Relationship between Shear Wave Velocity and Depth for Conventional Soils in the Bohai Sea Area
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摘要: 土层的剪切波速是岩土地震工程中重要的物理量，本文利用多年来在渤海海域地震安全性评价中积累的资料，研究了渤海常见土类剪切波速和埋深的关系。利用非线性最小二乘法，采用指数函数、一次函数、二次函数、幂函数、"幂函数+常数函数"、"幂函数+一次函数" 6种回归模型对各类土的剪切波速和埋深的关系进行了回归分析，以拟合优度以及最小二乘拟合的误差平方和为评价指标对比了各种模型拟合效果的优劣。结果表明，"幂函数+一次函数"回归模型的拟合效果最好。此外，本文给出了该海域常见的7类土在此回归模型下的拟合公式的系数，以供工程中参考。Abstract: Shear wave velocity of soil layers is an important physical index in geotechnical earthquake engineering. Based on the experimental data accumulated over the years in the seismic safety evaluation research projects of the Bohai sea area, relationship between shear wave velocity and depth of conventional soils has been studied. In order to achieve the best fitting of experimental data, 6 regression models including exponential function, linear function, quadratic function, power function, power function combined with constant function, power function combined with linear function, have been used for regression analysis through nonlinear least square fitting method. The goodness-of-fit has been used as an index to evaluate the matching effect. The results showed that, the proposed form of function which combining power function with linear function has the best matching effect for experimental velocity data. Furthermore, the fitting coefficients of proposed function for 7 kinds of conventional soils in the Bohai Sea area have been presented for reference in engineering.
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Key words:
- The Bohai Sea /
- Shear wave velocity /
- Depth /
- Regression analysis /
- Fitting
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图 3 粉质粘土在6种剪切波速-埋深回归模型下的拟合结果
Figure 3. Fitting curves of silty clay for 6 kinds of regression models
图 4 粉质细砂在6种剪切波速-埋深回归模型下的拟合结果
Figure 4. Fitting curves of silty fine sand for 6 kinds of regression models
图 5 粉砂在6种剪切波速-埋深回归模型下的拟合结果
Figure 5. Fitting results of silt for 6 kinds of regression models
图 6 粉土在6种剪切波速-埋深回归模型下的拟合结果
Figure 6. Fitting results of floury soil for six kind of regression models
图 7 砂质粉砂在6种剪切波速-埋深回归模型下的拟合结果
Figure 7. Fitting curves of sandy silt for 6 kinds of regression models
图 8 砂质粉土在6种剪切波速-埋深回归模型下的拟合结果
Figure 8. Fitting curves of sandy floury soil for 6 kinds of regression models
图 9 细砂在6种剪切波速-埋深回归模型下的拟合结果
Figure 9. Fitting curves of fine sand for 6 kinds of regression models
表 1 各类土在各回归模型下的拟合优度
Table 1. Goodness-of-fits of 7 kinds of soils under different regression models
拟合函数 土类 粉质粘土 砂质粉砂 粉砂 粉质细砂 细砂 砂质粉土 粉土 R2 RSS /105 R2 RSS /104 R2 RSS /104 R2 RSS /105 R2 RSS /104 R2 RSS /103 R2 RSS /104 （1）v=aebh 0.861 3.46 0.865 4.81 0.883 3.20 0.873 9.83 0.900 3.26 0.925 9.36 0.865 2.45 （2）v=ah+b 0.915 2.10 0.901 3.51 0.913 2.37 0.909 7.04 0.916 2.73 0.962 4.79 0.928 1.31 （3）v=ah2+bh+c 0.915 2.10 0.901 3.51 0.913 2.37 0.909 7.04 0.916 2.73 0.962 4.79 0.928 1.31 （4）v=ahb 0.935 1.61 0.926 2.64 0.901 2.71 0.946 4.19 0.922 2.55 0.992 1.03 0.979 0.38 （5）v=ahb+c 0.943 1.42 0.932 2.42 0.919 2.22 0.949 3.91 0.928 2.33 0.992 0.94 0.981 0.34 （6）v=ahb+ch+d 0.944 1.40 0.934 2.33 0.920 2.20 0.950 3.82 0.931 2.25 0.993 0.91 0.981 0.34 注：R2表示拟合优度，RSS表示误差平方和，其单位为m2/s2。 
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表 2 各土类采用v=ahb+ch+d形式拟合的系数
Table 2. Fitting coefficients for 7 kinds of soils while using the formula v=ahb+ch+d
v=ahb+ch+d拟合系数 土类 粉质粘土 砂质粉砂 粉砂 粉质细砂 细砂 砂质粉土 粉土 a 76.4017 123.9201 141.3937 120.0582 145.2684 101.4440 49.1360 b 0.2760 0.1907 0.1190 0.2241 0.1630 0.2769 0.4209 c 1.4209 1.1374 1.7891 0.7949 1.1223 0.4958 1.6224e-6 d 20.2951 0.0013 0.0049 3.0568e-5 5.2199e-5 1.0829e-5 62.3314
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