Slope-dependent erosion control by rock fragments: experiments and model improvements

• Rock fragment effectiveness in erosion control decreases exponentially with slope. • The coefficient b is quantified as a continuous function of slope gradient. • Slope shifts erosive force to runoff, weakening rock fragment erosion control. • A slope-dependent C-factor model is developed to enhance erosion prediction. Slope gradient and surface cover are key factors controlling soil erosion, but how their interaction influences the erosion control effectiveness of rock fragments remains unclear. In the commonly used exponential function that describes this effect ( C = a·exp(−b·R c ) ), the coefficient b determines the rate at which soil loss decreases with rock fragment coverage, but how b varies with slope is largely unknown. To address this, rainfall simulation experiments were conducted under 30 combinations of slope gradients (8.7%∼70.0%) and rock fragment coverage levels (0%∼80%) to investigate the slope-dependent erosion control by rock fragments. The results showed that rock fragment coverage and slope gradient had significant interactive effects on runoff and sediment concentration. Runoff and sediment concentration generally decreased with increasing coverage, while at steep slope and low coverage, the reduction efficiency was significantly weakened or even reversed. Soil loss rate exhibited a consistent exponential decline with increasing coverage across all slope gradients. However, the rate of this decline, represented by the coefficient b , systematically decreased from 0.0102 at slope 8.7% to 0.0032 at slope 70.0%. Further curve fitting revealed a significant exponential relationship between b and slope gradient. This study systematically quantifies the control of slope gradient on the erosion-reducing effectiveness of rock fragments and develops a slope-dependent formulation for the coefficient b . These findings provide a clear parameterization basis for improving the cover factor in existing soil erosion prediction models and help enhance the accuracy of erosion assessments in complex terrain regions.