A New Explicit Time Integration Algorithm for Nonlinear Seismic Response Analysis of Site
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摘要: 针对线弹性结构动力学方程，作者已提出一种具有良好稳定性的二阶精度单步显式时间积分算法。本文将该方法推广到求解材料非线性结构动力学方程中，采用带误差控制的修正欧拉算法计算单元应力，提高显式时间积分算法的精度。将求解非线性问题的显式算法应用于地震波垂直入射时非线性地震反应分析中，使用黏性边界模拟场地土层底部半空间基岩的辐射阻尼，并考虑地震动输入。与中心差分法计算结果进行对比，以表明新显式算法的有效性。Abstract: For the linear-elastic structure dynamics equation, the author has proposed a second-order precision single-step explicit time integration algorithm with good stability. In this paper, the method is extended to solve the nonlinear structural dynamics equations, and the modified Euler algorithm with error control is used to calculate the element stress and improve the accuracy of the explicit time integration algorithm. The explicit algorithm for solving nonlinear problems is applied to nonlinear site seismic response analysis. The viscous boundary is used to simulate the radiation damping of the bedrock underlying the soil layer, and the ground motion input is considered. The comparison with the calculation results of the central difference method shows the effectiveness of the new explicit algorithm.
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图 2 大开车站沿线土层纵断面构造
Figure 2. Site condition of the Daikai subway station in vertical direction
图 3 狄拉克脉冲速度和加速度时程图
Figure 3. Velocity and acceleration time history of the Dirac pulse
图 4 狄拉克脉冲入射时场地反应分析结果
Figure 4. Results of site analysis under the incident of Dirac pulse
图 5 实测地震动速度和加速度时程图
Figure 5. Velocity and acceleration time history of the seismic motion
图 6 实测地震动入射时场地反应分析结果
Figure 6. Results of site reaction analysis under the incident of the seismic motion
表 1 土层参数
Table 1. Parameters of soils
土质 深度/
m$\rho $/
（g/cm3）cs /
（m/s）v
-EN
-Rf
-c/
（MPa）θ/（°） D
-F
-人工填土 0—1.0 1.9 140 0.33 0.33 0.758 0.084 26.9 1.06 0.021 全新世砂土 1.0—5.1 1.9 140 0.32 0.33 0.758 0.084 26.9 1.06 0.021 全新世砂土 5.1—8.3 1.9 170 0.32 0.36 0.768 0.120 31.0 1.11 0.015 更新世粘土 8.3—11.4 1.9 190 0.40 0.44 0.822 0.188 28.4 1.01 0.012 更新世粘土 11.4—17.2 1.9 240 0.30 0.44 0.822 0.188 28.4 1.01 0.012 更新世砂土 17.2—22.2 2.0 330 0.26 0.51 0.840 0.300 30.0 1.02 0.011 基岩 ＞22.2 2.0 330 0.26 - - - - - - 
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