Efficient hybrid simulation method for seismic response analysis of underground structures
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摘要: 数值模拟是地下结构抗震分析的重要手段之一，然而地震动输入及边界效应、模型尺度规模等因素均会影响数值模拟的计算精度和效率，并且存在计算尺度、计算时间、计算精度之间的矛盾，因此如何高效、精确地模拟地下结构与地层相互作用体系的地震响应仍是亟待解决的关键问题。基于区域缩减法（DRM）将边界元和有限元相融合的核心思想，旨在建立能够合理模拟地下结构-地层系统地震响应特征的高效混合分析方法。首先将地下结构-地层整体模型划分为近场地层-结构内域子模型和远场地层外域子模型，通过构造重合节点保证内域-外域耦合边界处的位移连续性；其次，基于边界元求解外域自由场或地形影响下的非自由场地震动特征，并采用DRM构造矩阵方程将外域动力响应转化为等效地震荷载，可以在保证地震动合理输入的前提下极大地缩减外域模型尺寸，进而实现对内域中地下结构地震响应的快速参数化分析；最后，设计了两组典型算例以检验该方法的可靠性和高效性。结果表明：对于无地形影响下的双线隧道地震响应模拟，通过与远置边界参考解对比验证了方法的有效性；对于受地形条件影响下的双线隧道地震响应模拟，本方法在保证精度要求的基础上极大缩减了包括地形在内的外域模型范围，相比远置边界法和传统黏弹性法，可使计算模型尺度分别缩减97%和83%，计算时间减少72%和58%。此外，该方法还可推广到斜入射地震动作用下地下结构的动力响应分析。Abstract: The numerical simulation is critical for the seismic analysis of underground structures. However, its accuracy and efficiency are affected by the factors such as input of ground motion, boundary effect, model scale, which leads to the incompatibility among computational scale, time and accuracy. How to efficiently and accurately simulate the seismic response of the underground structure-ground interaction system is still an open question. A novel hybrid boundary element-finite element method in the framework of the domain reduction method (DRM) is proposed to efficiently simulate the seismic response characteristics of the subsurface structure-strata system. First, the overall subsurface structure-stratum model is divided into the inner domain sub-model of the near-field stratum structure and the outer domain sub-model of the far-field stratum, in which the displacement continuity at the inner-outer domain coupling boundary is ensured by overlapping nodes. Second, the non-free field vibration characteristics under the influences of free field and topography in the outer domain are solved by the boundary element method, and the dynamic response in the outer domain is converted into the equivalent seismic load by the DRM. The method greatly reduces the size of the outer domain, ensures the reasonable input of ground vibration, and realizes the rapid parametric analysis of the seismic response of subsurface structures in the inner domain. Further, two typical cases are designed to test the reliability and efficiency of the method. In the case of a two-line tunnel without the influences of topography, the accuracy of the method is validated by comparison with the reference solution. In another case of a two-line tunnel under the influences of terrain conditions, the numerical results show that compared with that of the remote boundary method and the traditional viscoelastic method, the computational cost is reduced by about 72% and 58%, respectively, and the computational scale is reduced by about 97% and 83%, respectively. In addition, the proposed method can be extended to the dynamic response analysis of subsurface structures under the action of oblique incident ground shaking.
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图 6 Chuetsu波加速度和位移时程曲线
Figure 6. Time-history curves of accelerations and displacement of Chuetsu waves
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图 12 Ricker波入射下观测点C处的位移时程
Figure 12. Time histories of displacement at observation point C from Ricker waves
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图 13 Chuetsu波入射下观测点C处的位移时程
Figure 13. Time histories of displacement at observation point C from Chuetsu waves
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图 14 Chuetsu不同角度入射下观测点C处的位移时程
Figure 14. Time histories of displacement at observation point C under different incident angles from Chuetsu waves
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图 15 Chuetsu不同角度入射下观测点D处的位移时程
Figure 15. Time histories of displacement at observation point D under different incident angles from Chuetsu waves
表 1 地层和衬砌的材料参数
Table 1 Material parameters of strata and linings
材料参数 弹性模量/MPa 泊松比 密度/(kg·m-3) 衬砌 32500 0.20 2500 地层 100 0.25 2000 
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表 2 计算模型和耗时
Table 2 Computational models and computational time
方法 单元数量 计算时间/s 远置边界 64089 3460 黏弹性边界 13218 1928 本文方法 5199 826
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