Unsaturated soil slope characterization with Karhunen–Loève and polynomial chaos via Bayesian approach

Abstract

Field measured data reflect real response of soil slopes under rainfall infiltration and can provide representative estimates of in situ soil properties. In this study, an efficient probabilistic back analysis method for characterization of spatial variability of soil properties is used to investigate the effects of field responses with various monitoring schemes on characterization of spatial variability in unsaturated soil slope. A hypothetical heterogeneous slope of spatially varied saturated hydraulic conductivity subjecting to steady-state rainfall infiltration is analyzed as a numerical example. The spatially varied soil saturated hydraulic conductivity is parameterized by the Karhunen–Loeve expansion (KLE) with a given covariance. The random variables corresponding to the truncated KLE terms are considered as variables to be estimated with Bayesian inverse method. Synthetic pore water pressure data corrupted with artificial noise are utilized as measurement data. Nine schemes with various locations, spacings and depths of monitoring sections are discussed. The results show that the local variability can be reduced substantially around the monitoring points of pore pressure. The spatial variability can be estimated more accurately with a smaller spacing of measurement points. When measurement points are installed with a spacing of 16.5 m, the posterior average COV of ks field is around 2% and the RMSE of the MAP field is only 5.90 × 10− 7 m/s. For schemes with different depths, the RMSEs of the MAP field does not change much but the posterior uncertainty of the estimated field is reduced with the increase of borehole depth.