Conditions of Hydraulic Heterogeneity under Which Bayesian Estimation is More Reliable

Abstract

Natural heterogeneity of soil hydraulic properties is significant for the design and construction of geotechnical structures, and should be adequately characterized. Accurate measurements of hydraulic properties remain a difficult job and do not always work well for further design and analysis. Field hydraulic monitoring data reflects the overall slope performance and provide a more representative estimation of in-situ soil hydraulic properties for back analysis. The objective of this study is to explore the conditions under which monitoring data can provide reliable estimates of hydraulic parameters. Different distributions of soil heterogeneity generate a total number of 500 sets of synesthetic monitoring data. Bayesian inversion with the integration of Karhunen-Loève (K-L) and polynomial chaos expansion (PCE) is chosen to estimate the spatially varied saturated coefficient of permeability ks. The results show that the method is accurate and reliable, with less than 3% percentage error and 0.08 coefficient of variation (COV) around the monitoring points. There are two characteristics of the best-estimated fields. First, the ranges of ks for best-estimated fields are much narrower than the worst estimated fields. Second, when the larger ks values are distributed in the unsaturated zone of slope crest, it will lead to the best estimation. It is suggested that monitoring data can provide a reliable estimation of heterogeneous ks when the ratio of ground surface flux to ks in the unsaturated zone of slope crest is less than 1/150. Small values of ks in the slope crest result in the response of pressure head far from the responses of homogenous ks in the unsaturated zone. This complex response of the pressure head further causes the ill identification of ks by Bayesian estimation.