Secondary consolidation of clay as an anomalous diffusion process

Abstract

International audienceSecondary 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, nu, and the fractional viscosity factor theta, 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-alpha measured independently are obtained: the fractional order nu, if experimentally calibrated, can be used as a reasonable estimator of the slope of the secondary consolidation portion of consolidation curve

Cam-Clay plasticity, Part VIII: A constitutive framework for porous materials with evolving internal structure

“…Several investigators have argued that secondary compression in clays can be attributed in part to delayed dissipation of excess pore pressures in the micropores of multiple porosity media [25,57,58]. Considering that many main is 0.1 m wide and 1.0 m tall, and discretized into 20 quadrilateral mixed elements with biquadratic displacement interpolation of displacement and bilinear interpolation of the macropore and micropore pressures.…”

A new simplified Hypothesis B method for calculating consolidation settlements of double soil layers exhibiting creep

“…Recently, researchers have undertaken some efforts to the double porosity model for two scales of porosity in the soil fabric structure. Cosenza and Korošak presented a heuristic approach that adopts two additional parameters of fractional order and fractional viscosity factor, to consider the ‘secondary consolidation’ of clayey soil as a result of pore water pressure diffusion from micro‐ to macro‐pores. Borja and Choo developed a framework of soil constitutive model to consider the pore water pressure dissipation in the macro‐ and micro‐scale, and used this model to simulate the ‘secondary compression’ in one‐dimensional (1D) consolidation, which agrees well with the experimental data.…”

Numerical simulations of the reuse of piled raft foundations in clay

“…By contrast, secondary consolidation is compression at constant effective stress, the underlying mechanisms of which remain very much open to question and the subject of numerous recent investigations. Two main hypotheses for the cause of the delayed compression associated with secondary consolidation have featured in the literature: (1) sliding of microparticles relative to each other inducing changes in microstresses and vice versa [54]; (2) drainage from micropores after macropores have experienced dissipation of pore pressure [3,6,13,47]. The latter theory is based on evidence that two different scales of porosity exist in many natural geomaterials, relating to (1) intra-aggregate micropores and (2) inter-aggregate macropores, e.g.…”