Correlation between shear wave velocity and buried depth of common soils in Liuzhou city of Guangxi region
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摘要:
基于广西柳州地区地震安全性评价中实测所获的钻孔资料，利用线性模型、幂函数模型和二次函数模型分别对该地区土层剪切波速与埋深之间的相关性进行了拟合分析，通过对比发现幂函数模型为二者间相关性拟合的最优选择，同时探讨了土体状态对二者相关性的影响。结果表明：除人工填土外，柳州地区内常见土层剪切波速与埋深之间具有较强的相关性，区域性对其相关性也具有影响。最后以实测钻孔为例，验证了本文模型的预测精度和可靠性，而且模型的预测精度可以通过区分土体状态得到明显提高。
Abstract:Based on the measured borehole data in the earthquake safety assessment of Liuzhou region, Guangxi, three models （linear, power function, quadratic function models） were used to fit and analyze the correlation between shear wave velocity of soil layer and burial depth in this area. And then the power function model was selected to analyze the correlation between the depth of the soil layer and corresponding shear wave velocity in the area, and the influence of the soil state on the correlation between the two parameters was also discussed, and finally the actual drilling was taken as an example to verify the accuracy and reliability of the model. The obtained results are as follows: ① except artificial filling, there is a strong correlation between the shear wave velocity and the buried depth of common soils in the area, and the correlation can be affected by the region where it is; ② the soil state can significantly improve the prediction accuracy of the model.
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Keywords:
- shear wave velocity /
- buried depth /
- soil state /
- regression model /
- correlation
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图 1 柳州地区Ⅱ类场地土层剪切波速与埋深之间的散点图
Figure 1. Shear wave velocity versus depth of soils for the class Ⅱ sites in Liuzhou region
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图 2 柳州地区人工填土剪切波速与埋深间的散点图
Figure 2. Shear wave velocity versus depth of artificial filled soils in Liuzhou region
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图 3 不同土类剪切波速与埋深间关系散点图
（a） 红黏土；（b） 粉质黏土；（c） 黏土
Figure 3. Shear wave velocity versus buried depth for different soils
（a） Red clay；（b） Silty clay；（c） Clay
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图 4 柳州地区红黏土（a）和粉质黏土（b）在不同土体状态下剪切波速与埋深间的散点图
Figure 4. Shear wave velocity versus depth of soils for red clay （a） and silty clay （b） with different soil states in Liuzhou region
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图 5 柳州地区红黏土（a）和粉质黏土（b）不同土体状态下剪切波速预测曲线
Figure 5. Prediction curves of shear wave velocity in red clay （a） and silty clay （b） with different soil states in Liuzhou region
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图 6 红黏土（a）和粉质黏土（b）不同土体状态下剪切波速与实测数据的对比
Figure 6. Comparison of shear wave velocity with measured data of red clay （a） and silty clay （b） in different soil states
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图 7 红黏土（a）和粉质黏土（b）土体状态对模型预测误差的影响
Figure 7. Influence of soil state on the predicted error from the model of red clay （a） and silty clay （b）
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图 8 本文模型与刘模型和规范模型所得剪切波速的对比
Figure 8. Comparison of shear wave velocties from the model of this study with those from Liu model and the normative model
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图 9 本文模型与刘模型和规范模型预测误差对比
Figure 9. Comparison of prediction errors from the model of this study with those from Liu model and normative model
表 1 柳州地区Ⅱ类场地常规土类的埋深范围
Table 1 Conventional soil depth range for the class Ⅱ sites in Liuzhou region
岩土类型 埋深范围/m 人工填土 0.2—12.2 红黏土 1.0—31.0 粉质黏土 0.8—25.0 黏土 3.8—25.7 
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表 2 柳州地区常规土类回归模型的拟合参数及拟合优度R2
Table 2 Fitting parameters and goodness R2 for three regressive models of conventional soils in Liuzhou region
岩土类型 线性模型 幂函数模型 二次函数模型 a b R2 c d R2 e f g R2 红黏土 243.80 4.237 3 0.803 2 215.93 0.129 7 0.813 1 240.02 5.059 4 −0.033 7 0.804 8 粉质黏土 224.22 6.325 4 0.772 4 201.86 0.149 6 0.824 2 223.02 5.777 0 −0.012 1 0.822 5 黏土 247.72 5.504 6 0.835 9 205.28 0.188 0 0.841 8 238.19 8.240 7 −0.077 8 0.840 3
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表 3 不同土体状态下红黏土和粉质黏土的幂函数模型拟合参数及拟合优度R2
Table 3 Fitting parameters and goodness R2 of power function model for red clay and silty clay with different plastic states
回归模型 c d R2 可塑状态 硬塑状态 可塑状态 硬塑状态 可塑状态 硬塑状态 红黏土 195.35 205.35 0.145 2 0.131 9 0.742 9 0.714 2 粉质黏土 192.30 207.14 0.168 2 0.155 5 0.748 4 0.763 8
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表 4 红黏土在不同土体状态下由回归模型按土体埋深所得剪切波速vS的预测值
Table 4 The predicted shear wave velocity vS from the regression model of red clay with plastic state according to the buried depth of soils
埋深/m 土体名称 土体状态 vS实测值
/（m·s−1）区分土体状态 不区分土体状态 vS计算值/（m·s−1） 误差 vS计算值/（m·s−1） 误差 0.70 杂填土 − 228 − − − − 2.00 红黏土 硬塑 230 225 2.2% 236 2.7% 3.00 红黏土 硬塑 242 237 1.9% 249 2.9% 4.00 红黏土 硬塑 255 247 3.3% 258 1.4% 5.00 红黏土 硬塑 260 254 2.3% 266 2.3% 6.00 红黏土 硬塑 263 260 1.1% 272 3.6% 7.00 红黏土 硬塑 267 265 0.6% 278 4.1% 8.00 红黏土 硬塑 264 270 2.3% 283 7.1% 9.00 红黏土 硬塑 264 274 3.9% 287 8.8% 10.00 红黏土 硬塑 272 278 2.3% 291 7.0% 11.00 红黏土 硬塑 272 282 3.6% 295 8.3% 12.00 红黏土 硬塑 273 285 4.4% 298 9.2% 13.00 红黏土 硬塑 269 288 7.1% 301 12.0% 14.00 红黏土 硬塑 272 291 6.9% 304 11.8% 15.00 红黏土 硬塑 279 294 5.2% 307 10.0% 16.50 红黏土 硬塑 286 297 3.9% 311 8.6% 18.00 红黏土 硬塑 296 301 1.6% 314 6.1%
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表 5 粉质黏土在不同土体状态下由回归模型按土体埋深所得剪切波速vS及视剪切波速预测值
Table 5 The shear wave velocity vS and predicted apparent shear wave velocity from the regression model of silty clay with plastic state according to the buried depth of soils
埋深/m 土体名称 土体状态 vS实测值
/（m·s−1）区分土体状态 不区分土体状态 vS计算值/（m·s−1） 误差 vS计算值/（m·s−1） 误差 0.40 耕植土 174 − − − − 2.00 粉质黏土 硬塑 235 231 1.8% 224 4.7% 3.00 粉质黏土 硬塑 245 246 0.3% 238 2.9% 4.00 粉质黏土 硬塑 253 257 1.6% 248 1.8% 5.00 粉质黏土 硬塑 260 266 2.3% 257 1.2% 6.00 粉质黏土 硬塑 271 274 1.0% 264 2.6% 7.00 粉质黏土 硬塑 279 280 0.5% 270 3.2% 8.00 粉质黏土 硬塑 288 286 0.6% 276 4.3% 9.00 粉质黏土 硬塑 298 292 2.2% 280 5.9% 10.00 粉质黏土 硬塑 303 296 2.2% 285 6.0% 11.00 粉质黏土 硬塑 314 301 4.2% 289 8.0% 12.50 粉质黏土 硬塑 328 307 6.5% 295 10.2%
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表 6 基于本文模型、刘模型和规范回归模型按土体埋深所得剪切波速预测值
Table 6 The predicted shear wave velocity vS based on the three models according to the buried depth of soils
埋深/m 土的名称 土的状态 vS实测值
/（m·s−1）本文模型 刘模型 规范模型 vS计算值/（m·s−1） 误差 vS计算值/（m·s−1） 误差 vS计算值/（m·s−1） 误差 0.80 素填土 200 − − − − 2.00 红黏土 硬塑 233 225 3.3% 221 5.0% 160 31.3% 3.00 红黏土 硬塑 236 238 0.7% 234 0.6% 181 23.4% 4.00 红黏土 硬塑 243 247 1.6% 244 0.6% 197 18.9% 5.00 红黏土 硬塑 253 254 0.4% 252 0.3% 211 16.7% 6.00 红黏土 硬塑 260 260 0.1% 259 0.4% 223 14.4% 7.00 红黏土 硬塑 264 266 0.6% 265 0.3% 233 11.7% 8.00 红黏土 硬塑 270 270 0.1% 270 0.1% 243 10.2% 9.00 红黏土 硬塑 279 275 1.6% 274 1.7% 251 9.9% 10.00 红黏土 硬塑 281 278 0.9% 279 0.9% 259 7.7% 11.00 红黏土 硬塑 280 282 0.7% 282 0.8% 267 4.7% 12.00 粉质黏土 硬塑 305 305 0.1% 260 14.6% 274 10.2% 13.00 粉质黏土 硬塑 303 309 1.9% 267 11.9% 281 7.4% 14.00 粉质黏土 硬塑 304 312 2.7% 273 10.3% 287 5.6% 15.00 粉质黏土 硬塑 326 316 3.2% 279 14.6% 293 10.1% 16.00 粉质黏土 硬塑 319 319 0.1% 284 11.0% 299 6.4% 17.00 粉质黏土 硬塑 319 322 0.9% 289 9.3% 304 4.7% 18.00 粉质黏土 硬塑 332 325 2.2% 294 11.4% 309 6.8% 19.00 粉质黏土 硬塑 351 327 6.7% 299 14.8% 314 10.4% 20.00 粉质黏土 硬塑 351 330 6.0% 304 13.5% 319 9.0% 21.00 粉质黏土 硬塑 359 333 7.4% 308 14.1% 324 9.7% 22.00 粉质黏土 硬塑 351 335 4.6% 313 10.9% 329 6.4% 23.00 粉质黏土 硬塑 369 337 8.6% 317 14.1% 333 9.8% 24.00 粉质黏土 硬塑 362 340 6.2% 321 11.4% 337 6.8% 25.00 粉质黏土 硬塑 368 342 7.1% 325 11.7% 341 7.2% 25.70 粉质黏土 硬塑 392 378 3.6% 336 14.2% 344 12.2% 注：刘模型引自刘红帅等（2010）以及刘华贵和蒋文宇（2015），规范模型引自中国人民共和国铁道部（2001）。
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