Application of the Beta Probability Density Function for Representing Infiltration of Water-Repellent Soil

Abstract

Laboratory experiments were conducted to investigate the infiltration of water-repellent soil. The most suitable mathematical model to represent infiltration of water-repellent soil was investigated and water infiltration into this column was measured for both hydrophilic and water-repellent soils of the Guishui River Basin. The results showed a monotonous increase and decrease in cumulative infiltration and infiltration rate over time within the hydrophilic soil, respectively. In contrast, the results for water-repellent soil showed: (1) The existence of a turning point in cumulative infiltration above which the infiltration rate increased sharply, with higher initial soil moisture content resulting in an earlier and larger increase in the infiltration rate; (2) A larger stable infiltration rate after the peak compared to that before the peak, with the overall infiltration rate presenting a single peak curve if the beginning of rapid infiltration is ignored. The applicability of the Kostiakov, segmented Kostiakov, Gaussian, segmented Gaussian, Beta and segmented Beta function infiltration models were analysed for the two soil types. The numerical analysis indicated that: (3) The Kostiakov and Beta function models showed better applicability for both hydrophilic and water-repellent soils; (4) For water-repellent soil, the Gaussian function infiltration model not only represented the monotonous decrease in infiltration rate, but also demonstrated a steady infiltration rate during the initial stage and a gradual increase and decrease in infiltration rate pre- and post-peak, respectively. Similarly, the Beta function model was able to represent the monotonous decrease in infiltration rate, and the segmented Beta function represented the U-shaped change in rapid infiltration before the threshold as well as the gradual increase and right-skewed distribution curve of infiltration pre- and post-turning point in water-repellent soil. The Beta function model achieved the highest simulation accuracy and showed the widest applicability.