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Numerical simulation of crack propagation in gravity dam heel under in-crack water pressure and earthquake action
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摘要: 为研究不同工况下，地震与缝面水压力共同作用对重力坝坝踵裂缝扩展的影响，以Koyna重力坝为例，利用扩展有限元法(XFEM)和相互作用积分理论，建立缝面水压力和地震共同作用下的重力坝坝踵裂缝断裂数学模型，研究不同的坝基与坝体弹模比、初始裂缝长度、缝面水压力分布对坝踵裂缝扩展的影响。计算结果表明：在缝面水压力均匀分布、初始裂缝长度一定的情况下，裂缝扩展长度随坝基与坝体弹模比的增大逐渐减小，扩展路径向坝基面靠拢；在坝基与坝体弹模比一定、缝面水压力均匀分布的情况下，裂缝扩展路径随着初始裂缝长度的增加逐渐增加且趋近坝基面；当坝基与坝体弹模比和初始裂缝长度一定时，随着缝面水压力系数的增大，裂缝扩展长度逐渐减小，裂缝逐渐向岩基扩展。
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关键词:
- 扩展有限元（XFEM） /
- 重力坝 /
- 裂缝扩展 /
- 坝踵 /
- 缝面水压力
Abstract: Aiming to study the influence from the collective effect of the pressure between earthquake and water in the construction joint to the gravity under various working conditions, we took advantages of extended finite element method (XFEM) and interaction integral theory to build a mathematical model of dam crack fracture under the collective effect of water pressure in the construction joint and earthquake, with Koyna gravity dam as an example. During the process, the effects of different dam foundation and dam elastic modulus ratios, length of initial crack and joint surface water pressure distribution on dam crack propagation were studied as well. It is proved by the calculation results that the expanded length of crack gets weakened with the increase of the dam base to dam body elastic modulus ratio on the condition that the crack water pressure distributes evenly and initial length of crack is fixed; when the elastic modulus ratio of dam and dam base is certain and the crack water pressure distributes evenly, the crack propagation route gradually increases with the increase of the initial length of crack and gradually approaches the dam base surface; when the elastic modulus ratio of the dam foundation and the dam body as well as the initial crack length are fixed, as the water pressure of the construction joint coefficient increases, the crack expanding length gradually decreases, and the crack gradually expands to the rock foundation. -
图 1 重力坝计算模型及网格划分示意
Figure 1. Gravity dam calculation model and grid partition schematic diagram
图 4 不同工况下的动态裂缝扩展路径
Figure 4. Dynamic crack propagation path under different working conditions
表 1 计算工况
Table 1. Calculation conditions
工况编号 E2/E1 a /m n 1 1.0,1.5,2.0,5.0,10.0 3 0 2 1.0,1.5,2.0,5.0,10.0 5 0 3 1.0,1.5,2.0,5.0,10.0 8 0 4 1.0 3, 5, 8 0 5 1.0 5 0, 1, 2 
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表 2 等效应力强度因子Keq
Table 2. Calculation table of equivalent stress intensity factor Keq
时间/s Keq/(MPa·m1/2) 时间/s Keq/(MPa·m1/2) 时间/s Keq/(MPa·m1/2) 时间/s Keq/(MPa·m1/2) 时间/s Keq/(MPa·m1/2) 10.1 2.69×106 11.5 4.58×106 12.9 1.31×105 14.3 6.75×106 15.7 5.31×106 10.2 2.94×106 11.6 4.32×106 13.0 1.66×105 14.4 6.45×106 15.8 4.88×106 10.3 3.21×106 11.7 3.89×106 13.1 3.83×105 14.5 7.38×106 15.9 4.66×106 10.4 3.49×106 11.8 3.47×106 13.2 6.47×105 14.6 6.88×106 16.0 4.03×106 10.5 3.79×106 11.9 2.94×106 13.3 1.19×106 14.7 7.23×106 16.1 3.70×106 10.6 4.09×106 12.0 2.49×106 13.4 1.72×106 14.8 7.42×106 16.2 2.97×106 10.7 4.37×106 12.1 1.99×106 13.5 2.37×106 14.9 7.31×106 16.3 2.53×106 10.8 4.63×106 12.2 1.56×106 13.6 2.91×106 15.0 7.30×106 16.4 1.83×106 10.9 4.86×106 12.3 1.11×106 13.7 3.62×106 15.1 6.92×106 16.5 1.20×106 11.0 5.02×106 12.4 7.65×105 13.8 4.18×106 15.2 6.65×106 16.6 5.22×105 11.1 5.12×106 12.5 4.91×105 13.9 4.85×106 15.3 6.93×106 16.7 3.81×104 11.2 5.14×106 12.6 2.70×105 14.0 5.32×106 15.4 6.41×106 16.8 9.26×102 11.3 4.93×106 12.7 1.70×105 14.1 6.15×106 15.5 6.20×106 16.9 4.85×103 11.4 4.86×106 12.8 9.48×104 14.2 6.68×106 15.6 5.41×106 17.0 2.30×105
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