边坡稳定可靠性研究
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摘要
安全系数法与可靠指标法是边坡工程稳定性分析中的典型方法。本论文以这两种方法为研究对象,对边坡稳定可靠性分析中的若干问题进行了探索和讨论:
(1)根据积分思想,推导了边坡圆弧滑裂面破坏时,有、无被动土体两种情况下的安全系数解析表达式;由该解析式编制相应的计算程序,借助土性参数对边坡稳定性分析的安全系数法与可靠指标法的差异性和关联性进行了研究:分析了土性参数统计特征、坡角等对纯粘性土和非纯粘性土边坡稳定性计算的影响作用和趋势;
(2)针对极限状态变量在“零”值附近的模糊性,建立了边坡模糊可靠性分析模型。研究了模糊失效概率隶属函数不同分布情况下,模糊区间宽度、偏度(相对零值的偏移程度)以及土性参数变异性等对模糊可靠指标的影响,并与确定性方法求解结果进行了对比分析;
(3)针对边坡圆弧滑裂面破坏形式,考虑土性参数变异性的影响,采用最优化方法求解各个假想滑弧的安全系数F和失效概率P_f~i;以P_f~i相应的可靠概率P_s~i=1-P_f~i度量F的可信程度,并对F进行折减(定义为折减安全系数F_R~i=F·P_s~i=F(1-P_f~i)),提出了以最小折减安全系数F_R=min(F_R~i)为评价标准的边坡稳定性评价体系;
(4)复杂工程的可靠性分析常伴随极限状态方程为隐式的情况,响应面法是解决这一困难的有效手段。样本点的选取决定了响应面法的精度,但因缺乏明确的理论指导,从样本点的选取角度对响应面法进行改良并未受到广泛关注。本论文提出了两种样本点选取策略,即方向余弦策略和有限步长策略,对响应面法进行改良;本方法一次性拟合响应面方程,避免了常规响应面法的复杂迭代运算,且对高非线性问题有较好的适用性。
(5)在实际的结构或岩土工程中,有学者提出用变量正态化转换多项式解决仅知道变量前几阶统计矩的可靠性分析问题。本文将三阶变量化转换多项式引入高阶矩法并用于边坡工程可靠性分析,解释了该方法具有一定的适用性,但仍需对其缺陷引起重视。首先,统计矩法往往不能给出小失效概率问题的准确预报。另外,对于功能函数物理意义相同但表达公式不同的问题可能得到完全不同的计算结果;
(6)针对二次二阶矩法展开研究。利用矩阵理论给出了求解曲率的简化算式,提出了一种相关变量可靠度计算的实用二次二阶矩法；
(7)借助某高边坡支护工程,详述了锚索极限抗拔试验和数值模拟。通过高边坡开挖、加固全过程数值模拟,联合可靠度计算结果肯定了支护效果。
Safety factor method and reliability index method are two typical stability analysis methods for slope. Some problems in the reliability analysis of slope are studied here. It's includes:
(1) A more accurate calculation formula of the safety factor for homogeneous soil slope with and without the resisting part of circle surface failure is established using analytical method. Based on the shear strength parameters, the relationship and difference between the safety factor method and the reliability index method for slope stability analysis are investigated. A program is developed accordingly; some regularity and the influence of statistical characteristics of soil strength parameters on stability analysis for pure clay slope and impure clay slope are studied.
(2)A model of the slope fuzzy-random reliability analysis is found basis of the fuzzy interval of the limit state variable near its zero value. The influences of width fraction and migration fraction is studied in different situations include the variability of common soil parameters and the distribution of membership function of fuzzy probability of failure. The results obtained by the fuzzy and deterministic method are studied based on contrastive analysis.
(3) The safety factor (F~i) and failure probability (P_f~i) of each slip surface is calculated for the soil slope with circle surface failure. The variable character of strength parameters is considered. The reliable probability (?) are used to estimate the creditability of F~i by calculating the reduced safety factor (?); A slope stability evaluation system is founded using the minimum reduced safety factor F_R=min(F_R~i).
(4) Response surface method (RSM) is an accepted and efficient technique in the reliability analysis of large and complex structures with implicit limit state function. It is noted that the accuracy of RSM is depended on the choice of sample points but the effect of varying their location has had little attention. In the present study, two sample point selection strategies, the direction cosines projected strategy (DCS) and the limit step length iteration strategy (LSS), are investigated to improve the fit of the RSM. Since it needs no iteration to fit the response surface function (only one response surface is fitted), and since it is more suitable for highly non-linear problems, the proposed improved RSM should be practical in actual reliability problems.
(5) The normal transformation polynomial is used by some researcher in practical probabilistic analysis in structural or civil engineering; especially when multivariate random variables with the probabilistic characteristics expressed using only statistical moments are involved. In this study, a moment method improved by the third-order normal transformation polynomial for practical slope reliability analysis with random variables having unknown distributions is discussed. Of particular importance in this work is the conclusion that although the application of the improved moment method to several examples is approving, its flaw should be recognized. First, the moment method cannot predict accurate results for some problems with small failure probability. Second, it may provide totally different estimate of reliability index for different equivalent formulations of the same performance function.
(6) An approximate second-order second-moment method (SORM) for structures with dependent random variables is investigated. A closed calculation form of the curvature is given based on the theory of matrix.
(7)A case study of high slope reinforcement is presented. The whole process of the uplift test and the computer simulation of cable are expatiated. The excavation of the slope with or without reinforcement is simulated by numerical method. Together with the conclusions of reliability analysis, the reinforcement is proved to be effective for stabilizing the slope.
(1)根据积分思想,推导了边坡圆弧滑裂面破坏时,有、无被动土体两种情况下的安全系数解析表达式;由该解析式编制相应的计算程序,借助土性参数对边坡稳定性分析的安全系数法与可靠指标法的差异性和关联性进行了研究:分析了土性参数统计特征、坡角等对纯粘性土和非纯粘性土边坡稳定性计算的影响作用和趋势;
(2)针对极限状态变量在“零”值附近的模糊性,建立了边坡模糊可靠性分析模型。研究了模糊失效概率隶属函数不同分布情况下,模糊区间宽度、偏度(相对零值的偏移程度)以及土性参数变异性等对模糊可靠指标的影响,并与确定性方法求解结果进行了对比分析;
(3)针对边坡圆弧滑裂面破坏形式,考虑土性参数变异性的影响,采用最优化方法求解各个假想滑弧的安全系数F和失效概率P_f~i;以P_f~i相应的可靠概率P_s~i=1-P_f~i度量F的可信程度,并对F进行折减(定义为折减安全系数F_R~i=F·P_s~i=F(1-P_f~i)),提出了以最小折减安全系数F_R=min(F_R~i)为评价标准的边坡稳定性评价体系;
(4)复杂工程的可靠性分析常伴随极限状态方程为隐式的情况,响应面法是解决这一困难的有效手段。样本点的选取决定了响应面法的精度,但因缺乏明确的理论指导,从样本点的选取角度对响应面法进行改良并未受到广泛关注。本论文提出了两种样本点选取策略,即方向余弦策略和有限步长策略,对响应面法进行改良;本方法一次性拟合响应面方程,避免了常规响应面法的复杂迭代运算,且对高非线性问题有较好的适用性。
(5)在实际的结构或岩土工程中,有学者提出用变量正态化转换多项式解决仅知道变量前几阶统计矩的可靠性分析问题。本文将三阶变量化转换多项式引入高阶矩法并用于边坡工程可靠性分析,解释了该方法具有一定的适用性,但仍需对其缺陷引起重视。首先,统计矩法往往不能给出小失效概率问题的准确预报。另外,对于功能函数物理意义相同但表达公式不同的问题可能得到完全不同的计算结果;
(6)针对二次二阶矩法展开研究。利用矩阵理论给出了求解曲率的简化算式,提出了一种相关变量可靠度计算的实用二次二阶矩法；
(7)借助某高边坡支护工程,详述了锚索极限抗拔试验和数值模拟。通过高边坡开挖、加固全过程数值模拟,联合可靠度计算结果肯定了支护效果。
Safety factor method and reliability index method are two typical stability analysis methods for slope. Some problems in the reliability analysis of slope are studied here. It's includes:
(1) A more accurate calculation formula of the safety factor for homogeneous soil slope with and without the resisting part of circle surface failure is established using analytical method. Based on the shear strength parameters, the relationship and difference between the safety factor method and the reliability index method for slope stability analysis are investigated. A program is developed accordingly; some regularity and the influence of statistical characteristics of soil strength parameters on stability analysis for pure clay slope and impure clay slope are studied.
(2)A model of the slope fuzzy-random reliability analysis is found basis of the fuzzy interval of the limit state variable near its zero value. The influences of width fraction and migration fraction is studied in different situations include the variability of common soil parameters and the distribution of membership function of fuzzy probability of failure. The results obtained by the fuzzy and deterministic method are studied based on contrastive analysis.
(3) The safety factor (F~i) and failure probability (P_f~i) of each slip surface is calculated for the soil slope with circle surface failure. The variable character of strength parameters is considered. The reliable probability (?) are used to estimate the creditability of F~i by calculating the reduced safety factor (?); A slope stability evaluation system is founded using the minimum reduced safety factor F_R=min(F_R~i).
(4) Response surface method (RSM) is an accepted and efficient technique in the reliability analysis of large and complex structures with implicit limit state function. It is noted that the accuracy of RSM is depended on the choice of sample points but the effect of varying their location has had little attention. In the present study, two sample point selection strategies, the direction cosines projected strategy (DCS) and the limit step length iteration strategy (LSS), are investigated to improve the fit of the RSM. Since it needs no iteration to fit the response surface function (only one response surface is fitted), and since it is more suitable for highly non-linear problems, the proposed improved RSM should be practical in actual reliability problems.
(5) The normal transformation polynomial is used by some researcher in practical probabilistic analysis in structural or civil engineering; especially when multivariate random variables with the probabilistic characteristics expressed using only statistical moments are involved. In this study, a moment method improved by the third-order normal transformation polynomial for practical slope reliability analysis with random variables having unknown distributions is discussed. Of particular importance in this work is the conclusion that although the application of the improved moment method to several examples is approving, its flaw should be recognized. First, the moment method cannot predict accurate results for some problems with small failure probability. Second, it may provide totally different estimate of reliability index for different equivalent formulations of the same performance function.
(6) An approximate second-order second-moment method (SORM) for structures with dependent random variables is investigated. A closed calculation form of the curvature is given based on the theory of matrix.
(7)A case study of high slope reinforcement is presented. The whole process of the uplift test and the computer simulation of cable are expatiated. The excavation of the slope with or without reinforcement is simulated by numerical method. Together with the conclusions of reliability analysis, the reinforcement is proved to be effective for stabilizing the slope.
引文
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