Fractional time-dependent Bingham model for muddy clay

In this short communication, based on fractional calculus, we present the fractional Bingham model which can describe the time dependent behavior in the fluid with yield strength. The pulling sphere tests under three different speed conditions are be used to investigate the time dependence of muddy clay. The experimental results illustrate the muddy clay is a noticeable time-dependent Bingham fluid. Experimental results show that the fractional Bingham model can well depict the mechanical behaviors of the muddy clay, and give a good agreement with the experimental data. In addition, this study also finds that the order of the fractional Bingham model is larger than 1 in some cases, which breaks the commonly used assumption that the order should be in the interval [0,1]. (C) 2012 Elsevier B.V. All rights reserved.