Impact of Statistical Uncertainty on Geotechnical Reliability Estimation

Because of limited information in site investigation, it is not possible to obtain the actual values for the trend ($t$), standard deviation ($\sigma$), and scale of fluctuation ($\delta$) of a spatially variable soil property of interest. The uncertainty in these soil parameters $\mathbf{\theta }=(t,\sigma ,\delta )$ is called the statistical uncertainty. The failure probability ($p_f$) of the geotechnical structure will increase as a result of the statistical uncertainty. This paper addresses the issue of incorporating the statistical uncertainty of $\mathbf{\theta }$ into the reliability calculation, to properly reflect the $p_f$ increase. A cone penetration test (CPT) sounding at the Wufeng District in Taichung City (Taiwan) is analyzed to illustrate the importance of treating statistical uncertainty in full and the limitations of the existing point-estimation and detrending approaches. It is shown that the statistical uncertainty can be fully characterized by drawing Markov chain Monte Carlo (MCMC) samples from the posterior PDF, $f(\mathbf{\theta }|\text{data})$. The resulting $p_f$ estimate will increase if some of these MCMC samples explore the high-risk region. The sample size in a thin soil layer is smaller than that in a thick layer. It follows that statistical uncertainty is larger for thin soil layers. It is also concluded that the point estimate for $\mathbf{\theta }$ cannot characterize the statistical uncertainty at all, nor can intermediate methods such as detrending first and then drawing MCMC samples from $f(\sigma ,\delta |t,\text{data})$ fully characterize the statistical uncertainty.