Proof of Nondeterministic Polynomial-Time Complete Problem for Soil Slope-Stability Evaluation

Abstract

Generally, slope-stability evaluation involves two coupled tasks: locating the critical slip surface and calculating its corresponding factor of safety. Various assessment methods have emerged in the past few decades, and the question of whether equivalence exists between these methods has become a controversial issue. Unfortunately, research that explores the roots of the slope-stability problem from the perspective of computational complexity is quite limited. This paper addresses this long-neglected but very important problem by rigorously proving that the evaluation of slope stability is essentially a nondeterministic polynomial-time complete problem, which is computationally one of the most difficult types of problems. A significant achievement of this proof is the inference that equivalence between the limit equilibrium method and the strength reduction method does not exist. The methods used throughout these routine analyses are exactly approximate and will not replace one another completely. The case study verified the aforementioned conclusions.