Generally

reliability analyscs of landslide stability under rainfall infiltration only consider the spatial variability of calculated parameters of soil materials

while the influence of non-uniform distribution of initial water is ignored. To solve this problem

the governing equation for Green-Ampt infiltration model with arbitrary distribution of initial water content under different rainfall conditions is derived

and a variable-step compound Simpson method is used to solve the governing equation for exploring the functional relation between wetting front depth and rainfall duration with different spatial distribution of initial water content. Then

the time-varying probability of landslide during the process of rainfall infiltration is calculated using multidimensional normal cumulative distribution function (Mvncdf). Finally

an actual case is used for verification through comparative analysis. The results show that different spatial distribution of initial water content has a significant impact on the time-varying reliability of landslide stability under rainfall conditions. Compared with the uniform and trapezoidal distribution of initial water content

the exponential distribution has the smallest decrease rate of time-varying reliability for landslide stability under the same rainfall condition. The improved model is feasible for arbitrary distribution of initial water content of soil

which is conducive to the universal application of Green-Ampt model in landslide stability evaluation.