Two‐Dimensional Probabilistic Infiltration Analysis in a Hillslope Using First‐Order Moment Approach

Abstract

A first-order moment analysis method is introduced to evaluate the pore-water pressure variability within a hillslope due to spatial variability in saturated hydraulic conductivity (K ) during rainfall. The influences of the variance of the natural logarithm of K (ln K ), spatial structure anisotropy of ln K , and normalized vertical infiltration flux (q) on the evaluations of the pore-water pressure uncertainty are investigated. Results indicate different responses of pressure head variability in the unsaturated region and the saturated region. In the unsaturated region, a larger variance of ln K , a higher spatial structure anisotropy, and a smaller q lead to a larger variability in pressure head, while in the saturated region, the variability in pressure head increases with the increase of variance of ln K , the decrease of spatial structure anisotropy, or the increase of q. These variables have great impacts on the range of fluctuation of the phreatic surface within the hillslope. The influences of these three variables on the variance of pressure head within the saturated region are greater than those within the unsaturated region, and the variance of ln K has the greatest impact. These results yield useful insight into the effects of heterogeneity on pressure head and uncertainty associated with predicted flow field.

Groundwater Responses of Foundation Subjected to Water Level Fluctuation of Reservoir Considering Variability of Layered Structure

“…The boundary AD is also defined as impermeable to represent distal end when the influence from the reservoir water level fluctuation is neglected. The boundary CD is defined as seepage faces [19], which varies from the Neumann boundaries with constant q in the unsaturated state to boundaries with zero pressure head in the saturated state. This takes into account both the possible rainfall and immersion, though they are not the focus of this study.…”

“…Since the variability in the layered structure of the foundation results in variation in the groundwater responses of the foundation, the uncertainty in groundwater flow should be estimated for a reliable analysis. Substituting the statistics in Table 2 into the first-order moment approach [17][18][19] yields the standard deviation of p, denoted as σ p , at each location of the foundation, representing the distribution of the uncertainty of p in the foundation. The σ p fields of foundation subjected to reservoir water level fluctuation at t = 3 days for the six cases are shown in Figure 7.…”