中文摘要：

矢量和法物理力学意义明确,计算简单,且能根据边坡当前的应力分布状态合理地评价其整体稳定性状态。其中边坡的应力状态通常是采用有限元法来求解。由于边界元法具有研究问题降阶、离散化带来的误差值仅产生在边界以及计算量小等优点,在工程中得到了广泛应用;对于平面问题,以源点作为原点,以所积分单元的切向和法向为坐标轴建立局部坐标系,对于线性单元可以得到所有积分的解析解。因此,可以得到计算区域内部任意点的场变量的解析解,这就保证了位于边界附近区域场变量的精度。利用边界元法得到二维边坡体内连续的应力分布状态,使用矢量和法对该边坡进行稳定性分析,并且与基于有限元的矢量和法、极限平衡法进行对比分析。边坡圆弧滑面和折线滑面的计算结果表明,基于边界元法得到的矢量和安全系数和基于有限元的矢量和法、极限平衡法基本一致;边界元法对应的矢量和安全系数对边界单元尺寸不敏感。

英文摘要：

The vector sum method （VSM） has clear physical and mechanical definition,simple calculation and gives reasonable assessment of whole stability according to slope stress distribution; and the stress distribution are usually obtained by finite element method （FEM）. The boundary element method （BEM） has gotten extensive application to engineering because of reduced order,discretization error only on the boundary and low computational complexity. For plane problem,using the source point serving as origin,the tangent and normal direction of integral element to establish local coordinate system,analytical solutions are obtained for all integrals of linear element. Therefore,analytical solutions for the variables in the region calculated can be acquired; and it guarantees the accuracy and continuity of the variables of region near the border. Using the stress distribution of two-dimensional slope obtained by BEM,together with VSM,the slope stability can be analyzed; the results obtained are compared and analyzed with the VSM based on FEM and the limit equilibrium method （LEM）. The results of circle and fold line slip surface slopes show that the vector sum safety factor based on BEM is very close to the VSM based on FEM and LEM; the vector sum factor of safety based on BEM is not sensitive to boundary element size.