Maximum Admissible Multi-Row Vegetation Spacing for Reducing Hydraulic Erosion Potential Under Overland Flow: Experimental and Theoretical Modelling

Vegetation distribution is important for regulating overland-flow hydraulics and reducing hydraulic erosion potential on slopes. However, quantitative procedures for determining the maximum admissible spacing of multi-row vegetation under specified soil and design rainfall conditions remain limited. This study combined fixed-bed flume experiments with a theoretical hydraulic model to determine the lateral and downslope vegetation spacings required to maintain the predicted overland-flow velocity below the critical velocity for soil-particle initiation. A total of 120 runoff tests were conducted at a slope gradient of 15° under eight flow discharges (0.3–1.0 L/s) and three vegetation configurations: single-row vegetation with varying lateral spacing b, multi-row vegetation with varying b at d = 0.030 m, and multi-row vegetation with varying downslope spacing d at b = 0.010 m. Flow depth and discharge were measured, and the cross-sectional mean velocity was calculated to evaluate the Reynolds number Re, Froude number Fr, and local resistance coefficient ξ. The measured Re and Fr ranged from 475 to 1770 and from 0.83 to 2.06, respectively, indicating laminar-to-transitional regimes based on Re and predominantly supercritical flow states based on Fr, with limited subcritical and critical cases. Increasing b, d, or Q generally reduced ξ, whereas multi-row vegetation produced greater flow resistance than single-row vegetation. At each Q level, the ξ–b and ξ–d relationships followed power functions with R2 ≥ 0.73. An improved local resistance formulation incorporating b, d, Re, and Fr was developed and evaluated using 129 measured data points, yielding R2 values of 0.77–0.90. The proposed model was further combined with SCS-CN runoff estimates and a critical initiation velocity criterion for five soil types characterized by mean particle diameter and particle density and five 1-h design rainfall depths of 25–125 mm. Model-derived vegetation-spacing estimates were obtained for 18 of the 25 soil–rainfall scenarios, and denser vegetation distributions were generally required as the design rainfall depth increased. These results provide experimentally informed, model-based guidance for estimating multi-row vegetation spacing under specified soil and rainfall conditions. The proposed relationships and spacing estimates are condition-specific to the fixed-bed experiments with artificial emergent vegetation at a slope gradient of 15° and to the investigated hydraulic and geometric ranges. They should not be interpreted as universal design criteria or direct predictions of field soil erosion; application beyond these conditions requires further calibration and validation.