Three-dimensional loosely coupled effective stress method for seismic soil-structure interactions
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摘要: 地震波传播至土–结构接触界面时会发生反射与透射现象，结构周围土体处于往复剪应力和正应力差耦合的三维循环剪切状态。采用三维等效剪应变算法和加卸载判据将一维Davidenkov非线性滞回模型与剪切–体积应变耦合的孔压增量模型拓展至三维应力空间。考虑循环加载过程中土骨架循环刚度退化与超静孔隙水压力增长的耦合关系，建立了三维应力空间中的弱耦合有效应力分析法。基于ABAQUS显式求解器，实现了该有效应力算法，可应用于大型三维可液化场地中的土–地下结构体系非线性地震反应分析。针对已完成可液化场地三层三跨地铁车站结构试验开展数值模拟，结果表明：超静孔隙水压力的累积导致土的性状变化显著影响土–地下结构动力相互作用，数值模拟得到的土–结构接触界面能量聚焦时刻以及该时刻对应的瞬时卓越频率与振动台试验结果均吻合较好，提出的三维弱耦合有效应力法能较为理想地反映振动台试验中土–地下结构动力相互作用特性。土骨架有效应力水平显著影响超孔压比的发展规律，振动台不完备的密度相似比设计会造成模型结构周围地基土与原型的超孔压比分布规律存在差异。
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关键词:
- 可液化场地 /
- 土–结构动力相互作用 /
- 弱耦合有效应力分析法 /
- 振动台试验
Abstract: Wave reflection and transmission phenomena occur when seismic ground motion propagates to the soil-structure interface, and the surrounding soil is under three-dimensional (3D) cyclic shearing with reciprocating change of shear stress and normal stress difference. The 3D equivalent shear strain algorithm and the loading-unloading criterion are used to extend the 1D Davidenkov hysteretic model in association with an incremental excess pore water pressure (EPWP) model to the 3D stress state. A weakly coupled effective stress method in 3D stress state is established considering the coupling between the cyclic degradation of soil stiffness and the EPWP generation during cyclic loading. Based on the ABAQUS explicit solver, the proposed method is implemented, allowing to perform nonlinear seismic response analysis of soil-structure interactions in 3D liquefiable site. The numerical simulation is carried out against a shaking table test on the subway station in liquefiable site. The results show that the EPWP generation leads to the degradation of soil stiffness, which significantly affects the dynamic soil-structure interactions. The energy-focusing time at the soil-structure interface obtained by numerical simulation and the corresponding instantaneous predominant frequency are in good agreement with the test results. The proposed effective stress method can capture the dynamic soil-structure interaction characteristics in the shaking table tests. However, the effective stress level at soil skeleton significantly affects the EPWP generation. The incomplete density similarity ratio design of the shaking table tests can cause the distribution of the EPWP ratio in the model soil deviated with the prototype. -
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图 3 地基土–车站结构的三维有限元分析模型
Figure 3. 3D finite element model for soil-subway station structure
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图 5 数值模拟与试验给出的孔压比时程曲线的对比
Figure 5. Comparison between predicted and measured results for time histories of pore pressure ratios
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图 6 数值模拟与试验给出的土中加速度计A1，A3的加速度时程与Fourier谱的对比
Figure 6. Comparison between predicted and measured results for time histories of acceleration and Fourier spectra for points A1 and A3 in model soil
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图 7 数值模拟与试验给出的土中峰值加速度放大系数随深度的变化关系
Figure 7. Comparison between predicted and measured results for peak acceleration amplification factors with model soil depth
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图 8 加速度反应的时-频-能量特性及与孔压比时域发展的相关性
Figure 8. Relationship between time-frequency-energy spectra of accelerations and time histories of EPWP ratio of model soil
表 1 黏土与南京细砂的模型参数
Table 1 Model parameters of clay and Nanjing fine sand
土层 密度/(g·cm-3) 动泊松比 Davidenkov模型 孔压增量模型 A B a1 a2 a3 C1 C2 C3 γtv/% m n 黏土 1.75 0.49 1.2 0.35 2.5×10-4 0 0 — — — — — — 南京细砂 1.83 0.49 1.02 0.43 4.1×10-4 0.5 0.45 1.051 0.143 1.25 0.02 0.345 6.689 
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表 2 微粒混凝土CDP模型的参数
Table 2 Model parameters of micro-concrete
弹性模量Eo /GPa 拉伸变量ωt 压缩变量ωc 泊松比 ψ/(°) ε fbo/fc Kc u 7.5 0 1 0.18 36.31 0.1 1.16 2/3 0.005
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表 3 振动台试验加载工况
Table 3 Schemes of shaking table tests
地震动 峰值加速度/g 工况 持时/s 松潘波 0.1 SP-1 100 0.5 SP-2 100 什邡八角波 0.1 SF-1 100 0.5 SF-2 100
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