确定滑面应力状态以及坡体滑动方向,是运用矢量和法进行边坡稳定性分析的关键。针对任意形状的滑移面,基于最小势能原理获取滑面上的应力,通过使得系统势能最小的虚位移求解滑面上的法向力以及剪切力。同时,将边坡整体运动趋势视为微面抗滑力矢量和的相反方向,构建了一种抗滑力方向的计算方法。将滑体上的所有力在滑动方向上进行投影得到抗滑力与下滑力,二者的比值定义为边坡的安全系数。相比以往的研究,文中方法无需假定主滑面,同时避免了初始滑动方向的确定。为验证该方法的可行性,用其计算了2个经典算例的安全系数、滑动方向以及法向应力,并将其应用于某实际工程。结果表明:该方法在2个经典算例中得到的结果与其余算法结果较为接近,验证了其合理性;在实际工程中,文中方法与其他算法的计算所得安全系数较为接近。研究成果为边坡稳定计算提供了新的思路。

Determining the stress state of sliding surface and the sliding direction of slope is the key to analyzing the stability of slope using the method of vector sum. The stress of any point on fixed sliding surface of arbitrary shape is ascertained based on the principle of minimum potential energy, and the normal stress and shear stress of sliding surface are obtained through the virtual displacement which produces minimum potential energy. Meanwhile, the slide-resistance direction of micro-unit is calculated by regarding the overall motion trend of the slope as in the opposite direction of the vector sum of the slide-resistance direction. Moreover, the ratio of slide-resistance to sliding stress which are acquired from projecting all the forces on the slope in the sliding direction is defined as the safety factor of slope. Compared to previous researches, the present method does not need to assume a major slide surface, and therefore, avoids the confirmation of initial sliding direction. The method is applied to calculating the safety factor, slide direction and normal stress of two classical calculation examples and also in a practical project. The results of two calculation examples verify the rationality of the present method; in practical engineering, the calculation result is also consistent with those of other methods.