Empirical relationship between overburden thickness and natural frequency based on borehole data in Beijing region
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摘要:
针对当前北京地区缺乏适用的覆盖层厚度与场地自振频率经验关系的现状，首先利用广泛收集的北京市地震安全性评价工作中获取的1 142个钻孔数据资料，采用幂函数模型对其进行回归拟合分析，获得了土体剪切波速随深度变化的关系式，然后对该关系式进行推导建立了适合北京地区场地特征的覆盖层厚度与场地自振频率之间的经验关系，藉此为北京市无剪切波速数据的工程场地提供vS20和vS30参考，并对土层剪切波速和覆盖层厚度进行预估。
Abstract:The thickness of the site overburden layer has a significant impact on the distribution of earthquake damage. Moreover, studies have shown that when calculating the surface ground motion parameters, the uncertainty of the overburden layer thickness will lead to obvious differences for the calculation results. Therefore, giving the thickness of the site overburden layer in a scientific, reasonable and accurate manner can improve the accuracy of calculating the ground motion parameters and better estimate the earthquake damage. Traditionally, the overburden layer thickness is obtained by borehole drilling. However, borehole drilling is expensive, time-consuming and unfriendly to the ecological environment. In order to obtain the thickness of the site overburden layer economically and efficiently, many researchers have conducted in-depth studies on the typical site indicators （site natural frequency, overburden layer thickness） and established the empirical relationship between the overburden layer thickness and the site natural frequency in various research areas. However, so far, no researchers have given the empirical relationship between the site natural frequency and the overburden layer thickness in Beijing. In view of this situation, this paper conducts research on the borehole data obtained in the seismic safety evaluation work in Beijing and obtains the following results:
1） According to the current Code for Seismic Design of Buildings in China, 1142 borehole data were classified, and 512 borehole data of class Ⅱ sites and 630 borehole data of class Ⅲ sites were obtained. Then, calculations and analyses were carried out on these borehole data, and the distribution characteristics of vS20 and vS30 of class Ⅱ sites and class Ⅲ sites in the main distribution areas of the boreholes were obtained, that is, the values of vS20 and vS30 in the west and southwest are higher than those in the east and northeast. As the geographical location moves from the southwest to the northeast, vS20 and vS30 are gradually decreasing.
2） Using the model y＝a （1＋x）b, the borehole data were fitted under the conditions of distinguishing the site categories or not, and the empirical relationship of the soil shear wave velocity changing with depth under different conditions were obtained. Without distinguishing the site categories: vS＝124.6 （0.6408＋Z）0.3074; class Ⅱ 1 site category: vS＝134.4 （0.1176＋Z）0.3085; class Ⅱ 2 site category: vS＝183.1 （−0.3965＋Z）0.2739; class Ⅲ site category: vS＝124.6 （0.6408＋Z）0.4115.
3） The empirical relationship of the soil shear wave velocity changing with depth obtained above were derived, and the empirical relationship between the overburden layer thickness and the site natural frequency were obtained. Without distinguishing the site categories: h＝84.33 fr−1.4438; class Ⅱ 1 site category: h＝94.54 fr−1.4461; class Ⅱ 2 site category: h＝124.63 fr−1.3772; class Ⅲ site category: h＝61.55 fr−1.6992. And the obtained empirical relationships were verified. The verification results show that the empirical relationship between the overburden layer thickness and the site natural frequency established in this paper can estimate the overburden layer thickness relatively accurately.
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Keywords:
- Beijing /
- shear-wave velocity /
- overburden layer thickness /
- fit analysis /
- natural frequency
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图 7 钻孔数据拟合图
（a） 所有钻孔数据；（b） Ⅱ 1类场地钻孔数据；（c） Ⅱ 2类场地钻孔数据；（d） Ⅲ类场地钻孔数据
Figure 7. Borehole data fitting
（a） All borehole data；（b） Data of boreholes on class Ⅱ 1 sites；（c） Data of boreholes on class Ⅱ 2 sites；（d） Data of boreholes on class Ⅲ sites
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图 1 北京地区的第四纪沉积物等厚线图（单位：m）
Figure 1. Isopach map of Quaternary sediment thickness in Beijing region （unit in m）
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图 3 Ⅱ类（左）和Ⅲ类（右）场地上不同终孔深度的钻孔数量（a）以及vS20分布（b）和vS30分布（c）的钻孔数量
Figure 3. The number of boreholes with different final depth （a），vS20 distribution （b） and vS30 distribution （c） at class Ⅱ （left panels） and class Ⅲ （right panels） sites
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图 4 北京地区vS20 （a）和vS30 （b）的空间分布
Figure 4. Spatial distribution of vS20 （a） and vS30 （b） in Beijing region
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图 6 北京地区Ⅱ 1 和Ⅱ 2 子类场地上的钻孔分布
Figure 6. Spatial distribution of boreholes on the Ⅱ 1-class and Ⅱ 2-class sites in Beijing region
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图 8 不同研究区域土层覆盖厚度h与场地共振频率fr的各关系式对比图
Figure 8. Comparison of relationship between overburden layer h and resonance frequency fr of different regions from this study with those from others
表 1 0—100 m深度范围内剪切波速vS与土体深度Z的拟合结果
Table 1 Fitting results of shear wave velocity vS and soil depth Z within the depth range of 0—100 m
拟合情况 拟合所得关系式 拟合标准差 拟合优度 未区分场地类别 vS＝124.6 （ 0.6408 ＋Z）0.3074 67.54 0.642 1 Ⅱ类场地Ⅱ 1子类 vS＝134.4 （ 0.1176 ＋Z）0.3085 63.94 0.689 4 Ⅱ类场地Ⅱ 2子类 vS＝183.1 （− 0.3965 ＋Z）0.2739 66.18 0.689 6 Ⅲ类场地 vS＝124.6 （ 0.6408 ＋Z）0.4115 54.21 0.760 9 
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表 2 不同研究区域土层覆盖厚度h与场地共振频率fr的关系式
Table 2 Relationship between overburden thickness h and resonance frequency fr in different regions
研究区域 来源 关系式 用于研究的钻孔数量 德国莱茵河 Ibs-von Seth和Wohlenberg （1 999） $ h＝96{f}_{\mathrm{r}}^{-1.388} $ 102 德国科隆 Parolai等（2 002） $ h＝108{f}_{\mathrm{r}}^{-1.551} $ 337 德国科隆 Hinzen 等（2 004） $ h＝137{f}_{\mathrm{r}}^{-1.190} $ 152 意大利拉奎拉 Del Monaco等（2 013） $ h＝53.461{f}_{\mathrm{r}}^{-1.4541} $ 25 美国马萨诸塞州 Fairchild等（2 013） $ h＝90.53{f}_{\mathrm{r}}^{-1.0} $ 164 澳大利亚悉尼 Harutoonian等（2 013） $ h＝73{f}_{\mathrm{r}}^{-1.170} $ 15 中国唐山 Bao等（2 019） $ h＝83{f}_{\mathrm{r}}^{-1.33} $ 21 中国新疆 李文倩等（2 019） $ h＝43.53{f}_{\mathrm{r}}^{-0.638} $ 18 中国济南 张若晗等（2 020） $ h＝61.34{f}_{\mathrm{r}}^{-0.874} $ 25 中国北京 本研究（不区分场地） $ h＝84.33{f}_{\mathrm{r}}^{-1.4438} $ 1142 本研究[Ⅱ类场地（Ⅱ 1子类）] $ h＝94.54 $$ {f}_{\mathrm{r}}^{-1.4461} $ 512 本研究[Ⅱ类场地（Ⅱ 2子类）] $ h＝124.63{f}_{\mathrm{r}}^{-1.3772} $ 本研究（Ⅲ类场地） $ h＝61.55{f}_{\mathrm{r}}^{-1.6992} $ 630
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表 3 本文关系式与Ibs-von Seht和Wohlenberg （1999）公式关于验证钻孔处覆盖层厚度的计算对比
Table 3 Comparison of overburden thickness estimation at the verification boreholes by the fitting expression in this study with that from Ibs-von Seht and Wohlenberg （1999）
钻孔编号 实际基岩深度/m 共振频率/Hz 本研究公式 Ibs-von Seht和Wohlenberg （1 999）公式 覆盖层计算深度/m 偏差率 覆盖层计算深度/m 偏差率 ZK07 315.0 0.405 310.98 1.27% 336.61 6.86% ZK08 478.0 0.300 479.64 0.34% 510.54 6.81% ZK14 284.8 0.393 324.79 14.36% 350.96 23.23% SHBZK1 227.0 0.460 258.76 13.98% 282.07 24.26% SHBZK2 70.0 1.190 75.41 6.28% 75.41 7.72% SHBZK3 120.0 0.860 104.85 12.63% 118.36 13.71%
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