基于严格平衡的安全系数统一求解格式

在边坡稳定性分析中宜采用严格极限平衡条分法，特别是对于任意形状滑动面。由于条间力假设的不同，产生了不同的边坡稳定安全系数求解格式，既造成计算及应用的不方便，又掩盖了各自方法的优劣。首次将现有严格极限平衡条分法对条间力的假定表示成统一形式，根据力和力矩的平衡，导出简单明了的条间力递推方程和条间力矩递推方程。根据这2个方程，通过Newton-Raphson法建立了传统意义下基于严格平衡的安全系数统一求解格式。所需有关导数均可用递推公式计算，其性质为解析解，因而计算格式具有良好的稳定性与收敛性。所有公式均为代数式，便于在工程中推广应用。

Unified calculating formulation for safety factor based on rigorous equilibrium

Rigorous limit equilibrium methods of slices should be used in slope stability analysis, especially for general slip surfaces. However, different assumptions regarding the inter-slice forces have resulted in different calculating formulations for the factor of safety of slope stability, thereby rendering the calculation process complicated and concealing the advantages and disadvantages of different procedures., In this paper, the assumptions regarding the inter-slice forces that made by the existing rigorous limit equilibrium methods of slices are expressed into the unified formulation for the first time, the simple and clear recurrence equations of the inter-slice forces and inter-slice moments are derived based on force equilibrium and moment equilibrium. Based on the recurrence equations of the inter-slice forces and inter-slice moments, the unified calculating formulation for the factor of safety based on rigorous equilibrium in the context of conventional methods of slices is developed by Newton-Raphson method. The relevant derivatives that it needs can be computed by using recurrence formulas, and its nature is analytic solution, therefore its computer formulation is of the good stability and convergence. All of its formulas are algebraic expressions. It facilitates the application and dissemination in engineering.