Evaluating and modeling rill detachment and resistance in different rates and particle sizes of biochar application on the Loess Plateau of China

The application of biochar can modify soil physicochemical properties, thereby influencing soil detachment capacity (D_c), rill erodibility (K_r) and critical shear stress (τ_c). However, the effects of biochar particle size on D_c, K_r and τ_c remain unexplored. This research investigated how apple branch-derived biochar with different biochar particle sizes and rates affects D_c, K_r, τ_c, and quantified their relationships with soil physicochemical properties through field experiment. Undisturbed soil samples were collected from field plots treated with biochar at 0 %, 1 %, 2.5 %, and 4 %, and particle sizes of 2–1, 1–0.5, and <0.5 mm for 3 months, using steel rings to a depth of 20 cm. The D_c, K_r, and τ_c of these samples were evaluated using a flume experiment, where soil samples were subjected to two flow discharge rates (0.25 and 0.65 L s⁻¹) and three slope gradients (17.63 %, 26.79 %, and 40.40 %). The results revealed that biochar application significantly reduced D_c and K_r, with the most pronounced reductions observed at the 4 % biochar rate (65 % and 174 %, respectively). Larger biochar particles (2–1 mm) were more effective in reducing D_c (64 %) and K_r (61 %) compared to smaller sizes. The total porosity (TP), cohesion (COH), mean weight diameter of soil aggregates (MWD) and soil organic carbon (SOC) were identified as critical factors influencing D_c and K_r. Power function equations effectively estimated D_c and K_r based on TP, COH, MWD and SOC under different biochar application rates. Similarly, the D_c and K_r were well predicted using power function equations incorporating SOC, soil crust hardness (SH) and >0.25 mm water-stable soil aggregate (SWA) under varying biochar particle sizes. These findings demonstrate that higher biochar application rates and larger particle sizes significantly enhance soil erosion resistance in loess soils, offering a promising strategy to mitigate rill erosion in degraded or degrading sloping farmlands on the Loess Plateau.