A Model Coupled with Fractional-Derivative and Peridynamic Theory for Water Migration in Unsaturated Expansive Clay

Abstract Expansive clay exhibits multiple fissures and undergoes deterioration due to fluctuations in moisture levels. To guarantee the stability of earth structures built on expansive clay in semiarid regions, significant emphasis has been placed on studying the effects of water migration. This paper introduces an innovative method that utilizes a nonlocal model and peridynamic theory as substitutes for the temporal and spatial derivative terms. Based on spatial integration, the peridynamic formulation effectively captures the path dependency of water transport in unsaturated expansive clay, enabling an accurate representation of the diffusion process. Furthermore, the use of a fractional derivative accurately characterizes subdiffusion phenomena arising from the fractal nature of heterogeneous media. The accuracy of the model was further confirmed by analyzing the measured data collected from migration experiments conducted in a closed system, where different temperatures and water potential gradients were applied. The findings indicate that the proposed model effectively captures the process of water migration in unsaturated clay, offering valuable insights into understanding the patterns governing water movement in expansive clay under unsaturated conditions.