Using the Richards’ equation of saturated-unsaturated seepage

the commercial Multiphysics finite element software COMSOL is adopted to deduce the governing equations of two boundary conditions with the pore water pressure as the control variable for the infiltration and seepage (overflow) boundary conditions in the rainfall infiltration problem of slope. Based on the two-dimensional soil column model and the published models

the value of the boundary coupling length scale L in the governing equation is discussed

and L equal to 0.001 m is found reasonable. A simple two-dimensional slope model is then established

and the governing equations of the above boundary conditions are applied to analyze the infiltration and seepage law of rainfall with different intensities (long and weak

short and strong). The results show that when the rainfall intensity is 4 mm/h

the actual infiltration rate is always equal to the rainfall intensity

and the water content of the surface soil has increased from 0.29 to 0.35. When the surface seepage has occurred for 75 h at the foot of the slope

the total infiltration of the study area at 200 h is 39.068 m3; when the rainfall intensity is 40 mm/h

the actual infiltration rate first equals the rainfall intensity

and then gradually decreases

and the water content of the surface soil increases from 0.29 to 0.415 (saturated). When the surface seepage has occurred for 4 h at the foot of the slope

the total infiltration of study area at 20 h is 26.908 m3

which is far less than the former. This conclusion is consistent with the existing rainfall infiltration law in slope

which further proves the reliability of the above boundary condition governing equations that provides a feasible method for the boundary condition problem in finite element analysis of rainfall in slope.