The objective of this study was to investigate the spatial relationship between the most likely distribution of saturated hydraulic conductivity (Ks) and the observed pressure head (P) distribution within a hillslope. The cross-correlation analysis method was used to investigate the effects of the variance of lnKs, spatial structure anisotropy of lnKs, and vertical infiltration flux (q) on P at some selected locations within the hillslope. The cross-correlation analysis shows that, in the unsaturated region with a uniform flux boundary, the dominant correlation between P and Ks is negative and mainly occurs around the observation location of P. A relatively high P value is located in a relatively low Ks zone, while a relatively low P value is located in a relatively high Ks zone. Generally speaking, P is positively correlated with q/Ks at the same location in the unsaturated region. In the saturated region, the spatial distribution of Ks can significantly affect the position and shape of the phreatic surface. We therefore conclude that heterogeneity can cause some parts of the hillslope to be sensitive to external hydraulic stimuli (e.g., rainfall and reservoir level change), and other parts of the hillslope to be insensitive. This is crucial to explaining why slopes with similar geometries would show different responses to the same hydraulic stimuli, which is significant to hillslope stability analysis

Analysis of the stability of slopes in fractured rock masses is not trivial and is fraught with uncertainty and risk. A DFN-DEC model (Discrete Fracture Network-Distinct Element Code) based on the MATLAB platform is developed to evaluate the stability of rock slopes with random fractures. Then, the influences of mean values of geometric characteristics (i.e., the trace length T, the dip D, and the spacing S) for both the horizontal (denoted with 1) and inclined (denoted with 2) fractures on the mean slope stability are investigated. The results indicate that the proposed DFN-DEC model based on the MATLAB platform is adequate, robust, and can generate more realistic fracture networks. By means of probabilistic analysis (i.e., Monte Carlo simulation), we can obtain a more accurate stability assessment result of fractured rock slopes. In addition, it is found that the ${\mu }_{Fs}$ (the mean of Fs) of slopes decreases with the increase in ${\mu }_{T_1}$, ${\mu }_{T_2}$ (the mean trace length of horizontal and inclined fractures, respectively) and ${\mu }_{D_1}$ (the mean dip of horizontal fractures), and increases gradually with the increase in ${\mu }_{D_2}$ (the mean dip of inclined fractures), ${\mu }_{S_1}$ and ${\mu }_{S_2}$ (the mean spacing of horizontal and inclined fractures, respectively). Furthermore, the geometric characteristics related to inclined fractures have a much greater influence on ${\mu }_{FS}$ than that related to horizontal fractures. This study can be well applied in engineering practice, e.g., preliminary evaluation of the slope stability according to the statistics of fracture geometric characteristics.