Abstract
The safety factor which may be defined as the ratio of the resistance of a structure to the applied loads is intended to cover all the uncertainties about strength, loads and mechanical theories. In this paper, at first, mathematical structures of these uncertainties in the stability problem of an embankment are considered. Some points are discussed about the "constancy of coefficient of variation" of undrained strength in a natural ground and this constancy plays the role to express the transition process of a state of ground. Sliding failure is naturally defined as a probabilistic event because of the probabilistic representation of inhomogeneity of a ground and some errors and hypotheses in a stability analysis.The parameters of a probability distribution of failure are estimated under the evaluation of the utility of an embankment. For this purpose, the loss function is defined by two factors, the one is a probability of failure and the other is a preference function. This definition shows that the Bayesian decision criterion is most reasonable.In a conventional safety factor method, the maximum likelihood estimator of strength is devided by a safety factor and a safety margin is subtracted from this quotient to get a design strength of a ground. This design method is compared with the presented optimum design.Some numerical examples show that the conventional safety factor does not always give a good approximation to the presented optimum design over the full range of a probable strength of a ground.
