Comparison of response acceleration methods suggested by different standards
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摘要: 《城市轨道交通结构抗震设计规范》和《核电厂抗震设计标准》给出了两种地下结构抗震分析的反应加速度法，其差异在于有效惯性加速度的确定，前者通过自由场剪应力计算水平有效惯性加速度，后者直接采用自由场加速度作为有效惯性加速度。通过理论分析和数值算例评价了两种反应加速度法的适用性，并比较研究了两种方法计算得到的水平有效惯性加速度随场地类型、场地剪切波速和地震动强度的变化规律。研究结果表明：是否考虑土体的阻尼是两种反应加速度法计算差异的主要来源，同时相邻土层的刚度比（波速比）也是产生差异的来源；两种规范方法计算得到的水平有效惯性加速度的差异随场地剪切波速的增大而减小，随地震动强度的增大而增大；当场地条件差或地震动强度大时，基于剪应力计算的水平有效惯性加速度更为合理，据此计算获得的位移场与动力时程法的计算结果一致，具有更为良好的计算精度。同时提出了一种通过自由场位移计算有效惯性加速度的反应加速度法——基于位移的反应加速度法，讨论和比较了采用位移确定有效加速度时的特点及用于反应加速度法时的计算精度，初步证明基于位移的反应加速度法具有良好的计算精度和更为广泛的适应性。
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关键词:
- 地下结构 /
- 地震反应分析 /
- 反应加速度法 /
- 基于位移的反应加速度法 /
- 有效惯性加速度
Abstract: The Chinese specifications, "Code for seismic design of urban rail transit structures" and "Standard for seismic design of nuclear power plants", give two response acceleration methods for the seismic analysis of underground structures. The difference lies in the determination of the effective inertial acceleration. The former calculates the horizontal effective inertia through free-field shear stress. However, the latter directly uses the free-field acceleration as the effective inertial acceleration. Their applicability is evaluated through the theoretical analysis and numerical examples, and the horizontal effective inertial acceleration calculated by the two methods is compared and studied with the site type, shear wave velocity and ground motion intensity. The research results show that whether to consider the damping of the soil is the main source of the difference in the calculation of the two response acceleration methods, and the stiffness ratio (wave velocity ratio) of the adjacent soil layers is also the source of the difference. The difference of the horizontal effective inertia calculated by the two standard methods decreases with the increase of shear wave velocity, and increases with the increase of ground motion intensity. When the site conditions are poor or the ground motion intensity is high, the horizontal effective inertial acceleration calculated based on the shear stress is more reasonable. The displacement obtained by this calculation is consistent with the calculated result by the dynamic time history method, thus it has better calculation accuracy. A new response acceleration method for calculating the effective inertial acceleration through free-field displacement is also proposed-displacement-based response acceleration method. The characteristics of using the free-field displacement to determine the effective acceleration and the calculation accuracy when used in the response acceleration method are discussed and compared, and it is preliminarily verified that the displacement-based response acceleration method has good calculation accuracy and wider adaptability. -
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图 3 不同场地水平有效惯性加速度随深度的分布曲线
Figure 3. Curves of effective response acceleration with depth by different soil models
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图 4 不同场地类型自由地表处加速度Fourier谱
Figure 4. Fourier spectra on free surface by different soil models
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图 5 不同土体初始剪切波速下水平有效惯性加速度随深度的分布曲线
Figure 5. Curves of effective response acceleration with depth by models with different soil parameters
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图 6 不同地震动强度水平下有效惯性加速度随深度的分布曲线
Figure 6. Curves of effective response acceleration with depth of different peak acceleration models
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图 7 均匀半空间场地水平位移随深度变化曲线
Figure 7. Curves of lateral displacement with depth of half space
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图 8 复杂场地水平位移随深度变化曲线
Figure 8. Curves of lateral displacement with depth of complex site
表 1 均匀半空间场地模型参数
Table 1 Parameters of models for half space
材料类型 密度/(kg·m-3) 厚度/m 初始剪切波速/(m·s-1) 基岩 2242.6 — 768.0 
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表 2 双覆盖层场地模型参数
Table 2 Parameters of models for double-covered site
材料类型 密度/(kg·m-3) 厚度/m 初始剪切波速/(m·s-1) 黏土 1890.0 35.4 120.0 砂土 2010.0 52.6 340.0 基岩 2242.6 — 768.0
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表 3 复杂场地模型参数
Table 3 Parameters of models for complex site
材料类型 密度/(kg·m-3) 厚度/m 初始剪切波速/(m·s-1) 黏土 1930.0 2.0 80.0 黏土 1830.0 6.0 88.0 砂土 1890.0 2.0 208.2 黏土 2010.0 23.4 111.5 黏土 1930.0 2.0 278.5 黏土 1920.0 16.8 147.5 砂土 1970.0 3.5 368.3 黏土 1930.0 25.5 200.1 黏土 2010.0 4.8 356.2 砂土 1970.0 2.0 455.7 基岩 2242.6 — 768.0
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表 4 岩土介质动力参数
Table 4 Dynamic parameters of soils
黏土 砂土 基岩 应变/% G/Gmax 阻尼比/% 应变/% G/Gmax 阻尼比/% 应变/% G/Gmax 阻尼比/% 0.0001 1.0000 1.50 0.0001 1.000 1.04 0.0001 1.000 1.00 0.0003 1.0000 1.60 0.0003 1.000 1.31 0.0003 1.000 — 0.0010 1.0000 1.88 0.0010 0.990 1.65 0.0010 1.000 1.42 0.0030 0.9840 2.81 0.0030 0.960 2.00 0.0030 0.981 — 0.0100 0.9470 4.65 0.0100 0.850 3.00 0.0100 0.950 2.80 0.0300 0.8470 7.51 0.0300 0.640 5.10 0.0030 0.850 — 0.1000 0.6560 11.69 0.1000 0.370 9.80 0.1000 0.725 6.14 0.3000 0.4380 16.16 0.3000 0.180 15.50 1.0000 0.550 13.59 1.0000 0.2380 21.00 1.0000 0.080 21.00 3.0000 0.1440 25.00 3.0000 0.050 25.00 10.0000 0.1100 28.00 10.0000 0.035 28.00
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表 5 均匀半空间场地结构位置处自由场变形相对误差
Table 5 Relative errors of free-field deformation at position of structures of half space
场地剪切波速/(m·s-1) 地震波 峰值加速度/g 规范一方法/% 规范二方法/% 基于位移法/% v0=100 Loma Prieta 0.40 -0.40 -10.99 -0.81 Kobe -0.22 -3.28 -0.80 Northridge -0.74 -1.52 0.17 v0=300 Loma Prieta 0.40 -0.39 1.36 0.13 Kobe 0.73 1.43 -0.23 Northridge -0.28 4.29 -0.37 v0=768 Loma Prieta 0.40 15.93 16.11 0.17 Kobe 8.28 8.10 1.06 Northridge -1.96 -0.61 -0.40
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表 6 复杂场地结构位置处自由场变形相对误差
Table 6 Relative errors of free-field deformation at position of structures of complex site
场地模型 地震波 峰值加速度/g 规范一方法/% 规范二方法/% 基于位移法/% Loma Prieta 0.10 -1.16 4.06 -0.16 Kobe -0.56 -4.23 -2.10 Northridge -1.00 2.48 0.26 复杂场地
（vse=149.52 m/s）Loma Prieta 0.20 -1.32 5.33 -0.01 Kobe -0.31 -5.70 -1.27 Northridge -0.44 -4.99 -1.06 Loma Prieta 0.40 -0.93 21.25 -0.39 Kobe -1.76 -7.67 -1.75 Northridge -0.52 -5.99 -1.37
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