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黄土高填方场地工后沉降预测模型性能评估方法

于永堂 郑建国 孙茉 黄鑫 韩文斌

于永堂,郑建国,孙茉,等. 黄土高填方场地工后沉降预测模型性能评估方法[J]. 中国地质灾害与防治学报,2023,34(0): 1-10 doi: 10.16031/j.cnki.issn.1003-8035.202211003
引用本文: 于永堂,郑建国,孙茉,等. 黄土高填方场地工后沉降预测模型性能评估方法[J]. 中国地质灾害与防治学报,2023,34(0): 1-10 doi: 10.16031/j.cnki.issn.1003-8035.202211003
YU Yong-tang,ZHENG Jian-guo,SUN Mo,et al. Evaluation mthods for performance of post-construction settlement prediction models in thick loess filled ground[J]. The Chinese Journal of Geological Hazard and Control,2023,34(0): 1-10 doi: 10.16031/j.cnki.issn.1003-8035.202211003
Citation: YU Yong-tang,ZHENG Jian-guo,SUN Mo,et al. Evaluation mthods for performance of post-construction settlement prediction models in thick loess filled ground[J]. The Chinese Journal of Geological Hazard and Control,2023,34(0): 1-10 doi: 10.16031/j.cnki.issn.1003-8035.202211003

黄土高填方场地工后沉降预测模型性能评估方法

doi: 10.16031/j.cnki.issn.1003-8035.202211003
基金项目: 陕西省秦创原“科学家+工程师”队伍建设项目(2022KXJ-086);陕西省技术创新引导专项(基金)计划项目(2020CGHJ-002);国家自然科学基金项目(42072302)
详细信息
    作者简介:

    于永堂(1983–),男,辽宁鞍山人,博士,正高级工程师,从事岩土工程测试与监测技术、特殊土工程性质评价与地基处理技术的研发与应用。E-mail:yuyongtang@126.com

  • 中图分类号: TU444

Evaluation mthods for performance of post-construction settlement prediction models in thick loess filled ground

  • 摘要: 工后沉降预测结果是黄土高填方场地变形稳定性评价和建筑物规划布局的重要参考依据。为遴选适合黄土高填方场地的工后沉降预测模型,基于某典型黄土高填方工程的实测沉降数据,分析了工后沉降曲线的变化规律和发展趋势,建立了17种回归参数模型,提出了模型预测效果的评价指标和方法。结果表明,该工程填方区工后沉降历时曲线呈“缓变型”变化,土方填筑完工初期无陡增段,随时间增加沉降速率逐步降低,尚未出现沉降趋于稳定的水平段;将外推预测误差、内拟合误差和后验误差比最小化作为综合控制目标,可遴选出理想的回归参数模型;MMF模型(Ⅱ型)和双曲线模型具有较高的预测精度、较好的稳定性和较强的适应性,在17种模型中的预测效果最佳;沉降数据的变化越平稳,模型预测效果越好;增大建模数据的时间跨度,会提升预测精度,但增大至一定值后,预测精度提升效果不再显著。
  • 图  1  试验场地内的代表性地表沉降监测点平面位置图

    Figure  1.  Distribution map of representative surface settlement monitoring points of post-construction settlement within the test site

    图  2  试验场地内代表性监测点的工后沉降曲线

    Figure  2.  Post-construction settlement curve of representative monitoring points within the test site

    图  3  各模型的内拟合及外推预测曲线

    Figure  3.  Internal-fitting and extrapolation prediction curves of each model

    图  4  各模型对实测沉降数据的拟合及预测误差

    Figure  4.  Fitting and prediction errors of each model for measured settlement data

    图  5  优选模型在建模数据不同时间跨度时的拟合及预测曲线

    Figure  5.  Curve Fitting and prediction results of the optimal model with different time span

    表  1  沉降预测中常用的回归参数预测模型

    Table  1.   Summary of regression parameter prediction models for settlement prediction

    类型模型名称数学表达式沉降速率备 注
    第Ⅰ类模型Logistic${\hat s_t} = a/(1 + b{{\text{e}}^{ - ct}})$${\hat s'_t} = abc{{\text{e}}^{ - ct}}/{(1 + b{{\text{e}}^{ - ct}})^2}$收敛模型
    Gompertz${\hat s_t} = a{{\text{e}}^{ - {{\text{e}}^{b - ct}}}}$${\hat s'_t} = ac{{\text{e}}^{ - {{\text{e}}^{b - ct}}}}{{\text{e}}^{b - ct}}$收敛模型
    Usher${\hat s_t} = a/{(1 + b{{\text{e}}^{ - ct}})^d}$${\hat s'_t} = abcd{{\text{e}}^{ - ct}}{(1 + b{{\text{e}}^{ - ct}})^{ - 1 - d}}$收敛模型
    Weibull${\hat s_t} = a(1 - b{{\text{e}}^{ - c{t^d}}})$${\hat s'_t} = abcd{{\text{e}}^{ - c{t^d}}}{t^{ - 1 + d}}$收敛模型
    MMF-Ⅰ${\hat s_t} = (ab + c{t^d})/(b + {t^d})$${\hat s'_t} = cd{t^{d - 1}}/(b + {t^d}) - d{t^{d - 1}} \cdot (ab + c{t^d})/{(b + {t^d})^2}$收敛模型
    MMF-Ⅱ${\hat s_t} = a{t^b}/(c + {t^b})$${\hat s'_t} = ab{t^{b - 1}}/(c + {t^b}) - ab{t^{2b - 1}}/{(c + {t^b})^2}$收敛模型
    Richards${\hat s_t} = a{(1 - b{{\text{e}}^{ - ct}})^{1/(1 - d)}}$${\hat s'_t} = abc{{\text{e}}^{ - ct}}{(1 - b{{\text{e}}^{ - ct}})^{d/(1 - d)}}/(1 - d)$收敛模型
    Knothe-Ⅰ${\hat s_t} = a{(1 - {{\text{e}}^{ - b{t^c}}})^d}$${\hat s'_t} = abcd{t^{c - 1}}{{\text{e}}^{ - b{t^c}}} \cdot {(1 - {{\text{e}}^{ - b{t^c}}})^{d - 1}}$收敛模型
    Knothe-Ⅱ${\hat s_t} = a{(1 - {{\text{e}}^{ - bt}})^c}$${\hat s'_t} = abc{{\text{e}}^{ - bt}}{(1 - {{\text{e}}^{ - bt}})^{c - 1}}$收敛模型
    Bertalanffy${\hat s_t} = {[{a^{1/3}} - {(a - b)^{1/3}} \cdot {{\text{e}}^{ - ct}}]^3}$${\hat s'_t} = 3{(a - b)^{1/3}}c{{\text{e}}^{ - ct}} \cdot {[{a^{1/3}} - {(a - b)^{1/3}} \cdot {{\text{e}}^{ - ct}}]^2}$收敛模型
    邓英尔${\hat s_t} = a/(1 + b{{\text{e}}^{ - c{t^d}}})$${\hat s'_t} = abcd{{\text{e}}^{ - c{t^d}}}{t^{d - 1}}/{(1 + b{{\text{e}}^{ - c{t^d}}})^2}$收敛模型
    第Ⅱ类模型Spillman${\hat s_t} = a - (a - b){{\text{e}}^{ - ct}}$${\hat s'_t} = (a - b)c{{\text{e}}^{ - ct}}$收敛模型
    指数曲线${\hat s_t} = a(1 - {{\text{e}}^{ - bt}})$${\hat s'_t} = ab{{\text{e}}^{ - bt}}$收敛模型
    双曲线${\hat s_t} = t/(a + bt)$${\hat s'_t} = a/{(a + bt)^2}$收敛模型
    幂函数${\hat s_t} = a{t^b}$${\hat s'_t} = ab{t^{b - 1}}$发散模型
    平方根函数${\hat s_t} = a + b\sqrt t $${\hat s'_t} = b/2\sqrt t $发散模型
    对数函数${\hat s_t} = a\ln t + b$${\hat s'_t} = a/t$发散模型
    对数抛物线${\hat s_t} = a{(\lg t)^2} + b\lg t + c$${\hat s'_t} = \lg {\text{e}} \cdot (b + 2a\lg t) \cdot {t^{ - 1}}$发散模型
    星野法${\hat s_t} = {s_0} + \dfrac{ {ab\sqrt {t - {t_0} } } }{ {\sqrt {1 + {b^2}\left( {t - {t_0} } \right)} } }$${\hat s'_t} = \dfrac{ {ab} }{ {2\sqrt {[1 + {b^2}(t - {t_0})](t - {t_0})} } } - \dfrac{ {a{b^3}\sqrt {t - {t_0} } } }{ {2{ {[1 + {b^2}(t - {t_0})]}^{3/2} } } }$收敛模型
    下载: 导出CSV

    表  2  各模型对典型监测点S6实测数据的内拟合及外推预测结果

    Table  2.   Internal-fitting and extrapolation prediction results of each model for the measured settlement data at a typical monitoring point, S6

    类型模型名称模型参数内拟合效果外推预测效果后验误差
    Ci
    abcdMAPE* /%SSERMSER2MAPE /%MADMSEMFE




    Logistic39.75407.60800.0252/9.888.060.950.992821.6611.77179.3211.772.19
    Gompertz43.78540.93950.0150/6.103.090.590.997316.398.99111.118.992.69
    Usher64.0873−0.99310.0049−1.01495.162.720.520.99815.032.7410.972.310.98
    Weibull3.3377−52.224814.7577−0.42323.582.040.450.99863.091.653.871.210.86
    MMF-Ⅰ2.4888869.749868.87151.31993.261.710.440.99857.183.9321.543.622.20
    MMF-Ⅱ113.91600.9777329.4676/5.843.040.550.99792.051.051.770.410.35
    Richards51.88740.86870.00850.37243.181.660.430.99859.985.4942.785.253.13
    Knothe-Ⅰ41.09490.00004.06870.20984.492.170.490.998118.7510.31147.8010.314.18
    Knothe-Ⅱ68.6817240.20710.9562/5.652.870.560.99753.792.056.411.580.67
    Bertalanffy46.897236.19480.0116/4.452.030.470.998213.427.3976.867.323.02
    邓英尔3.2623−0.955828.7664−1.23683.241.810.420.99876.323.4516.623.111.95




    Spillman68.57270.70740.0043/4.502.470.520.99783.591.935.671.380.80
    指数曲线62.62260.0050//5.953.010.580.99735.713.1213.952.740.96
    双曲线3.12210.0095//6.003.060.550.99792.751.463.160.930.46
    幂函数0.64250.7852//4.345.380.730.996311.676.1542.57-6.152.69
    平方根函数−8.95053.3748//13.1814.001.250.98762.901.542.781.360.22
    对数函数11.6931−28.2990//26.75113.313.550.899324.2012.77182.5812.770.90
    对数抛物线21.4982−43.538525.8604/4.122.830.560.99752.751.462.831.070.67
    星野法1367.00000.0018//32.50114.393.380.920516.818.8084.058.800.52
    下载: 导出CSV

    表  3  优选模型对不同监测点沉降数据的内拟合和外推预测结果

    Table  3.   Internal-fitting and extrapolation prediction of settlement data for different monitoring points using the optimal model

    监测点模型名称模型参数内拟合效果R2外推预测效果后验误差比Ci
    abcMAPE /%MFE
    S2双曲线15.82650.0747/0.98058.33−0.600.58
    MMF-Ⅱ7.49421.5515829.14000.98807.420.560.55
    S3双曲线4.96100.0145/0.99693.281.310.73
    MMF-Ⅱ64.77241.0199344.13450.99694.111.600.88
    S4双曲线3.44750.0099/0.99730.780.560.12
    MMF-Ⅱ90.25251.0341350.09080.99742.211.280.32
    S5双曲线3.76770.0095/0.99902.341.290.64
    MMF-Ⅱ86.20611.0584397.98120.99914.822.511.14
    S6双曲线3.12470.0095/0.99781.420.920.24
    MMF-Ⅱ112.90760.9804329.86600.99790.570.460.10
    S7双曲线4.42750.0108/0.99442.15−0.750.22
    MMF-Ⅱ71.24081.0794416.68110.99461.300.640.13
    S8双曲线9.80390.1899/0.941931.962.243.26
    MMF-Ⅱ−1.03960.1205−2.30300.98140.55−0.050.11
    S9双曲线7.94480.0288/0.98168.111.790.54
    MMF-Ⅱ35.32010.9936274.50820.99997.881.740.53
    S10双曲线5.52940.0167/0.99084.161.370.40
    MMF-Ⅱ166.37110.8423540.34700.99173.30−0.980.36
    S11双曲线4.00730.0100/0.99813.511.750.69
    MMF-Ⅱ143.15990.9305451.83950.99820.260.220.06
    S12双曲线3.08850.0101/0.99815.403.111.01
    MMF-Ⅱ139.22670.9179325.71700.99841.821.140.40
    S13双曲线3.65370.0104/0.99892.591.370.68
    MMF-Ⅱ145.90220.9138397.92440.99921.51−0.600.72
    S14双曲线4.42230.0123/0.99863.521.520.73
    MMF-Ⅱ74.27161.0255358.68420.99864.611.960.94
    S15双曲线3.81730.0093/0.99821.931.120.38
    MMF-Ⅱ77.34641.1049426.31570.99866.283.261.20
    S16双曲线3.39890.0084/0.99671.541.020.22
    MMF-Ⅱ160.00720.9428447.04790.99681.24−0.510.20
    S17双曲线3.27200.0110/0.99685.663.080.78
    MMF-Ⅱ100.13780.9706296.39210.99684.462.460.63
    下载: 导出CSV
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  • 收稿日期:  2022-11-02
  • 录用日期:  2023-03-30
  • 修回日期:  2023-03-15
  • 网络出版日期:  2023-04-04

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