Reliability based risk index for the design of reinforced earth structures

Abstract

The design methods currently used for earth reinforcement are mostly based on deterministic properties of both the soil and the construction materials used. Nowadays, however, the general trend is designing at a specific degree of reliability. This is even more true where the raw data such as soil properties exhibit significant variation. Deterministic solutions, in this case, may not suffice. Therefore, this paper will attempt to use probabilistic formulations thereby modifying the existing design procedure of reinforced earth retaining walls to account for uncertainties and variabilities. Through a first order Taylor's series expansion about the mean, the mean and variance of the strip reinforcing components, namely width and length, are derived in terms of the variations in the soil properties. Design charts that enable estimation of both mean and variance are developed to avoid extensive partial differentiation involved in the computations. Using appropriate probability distributions along with the mean and variance, the final design outputs are determined for a selected failure probability by introducing what is refered to as 'risk index'. The results indicate that the risk index increases with an increase in the coefficient of variations and a decrease in failure probability. Furthermore, it is shown that in some cases, depending on the variabilities of the soil properties, the classical design technique produced a relatively high failure probability.