中文摘要：

在二维矢量和法的基础上提出三维矢量和法中整体下滑趋势方向的确定方法，需首先计算整体下滑方向的初值，然后进行投影计算得到其整体下滑趋势方向及矢量和法安全系数。运用该方法对几个三维边坡算例进行分析，结果表明矢量和法安全系数与三维极限平衡法结果基本一致，且对于滑移面单元尺寸不敏感。最后，以三峡大坝26#坝段抗滑稳定性分析为工程实例，针对通过详细勘察而指定的4种滑移面进行平面矢量和分析及三维矢量和分析，结果表明三维矢量和分析结果均较二维矢量和结果要大，且深层滑移面得到的安全系数比浅层滑移面稍大，其抗滑安全系数远大于1．0，说明坝基是安全的。该方法具有明确的物理和力学意义，只需一次弹性或弹塑性数值计算，不需过多的人为假设，即可得到三维矢量和法安全系数。该方法具有三维极限平衡法及强度折减法无法相比的优势，计算过程简单，便于在工程实践中运用。

英文摘要：

Based on two-dimensional vector sum method（VSM）, the determination of the whole sliding direction of slope with 3D vector sum method is put forward; and initial sliding direction can be obtained by current stress state. Then the whole sliding direction and the factor of safety with this method is solved. This method is used in several 3D examples; and the results demonstrate that the factors of safety are in good agreement with that of the limit equilibrium method, and the results are not sensitive to element sizes of the slip surfaces. Finally, this new method is applied to the foundation stability analysis of dam section No.26 in the Three Gorges Project. Four slip paths designated through detailed investigation are analyzed with the plane vector sum method and the 3D vector sum method. The calculating results with the 3D vector sum method show that the factors of safety with the 3D vector sum method are larger than that with the 2D method; and the factor of safety of the deep slip paths is larger than the shallow ones, greater than 1.0. Therefore, the dam section No.26 under the current loads in the Three Gorges Project is safe. This new method is clear in physics and mechanics, and only one time elastic calculation or elastoplastic calculation, and the 3D factor of safety of potential sliding mass can be achieved without too many artificial assumptions. The process of this new analysis method is simple and easy to use in practical engineering projects.