Quantification of the hydraulic diffusivity of a bentonite-sand mixture using the water head decrease measured upon sudden flow interruption

This paper presents a new modelling approach to quantify the hydraulic diffusivity of low-permeability unconsolidated porous media under confined saturated-flow conditions in the laboratory. The derived analytical solution for the transient variation of the hydraulic head after flow interruption was applied to experimental data obtained from continuous measurements of the water pressure at two locations in the soil column. Three soil samples made of a mixture of natural bentonite (at different mass fractions) and medium sand were studied during a series of stepwise constant flow rates of water. The numerical results well fit the experimentally measured decrease of the dimensionless hydraulic head. The study shows that the increase of the mass fraction of bentonite in the soil sample from 10 to 30% is accompanied by a strong decrease of the hydraulic diffusivity from 2.4 × 10⁻² to 1.1 × 10⁻³ m² s⁻¹, which is clearly due to the decrease of the hydraulic conductivity of the soil sample. The specific storages obtained for each of the three samples are in the same order of magnitude and seem to decrease with the increase of mass fraction of bentonite. However, they clearly reflect the predominant portion of the compressibility of the porous medium compared with that of water. Compared with reported literature values for clayey soils, the specific storage values in this study are slightly higher, varying within the range of 2 × 10⁻³ to 8.1 × 10⁻³ m⁻¹._. The experimental results also give insight into the limitations of the modelling approach. In the case of low-permeability soils (K < 2 × 10⁻⁶ ms⁻¹) and steady-flow conditions with low Reynolds numbers, for example, Re < 0.003, it is recommended to choose a time duration for flow interruption between subsequent flow rate steps of longer than 5 s. For high-permeability porous media, to increase the precision of the quantified hydraulic diffusivity, it might be useful to select a measuring frequency significantly higher than 1 Hz.