Optimal reconstruction of constrained janbu method with ADP and non-integral safety factor.

• Compared with the classical Janbu method, the addition of an adaptive dynamic programming algorithm has the following advantages. • In the limit equilibrium analysis of each slice, the individual safety factor is directly added to solve the critical instability trajectory iteratively. Instead of first solving the fractional average and safety factor of the sliding surface, judging the rationality, and then searching for the critical sliding surface, the computational task is vast. • When dealing with a complex engineering background, the reconstructed framework is based on a neural network to complete an iterative solution. The fuzzy relationship of safety factors between adjacent strips can be simplified and integrated into the model network. The interactive iterative update of the action and critic networks can complete the boundary curve corresponding to the limit sliding state. At the same time, in order to further simplify the calculation, the critic network uses a dual network design. Notwithstanding the rich research on the slicing method, it is still impossible to accomplish the limit equilibrium analysis of all phases before the evaluation of the safety factor. Bearing this dilemma in view, in this paper, the Janbu method is optimized and reformulated by introducing adaptive dynamic programming (ADP). The fractional average safety factor is no longer used; instead, a sequence of safety factors is used. The critical slip state is chosen as the equilibrium point, the nonlinearity of safety coefficients of adjacent blocks is approximated by the neural network, and the remaining variables and constraints of the system are added to assist in transforming the original redundant safety coefficient evaluation-finding optimal solution problem into a Janbu-qualified cost function. The action network and critic network of ADP accomplish the boundary trajectory solving and safety evaluation, respectively. The validity of the method is verified when the optimized and reorganized framework is applied to solve the critical slip surface of a clay slope. [ABSTRACT FROM AUTHOR]