吕爱钟, 贾晓阳. 2022. 边坡危险滑动面及稳定安全系数的力学解析方法[J]. 工程地质学报, 30(1): 110-116. doi: 10.13544/j.cnki.jeg.2020-568.
    引用本文: 吕爱钟, 贾晓阳. 2022. 边坡危险滑动面及稳定安全系数的力学解析方法[J]. 工程地质学报, 30(1): 110-116. doi: 10.13544/j.cnki.jeg.2020-568.
    Lü Aizhong, Jia Xiaoyang. 2022. Mechanical analysis method for dangerous sliding surface and factor of safety[J]. Journal of Engineering Geology, 30(1): 110-116. doi: 10.13544/j.cnki.jeg.2020-568.
    Citation: Lü Aizhong, Jia Xiaoyang. 2022. Mechanical analysis method for dangerous sliding surface and factor of safety[J]. Journal of Engineering Geology, 30(1): 110-116. doi: 10.13544/j.cnki.jeg.2020-568.

    边坡危险滑动面及稳定安全系数的力学解析方法

    MECHANICAL ANALYSIS METHOD FOR DANGEROUS SLIDING SURFACE AND FACTOR OF SAFETY

    • 摘要: 为了分析边坡的稳定性,提出了一种基于极限平衡理论的分析方法。假定坡体为只受重力作用的弹性体,通过弹性力学解析解求得应力分布,将滑动面用分段二次多项式函数表示,当分段间隔足够小时,这种表示方式可以描述任意曲面形状,根据坡体滑面所满足的Mohr-Coulomb准则,定义边坡稳定安全系数,其为多项式系数的函数。通过混和罚函数优化方法可以求出最危险滑动面对应的多项式系数,获得边坡的稳定安全系数,从而判定边坡的稳定性。所提出的方法与以往方法不同,不用将滑体划分成垂直条块,不用假定滑面上的法向应力分布形式,而直接利用已有的坡体弹性应力解。算例表明:本文方法所得到的结果与简化Bishop法和有限元强度折减法获得的结果非常接近,且基本介于有限元法和简化Bishop法之间。

       

      Abstract: In order to analyze the stability of slope,a method based on limit equilibrium theory is proposed. Assuming that the slope is made up with elastomer only affected by gravity,the stress distribution can be obtained by analytical solution of elastic mechanics. The sliding surface is described by piecewise quadratic polynomial function. When the piecewise interval is short enough,this description method can reflect arbitrary curved shape. According to the Mohr-Coulomb criterion,the factor of safety is defined,which can be expressed as a function of polynomial coefficient. The polynomial coefficient of the most dangerous sliding surface can be obtained by using the mixed penalty function optimization method,then the factor of safety can be obtained to analyze the stability of the slope. The proposed method is different from the previous methods. It does not need to divide the landslide body into vertical slices and to assume the normal stress distribution form on the sliding surface. It directly uses the existing slope body elastic stress solution. The results of the calculation examples show that the factor of safety obtained by the method in the paper is very close to the results obtained by the simplified Bishop method and the finite element strength reduction method. They are basically between the finite element method and the simplified Bishop method.

       

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