FRACTAL DERIVATIVE MODEL OF WATER ANOMALOUS ADSORPTION IN SWELLING SOIL¹⁾

In this paper the fractal derivative model of water adsorption in swelling soil was constructed based on the material coordinates, which correlates the moisture content with the spatial position. The cumulative adsorption of water in swelling soil was also derived. The cumulative adsorption in swelling soil underlying the fractal derivative model is a function of the fractal derivative of time and the diffusion coefficient. The fractal derivative order can be used to classify the adsorption process and to characterize the heterogeneity of soil. The feasibility of the fractal derivative model is verified by analyzing the experimental data of the water cumulative adsorption in the black soil and sand, and the proposed model exhibits higher accuracy than the traditional integer order model.