张年学, 李晓, 盛祝平. 2018: 用拐点原理计算滑坡后沿张裂缝深度的新公式. 工程地质学报, 26(1): 157-163. DOI: 10.13544/j.cnki.jeg.2018.01.017
    引用本文: 张年学, 李晓, 盛祝平. 2018: 用拐点原理计算滑坡后沿张裂缝深度的新公式. 工程地质学报, 26(1): 157-163. DOI: 10.13544/j.cnki.jeg.2018.01.017
    ZHANG Nianxue, LI Xiao, SHENG Zhuping. 2018: THE NEW FORMULA OF CALCULATING DEPTH OF A TENSION CRACK IN THE UPPER SURFACE OF A SLIDING SLOPE USING INFLECTION PRINCIPLE. JOURNAL OF ENGINEERING GEOLOGY, 26(1): 157-163. DOI: 10.13544/j.cnki.jeg.2018.01.017
    Citation: ZHANG Nianxue, LI Xiao, SHENG Zhuping. 2018: THE NEW FORMULA OF CALCULATING DEPTH OF A TENSION CRACK IN THE UPPER SURFACE OF A SLIDING SLOPE USING INFLECTION PRINCIPLE. JOURNAL OF ENGINEERING GEOLOGY, 26(1): 157-163. DOI: 10.13544/j.cnki.jeg.2018.01.017

    用拐点原理计算滑坡后沿张裂缝深度的新公式

    THE NEW FORMULA OF CALCULATING DEPTH OF A TENSION CRACK IN THE UPPER SURFACE OF A SLIDING SLOPE USING INFLECTION PRINCIPLE

    • 摘要: 当坡体后沿产生张裂缝时,通常意味着坡体接近极限平衡状态,滑坡可能发生,若遇降雨,张裂缝充水产生的水压往往是滑坡发生的启动因素,因为水压的大小与张裂缝的深度估算有关,是边坡稳定分析的重要条件之一。建立了一个坡体后部潜在三角形极限平衡体拉张模型,导出裂缝深度公式。应用拐点的数学性质原理,解出裂缝处与内摩擦角相应的滑面倾角,计算张裂缝深度系数,绘制了应用于实际的张裂缝深度系数的数值解曲线图。解释了张裂缝发生条件:裂缝处的滑面倾角必须小于裂缝深度系数的一阶导数的极值点确定的与土层内摩擦角对应的倾角α。给出了圆弧滑面和一种非圆弧滑面发生张裂缝位置的公式。与Spencer裂缝公式进行了比较,表明本文方法具有实用价值。

       

      Abstract: When a tension crack appears in a slope, it usually indicates the slope is reaching limited equilibrium and a landslide is most likely to occur. With a rainfall, pressure by the filling water in the tension crack becomes a triggering factor for the slope failure. Therefore the crack depth is one of the important factors in slope stability analysis since it determines the water pressure in the tension crack. This paper presents a potential triangle block model created by a tension crack in the upper slope. The crack depth equation is derived by the force balance. The angle of the sliding surface associated to angle of international friction at the tension crack is obtained by the inflection principle. The crack depth coefficient is calculated afterward. The analytical solution curves are prepared for practical determination of crack depth coefficients. The conditions for generation of a tension crack are identified as follows:the angle of the sliding surface at the tension crack should be smaller than the angle corresponding to the angle of internal friction determined by the limited values of the first degree derivative. The crack location formula are also given for both circular failure and non-circular failure slopes. The results are compared with the Spencer Method, proving potential for its applications in slope engineering.

       

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