Analytical solution for longitudinal response of pipeline structure under fault dislocation based on Pasternak foundation model
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摘要: 断层错动引起场地上覆土体破裂对跨断层上覆土层的地下管线结构造成巨大破坏。针对断层错动作用下跨断层上覆土层管线结构的纵向响应开展研究，考虑到管线–地基间的非线性相互作用引入了双参数Pasternak地基模型，并结合补余误差函数推导了断层错动下地下管线结构纵向响应解析解。解析解计算结果和模型试验与数值模拟结果基本吻合，证明了解析解的正确性。通过参数敏感性分析讨论了地基剪切刚度、地基反力系数和断层倾角对地下管线结构纵向响应的影响。研究结果表明：基于双参数Pasternak地基模型的断层错动下管线结构纵向响应解析解比传统Winkler地基模型更精确。地基剪切刚度和地基反力系数会改变地下管线结构的弯矩和剪力最大值，而地基反力系数和断层倾角会改变弯矩和剪力的影响区域和最大值的出现位置。在影响区域内管线结构弯矩和剪力值数倍于其它区域，结构易出现剪切破坏，为主要灾害发生区域。
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关键词:
- 断层错动 /
- 解析解 /
- Pasternak地基模型 /
- 补余误差函数 /
- 纵向响应
Abstract: The fault dislocation causes the rupture of the overlying soil on the site, resulting in enormous damage to the underground pipeline structures across the overlying soil. Through the researches on the longitudinal response of the pipeline structures of the overlying soil layer under the fault dislocation, the Pasternak double-parameter model is introduced so as to take the nonlinear interaction between the pipeline and the foundation into consideration, and an analytical solution for the longitudinal response of the pipeline structures is derived using the complementary error function. The calculated results of analytical solution are consistent with those of the model tests and numerical simulations, which proves the correctness of the analytical solution. Through the parameter sensitivity analysis, the influences of the shear stiffness of the elastic layer, the coefficient of subgrade reaction and the fault dip on the longitudinal response of the underground pipeline structures are discussed. The research results show that the longitudinal response of the pipeline structures under fault dislocation based on the two-parameter Pasternak foundation model is more accurate than that of the Winkler foundation model. The shear stiffness and reaction coefficient of the subgrade will change the maximum bending moment and shear force of the underground pipeline structures. In contrast, the coefficient of subgrade reaction and fault dip will change the influence area and the maximum value of the bending moment and shear force. In the influence area, the bending moment and shear force of the pipeline structures are several times higher than those in other locations, and the structures are prone to shear failure, which is the main disaster occurrence area. -
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图 3 断层诱发理想地表变形机制和双参数Pasternak地基梁
Figure 3. Idealized ground deformation mechanism induced by fault and double-parameter Pasternak foundation beam
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图 6 管道位移沿纵向分布规律对比
Figure 6. Comparison of displacement distribution of pipelines along longitudinal direction
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图 7 管道弯矩沿纵向分布规律对比
Figure 7. Comparison of bending moment distribution of pipelines along longitudinal direction
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图 12 管线结构弯矩沿纵向分布规律
Figure 12. Bending moments of pipelines along longitudinal direction
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图 15 管线结构弯矩沿纵向分布规律
Figure 15. Bending moments of pipelines along longitudinal direction
表 1 原型和模型材料的物理力学参数
Table 1 Physical and mechanical parameters of prototype and model materials
参数 原型 模型 测量值 相似比 密度/(kg·m-3) 2400~2500 2400 2300~2400 1 杨氏模量/MPa 33500 111.67 900~980 34.8 泊松比 0.20 0.20 0.20~0.25 1 抗压强度/MPa 20.1 0.67 0.762 26.4 摩擦角/(°) 50 50 50~54 1 
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表 2 围岩和衬砌结构计算参数
Table 2 Physical and mechanical parameters
隧道结构 围岩 断层位移/m 断层倾角/(°) 杨氏模量/MPa 洞跨/m 厚度/m 杨氏模量/MPa 泊松比 33500 4.8 0.6 18 0.4 0.8 45
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表 3 混凝土损伤参数（C45）
Table 3 Damage parameters of concrete (C45)
压缩应力/MPa 非弹性应变/10-3 压缩损伤因子 拉伸应力/MPa 开裂应变/10-3 拉伸损伤因子 5.82 0.0000 0.0000 1.26 0.0000 0.0000 20.10 0.8018 0.3577 2.01 0.0282 0.2256 17.91 1.6030 0.5194 1.18 0.1608 0.5462 14.41 2.5196 0.6460 0.81 0.2729 0.7246 11.66 3.4112 0.7315 0.63 0.3789 0.8150 10.11 4.0630 0.7773 0.53 0.4824 0.8661 8.21 5.1264 0.8313 0.46 0.5848 0.8979 6.65 6.3782 0.8735 0.40 0.6866 0.9192 5.29 8.0237 0.9087 0.36 0.7879 0.9341 4.58 9.2474 0.9260 0.33 0.8889 0.9451 4.29 9.8571 0.9329 0.31 0.9897 0.9534
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