Risk-reduction factor for bearing capacity of shallow foundations

Abstract

In this paper an ultimate bearing capacity risk-reduction factor is proposed to account for the variation and randomness in soil properties. Through a first-order Taylor series expansion, the mean and variance of the ultimate bearing capacity were assessed. Consequently, the variation of the ultimate bearing capacity is expressed as a function of the variation in cohesion and internal friction angle. To develop a risk-reduction factor, several probability density functions were utilized. The asymptotic type II extreme-value distribution for maxima was found best suited to represent the ultimate bearing capacity. The results indicate that the risk-reduction factor FR decreases with an increase in the coefficient of variation of ultimate bearing capacity and a decrease in the selected probability of failure pf. For pf = 0.0001, however, FR was found to range between 0.20 and 1.0. A numerical example is presented to illustrate the use of the proposed reduction factor. Key words : bearing capacity, coefficient of variation, probability distribution, probability of failure, risk factor, shallow foundations.