Reliability analysis and design of cantilever RC retaining walls against sliding failure

Abstract Among the various modes of failure of reinforced concrete (RC) cantilever retaining walls, the sliding mode of failure is invariably seen to be the critical mode governing the proportions of the wall. Traditionally, a constant factor of safety (usually 1.5) is adopted in the design of cantilever retaining walls against sliding and overturning instability, regardless of the actual uncertainties in the various design variables. This paper presents the stability analysis of cantilever retaining walls, accounting for uncertainties in the design variables in the framework of probability theory. The first order reliability method (FORM), second order reliability method (SORM) and Monte Carlo simulation (MCS) method are used as alternative ways to evaluate the probability of failure associated with the sliding failure of retaining walls of various heights (ranging from 4 to 8 m). Sensitivity analysis has shown that the angle of internal friction (Φ) and the coefficient of friction below the concrete base slab (μ) are the most sensitive random variables. It is shown that cantilever retaining walls, optimally proportioned to achieve a factor of safety of 1.5 against sliding failure, can have significant variations in the reliability index (or probability of failure). In order to achieve consistently a ‘target’ reliability index (β = 2.5 or 3.0), the factor of safety must be appropriately chosen, accounting for uncertainties, especially with regard to Φ and μ. In this paper, easy-to-use design tables have been developed for this purpose.