New Green-Ampt model based on fractional derivative and its application in 3D slope stability analysis

The infiltration process in slopes is an essential issue in geotechnical engineering. A new Green-Ampt model for describing the two-stage infiltration in slopes based on fractional derivatives was proposed in this paper. The Green and Ampt (1911)'s model, and Chen and Young (2006)'s model are two special cases of the proposed model. A 1D loess soil column test in the literature as well as a laboratory rainfall test of loess slope were used to validate the proposed model. The travel curve of wetting front obtained by the proposed model was obviously closer to the actual test value than that obtained by the Chen and Young's model, indicating that the performance of the proposed model is superior to the Chen and Young's model due to the use of fractional derivatives. The proposed Green-Ampt model was combined with a rigorous 3D limit equilibrium method to obtain the real-time safety factor of the slope during rainfall. The calculated failure time of the loess slope by the proposed method is close to the actual failure time of the laboratory test, while the corresponding of Chen and Young's model is obviously shorter than the actual status. Six parameters are included in the proposed model, and sensitivity analysis shows that the fractional derivative has the most significant impact on the wetting front depth, followed by the permeability coefficient, moisture content difference, suction head, rainfall intensity, and slope angle.

Automated summary

A new Green-Ampt model based on fractional derivatives was proposed in this paper to describe the two-stage infiltration in slopes, showing superior performance compared to traditional models. The proposed model combined with a rigorous 3D limit equilibrium method can provide real-time safety factors of slopes during rainfall, with sensitivity analysis identifying the significant impacts of different parameters on the model.