Secondary consolidation of clay as an anomalous diffusion process

Secondary consolidation of clay soil is considered as a result of anomalous diffusion of pore water pressure from the micropores to the macropores. By using simplified pore geometry, a heuristic approach allows us to infer the expression of the associated rate of vertical secondary deformation written as a fractional derivative of the pore pressure. The insertion of this expression into the 1D Terzaghi's theory leads to a particular type of time‐fractional diffusion equation of the pore pressure that is solved semi‐analytically. The advantage of such theoretical approach stems from the concise and compact way of treating the secondary consolidation. Only two additional parameters are needed: the fractional order, ν, and the fractional viscosity factor, θ, both accounting for the physicochemical interactions between pore fluid and clay particles. This theoretical approach is tested on experimental data obtained from the Cubzac‐les‐Ponts clay soil intensively studied for secondary consolidation. This application shows a good agreement between the data and the predicted values confirming the interest of the initial assumption and the use of the fractional derivatives formalism. Moreover, good correlations between the inverted fractional parameters and the empirical secondary consolidation index C_α measured independently are obtained: the fractional order ν, if experimentally calibrated, can be used as a reasonable estimator of the slope of the secondary consolidation portion of consolidation curve. Copyright © 2014 John Wiley & Sons, Ltd.