Abstract: Compared with limit equilibrium method and finite element method, limit analysis has a more rigorous and precise theoretical basis and clearer physical meaning in slope stability analysis. But traditional limit upper bound relies on the overload factor to avoid nonlinear programming whereas most engineering slopes are analyzed by using the factor of strength reduction. In view of this, we introduce the principle of limit upper bound of finite element analysis and introduce the strength reduction factor into the limit upper bound method. Since the relationship between strength reduction coefficient and overload coefficient is approximately hyperbolic, we present a hyperbolic iteration method to solve the strength reduction factor. This method has a faster convergence speed, and overcomes the shortage of traditional strength reduction method which needs artificial trials. The effectiveness of this method is proved by a numerical example compared with the limit equilibrium method and finite element method.

Key words: limit analysis, upper bound finite element, stability analysis, strength reduction, hyperbolic iteration