Material coordinate driven time-space scaled models for anomalous water absorption in swelling soils

Abstract

Anomalous water absorption in soils usually causes changes in the volume, structure and related properties of soils, especially in swelling soils. In this paper, time and space scaled models based on the fractal derivatives are introduced in the diffusion equation in the material coordinate to characterize the anomalous absorption of water in swelling soils, and to derive solutions for both cumulative absorption and absorption rates. Interestingly, the cumulative absorptions given by the fractal and fractional derivative models in terms of the material coordinate are the same. The fractal derivative model provides a different physical mechanism compared with the fractional derivative model. The differences and unity of the time and space fractal derivative models are verified by using the experimental data of water absorption in no tillage-soil and Xerochrept soil.