Equivalence between Bearing-Capacity, Lateral Earth-Pressure, and Slope-Stability Problems by Slip-Line and Extremum Limit Equilibrium Methods

Abstract

Classically, lateral earth-pressure, bearing-capacity, and slope-stability problems are considered separately, although these problems are all related to the ultimate limit state of a system. The authors see that these problems are governed by similar ultimate requirements and should be equivalent in terms of the failure mechanism, and these problems can be considered as a different view of the ultimate limit state of the system. It is interesting to note that, although there are many applications of the method of characteristics in various geotechnical problems, there is none that is devoted to the unification of these geotechnical problems. Bearing-capacity, slip-line, and slope-stability problems have been treated as individual topics in all previous works. In the present study, based on the method of characteristics, the authors determined the bearing capacity factors (Nc, Nq, and Nγ) for a shallow foundation and the lateral earth-pressure coefficients (Kac, Kaq, and Kpγ) for a retaining wall. Through the method of characteristics, Kac, Kaq, and Kpγ were demonstrated to be related to Nc, Nq, and Nγ, so these two problems can be unified, and each problem can be viewed as the inverse of the other problem. The authors also applied the extremum principle to demonstrate the equivalence between the lateral active-pressure, bearing-capacity, and slope-stability problems. Overall, these three problems can be considered as equivalent in the basic principles, and the classification of a problem is simply a matter of convenience.