二维边坡稳定方法的统一计算公式

根据条分法的概念，本文推导出二维边坡稳定分析的统一计算公式。根据不同的计算假定，可以得到相应的刚体极限平衡方法，包括Bishop简化法、Janbu简化法，美国陆军工程师团法、Lowe和Karafiath法、传力系数法、分块极限平衡法、严格Janbu法、Spencer法和Morgen-stern-Price法等。本文的计算公式简单，易于理解，适用于用有限差分求异的各种数值方法，避免了繁琐的求异计算。文中统一采用带线性搜索的高斯牛顿法，通过考题的比较，证明了计算公式的可靠性和正确性，也证实了不论计算假定如何，满足合理性条件和所有平衡条件的安全系数就是合理的，而且它们之间的相对误差应少于5%。

Uniform formulation for 2D slope stability analysis

Uniform formulation about limit equilibrium slope stability analysis method is developed, based on the idea of slice method According to different assumption, Bishop Simplified Method, Janbu's Simplified Method, Lowe and Karafiath Method, US Army Corps of Engineer's Method, Load Transfer factor Method, Blocking Limit Equilibrium Method, Janbu's Generalized Method, Spencer Method and Morgenstern-Price Method can be derived. The formulation is simple and easy to understand. Gauss-Newton Method with a line search step-selection strategy is adopted. Jacobian matrix is obtained by finite-differences. Finally, several examples are used to verify the formulation. It also proves that factor of safety(FOS)is accurate when satisfying all equlibrium equations and acceptability conditions. The factor of safety using any of these methods differs by no more than 5%.