Impact of Autocorrelation Function Model on the Probability of Failure

Abstract

The scale of fluctuation (SOF) of a spatially variable soil property has been known to be the most important parameter that characterizes the effect of spatial averaging, whereas the type of the autocorrelation model (e.g., single exponential versus squared exponential model) is thought to be of limited impact. This paper shows that when extending this statement (SOF is the most important parameter) to the probability of failure, one must be cautious regarding whether the limit-state function is completely governed by spatial averaging. Spatial averaging is a function of the input random field in its classical form—it is not related to the limit-state function. For a limit state that happens to be completely governed by spatial averaging, e.g., a friction pile under axial compression, the statement is indeed true, but for a limit state that is not completely governed by spatial averaging, the statement may not be true and the type of autocorrelation model can have significant impact. This paper shows that the second type of limit-state functions are not uncommon. In particular, this paper shows that the sample path smoothness can be another important feature that signifcantly affects the probability of failure for this type of limit-state function. An autocorrelation model that can control the sample path smoothness using a smoothness parameter ν is adopted in this paper. Five practical examples are presented to illustrate the effect of ν. It is observed that ν, which is another characteristic of the autocorrelation model that is distinctive from the scale of fluctuation, can have significant impact on the probability of failure for these examples.