Sampling schemes for hillslope hydrologic processes and stability analysis based on cross-correlation analysis

Cost-effective sampling strategies to understand hydrologic processes in a hillslope are essential to the estimation of hillslope seepage and to the evaluation of slope stability. The objectives of this paper are (a) to introduce a stochastic cross-correlation analysis to hillslope hydrologic processes and stability investigation and (b) to develop a cost-effective sampling strategy to reduce the pore-water pressure uncertainty at the region of our interest. The concept of stochastic representation of spatial variabilities of soil hydraulic properties is introduced first. We then develop a first-order analysis method to determine spatiotemporal distribution of pore-water pressure head (P) variance (unconditional variance or uncertainty) due to spatial variability of saturated hydraulic conductivity (Ks) in a variably saturated hillslope during rainfall. Subsequently, a cross-correlation analysis is presented, which quantifies the spatial correlation between P at a given location and Ks at any part of a hillslope under a transient infiltration event. We afterward formulate a first-order approximation of residual P variance (conditional variance or uncertainty) due to inclusions of Ks measurements. The developed methodology is applied to synthetic, heterogeneous, two-dimensional hillslopes to investigate the effectiveness of several Ks sampling schemes. Results of this investigation show that boreholes and sampling locations should be placed at an interval of one correlation scale. They should be distributed over an area covering several correlation scales, rather than clustered together at the largest cross-correlation region or at regions where prediction uncertainty is large (where our interest and concern are). Further, the results demonstrate that increasing the sampling density is useful but inefficient. Layering structures of hillslopes reduce the number of boreholes and samples required. At last, a cost-effective sampling strategy for study of slope stability based on cross-correlation is suggested, which minimizes the prediction uncertainty of P at critical locations.