基于矢量和法安全系数的边坡稳定性研究
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摘要
对边坡稳定性的研究一直是岩土工程界关注的话题。随着在工程建设中出现的边坡数量及规模的增大,加强对滑坡机理的研究具有重大的意义。本文对现有的边坡稳定性分析方法做了归纳总结,以葛修润院士提出的矢量和法安全系数为出发点提出了包括有限元模型建立、应力插值、临界滑裂面搜索的边坡稳定性分析方法,并编制了相应的计算程序“GAKV”。
本文边坡稳定性分析方法的实现方式包括:应用有限元软件ANSYS建立边坡的弹塑性模型,对其作适当的网格剖分后计算得到有限元节点的应力文件;将坡体内的应力值视为区域化变量,文中采用球状模型构建理论变差函数,将克立格插值方法应用到滑面的点应力插值上;通过引进罚函数,最优保留等策略对简单遗传算法做了改进,构建以与矢量法安全系数相关联的适值函数,分别对圆弧型滑面与非圆弧滑面作了算法设计。此外,文中介绍了实现以上算法的程序编写方法与步骤,详细说明了滑面生成方式、初始种群的合理性约束、适值函数变量取值范围的确定在程序上的实现方法。
文中选用澳大利亚计算机应用协会(ACADS)的两个算例EX1(a)和EX1(c)对本文所述的边坡稳定性分析方法作了验证,验证结果表明本文方法计算结果与标准答案相接近,误差控制在4%以内。应用本文计算方法,文中对对福建某码头的护岸工程做了稳定性计算,计算所得安全系数为1.514,能够满足规范要求。
本文研究结果表明:(1)矢量法安全系数定义方式简明,物理意义明确,是定义在滑面应力分析基础之上的,能够充分利用有限元的计算结果,计算结果可靠;(2)计算矢量法安全系数时只需要知道滑面上的点应力,在边坡应力场已知的条件下,矢量法安全系数与遗传算法相结合时只需对控制滑面的位置变量进行编码、组串即可,这大大简化了遗传算法中染色体的初始化和遗传操作的实现;(3)通过对简单遗传算法的改进明显提高了算法的搜索效率和可靠性;(4)通过回归反证及与其它插值结果相互比较,用克立格插值法得到点应力比较可靠,插值结果基本上能反映滑面的真实应力状态。
The research of slope’s stability is always a focus in the geotechnical engineering. Along with the aggrandizement of slope’s amount and scale in engineering, enhancing the mechanism research of landslide has a great significance. This dissertation makes a summarization to the existing method of slope’s stability analysis. Based on the vector method safety factor which was put forward by academician Ge Xiurun, this paper puts forward the method of slope’s stability analysis includes establishing finite element model, stress interpolation and searching critical slip surface, and write the corresponding computational procedures“GAKV”.
The method in this paper has some critical parts. The slope’s elastic-plastic model is established by using finite element software ANSYS and the nodes’stress can be calculated after meshing the slope’s model properly. Regarding the slope’s stress as regional variable, this paper uses spherical model constructs the theoretical variogram and applies the kriging interpolation method to interpolate the slide surface’s stress. Through indraught the penalty function and strategy of retaining optimal chromosomes to improve the simple genetic algorithm, this dissertation constructs the fitness function related to the vector method safety factor and designs the arithmetic of circle-slide surface and noncircle-slide surface. In addition, how realize the above method by procedure is presented and the method of generating slide surface, restricting initial population rationally and fixing the scope of fitness function’s variable are introduced detailedly.
The two examples EX1(a) and EX1(c) come from ACADS are used to identify the method of slope’s stability analysis put forward in this paper and show that its results is close to critical results and the error can be controlled in 4%. The stability of the dock in Fujian is caculated by this pqper’s method, the safety factor of it is 1.2 that can fit the specification.
The results show that: (1) the definition of vector safety factor is consice and has a clear physical meaning. Because vector safety factor based on slide surface’s stress analysis, it can take full advantage of the finite element calculations to calculate reliable results; (2) calculating the vector safety factor only need to know the dot’s stress on slide surface. If have already knew the slope’s stress field, the combination of vector safety factor and genetic algorithm just have to control the variable which deside the location of slide surface, which greatly simplifies the initialization of chromosome and realization of genetic manipulation; (3)the search efficiency and reliability of genetic algorithm are improved after improving the simple genetic algorithm;(4) through the return validating and comparing the results of interpolation with other method, kriging interpolation method shows its reliability.
本文边坡稳定性分析方法的实现方式包括:应用有限元软件ANSYS建立边坡的弹塑性模型,对其作适当的网格剖分后计算得到有限元节点的应力文件;将坡体内的应力值视为区域化变量,文中采用球状模型构建理论变差函数,将克立格插值方法应用到滑面的点应力插值上;通过引进罚函数,最优保留等策略对简单遗传算法做了改进,构建以与矢量法安全系数相关联的适值函数,分别对圆弧型滑面与非圆弧滑面作了算法设计。此外,文中介绍了实现以上算法的程序编写方法与步骤,详细说明了滑面生成方式、初始种群的合理性约束、适值函数变量取值范围的确定在程序上的实现方法。
文中选用澳大利亚计算机应用协会(ACADS)的两个算例EX1(a)和EX1(c)对本文所述的边坡稳定性分析方法作了验证,验证结果表明本文方法计算结果与标准答案相接近,误差控制在4%以内。应用本文计算方法,文中对对福建某码头的护岸工程做了稳定性计算,计算所得安全系数为1.514,能够满足规范要求。
本文研究结果表明:(1)矢量法安全系数定义方式简明,物理意义明确,是定义在滑面应力分析基础之上的,能够充分利用有限元的计算结果,计算结果可靠;(2)计算矢量法安全系数时只需要知道滑面上的点应力,在边坡应力场已知的条件下,矢量法安全系数与遗传算法相结合时只需对控制滑面的位置变量进行编码、组串即可,这大大简化了遗传算法中染色体的初始化和遗传操作的实现;(3)通过对简单遗传算法的改进明显提高了算法的搜索效率和可靠性;(4)通过回归反证及与其它插值结果相互比较,用克立格插值法得到点应力比较可靠,插值结果基本上能反映滑面的真实应力状态。
The research of slope’s stability is always a focus in the geotechnical engineering. Along with the aggrandizement of slope’s amount and scale in engineering, enhancing the mechanism research of landslide has a great significance. This dissertation makes a summarization to the existing method of slope’s stability analysis. Based on the vector method safety factor which was put forward by academician Ge Xiurun, this paper puts forward the method of slope’s stability analysis includes establishing finite element model, stress interpolation and searching critical slip surface, and write the corresponding computational procedures“GAKV”.
The method in this paper has some critical parts. The slope’s elastic-plastic model is established by using finite element software ANSYS and the nodes’stress can be calculated after meshing the slope’s model properly. Regarding the slope’s stress as regional variable, this paper uses spherical model constructs the theoretical variogram and applies the kriging interpolation method to interpolate the slide surface’s stress. Through indraught the penalty function and strategy of retaining optimal chromosomes to improve the simple genetic algorithm, this dissertation constructs the fitness function related to the vector method safety factor and designs the arithmetic of circle-slide surface and noncircle-slide surface. In addition, how realize the above method by procedure is presented and the method of generating slide surface, restricting initial population rationally and fixing the scope of fitness function’s variable are introduced detailedly.
The two examples EX1(a) and EX1(c) come from ACADS are used to identify the method of slope’s stability analysis put forward in this paper and show that its results is close to critical results and the error can be controlled in 4%. The stability of the dock in Fujian is caculated by this pqper’s method, the safety factor of it is 1.2 that can fit the specification.
The results show that: (1) the definition of vector safety factor is consice and has a clear physical meaning. Because vector safety factor based on slide surface’s stress analysis, it can take full advantage of the finite element calculations to calculate reliable results; (2) calculating the vector safety factor only need to know the dot’s stress on slide surface. If have already knew the slope’s stress field, the combination of vector safety factor and genetic algorithm just have to control the variable which deside the location of slide surface, which greatly simplifies the initialization of chromosome and realization of genetic manipulation; (3)the search efficiency and reliability of genetic algorithm are improved after improving the simple genetic algorithm;(4) through the return validating and comparing the results of interpolation with other method, kriging interpolation method shows its reliability.
引文
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[5]张金山,袁绍国,雷化南.露天矿边坡稳定性分析专家系统[J].中国矿业,1995,4(3):57–62.
[6]夏元友,朱瑞赓.边坡稳定性分析专家系统研制[J].灾害学,1997,12(4):10–14.
[7] Hassan Ahmed Mohamed. A practical approach to combined probabilistic analysis of slope stability and seepage problems[PhD thesis][D].East Lansing:Michigan State University,1998.
[8] Alonso E E.Risk analysis of slopes and its application to slopes in Canadian sensitive clays[J]. Géotechnique,1976,26(3):453–472.Chowdhury R N,Tang W H,Sidi I. Reliabilistic model of progressive failure of slopes[J].Géotechnique,1987,37(4):467–481.
[9]谢全敏,夏元友.岩体边坡治理决策的模糊层次分析方法研究[J].岩石力学与工程学报,2003,22(7):1117–1120.
[10] Xie Quanmin,Zhu Ruigeng. Grey classification for evaluating the stability of dangerous rock—block masses[J].Journal of Wuhan University of Technology(Materials Science),2000,15(1):73–77.
[11]夏元友.滑坡灰色系统预测模型及其应用[J].自然灾害学报,1995,4(1):74–78.
[12]谢全敏,夏元友.基于遗传算法的边坡稳定性评价的动态聚类法[J].岩土力学,2002,23(2):170–173.
[13]冯夏庭,王泳嘉,丁恩保.智能化的边坡稳定性分析方法[J].东北大学学报(自然科学版),1995,16(5):453–457.
[14]刘金龙.边坡稳定性及路堤变形与破坏机理研究[博士学位论文][D].武汉:中国科学院武汉岩土力学研究所,2006.
[15]冯夏庭.智能岩石力学导论[M].北京:科学出版社,2000.
[16]赵杰,邵龙潭.平面应变条件下两类有限元边坡稳定分析方法比较研究[J].大连理工大学学报,2007(6).
[17]陈祖煜.土质边坡稳定分析[M].北京:中国水利水电出版社,2003.
[18] Janbu N. Slope stability computations[A].In:Hirschfield R C,Poulos S J.ed. Embankment-Dam Engineering[C].New York:John Wiley & Sons,1973,Casagrande Volume,47–86.
[19] Bishop A W. The use of the slip circle in the stability analysis of slopes[J].Géotechnique,1955,5(1):7–17.
[20]赵杰,邵龙潭.土体结构极限承载力的有限元分析[J].岩石力学与工程学报, 2007. S1.
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