多点估计法的改进及其在边坡中的应用
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摘要
边坡工程稳定性研究一直以来是岩土工程领域中的一个研究热点。组成边坡的结构构造和岩土体都存在不均匀性和强烈的时空变异性,采用以中值安全系数为评价标准的传统边坡安全度评价方法难以体现边坡工程的不确定性,而充分考虑岩土体参数随机性的边坡稳定可靠度分析方法,更具实际意义。由于边坡工程本身的复杂性,其稳定性极限功能函数一般为多极值点、非凸性的隐函数,因此,采用一般的可靠度计算方法如一次二阶矩法计算可靠度时存在求导困难,而响应面法、随机有限元法等都存在不同的局限性。
点估计法作为一种简单、高效的可靠度计算方法,目前已在建筑结构工程、路基工程等领域应用,并取得了较好的结果。为此,本文致力于研究基于点估计法求解功能函数的统计矩,并利用皮尔逊曲线模拟边坡稳定功能函数的近似概率密度函数,再在失效区域直接积分求解可靠度的可靠性分析的方法,希望能给这方面的研究者一些参考意义。
针对以上问题,本文主要对以下内容进行了研究:
(1)将Gauss—Hermit数值积分原理和矩点估计法结合起来,以边坡稳定极限平衡分析的毕肖普模式为例,建立了一种七点估计法的边坡可靠度计算方法。
(2)针对常用的边坡可靠度计算方法的局限性和不足,引入多点估计法和皮尔逊曲线,推导了基于皮尔逊曲线的功能函数的密度函数的求解方法,建立了相应的可靠度计算公式,并对其性能与基于最大熵法的近似直接积分法和蒙特卡洛模拟法作了对比。
(3)通过室内试验测试了衡桂高速公路边坡岩土体物理力学参数,分析了红砂岩崩解分形模型,以及边坡岩土体含水量变化导致岩土体强度变化趋势,对雨水入渗导致边坡土体抗剪强度变化的路堤边坡的稳定性进行了分析,为工程提供了参考依据。
Slope stability study has long been a hotspot in the geotechnical engineering field. Structure and composition of the slope rock and mass are uneven and there is a strong spatial and temporal variability, as the value of the safety factor used to evaluate the slope of the standard evaluation of traditional methods can not reflect the uncertainty in slope engineering, and the reliability analysis methods of rock and soil slope stability full account of random parameters, have more practical significance. As the complexity of engineering itself, its stability limited performance function is generally more extreme point, non-convex of the implicit function, so the reliability of using the general method such as first order second moment reliability method exists difficult to calculate derivatives, and response surface methods, stochastic finite element method and so have different limitations.
Point estimate method as a simple and efficient method of reliability analysis, has been applied in the building structural engineering, foundation engineering and other field, and achieved good results. Therefore, the paper dedicated to the research for a reliability analysis of reliability method, which based on point estimate method to caculate statistical moments of the function and use Pearson curves to simulate approximate probability density function of slope stability performance function, and Then direct integration in the failure zone to calculate the reliability. Hoping to give some reference value to the researchers.
For the above problems, this paper conducted a study of the following:
(1) Combined The principle of Gauss-Hermit numerical integration with point estimate method , Take the Bishop model of slope stability limit equilibrium analysis as an example, established a seven-point estimate method of slope reliability analysis.
(2) For the limitations and shortcomings of the commonly used slope reliability compute method, introduced the multi-point estimate method and Pearson curve, simulation of the approximate performance function slope stability probability density function, and compared its performance with approximate direct integration method which based on maximum entropy method and Monte Carlo simulation.
(3) The physical mechanics parameter of rock and soil along the Henggui highway's side slope has tested through the indoor experiment, analyzed the the fractal model of red sandstone collapse, and analyzed the rock and soil of side slope’s water content change to cause the intensity change tendency of rock and soil intensity, for the infiltration of rain water caused changes in soil shear strength of the slope stability of embankment slope were analyzed, provide a reference for project.
点估计法作为一种简单、高效的可靠度计算方法,目前已在建筑结构工程、路基工程等领域应用,并取得了较好的结果。为此,本文致力于研究基于点估计法求解功能函数的统计矩,并利用皮尔逊曲线模拟边坡稳定功能函数的近似概率密度函数,再在失效区域直接积分求解可靠度的可靠性分析的方法,希望能给这方面的研究者一些参考意义。
针对以上问题,本文主要对以下内容进行了研究:
(1)将Gauss—Hermit数值积分原理和矩点估计法结合起来,以边坡稳定极限平衡分析的毕肖普模式为例,建立了一种七点估计法的边坡可靠度计算方法。
(2)针对常用的边坡可靠度计算方法的局限性和不足,引入多点估计法和皮尔逊曲线,推导了基于皮尔逊曲线的功能函数的密度函数的求解方法,建立了相应的可靠度计算公式,并对其性能与基于最大熵法的近似直接积分法和蒙特卡洛模拟法作了对比。
(3)通过室内试验测试了衡桂高速公路边坡岩土体物理力学参数,分析了红砂岩崩解分形模型,以及边坡岩土体含水量变化导致岩土体强度变化趋势,对雨水入渗导致边坡土体抗剪强度变化的路堤边坡的稳定性进行了分析,为工程提供了参考依据。
Slope stability study has long been a hotspot in the geotechnical engineering field. Structure and composition of the slope rock and mass are uneven and there is a strong spatial and temporal variability, as the value of the safety factor used to evaluate the slope of the standard evaluation of traditional methods can not reflect the uncertainty in slope engineering, and the reliability analysis methods of rock and soil slope stability full account of random parameters, have more practical significance. As the complexity of engineering itself, its stability limited performance function is generally more extreme point, non-convex of the implicit function, so the reliability of using the general method such as first order second moment reliability method exists difficult to calculate derivatives, and response surface methods, stochastic finite element method and so have different limitations.
Point estimate method as a simple and efficient method of reliability analysis, has been applied in the building structural engineering, foundation engineering and other field, and achieved good results. Therefore, the paper dedicated to the research for a reliability analysis of reliability method, which based on point estimate method to caculate statistical moments of the function and use Pearson curves to simulate approximate probability density function of slope stability performance function, and Then direct integration in the failure zone to calculate the reliability. Hoping to give some reference value to the researchers.
For the above problems, this paper conducted a study of the following:
(1) Combined The principle of Gauss-Hermit numerical integration with point estimate method , Take the Bishop model of slope stability limit equilibrium analysis as an example, established a seven-point estimate method of slope reliability analysis.
(2) For the limitations and shortcomings of the commonly used slope reliability compute method, introduced the multi-point estimate method and Pearson curve, simulation of the approximate performance function slope stability probability density function, and compared its performance with approximate direct integration method which based on maximum entropy method and Monte Carlo simulation.
(3) The physical mechanics parameter of rock and soil along the Henggui highway's side slope has tested through the indoor experiment, analyzed the the fractal model of red sandstone collapse, and analyzed the rock and soil of side slope’s water content change to cause the intensity change tendency of rock and soil intensity, for the infiltration of rain water caused changes in soil shear strength of the slope stability of embankment slope were analyzed, provide a reference for project.
引文
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