Applicability of VS30 Estimation Models for the Beijing Plain Area
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摘要: 本文使用基于钻孔测井数据的3类模型，即常速度外推模型、速度梯度模型、双深度参数外推模型，通过对北京地区460个深度超过30m的钻孔剪切波速资料进行分析，详细探究了VS30估算模型在本研究区的适用性。研究结果表明双深度参数外推模型在估算VS30上准确度很高，其不需要大量的数据进行回归分析，且不具有区域独立性，可以为全球包括北京地区场地类别划分提供依据，进而在震害快速评估中用于确定场地影响，是一种值得推广的估算模型。Abstract: Using three models i.e. bottom-layer constant velocity model, velocity gradient model and the extrapolation model with the travel-time averaged shear-wave velocities at two different depths, we investigated the data from 460 boreholes in Beijing plain area in which the shear-wave velocity profile reaches over 30m. Through the detailed research, we found that the last method can estimate VS30 with high accuracy, which does not need any regression analysis to derive empirical relations from a large number of data. Meanwhile, this method is not regionally dependent, and has a remarkable improvement in the accuracy. Therefore, it is potentially useful for many parts of the world including Beijing. It provides a basis for site classification, and then can extend the application to evaluation of site effect in a rapid assessment of earthquake damage, thus being worth to be extensively applied.
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图 3 VS20和VS30的对应关系(虚线代表 1: 1分割线)
Figure 3. Relation of VS20 and VS30 (The dashed lines represent the 1:1 curve)
图 4 不同深度下常速度模型(BCV)剪切波速估算值VSE30和实测值VS30对比图
Figure 4. Comparison between the estimate VSE30 and the measured VS30 in BCV model at different depths
图 5 不同深度下北京平原及Boore(2004)加州和Boore等(2011)日本地区数据回归分析图
Figure 5. Regression analysis based on the data of Beijing plain area, California (Boore, 2004) and Japan (Boore et al., 2011) at different depths
图 6 速度梯度模型线性回归分析(左图)及Wang等(2015)模型(中及右图)得出的VS30和VSE30对比图
Figure 6. Correlations between VS30 and VSE30 using method of velocity gradient linear regression model (left column) and Wang et al. (2015) method (middle and right column), respectively
表 1 BCV法VSE30与VS30的相关系数及残差标准差
Table 1. List of parameters (and defective standard deviation r and σRES) of VSE30 and VS30 for BCV
深度/m r σRES 6 0.830 0.104 7 0.860 0.089 8 0.877 0.080 9 0.901 0.069 10 0.903 0.064 11 0.920 0.053 12 0.917 0.046 13 0.924 0.039 14 0.931 0.035 15 0.945 0.029 16 0.950 0.027 17 0.957 0.025 18 0.963 0.022 19 0.972 0.020 20 0.978 0.018 21 0.982 0.016 22 0.986 0.014 23 0.991 0.011 24 0.994 0.009 25 0.996 0.006 26 0.998 0.005 27 0.999 0.003 28 1.000 0.002 29 1.000 0.001 
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表 2 基于公式(4)的线性回归模型的回归系数
Table 2. List of coefficients a0, a1, r and σRES of equation (4) based on Linear Regression Model
深度/m a0 a1 r σRES 5 0.847 0.696 0.728 0.045 6 0.680 0.766 0.776 0.041 7 0.562 0.814 0.812 0.038 8 0.478 0.847 0.840 0.035 9 0.399 0.878 0.867 0.033 10 0.340 0.901 0.886 0.030 11 0.290 0.919 0.904 0.028 12 0.242 0.937 0.919 0.026 13 0.196 0.954 0.931 0.024 14 0.161 0.966 0.943 0.022 15 0.133 0.975 0.953 0.020 16 0.118 0.978 0.960 0.018 17 0.108 0.980 0.967 0.017 18 0.100 0.981 0.973 0.015 19 0.089 0.983 0.977 0.014 20 0.074 0.988 0.982 0.012 21 0.060 0.991 0.985 0.011 22 0.050 0.994 0.988 0.010 23 0.042 0.995 0.991 0.009 24 0.034 0.997 0.993 0.008 25 0.028 0.998 0.995 0.006 26 0.023 0.998 0.997 0.005 27 0.017 0.998 0.998 0.004 28 0.011 0.999 0.999 0.003 29 0.005 1.000 1.000 0.001
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表 3 基于公式(5)的二次回归模型的回归系数
Table 3. List of coefficients b0, b1, b2, r and σRES of equation (5) based on Quadratic Regression Model
深度/m b0 b1 b2 r σRES 5 3.487 -1.672 0.530 0.734 0.044 6 4.280 -2.442 0.714 0.783 0.041 7 4.603 -2.763 0.791 0.820 0.037 8 4.344 -2.553 0.747 0.846 0.035 9 3.876 -2.162 0.664 0.871 0.032 10 3.357 -1.724 0.570 0.890 0.030 11 2.850 -1.297 0.479 0.906 0.028 12 2.403 -0.926 0.401 0.920 0.026 13 2.079 -0.663 0.347 0.932 0.024 14 1.868 -0.496 0.312 0.943 0.022 15 1.768 -0.420 0.297 0.953 0.020 16 1.682 -0.352 0.283 0.961 0.018 17 1.567 -0.258 0.262 0.967 0.017 18 1.451 -0.162 0.241 0.973 0.015 19 1.246 0.007 0.206 0.978 0.014 20 0.949 0.251 0.155 0.982 0.012 21 0.670 0.480 0.107 0.985 0.011 22 0.477 0.636 0.075 0.988 0.010 23 0.338 0.747 0.052 0.991 0.009 24 0.191 0.866 0.027 0.993 0.008 25 0.081 0.953 0.009 0.995 0.006 26 -0.013 1.027 -0.006 0.997 0.005 27 -0.031 1.038 -0.008 0.998 0.004 28 -0.032 1.035 -0.007 0.999 0.003 29 -0.003 1.006 -0.001 1.000 0.001
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表 4 Wang等(2015)计算的VSE30和VS30相关性及残差标准差
Table 4. List of coefficients and defective standard deviation r and σRES of VSE30 and VS30 from Wang et al. (2015)
(z1，z2) r σRES (5，10) 0.876 0.052 (5，15) 0.947 0.03 (5，20) 0.978 0.018 (5，25) 0.995 0.009 (10，15) 0.943 0.025 (10，20) 0.977 0.016 (10，25) 0.995 0.008 (15，20) 0.975 0.016 (15，25) 0.995 0.007 (20，25) 0.994 0.008
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