Probabilistic Analysis of Highly Nonlinear Models by Adaptive Sparse Polynomial Chaos: Transient Infiltration in Unsaturated Soil

Abstract

Polynomial chaos expansion (PCE) is widely adopted in geotechnical engineering as a surrogate model for probabilistic analysis. However, the traditional low-order PCE may be unfeasible for unsaturated transient-state models due to the high nonlinearity. In this study, a temporal-spatial surrogate model of adaptive sparse polynomial chaos expansions (AS-PCE) is established based on hyperbolic truncation with stepwise regression as surrogate models to improve computational efficiency. The uncertainty of pore water pressure of an unsaturated slope under transient-state rainfall infiltration considering hydraulic spatial variability is studied. The saturated coefficient of permeability [Formula: see text] is chosen to be spatial variability to account for the soil hydraulic uncertainty. The effects of location and time and the performances of AS-PCE are investigated. As rainfall goes on, the range of the pore pressure head becomes larger and the spatial variability of [Formula: see text] has little influence in the unsaturated zone with high matric suction. The pore pressure head under the water table suffers more uncertainty than it in the unsaturated zone. The [Formula: see text] in the high matric suction zone has a trend of rising first and then falling. Except for the high matric suction zone, the [Formula: see text] rise over time and they are almost 1 at the end of the time. It can be concluded that the AS-PCE performs better for low matric suction and positive pore pressure head and the fitting effect gradually increases as the rainfall progresses. The quartiles and at least up to second statistical moments can be characterized by the AS-PCE for transient infiltration in unsaturated soil slopes under rainfall.