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岩土工程简化可靠度设计方法——修正分位数法

杨智勇, 唐栋, 张蕾, 祁小辉

杨智勇, 唐栋, 张蕾, 祁小辉. 岩土工程简化可靠度设计方法——修正分位数法[J]. 岩土工程学报, 2020, 42(8): 1456-1464. DOI: 10.11779/CJGE202008010
引用本文: 杨智勇, 唐栋, 张蕾, 祁小辉. 岩土工程简化可靠度设计方法——修正分位数法[J]. 岩土工程学报, 2020, 42(8): 1456-1464. DOI: 10.11779/CJGE202008010
YANG Zhi-yong, TANG Dong, ZHANG Lei, QI Xiao-hui. Simplified reliability-based design method for geotechnical structures —modified quantile value method[J]. Chinese Journal of Geotechnical Engineering, 2020, 42(8): 1456-1464. DOI: 10.11779/CJGE202008010
Citation: YANG Zhi-yong, TANG Dong, ZHANG Lei, QI Xiao-hui. Simplified reliability-based design method for geotechnical structures —modified quantile value method[J]. Chinese Journal of Geotechnical Engineering, 2020, 42(8): 1456-1464. DOI: 10.11779/CJGE202008010

岩土工程简化可靠度设计方法——修正分位数法  English Version

基金项目: 

台湾大学高等教育深耕计划项目 107L4000

湖南省自然科学基金项目 2019JJ50642

山西省应用基础研究项目 201801D221046

水沙科学与水灾害防治湖南省重点实验室开放基金项目 2019SS04

湖南省教育厅科学研究项目 18C0191

详细信息
    作者简介:

    杨智勇(1989—),男,山西柳林人,博士,主要从事岩土工程可靠度与风险分析方面的研究工作。E-mail:yzywhu@163.com

    通讯作者:

    唐栋, E-mail:tangdong@csust.edu.cn

  • 中图分类号: TU43

Simplified reliability-based design method for geotechnical structures —modified quantile value method

  • 摘要: 现阶段多数规范推荐的半概率设计方法分项系数法与传统容许应力设计法具有相似的设计过程,易于被岩土工程师接受。然而,当实际岩土体参数统计量及分布类型等与分项系数设计法校准过程所采用的不一致时,分项系数法的设计结果往往会产生较大偏差。分位数设计法与分项系数法设计过程相似,且能够解决分项系数法设计偏差较大的问题。遗憾的是,该方法需要事先通过大量可靠度分析建立岩土结构物设计参数与有效随机维度间的回归函数,该过程不仅计算量较大而且十分繁琐,不利于工期紧迫条件下的快速可靠度设计。为此,提出了基于修正分位数法的岩土工程简化可靠度设计方法。首先介绍了原始有效随机维度–分位数设计法(ERD-QVM)和分位一阶二次矩可靠度分析方法,在此基础上提出了基于简单迭代算法的修正分位数法。最后以桩基础设计和方形基础设计为例阐明了所提方法的有效性。结果表明:修正分位数法为工期紧迫的岩土结构物可靠度设计提供了一种有效分析工具。修正分位数法不仅能够有效地避免原始ERD-QVM需要建立关于设计参数回归函数的问题,极大地降低原始ERD-QVM的计算量,而且能够得到合理的岩土结构物设计结果。修正分位数法设计结果更保守,原始ERD-QVM可能产生偏危险的设计,这对岩土结构物稳定性非常不利。两种设计方法具有相似的设计稳健性。
    Abstract: Currently, the partial factor design method is recommended by most international design codes as a semi-probability design method. This popularity might be partly because the partial factor design method shares a similar design procedure as that of the conventional allowable-stress-design method and therefore is likely to be accepted by practical geotechnical engineers. However, the partial factor design method might produce significantly biased design schemes especially when the design condition (e.g., statistical and probabilistic distributions of soil properties) is different from that used in the code for partial factor calibrations. The quantile value method (i.e., effective random dimension-quantile value method, ERD-QVM) shares a similar design procedure as the partial factor design method. But it needs to calibrate the relationship between ERD and design parameters, which is tedious and computationally expensive. Consequently, it is not feasible to apply this method when the time schedule of the engineering is tight. This study proposes a simplified reliability-based design method for geotechnical structures, namely modified quantile value method (MQVM). The original ERD-QVM and the quantile first-order second-moment method (QFOSM) are reviewed. Based on the QFOSM, the MQVM is developed. A pile foundation example and a pad footing example are employed to illustrate the performance of the proposed method. It is shown that the proposed method can provide an effective tool for rapid reliability-based designs. The proposed MQVM can avoid the calibration procedure of the relationship between ERD and design parameters and yield rational design schemes. The original ERD-QVM might produce an unsafe design scheme, which poses an enormous threat to geotechnical structures. By contrast, the design scheme of MQVM is relatively conservative. Moreover, the MQVM has a robustness similar to that of ERD-QVM.
  • 图  1   桩基础示意图

    Figure  1.   Schematic of pile foundation

    图  2   不同目标可靠度下ERD-QVM和修正分位数法设计结果对比

    Figure  2.   Comparison of results by ERD-QVM and MQVM under various values of βT

    图  3   方形基础示意图

    Figure  3.   Schematic of pad footing

    图  4   ERD回归函数验证

    Figure  4.   Verification for regression function of ERD

    图  5   不同目标可靠度下ERD-QVM和修正分位数法设计结果对比

    Figure  5.   Comparison of results by ERD-QVM and MQVM under various values of βT

    表  1   桩基础的随机变量统计值

    Table  1   Statistics of random variables for pile example

    随机变量均值变异系数/%分布类型
    静荷载DL(kN)μDL10对数正态
    活荷载LL(kN)μLL20对数正态
    不排水抗剪强度参数su(kPa)μsu30对数正态
    砂土平均SPT锤击数NμN30对数正态
    黏土转换不确定性因子εα1.0532对数正态
    砂土转换不确定性因子εN1.2270对数正态
    下载: 导出CSV

    表  2   桩基础设计参数可行域

    Table  2   Feasible ranges for pile design parameters

    设计参数下界上界分布类型
    桩直径B/m0.52.0均匀分布
    桩长L = Lc+ Ls/m1080均匀分布
    砂土深度与桩长的比值ts=Ls/L01均匀分布
    动荷载与静荷载比值rL/D=μLL/μDL0.11.0均匀分布
    静荷载均值μDL/kN20002500均匀分布
    不排水抗剪强度参数均值μsu/kPa50200均匀分布
    砂土平均SPT锤击数N均值μN1050均匀分布
    下载: 导出CSV

    表  3   基于1000组随机设计参数的可靠度指标统计

    Table  3   Statistics of actual reliability index for 1000 verification cases

    统计量βT=1.5βT=2.0βT=2.5βT=3.0
    βMQ/βTβEQ/βTβMQ/βTβEQ/βTβMQ/βTβEQ/βTβMQ/βTβEQ/βT
    均值1.061.011.061.011.061.011.061.02
    变异系数0.030.040.020.020.020.010.020.02
    最大值1.101.071.101.061.101.061.111.07
    最小值0.990.940.990.960.990.960.990.96
    注:βMQ为修正分位数法估计的基础宽度对应的实际可靠度指标;βEQ为ERD-QVM估计的基础宽度对应的实际可靠度指标。
    下载: 导出CSV

    表  4   方形基础的随机变量统计值

    Table  4   Statistics of random variables for square footing problem

    随机变量均值变异系数分布类型
    黏聚力c/kPaμcVc对数正态
    摩擦角φ/(°)μφVφ对数正态
    水平荷载H/kNμH15%对数正态
    垂直荷载VD/kNμV10%对数正态
    影响变量(ic,iq,iγ)的垂直荷载VS/kNμV10%对数正态
    下载: 导出CSV

    表  5   方形基础设计参数可行域

    Table  5   Feasible ranges for square footing design parameters

    设计参数下界上界分布类型
    基础宽度B/m1.53均匀分布
    黏聚力均值μc/kPa10100均匀分布
    摩擦角均值μφ/(°)1530均匀分布
    黏聚力变异系数Vc0.10.3均匀分布
    摩擦角变异系数Vφ0.10.3均匀分布
    黏聚力与摩擦角间相关系数ρ−0.80.0均匀分布
    水平荷载均值μH/kN200400均匀分布
    垂直荷载均值μV/kN7001000均匀分布
    下载: 导出CSV

    表  6   基于1000组随机设计参数的实际可靠度指标统计

    Table  6   Statistics of actual reliability index for 1000 verification cases

    统计量βT=2.0βT=2.5βT=3.0βT=3.5
    βMQ/βTβEQ/βTβMQ/βTβEQ/βTβMQ/βTβEQ/βTβMQ/βTβEQ/βT
    均值1.041.011.041.011.031.011.021.01
    变异系数0.030.020.030.020.030.020.030.02
    最大值1.191.131.201.101.221.081.241.06
    最小值0.990.870.990.880.990.880.990.89
    注:βMQ为修正分位数法估计的基础宽度对应的实际可靠度指标;βEQ为ERD-QVM估计的基础宽度对应的实际可靠度指标。
    下载: 导出CSV
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出版历程
  • 收稿日期:  2019-06-21
  • 网络出版日期:  2022-12-05
  • 刊出日期:  2020-07-31

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