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

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

杨智勇^1,,
唐栋^2, ,,
张蕾³,
祁小辉⁴

1.
台湾大学土木工程学系,台湾　台北
2.
长沙理工大学水利工程学院,湖南　长沙　410114
3.
太原理工大学水利科学与工程学院,山西　太原　030024
4.
南洋理工大学土木环境工程学院,新加坡

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
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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

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

1.
Department of Civil Engineering, Taiwan University, Taipei China
2.
School of Hydraulic Engineering, Changsha University of Science & Technology, Changsha 410114, China
3.
College of Hydro Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, China
4.
School of Civil and Environmental Engineering, Nanyang Technological University, Singapore

摘要

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。
- 岩土结构物 /
- 可靠度设计 /
- 分项系数法 /
- 修正分位数法 /
- 分位一阶二次矩法
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.
- geotechnical structure /
- reliability-based design /
- partial factor design method /
- modified quantile value method /
- quantile first-order second-moment method

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图 1 桩基础示意图

Figure 1. Schematic of pile foundation

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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 β_T

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图 3 方形基础示意图

Figure 3. Schematic of pad footing

下载: 全尺寸图片幻灯片

图 4 ERD回归函数验证

Figure 4. Verification for regression function of ERD

下载: 全尺寸图片幻灯片

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 β_T

下载: 全尺寸图片幻灯片

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)	μ_DL	10	对数正态
活荷载LL(kN)	μ_LL	20	对数正态
不排水抗剪强度参数s_u(kPa)	μ_su	30	对数正态
砂土平均SPT锤击数N	μ_N	30	对数正态
黏土转换不确定性因子ε_α	1.05	32	对数正态
砂土转换不确定性因子ε_N	1.22	70	对数正态

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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/m	0.5	2.0	均匀分布
桩长L = L_c+ L_s/m	10	80	均匀分布
砂土深度与桩长的比值t_s=L_s/L	0	1	均匀分布
动荷载与静荷载比值 $r_{L/D} = μ_{LL} / μ_{DL}$	0.1	1.0	均匀分布
静荷载均值 $μ_{DL}$ /kN	2000	2500	均匀分布
不排水抗剪强度参数均值μ_su/kPa	50	200	均匀分布
砂土平均SPT锤击数N均值 $μ_{N}$	10	50	均匀分布

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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	β_T=1.5		β_T=2.0		β_T=2.5		β_T=3.0
统计量	β_MQ/β_T	β_EQ/β_T	β_MQ/β_T	β_EQ/β_T	β_MQ/β_T	β_EQ/β_T	β_MQ/β_T	β_EQ/β_T
均值	1.06	1.01	1.06	1.01	1.06	1.01	1.06	1.02
变异系数	0.03	0.04	0.02	0.02	0.02	0.01	0.02	0.02
最大值	1.10	1.07	1.10	1.06	1.10	1.06	1.11	1.07
最小值	0.99	0.94	0.99	0.96	0.99	0.96	0.99	0.96
注：β_MQ为修正分位数法估计的基础宽度对应的实际可靠度指标；β_EQ为ERD-QVM估计的基础宽度对应的实际可靠度指标。

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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/kPa	μ_c	V_c	对数正态
摩擦角 $φ$ /(°)	$μ_{φ}$	$V_{φ}$	对数正态
水平荷载H/kN	μ_H	15%	对数正态
垂直荷载V_D/kN	μ_V	10%	对数正态
影响变量(i_c,i_q,i_γ)的垂直荷载V_S/kN	μ_V	10%	对数正态

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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/m	1.5	3	均匀分布
黏聚力均值μ_c/kPa	10	100	均匀分布
摩擦角均值 $μ_{φ}$ /(°)	15	30	均匀分布
黏聚力变异系数V_c	0.1	0.3	均匀分布
摩擦角变异系数 $V_{φ}$	0.1	0.3	均匀分布
黏聚力与摩擦角间相关系数ρ	−0.8	0.0	均匀分布
水平荷载均值 $μ_{H}$ /kN	200	400	均匀分布
垂直荷载均值 $μ_{V}$ /kN	700	1000	均匀分布

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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	β_T=2.0		β_T=2.5		β_T=3.0		β_T=3.5
统计量	β_MQ/β_T	β_EQ/β_T	β_MQ/β_T	β_EQ/β_T	β_MQ/β_T	β_EQ/β_T	β_MQ/β_T	β_EQ/β_T
均值	1.04	1.01	1.04	1.01	1.03	1.01	1.02	1.01
变异系数	0.03	0.02	0.03	0.02	0.03	0.02	0.03	0.02
最大值	1.19	1.13	1.20	1.10	1.22	1.08	1.24	1.06
最小值	0.99	0.87	0.99	0.88	0.99	0.88	0.99	0.89
注：β_MQ为修正分位数法估计的基础宽度对应的实际可靠度指标；β_EQ为ERD-QVM估计的基础宽度对应的实际可靠度指标。

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