A new fractal model for nonlinear seepage of saturated clay considering the initial hydraulic gradient of microscopic seepage channels

It is crucial to investigate nonlinear seepage phenomena in low-permeability soils. Currently, empirical formulas account for the majority of nonlinear seepage model formulations. Some theoretical prediction models have been proposed; however, they tend to be computationally complex, and their predictive performance must be enhanced. Considered an indirect indicator, the soil–water characteristic curve reflects the permeation channels of soil pores of varying diameters. A nonlinear seepage model for saturated clay has been devised, taking into account the initial hydraulic gradient of microscopic seepage channels. This paper derives and solves the fractal dimension of the soil–water characteristic curve fractal model and establishes a new nonlinear seepage fractal model for saturated clay under various hydraulic gradients. The new seepage fractal model proposed in this paper is used to predict the seepage velocity of saturated Hunan clay under various hydraulic gradients and is compared to the results of its nonlinear seepage test. Overall, the results indicate that the predicted values of the seepage fractal model presented in this paper closely match the experimental values, and the accuracy of the prediction of the seepage velocity of saturated clay with a higher dry density exceeds that of present theoretical models.