An adjustment method for the characteristic period of site acceleration response spectra with soft layers
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摘要:
在分析场地条件对地震震害影响及国内外关于软弱土层对场地地震反应影响的基础上，采用实际含淤泥质土层场地资料，建立了12个含软弱土层的场地模型，在不同输入地震动水平下进行了场地地震反应一维等效线性化分析，讨论了软弱土层厚度和埋深对场地地震反应的影响。结果表明：随着软弱土层的埋深或厚度的增加，反应谱特征周期逐渐增大；输入地震动峰值增加，反应谱特征周期亦增大。继而依据软弱土层厚度、埋深及输入地震动强度对场地加速度反应谱特征周期的影响特征，提出了含软弱土层场地地震动加速度反应谱特征周期调整方法。
Abstract:In recent years, the impact of soft soil on the seismic response of soil layers in sites has attracted attention. Some scholars have conducted in-depth analysis from different perspectives, and the research results show that soft soil increases the dominant period and response spectrum characteristic period of the site to a certain extent. As the position of the soft interlayer deepens, the amplification effect of the site decreases, and the dominant period and response spectrum characteristic period of the site increase. Compared with the Code for Seismic Design of Buildings （GB 50011−2010） in China, the characteristic period of the seismic acceleration response spectrum for sites containing weak soil layers after regulation is much larger than the value specified in the code. At present, although there is an analysis of the impact of weak soil layers on site seismic response, there is little research on the adjustment methods of characteristic periods of site response spectra containing weak soil layers.Based on the analysis for the effect of site conditions on earthquake damage and the influence of soft layers on site seismic response at home and abroad, 12 site models are established, by means of drilling data from sites containing soft layers. The one-dimensional equivalent linearization site seismic response analysis is carried out under different input acceleration peak, and the influence of soft layer thickness, buried depth and input peak acceleration on site seismic response is discussed. The results show that under the same input acceleration peak, as the burial depth and thickness of soft layer increase, the characteristic period of the site acceleration response spectra gradually increases and the peak ground acceleration decreases. As the input peak acceleration increases, while the thickness and burial depth of the soft layer remain unchanged, the characteristic period of the site acceleration response spectra and the peak ground acceleration increases. Finally an adjustment method for the characteristic period of site acceleration response spectra with soft layers was proposed.
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图 1 输入地震动加速度时程 （a，b，c） 及反应谱 （d）
Figure 1. Acceleration time histories of input ground motion （a，b，c） and conresponding response spectrum （d）
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图 2 地表峰值加速度随软弱土层埋深的变化特征
Figure 2. Variation characteristics of peak ground acceleration with buried depths of soft soil layers
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图 3 地表峰值加速度动力放大系数随软弱土层埋深的变化特征
Figure 3. Variation characteristics of peak acceleration dynamic amplification coefficient with buried depths of soft soil layer
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图 4 不同输入地震动下含一层（a）和含两层（b）淤泥的各分析模型场地相关加速度反应谱
Figure 4. Site-related acceleration response spectra of each analysis model with one-layer （a） and two-layers （b） of silt under different input ground motions
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图 5 输入不同地震动下含一层淤泥（a）和含两层淤泥（b）的各计算模型场地相关归一化反应谱
Figure 5. Site-related normalized acceleration spectrum of each calculation model with one-layer （a） and two-layers （b） of silt under different input ground motions
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图 6 输入不同峰值加速度时含一层淤泥（a）和含两层淤泥（b）的各分析模型场地加速度反应谱
Figure 6. Site acceleration response spectrum of each analysis model with one-layer of silt （a） and two-layers of silt （b） under different input ground motion with peak ground acceleration
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图 9 不同输入地震动下补充模型1、2与分析模型2场地相关加速度反应谱
（a） 输入PGA＝25 cm/s2；（b） 输入PGA＝50 cm/s2；（c） 输入PGA＝100 cm/s2
Figure 9. The site-related acceleration response spectra of supplementary model 1，2 and analysis model 2 under different input ground motions
（a） Input PGA＝25 cm/s2；（b） Input PGA＝50 cm/s2；（c） Input PGA＝100 cm/s2
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图 7 不同地震动输入水平下各模型的场地相关加速度反应谱
Figure 7. Site-related acceleration response spectrum of model 1 under different input ground motion
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图 8 弹簧−质量单自由度体系分析示意图
图中h，v和ρ分别表示土层厚度、剪切波速、密度；下标su，s，sd分别表示上覆土层、软弱夹层、下伏土层
Figure 8. Schematic diagram of spring mass single degree of freedom system analysis
In the figure，h，v and ρ respectively represent soil layer thickness，shear wave velocity， and density；subscriptsu，s and sd represent the overlying soil layer，weak interlayer，and underlying soil layer respectively
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图 10 不同输入地震动下含一层 （a） 和含两层 （b） 淤泥的各分析模型场地反应谱特征周期随软弱土层厚度及埋深的变化关系
Figure 10. Variation of the characteristic period of the site response spectrum with the thickness and burial depth of the weak soil layer for the analysis models with one-layer （a） and two-layer （b） silt under different input ground motions
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图 11 不同输入地震动水平下场地反应谱特征周期随软弱土层厚度及埋深的变化
Figure 11. Variation of characteristic period of site response spectrum with thickness and buried depth of soft soil layer under different input ground motions
表 1 分析模型1和模型7的剖面和力学特性参数
Table 1 Profile and mechanical characteristic parameters of Analysis model 1
模型 土层
序号岩土名称 土类号 层底深度
/m层厚
/m剪切波速
/（m·s−1）密度
/（kg·m−3）模型1 1 淤泥 1 5.0 5.0 112 1580 2 粉质黏土 3 9.5 4.5 160 1860 3 粉质黏土 4 13.0 3.5 165 1870 4 粉质黏土 5 17.0 4.0 199 1880 5 粉质黏土 6 21.0 4.0 212 1960 6 粉质黏土 7 24.0 3.0 242 1980 7 圆砾 8 27.0 3.0 258 2200 8 全风化安山岩 8 30.0 3.0 393 2250 9 计算基底 9 516 2650 模型7 1 淤泥 1 5.0 5.0 112 1580 2 淤泥 2 10.0 5.0 112 1660 3 粉质黏土 3 14.5 4.5 160 1860 4 粉质黏土 4 18.0 3.5 165 1870 5 粉质黏土 5 22.0 4.0 199 1880 6 粉质黏土 6 26.0 4.0 212 1960 7 粉质黏土 7 29.0 3.0 242 1980 8 圆砾 8 32.0 3.0 258 2200 9 全风化安山岩 8 35.0 3.0 393 2250 10 计算基底 9 516 2650 
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表 2 各土层不同剪应变水平下的动力剪切非线性参数
Table 2 Nonlinear parameters of dynamic shear of all soils under different shear strain levels
土类号 土层名称 参数 剪应变/（10−4） 0.05 0.1 0.5 1 5 10 50 100 1 淤泥 模量比G/Gmax 0.990 2 0.9808 60.910 5 0.835 8 0.504 5 0.337 4 0.092 3 0.048 3 阻尼比ζ 0.017 3 0.024 4 0.052 5 0.071 1 0.123 6 0.142 9 0.167 2 0.171 2 2 淤泥 模量比G/Gmax 0.991 3 0.982 7 0.918 9 0.850 0 0.531 3 0.361 7 0.101 8 0.053 6 阻尼比ζ 0.008 8 0.013 5 0.035 6 0.052 5 0.107 3 0.130 3 0.161 5 0.166 9 3 粉质黏土 模量比G/Gmax 0.991 8 0.983 8 0.924 1 0.858 8 0.548 9 0.378 3 0.108 5 0.057 3 阻尼比ζ 0.013 8 0.019 9 0.045 9 0.064 1 0.120 1 0.142 8 0.173 5 0.178 8 4 粉质黏土 模量比G/Gmax 0.992 5 0.985 1 0.929 6 0.868 4 0.568 9 0.397 5 0.116 6 0.061 9 阻尼比ζ 0.012 3 0.017 6 0.040 2 0.056 1 0.105 3 0.125 8 0.154 2 0.159 2 5 粉质黏土 模量比G/Gmax 0.993 9 0.987 8 0.941 9 0.890 3 0.618 7 0.447 9 0.139 6 0.075 0 阻尼比ζ 0.015 7 0.021 8 0.046 1 0.062 6 0.113 6 0.135 6 0.167 7 0.173 6 6 粉质黏土 模量比G/Gmax 0.994 3 0.988 7 0.946 0 0.897 5 0.636 5 0.466 8 0.149 0 0.080 5 阻尼比ζ 0.018 1 0.024 9 0.051 2 0.068 8 0.123 4 0.147 3 0.182 7 0.189 4 7 粉质黏土 模量比G/Gmax 0.995 0 0.990 1 0.952 4 0.909 2 0.666 9 0.500 3 0.166 8 0.091 0 阻尼比ζ 0.010 6 0.015 2 0.034 2 0.047 8 0.093 6 0.115 4 0.150 4 0.157 0 8 圆砾及卵石 模量比G/Gmax 0.990 0.970 0.900 0.850 0.700 0.550 0.320 0.200 阻尼比ζ 0.004 0.006 0.019 0.030 0.075 0.090 0.110 0.120 9 基岩 模量比G/Gmax 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 阻尼比ζ 0.004 0.008 0.010 0.015 0.021 0.030 0.036 0.046
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表 3 各分析模型地表峰值加速度和地震反应动力放大系数
Table 3 The peak acceleration and dynamic amplification coefficient for surface seismic response of each analysis model
模型 输入不同峰值加速度的地表水平向峰值加速度/（cm·s−2） 模型 输入不同峰值加速度的地表水平向地震反应动力放大系数 PGA＝25 cm/s2 PGA＝50 cm/s2 PGA＝100 cm/s2 PGA＝25 cm/s2 PGA＝50 cm/s2 PGA＝100 cm/s2 模型1 53.1 97.1 193.2 模型1 2.124 1.942 1.932 模型2 43.8 86.5 152.3 模型2 1.752 1.73 1.523 模型3 41.2 72.4 118.7 模型3 1.648 1.448 1.187 模型4 38.7 58.2 109.9 模型4 1.548 1.164 1.099 模型5 36.4 52.6 100.6 模型5 1.456 1.052 1.006 模型6 30.6 45 87.4 模型6 1.224 0.900 0.874 模型7 48.9 96 174.2 模型7 1.956 1.92 1.742 模型8 38.7 62.6 110.1 模型8 1.548 1.252 1.101 模型9 33.7 55.2 102.8 模型9 1.348 1.104 1.028 模型10 31.1 53.9 83.9 模型10 1.244 1.078 0.839 模型11 30.4 48.2 69.4 模型11 1.216 0.964 0.694 模型12 29.6 46.4 64.6 模型12 1.184 0.928 0.646
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表 4 分析模型的场地参数及场地类别
Table 4 Site parameters and categories of analysis models
分析
模型覆盖层
厚度/m等效剪切
波速/m·s−1场地
类别分析
模型覆盖层
厚度/m等效剪切
波速/m·s−1场地
类别模型1 30 156.0 Ⅱ 模型7 35 134.5 Ⅲ 模型2 30 156.0 Ⅱ 模型8 35 134.5 Ⅲ 模型3 30 156.0 Ⅱ 模型9 35 134.5 Ⅲ 模型4 30 156.0 Ⅱ 模型10 35 142.0 Ⅲ 模型5 30 161.3 Ⅱ 模型11 35 161.3 Ⅱ 模型6 30 182.4 Ⅱ 模型12 35 182.4 Ⅱ
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表 5 各分析模型场地规准反应谱特征周期Tg
Table 5 The characteristic periodic values of site standard response spectrum of each analysis model
模型 输入不同峰值加速度各模型的反应谱特征周期 模型 输入不同峰值加速度各模型的反应谱特征周期 PGA＝25 cm/s2 PGA＝50 cm/s2 PGA＝100 cm/s2 PGA＝25 cm/s PGA＝50 cm/s2 PGA＝100 cm/s2 模型1 0.5 0.55 0.6 模型7 0.7 0.75 0.95 模型2 0.6 0.65 0.8 模型8 0.9 0.95 1.2 模型3 0.7 0.75 0.85 模型9 1 1.05 1.35 模型4 0.75 0.8 1.05 模型10 1.1 1.2 1.45 模型5 0.8 0.9 1.1 模型11 1.15 1.3 1.5 模型6 0.85 0.95 1.2 模型12 1.25 1.35 1.65
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表 6 输入不同地震动水平下模型1—6的反应谱特征周期Tg
Table 6 Characteristic periods Tg of model 1−6 under different input ground motion
分析模型 不同地震动输入水平下的反应谱特征周期 PGA＝25 cm/s2 PGA＝50 cm/s2 PGA＝100 cm/s2 PGA＝150 cm/s2 PGA＝200 cm/s2 PGA＝300 cm/s2 模型1 0.50 0.55 0.60 0.65 0.70 0.75 模型2 0.60 0.65 0.70 0.75 0.80 0.90 模型3 0.70 0.75 0.80 0.85 0.90 0.95 模型4 0.75 0.80 0.85 0.90 0.95 1.00 模型5 0.80 0.85 0.90 0.95 1.00 1.05 模型6 0.85 0.90 0.95 1.00 1.05 1.20 注：输入峰值加速度25 cm/s2的各模型特征周期来自于表5
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表 7 原分析模型剖面和力学特性参数
Table 7 The original analysis model
序号 土层名称 土类号 层底深度
/m层厚
/m剪切波速
/（m·s−1）密度
/（kg·m−3）1 粉质黏土 3 4.5 4.5 160 1860 2 淤泥 1 9.5 5.0 112 1580 3 粉质黏土 4 13.0 3.5 165 1870 4 粉质黏土 5 17.0 4.0 199 1880 5 粉质黏土 6 21.0 4.0 212 1960 6 粉质黏土 7 24.0 3.0 242 1980 7 圆砾 8 27.0 3.0 258 2200 8 全风化安山岩 8 30.0 3.0 393 2250 9 计算基底 9 516 2650
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表 8 补充分析模型1
Table 8 The supplementary analysis model 1
土层序号 土层名称 土类号 层底深度
/m层厚
/m剪切波速
/（m·s−1）密度
/（kg·m−3）1 粉质黏土 3 4.5 4.5 160 1860 2 粉质黏土 3 9.5 5.0 160 1860 3 粉质黏土 4 13.0 3.5 165 1870 4 粉质黏土 5 17.0 4.0 199 1880 5 粉质黏土 6 21.0 4.0 212 1960 6 粉质黏土 7 24.0 3.0 242 1980 7 圆砾 8 27.0 3.0 258 2200 8 全风化安山岩 8 30.0 3.0 393 2250 9 计算基底 9 516 2650
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表 9 补充分析模型2
Table 9 The supplementary analysis model 2
土层序号 土层名称 土类号 层底深度
/m层厚
/m剪切波速
/（m·s−1）密度
/（kg·m−3）1 粉质黏土 3 4.5 4.5 160 1860 2 粉质黏土 4 9.5 5.0 165 1870 3 粉质黏土 4 13.0 3.5 165 1870 4 粉质黏土 5 17.0 4.0 199 1880 5 粉质黏土 6 21.0 4.0 212 1960 6 粉质黏土 7 24.0 3.0 242 1980 7 圆砾 8 27.0 3.0 258 2200 8 全风化安山岩 8 30.0 3.0 393 2250 9 计算基底 9 516 2650
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表 10 不同输入地震动水平下场地反应谱特征周期拟合结果
Table 10 Fitting results of characteristic period of site response spectrum under different input ground motions
输入地震动/（cm·s−2） 模型1—6 输入地震动/（cm·s−2） 模型7—12 a b R2 a b R2 25 0.838 −0.066 0.999 80 25 0.972 −0.297 0.999 12 50 0.941 −0.166 0.999 05 50 1.050 −0.410 0.999 64 100 1.231 −0.270 0.999 72 100 1.246 −0.223 0.999 38
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表 11 不同输入水平下模型1−模型6的反应谱特征周期拟合结果
Table 11 Fitting results of characteristic periods of model 1−6 at different input ground motions
分析模型 α β R2 模型1 0.501 5 0.000 9 0.962 4 模型2 0.588 4 0.001 0 0.993 7 模型3 0.701 5 0.000 9 0.962 4 模型4 0.751 5 0.000 9 0.962 4 模型5 0.801 5 0.000 9 0.962 4 模型6 0.825 4 0.001 2 0.995 3
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