岩土参数随机性分析与边坡稳定可靠度研究
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摘要
边坡的稳定性评价一直是岩土工程中非常重要的研究课题。迄今,边坡稳定性评价方法已有安全系数法和可靠性方法两类,但这些方法尚存在以下不足:安全系数法不能考虑边坡的土性参数、孔隙水压等因素中客观存在的较大不确定性,由此导致具有相同安全系数的不同边坡可能具有相去甚远的失效风险水平;可靠性方法虽考虑了参数的随机性,但其相关统计资料、统计方法和边坡稳定可靠性分析方法尚不完善,导致该法在计算量、收敛性、精度和工程实用性上存在诸多缺陷。本文针对以上问题,深入研究了岩土参数随机性统计方法,在广泛收集边坡测试资料和补充试验的基础上,统计分析了典型岩土的力学参数的概率分布规律;分析了具有单一失效模式的边坡可靠度计算中存在的关键问题,提出了相应的解决办法;针对多失效模式的边坡,改进了基于矩阵的体系可靠度法(MSR法),应用该法解决了复杂边坡体系的稳定可靠度计算问题;在以上分析基础上,开发了边坡稳定可靠性计算程序。主要工作及成果如下:
1、研究了岩土参数不确定性的量化方法;统计分析了我国部分典型土性参数的随机性特征;收集了23个岩石边坡的1500多组岩土力学参数的测试数据和统计资料,进行了岩石力学性质的补充试验,并统计了我国部分典型岩体的强度参数概率分布规律,为边坡可靠性分析提供了基础数据。
2、针对经典的假设检验法不适用于样本量很多或很少的极端情况,提出了新的岩土参数统计方法:
(1)针对“大样本”:为弥补信息熵推断法的准确性受参数边界影响较大、最佳平方逼近法在多项式次数较高时结果不稳定等缺点和不足,提出了采用正交多项式拟合岩土参数概率密度函数的方法,利用样本统计矩的信息,推导了勒让德(Legendre)正交多项式和切尔雪夫(Chebyshev)多项式的拟合公式。通过仿真实验和工程实例验证了其正确性和优势。
(2)针对“小样本”:首次引入Bootstrap法进行岩土参数的统计分析,通过计算机仿真解决样本量很少时参数分布的推断问题;采用Bayes原理及其推广公式,充分利用验前信息,修正和完善岩土参数的概率模型;利用多源信息,首次将“K-L信息距离”引入到参数概率分布推断中,提出了K-L信息融合法,使多源信息融合方法的客观性和可信性得到了较大幅度的提高。仿真实例和工程实例证明了上述方法能较好地解决小样本的统计问题。
3、针对单一失效模式的边坡可靠性分析中的几个关键问题(边坡稳定极限平衡方程的构建、滑面的模拟技术、关键概率滑面的搜索和可靠指标的求解),分别提出了相应的解决方法:基于边坡极限平衡原理建立了稳定极限平衡方程(或方程组);通过选用圆弧滑面的基本控制参数避免出现无效滑面或遗漏关键滑面;通过约束非圆弧滑面底边的倾角以控制其中间顶点的生成,且通过逐渐增加顶点个数来提高滑面模拟效率;改进遗传算法搜索最小可靠指标以提高搜索的效率和质量。测试算例和工程实例结果表明:该法比安全系数法更能反映工程实际情况;与已有可靠度分析方法相比,省却了求解安全系数的过程,显著降低了计算量,提高了收敛性。
4、以系统的观点研究了具有多个失效模式的边坡稳定可靠性问题,提出了MSR法中事件向量c的构造公式,并与线性规划(LP)法和多尺度法相结合,解决了复杂边坡体系可靠性的计算难题。研究表明:该法大大简化了事件向量c的识别过程,便于实现计算机自动识别;结合LP法和多尺度法,可将MSR法用于复杂边坡的体系可靠度计算,且优化过程易于实现,结果精度较高。
Stability evaluation of slope has been an important research subject in geotechnical engineering. Until now, there are Safety Factor Methods and Reliability Methods for it. However, these methods have such defects as the following: Safety Factor Methods cann't consider the significant uncertainty existing in geotechnical parameters, pore-water pressure and other influencing factors of slope stability, which may lead to quite different risk levels associated with a same safety factor in different slopes; the existing Reliability Methods take the randomness into account, however, they are still imperfect in the accumulation of statistical data, statistical methods for geotechnical parameters and the reliability methods for calculating slope stability so that many shortcomings were brought about in calculation load, convergence, accuracy and practical values. In view of the above problems, the statistical methods of geotechnical parameters were studied further and the probabilistic distribution rules of typical rock and soil parameters were analyzed statistically based on extensively accumulating statistical data related to the randomness of geotechnical parameters and complement experiments. Some key problems in slope reliability analysis with one-mode failure were studied, followed by corresponding solutions. According to multi-failure mode slopes, the matrix-based system reliability method (MSR method) was improved and the difficulties in system reliability calculation of complex rock slopes were overcame by the proposed method and a computer program was developed to realize the above functions. The main work and conclusions are summarized as follows:
1、The quantitative methods of rock and soil parameters uncertainties were studied and stochastic characteristics of partly typical soil parameters were statistically analyzed; more than 1500 groups of test data of strength parameters and statistical material extracted from 23 rock slopes were classified and reprocessed and some supplemental tests associated with mechanical parameters of rocks were carried out for quantifying the uncertainties, and the distribution rules of strength parameters were gained for partly typical rock mass. All of the above provide basic data for the reliability analysis of slopes .
2、Due to the hypothesis test can't be applied to the extreme cases that there is few or too many data for statistical analysis, new methods were proposed to solve the difficulties:
(1) The case of large sample: an information entropy inference method and the least square approximation were studied; considering that the result by the former is sensitive to the borders of parameters and the result by the latter is unstable when the order of polynomial is high, orthogonal polynomial fitting methods were proposed and the calculation formula of Chebyshev polynomials and Legendre polynomials were deduced by utilizing the information of statistical moments of sample. The validity and advantages were proved by a simulation example and a project case.
(2) The case of small sample: Bootstrap method was introduced into the distributions inference of geotechnical parameters for the first time in order to solve parameter distribution inferring by means of computer simulation on condition that statistical data are rather few; Bayes theory and its extension were adopted to utilize prior information fully so as to modify and improve the probabilistic model of geotechnical parameters continuously; in order to utilize multi-source information, "K-L information distance" was introduced into parameter distribution inferring firstly and K-L information fusion method was suggested. As a result, the objectivity and credibility of results by the multi-source information fusion method were improved greatly. It was shown by a simulation and a project case that these methods are good measures to infer the parameter distributions in the case of few data.
3、Aim at some key problems to be solved concerned with reliability calculation for the slopes with one-failure mode (the establishment of limit equilibrium equations of slope, simulation technique and search tools for critical probabilistic slip surface and solving for the least reliability index), the corresponding solutions were proposed: based on limit equilibrium theory, the limit equilibrium equations of slopes were deduced with the safety factor Fs not being contained; suitable control parameters were chosen for circular surfaces to avoid generating invalid surfaces or leaving out key ones; the generation of non-circular surfaces was controlled by angles of interior vertices and by increasing the number of vertices gradually so as to improve simulation efficiency; the standard genetic algorithm for searching for the lowest reliability index was improved so as to enhance the efficiency and quality of the algorithm. It is shown by a test example and a case history that the results were in agreement with the actual situation; being different from the existing reliability methods, this method goes without the solving process of the safety factor so the calculation load was decreased remarkably and the convergence was improved.
4、The slope stable reliability with multi-failure mode was studied from the viewpoint of system, a construction formula of event vector c in MSR method was suggested and the difficulty in calculating complex slope system reliability was overcame by adopting the modified MSR method combining with linear programming and multi-scale method. The results of the project application indicate that the method simplifies the identification of event vectors of components greatly and makes it easy to carry out the computer automatic recognition; combining with the linear programming and multi-scale method, the MSR method can be applied to calculate the complex system reliability for slopes and the optimization process can be implemented conveniently with good precision.
1、研究了岩土参数不确定性的量化方法;统计分析了我国部分典型土性参数的随机性特征;收集了23个岩石边坡的1500多组岩土力学参数的测试数据和统计资料,进行了岩石力学性质的补充试验,并统计了我国部分典型岩体的强度参数概率分布规律,为边坡可靠性分析提供了基础数据。
2、针对经典的假设检验法不适用于样本量很多或很少的极端情况,提出了新的岩土参数统计方法:
(1)针对“大样本”:为弥补信息熵推断法的准确性受参数边界影响较大、最佳平方逼近法在多项式次数较高时结果不稳定等缺点和不足,提出了采用正交多项式拟合岩土参数概率密度函数的方法,利用样本统计矩的信息,推导了勒让德(Legendre)正交多项式和切尔雪夫(Chebyshev)多项式的拟合公式。通过仿真实验和工程实例验证了其正确性和优势。
(2)针对“小样本”:首次引入Bootstrap法进行岩土参数的统计分析,通过计算机仿真解决样本量很少时参数分布的推断问题;采用Bayes原理及其推广公式,充分利用验前信息,修正和完善岩土参数的概率模型;利用多源信息,首次将“K-L信息距离”引入到参数概率分布推断中,提出了K-L信息融合法,使多源信息融合方法的客观性和可信性得到了较大幅度的提高。仿真实例和工程实例证明了上述方法能较好地解决小样本的统计问题。
3、针对单一失效模式的边坡可靠性分析中的几个关键问题(边坡稳定极限平衡方程的构建、滑面的模拟技术、关键概率滑面的搜索和可靠指标的求解),分别提出了相应的解决方法:基于边坡极限平衡原理建立了稳定极限平衡方程(或方程组);通过选用圆弧滑面的基本控制参数避免出现无效滑面或遗漏关键滑面;通过约束非圆弧滑面底边的倾角以控制其中间顶点的生成,且通过逐渐增加顶点个数来提高滑面模拟效率;改进遗传算法搜索最小可靠指标以提高搜索的效率和质量。测试算例和工程实例结果表明:该法比安全系数法更能反映工程实际情况;与已有可靠度分析方法相比,省却了求解安全系数的过程,显著降低了计算量,提高了收敛性。
4、以系统的观点研究了具有多个失效模式的边坡稳定可靠性问题,提出了MSR法中事件向量c的构造公式,并与线性规划(LP)法和多尺度法相结合,解决了复杂边坡体系可靠性的计算难题。研究表明:该法大大简化了事件向量c的识别过程,便于实现计算机自动识别;结合LP法和多尺度法,可将MSR法用于复杂边坡的体系可靠度计算,且优化过程易于实现,结果精度较高。
Stability evaluation of slope has been an important research subject in geotechnical engineering. Until now, there are Safety Factor Methods and Reliability Methods for it. However, these methods have such defects as the following: Safety Factor Methods cann't consider the significant uncertainty existing in geotechnical parameters, pore-water pressure and other influencing factors of slope stability, which may lead to quite different risk levels associated with a same safety factor in different slopes; the existing Reliability Methods take the randomness into account, however, they are still imperfect in the accumulation of statistical data, statistical methods for geotechnical parameters and the reliability methods for calculating slope stability so that many shortcomings were brought about in calculation load, convergence, accuracy and practical values. In view of the above problems, the statistical methods of geotechnical parameters were studied further and the probabilistic distribution rules of typical rock and soil parameters were analyzed statistically based on extensively accumulating statistical data related to the randomness of geotechnical parameters and complement experiments. Some key problems in slope reliability analysis with one-mode failure were studied, followed by corresponding solutions. According to multi-failure mode slopes, the matrix-based system reliability method (MSR method) was improved and the difficulties in system reliability calculation of complex rock slopes were overcame by the proposed method and a computer program was developed to realize the above functions. The main work and conclusions are summarized as follows:
1、The quantitative methods of rock and soil parameters uncertainties were studied and stochastic characteristics of partly typical soil parameters were statistically analyzed; more than 1500 groups of test data of strength parameters and statistical material extracted from 23 rock slopes were classified and reprocessed and some supplemental tests associated with mechanical parameters of rocks were carried out for quantifying the uncertainties, and the distribution rules of strength parameters were gained for partly typical rock mass. All of the above provide basic data for the reliability analysis of slopes .
2、Due to the hypothesis test can't be applied to the extreme cases that there is few or too many data for statistical analysis, new methods were proposed to solve the difficulties:
(1) The case of large sample: an information entropy inference method and the least square approximation were studied; considering that the result by the former is sensitive to the borders of parameters and the result by the latter is unstable when the order of polynomial is high, orthogonal polynomial fitting methods were proposed and the calculation formula of Chebyshev polynomials and Legendre polynomials were deduced by utilizing the information of statistical moments of sample. The validity and advantages were proved by a simulation example and a project case.
(2) The case of small sample: Bootstrap method was introduced into the distributions inference of geotechnical parameters for the first time in order to solve parameter distribution inferring by means of computer simulation on condition that statistical data are rather few; Bayes theory and its extension were adopted to utilize prior information fully so as to modify and improve the probabilistic model of geotechnical parameters continuously; in order to utilize multi-source information, "K-L information distance" was introduced into parameter distribution inferring firstly and K-L information fusion method was suggested. As a result, the objectivity and credibility of results by the multi-source information fusion method were improved greatly. It was shown by a simulation and a project case that these methods are good measures to infer the parameter distributions in the case of few data.
3、Aim at some key problems to be solved concerned with reliability calculation for the slopes with one-failure mode (the establishment of limit equilibrium equations of slope, simulation technique and search tools for critical probabilistic slip surface and solving for the least reliability index), the corresponding solutions were proposed: based on limit equilibrium theory, the limit equilibrium equations of slopes were deduced with the safety factor Fs not being contained; suitable control parameters were chosen for circular surfaces to avoid generating invalid surfaces or leaving out key ones; the generation of non-circular surfaces was controlled by angles of interior vertices and by increasing the number of vertices gradually so as to improve simulation efficiency; the standard genetic algorithm for searching for the lowest reliability index was improved so as to enhance the efficiency and quality of the algorithm. It is shown by a test example and a case history that the results were in agreement with the actual situation; being different from the existing reliability methods, this method goes without the solving process of the safety factor so the calculation load was decreased remarkably and the convergence was improved.
4、The slope stable reliability with multi-failure mode was studied from the viewpoint of system, a construction formula of event vector c in MSR method was suggested and the difficulty in calculating complex slope system reliability was overcame by adopting the modified MSR method combining with linear programming and multi-scale method. The results of the project application indicate that the method simplifies the identification of event vectors of components greatly and makes it easy to carry out the computer automatic recognition; combining with the linear programming and multi-scale method, the MSR method can be applied to calculate the complex system reliability for slopes and the optimization process can be implemented conveniently with good precision.
引文
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