基于区间参数反演的重力坝非概率可靠性分析

魏博文; 占良红; 李火坤; 徐镇凯

doi:10.11779/CJGE202002014

基于区间参数反演的重力坝非概率可靠性分析 English Version

南昌大学建筑工程学院,江西　南昌330031

基金项目:

国家自然科学基金项目 51779115

国家自然科学基金项目 51869011

国家自然科学基金项目 51879126

江西省水利厅科研课题 201820YBKT29

江西省青年科学重点项目 20192ACB21022

江西省杰出青年基金项目 2018ACB21018

南昌大学研究生创新专项资金项目 CX2018052

详细信息

作者简介:
魏博文（1981— ）,男,副教授,博士生导师,主要从事数值安全监控及水工结构方面的科研工作。E-mail：bwwei@ncu.edu.cn

通讯作者:
李火坤, E-mail：lihuokun@126.com

中图分类号: TV642.3
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出版历程
- 收稿日期: 2018-09-27
- 网络出版日期: 2022-12-07
- 刊出日期: 2020-01-31

Non-probabilistic reliability analysis of gravity dams based on inversion of interval parameters

School of Civil Engineering and Architecture, Nanchang University, Nanchang 330031, China

摘要

摘要: 传统概率可靠性分析方法应用重力坝结构性能和服役性态评估过程中,其受不确定参数严格随机性、计算结果对参数过敏感性及其功能函数高度非线性等多因素制约。提出了基于区间参数的重力坝单元和体系非概率可靠性（Nonprobabilistic Reliability,NR）分析方法。首先,充分依据重力坝原型监测资料、数学模型和物理模型计算成果获取重力坝区间参数的界限,综合运用区间数学和NR等理论和方法,构建了基于区间参数的重力坝单元与体系NR计算模型,发展了一种基于响应面方法的重力坝NR指标（NR-η）计算方法。其次,从重力坝系统可能失效路径及失效模式入手,剖析单一和多重失效模式下重力坝体系的安全性。最后,通过某重力坝工程表明：方法能够有效地揭示重力坝局部和整体可靠状态,计算结果符合重力坝运行特点前提下与该大坝服役背景状况高度吻合。
- 重力坝 /
- 非概率可靠性 /
- 区间参数 /
- 失效模式 /
- 服役可靠度
Abstract: In the evaluation of structural performance and service behavior of gravity dams, the traditional probabilistic reliability analysis method is restricted by many factors, such as strict randomness of uncertain parameters, oversensitivity of calculated results and high nonlinearity of function function. A non-probabilistic reliability (NR) analysis method for gravity dam elements and system based on the interval parameters is proposed. First, according to the prototype monitoring data and the achievements of physical and mathematical models for gravity dams, the interval parameter boundary of the gravity dam is obtained. A NR model based on the interval parameters is established, and a method for calculating NR index (NR-η) based on response surface method is developed by using the interval mathematics and NR theory. Then, the safety of the gravity dam system in single and multiple failure modes is analyzed from the possible failure paths and modes. Finally, based on a gravity dam, the results indicate that the proposed method can effectively reveal the local and overall reliable states of the gravity dam. The calculated results are in good agreement with the background conditions of the dam under the premise of the operating characteristics of the gravity dam.
- gravity dam /
- non-probabilistic reliability /
- interval parameter /
- failure mode /
- service reliability

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图 1 失效模式搜索示意图

Figure 1. Schematic diagram of failure mode search

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图 2 重力坝体系NR-η_s计算流程

Figure 2. Flow chart of NR-η_s evaluation for gravity dam system

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图 3 重力坝有限元模型

Figure 3. Finite element model for gravity dam

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图 4 环境量监测曲线

Figure 4. Graph of environmental variables

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图 5 D35水平位移实测值、拟合值及残差值曲线

Figure 5. Actual values, fitted values and residuals curves of horizontal displacement of D35

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图 6 单元NR- $η_{e}$ 分布云图

Figure 6. Contour map of NR- $η_{e}$ for dam elements

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图 7 坝体单元NR- $η_{e}$ 统计图

Figure 7. Statistical graph of NR- $η_{e}$ for dam body elements

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图 8 初始失效单元

Figure 8. Initial failure elements

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图 9 初始单元失效模式

Figure 9. Failure modes for initial elements

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图 10 组合单元失效模式

Figure 10. Failure modes for combination elements

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表 1 水压分量拟合系数

Table 1 Fitting coefficients of water pressure component

系数	a₁₁	a₁₂	a₁₃	a₂₁-a₁₁	a₂₂-a₁₂	a₂₃-a₁₃
D35	0.44253	-0.01015	0.00014	0.10270	-0.00295	0.00002
注：各系数定义参考文献[26]。

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表 2 参数界限反演结果

Table 2 Inversion results of interval parameters

水压调整系数区间值		弹性模量区间值/GPa
$X_{I}$	$Y_{I}$	$E_{c I}^{}$	$E_{r I}^{}$
[0.858, 0.936]	[0.898, 0.982]	[18.02, 19.66]	[14.37, 15.71]
注： $X_{I}^{} = E_{c0} / E_{c I}^{}$ 和 $Y_{I} = E_{r0} / E_{r I}^{}$ 。

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表 3 主要区间参数界限

Table 3 Boundaries of main interval parameters

荷载	材料参数	界限范围	均值	离差
荷载	扬压力系数α	[0.28, 0.32]	0.30	0.02
坝体	混凝土抗拉强度f_t/MPa	[1.40, 1.70]	1.55	0.15
	混凝土抗压强度f_c/MPa	[16.00, 18.50]	17.25	1.25
	坝体弹性模量E_c/GPa	[18.02, 19.66]	18.84	0.82
岩基	岩基抗拉强度f_t′/MPa	[1.12, 1.44]	1.28	0.16
	岩基抗压强度f_c′/MPa	[14.60, 17.20]	15.90	1.30
	岩基弹性模量E_r/GPa	[14.37, 15.71]	15.04	0.67
岩基面	滑移面摩擦系数f_′	[0.82, 1.08]	0.95	0.13
岩基面	滑移面凝聚力c′/MPa	[0.80, 0.96]	0.88	0.08
注：上游水位为正常蓄水位定值,混凝土重度取定值γ_c = 2350 kg·m^-3。

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表 4 各失效模式下NR-η

Table 4 NR-η of each failure mode

失效模式	失效模式1	失效模式2	失效模式3	失效模式4	失效模式5	失效模式6	^#5225—^#4595	^#7813—^#6017
NR-η	0.916	1.301	0.854	0.872	0.914	0.919	0.732	0.835

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