边坡稳定性分析最小二乘法
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摘要
利用经典土压力理论设定合理土条推力线位置,对土条底滑面采用摩尔-库伦破坏准则,根据静力平衡及力矩平衡条件建立线性超定方程组,应用MATLAB软件基于最小二乘法原理对此方程组求解,得到比较精确的安全系数。该法从设定合理土条推力线位置出发,避免了对条间力函数的不合理设定,采用MATLAB求解线性超定方程组得解,克服了求解非线性方程组不能迭代收敛得解的缺点,经算例验证其在精度方面比较可靠,对于评价边坡的稳定性具有参考意义。
In this article, the author points out that using MATLAB program and the principle of the least squares to calculate the liner equations can get a more accurate safety factor when under the following situations. Firstly, the author use the classical earth pressure theory and Mohr-Coulomb failure criterion to set-up the reasonable thrust line position of soil slice. Secondly, according to static equilibrium equation and torque equilibrium equation, the liner equations are established. This assumption is set by a reasonable thrust line position and avoiding any unreasonable interaction forces. MATLAB is the method for solving linear equations, it overcomes the shortcomings, in which other methods to solve nonlinear equations cannot iterative to converge. The results show the xassumption is more reliable in precision. The study is a guide for evaluating the stability of slopes.
In this article, the author points out that using MATLAB program and the principle of the least squares to calculate the liner equations can get a more accurate safety factor when under the following situations. Firstly, the author use the classical earth pressure theory and Mohr-Coulomb failure criterion to set-up the reasonable thrust line position of soil slice. Secondly, according to static equilibrium equation and torque equilibrium equation, the liner equations are established. This assumption is set by a reasonable thrust line position and avoiding any unreasonable interaction forces. MATLAB is the method for solving linear equations, it overcomes the shortcomings, in which other methods to solve nonlinear equations cannot iterative to converge. The results show the xassumption is more reliable in precision. The study is a guide for evaluating the stability of slopes.
引文
[1]郑颖人,陈祖煜,王恭先,等.边坡与滑坡工程治理[M].北京:人民交通出版社,2007.
[2]童志怡,陈从新,徐健,等.边坡稳定性分析的条块稳定系数法[J].岩土力学,2009,30(5):1393-1398.
[3]李广信.高等土力学[M].北京:清华大学出版社,2004.
[4]郑颖人,沈珠江,龚晓南.岩土塑性力学原理[M].北京:中国建筑工业出版社,2002.
[5]殷宗泽.土工原理[M].北京:中国水利水电出版社,2007.
[6]朱大勇,李焯芬,黄茂松,等.对3种著名边坡稳定性计算方法的改进[J].岩石力学与工程学报,2005,24(2):184-194.
[7]陈昌富,杨宇,龚晓南.基于遗传算法地震荷载作用下边坡稳定性分析水平条分法[J].岩石力学与工程学报,2003,22(11):1919-1923.
[8]邹广电,魏汝龙.土坡稳定性分析普遍极限平衡法数值解的理论及方法研究[J].岩石力学与工程学报,2006,25(2):363-370.
[2]童志怡,陈从新,徐健,等.边坡稳定性分析的条块稳定系数法[J].岩土力学,2009,30(5):1393-1398.
[3]李广信.高等土力学[M].北京:清华大学出版社,2004.
[4]郑颖人,沈珠江,龚晓南.岩土塑性力学原理[M].北京:中国建筑工业出版社,2002.
[5]殷宗泽.土工原理[M].北京:中国水利水电出版社,2007.
[6]朱大勇,李焯芬,黄茂松,等.对3种著名边坡稳定性计算方法的改进[J].岩石力学与工程学报,2005,24(2):184-194.
[7]陈昌富,杨宇,龚晓南.基于遗传算法地震荷载作用下边坡稳定性分析水平条分法[J].岩石力学与工程学报,2003,22(11):1919-1923.
[8]邹广电,魏汝龙.土坡稳定性分析普遍极限平衡法数值解的理论及方法研究[J].岩石力学与工程学报,2006,25(2):363-370.
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