Transient stochastic analysis on influence of hydraulic heterogeneity on drainage in soils

Abstract: Water draining and redistribution from soil profiles is important for both ecological and hydrological modeling. In reality, the vertical hydraulic conductivity is highly variable because of the heterogeneity of soil. Therefore, the objectives of this study were 1) to conduct the stochastic analysis of a one-dimensional transient drainage problem under a unit gradient assumption; 2) to quantify the influence of uncertainty of the hydraulic conductivity using the perturbation method and kinematic wave model; and 3) to verify the stochastic analysis and the analytical solution. Field experiments were carried out at 2 experimental sites (site A: 57°05'57'' N, 111°38'54'' W and site B: 56°56'36'' N, 111°31'57'' W) in the north of Fort McMurray, northeastern Alberta, Canada. A double-ring infiltrometer consisted of 2 metal rings with the inner ring diameter of 60 cm and the outer ring diameter of 120 cm was used to measure soil infiltration and drainage. In addition, soil water content was determined by EnviroSCAN probe (EnviroSCAN, Sentek Pty Ltd., South Australia). The parameters in Brooks-Corey model for homogeneous soil (site A) and heterogeneous soil (site B) were obtained from the particle size distribution (PSD) data. The results showed that the saturated water content (θs) of site A and site B were 0.483 and 0.415 cm3/cm3, respectively. The PSD index expected value of site A and site B were 3 and 4.09, respectively. The saturated hydraulic conductivity of site A and site B were 937 and 3 049 cm/d, respectively. The water draining process was slowly decreased when the variance of hydraulic conductivity was increased from 0 to 0.5. There was the same relative water storage when the saturated hydraulic conductivity of site A and site B were 1 691.56 and 3 049 cm/d, respectively; and the variance of hydraulic conductivity were 0 and 0.5, respectively. The relative water storage difference among heterogeneous soil was remarkable when the time was more than 9.6 hours, and the trend was that at long time limit, the larger the soil water storage capacity should be. The draining of water was sensitive to the variance of hydraulic conductivity, but it was less sensitive to the fluctuation of PSD index, as well as to the covariance of hydraulic conductivity and PSD index. The larger the heterogeneity of soil hydraulic conductivity was, the smaller the effective saturated hydraulic conductivity was. The introduction of heterogeneities would slow down the draining and increase the water storage ability. Taking the heterogeneous characteristic into account, the site B had larger water storage capacity than the site A when time was more than 4.8 hours. However, the 2 sites had nearly the same water storage ability after 12 hours, when no stochastic characteristic in parameters of Brooks-Corey model was considered, such as soil hydraulic conductivity and PSD index. Two field experiments were in agreement with the theoretical predictions. The ratio of the variance and the expected value operator of hydraulic conductivity were 0.11 and 0.58 for site A and site B, respectively. The heterogeneous site B would hinder the draining of water and increase the water storage ability, which was also coincident with the theoretical prediction. The variance of hydraulic conductivity would cause the slowing down of the drainage process and thus result in a smaller effective saturated hydraulic conductivity. In conclusion, we could improve the water storage ability of soil by introducing heterogeneity in soil structure or particle size distribution. The analytical result agreed with the experimental observation, which hinted that making soil heterogeneous would be better for improving the water storage ability. This study is useful for soil reclamation whose objective is to produce a long-term self-sustaining ecosystem with high field capacity.