Dimensional analysis of pore-water pressure response in a vegetated infinite slope

Pore-water pressure (PWP) induced by root water uptake has usually been investigated by individual physical quantities. Limited dimensional analysis has been available for investigating PWP response in a vegetated slope. In this study, dimensional analysis was conducted to explore dimensionless numbers controlling PWP distributions in a vegetated slope. Three dimensionless numbers governing unsaturated seepage were proposed, including capillary effect number (CN, describing the relative importance of water flow driven by PWP gradient over that driven by gravity), root water uptake number (RN, representing the effects of root water uptake), and water transfer-storage ratio (WR, ratio of water transfer to water storage rate). Dimensionless relationships were further proposed to estimate PWP and root influence zone in a vegetated slope. Then analytical parametric studies were conducted to study effects of RN, CN, and WR on PWP distributions. Thereafter, the proposed relationships were validated by published field and centrifuge tests. During the drying period, the effects of root water uptake on PWP and the root influence zone become more significant as CN decreases or RN increases. During the wetting period, the larger the WR, the deeper the wetting front moves and more reduction of negative PWP occurs. The proposed dimensionless relationships can determine PWP and the root influence zone in a vegetated soil reasonably well.