Random Field Modelling for the effect of Cross-Correlation

Probabilistic approaches are being used increasingly in the modelling of geotechnical problems, some of the assumptions made in most analyses to simplify the calculations in stochastic modelling have to be reviewed. One of those assumptions is that of zero correlation between soil strength parameters (cohesion and internal friction) in the analysis of soil slope stability. In the paper, it is shown that this assumption is far too conservative. A random field is used to model the covariance function of cohesion and internal friction. The first order second moment (FOSM) method and method of slices are then used to calculate the probability of failure of a slope by defining the performance function as the safety margin. Such a realistic soil model has not been adopted elsewhere and its use results in considerably increased reliabilities for slopes. The effect of this change is demonstrated by some examples.