Semi-analytical solution of pore-water pressure in unsaturated ground and infinite slope considering highly nonlinear soil hydraulic properties

A multi-exponential function (ME) is proposed to depict the highly nonlinear soil water retention curve and hydraulic conductivity function. Then, semi-analytical solution of pore-water pressure in an unsaturated infinite slope at steady state is derived using ME to depict soil hydraulic properties. The solution is verified with experimental and numerical results. It is found that ME can better describe the highly nonlinear hydraulic properties of soil than the single exponential function (SE), which is commonly-used previously. At steady state, the adoption of SE results in overestimating negative pore-water pressure (PWP; i.e., matric suction) by about 25 kPa and slope's factor of safety (FOS) by 100% under rainfall, but underestimating negative PWP by about 50 kPa under evaporation. The difference between PWP and FOS calculated by using SE and ME becomes more significant for soil with bimodal hydraulic conductivity function than that with unimodal one. This difference reduces at a larger slope angle and deeper depth. Moreover, this difference generally increases at a lower SME/ SSE, where SME and SSE represent the suction at which the unsaturated hydraulic conductivity expressed by ME and SE equals the applied rainfall intensity or evaporation rate, respectively. When SME/SSE is greater than 0.1, the difference basically diminishes.