.69 1.96 2.03 1.13 –0.37 –5.01 2.88 0.95
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