Rules-of-thumb for predicting air-entry value of disturbed sands from particle size

With the goal of finding empirical direct relationships between the air-entry values (AEV) and characteristic particle diameters (i.e., d ₁₀, d₂₀, d₃₀, d₉₀,) determined from the particle-size distribution, we examined the AEV values for a variety of disturbed sands. It was found that the AEVs were, in general, strongly correlated to the characteristic diameters. The correlation was more distinct for uniform sands with uniformity coefficient of 2 or smaller. For those with larger uniformity coefficient values, the AEVs were highly correlated to smaller characteristic particle sizes d₁₀ to d₅₀ but less with larger characteristic particle sizes, d₆₀ to d₉₀. For all the sands examined in this study, the AEVs showed the least scatter when plotted against d₃₀. The large particles do not necessarily control the AEVs because the pores between the large particles are often filled with smaller particles. The following best-fit power functions with respect to the frequently used characteristic particle diameters were found to have high r2 values; AEV = 8.2 d₃₀^-0.99and AEV =9.5 d₅₀ ^-1.05(with AEV in cm and d in mm). The exponent close to -1 in both relationships confirms a strong "inverse" proportionality. The effective pore diameter, d_e′, estimated from the AEVs agreed closely with the mean pore diameters measured with mercury porosimetry and X-ray micro-tomography. All these findings suggest that the AEVs are strongly controlled by the particle sizes which determine the mean pore size, and that the capillary rise theory is applicable in terms of the effective pore diameter. Finally, easy-toimplement rule-of-thumb expressions, AEV [cm] = 8/d ₃₀[mm] and AEV [cm] =10/d₅₀[mm] were proposed with some limitations for a quick but reasonably accurate prediction of the AEV.