The saturated hydraulic conductivity is inherently variable. An extension infiltration model considering the variability of saturated hydraulic conductivity is established using the classic Green-Ampt model; and then the corresponding depth of the wetting front and the distribution of water content are determined. Meanwhile

a closed form of the limit state function is presented

based on the combination of the extension of the Green-Ampt model and the infinite slope stability model. Random number sequences of saturated hydraulic conductivity are generated following a lognormal distribution using the Monte Carlo simulation method. For a hypothetical slope that is subjected to steady-state rainfall infiltration

a series of parameter analyses is conducted. The results show that the cases with a smaller coefficient of variability have a smaller failure probability in the initial stage of rainfall infiltration. However

as rainfall progresses

the cases with a smaller coefficient of variability have a larger probability of failure instead. The most likely failure time of the slope is not affected by the coefficient of variability

but depends on the intensity of rainfall. The corresponding probability of the most likely failure time decreases with the increase of the variability.