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The influence of slope gradient on interrill erosion processes is a key scientific problem in the decision-making process regarding soil erosion control in Loess Plateau. The relationship of time to runoff (RT), flow velocity (V), runoff rate (RR) and interrill erosion rate (IER) with slope gradient was investigated to derive accurate experimental model to evaluate and quantify the influence of slopes on interrill erosion processes. The experimental soil was collected from Ansai County of Shaanxi Province, China. The average diameter of the test soil was 0.041 mm. The experiment was conducted at slopes of 8.74%, 17.62%, 26.78%, 36.38%, 46.6%, 57.70% and 69.97% under I of 90, 120 and 150 mm h−1, respectively, using indoor simulated rainfall. Time to runoff, flow velocity, runoff rate and interrill erosion rate were measured for each combination. Results showed that the time to runoff decreased as a linear function with increasing slope gradient. Slope gradient was a good predictor of time to runoff for different rainfall intensities with NSE from 0.90 to 0.97 and MSE from 0.1 to 0.25 and R2 from 0.90 to 0.97. The flow velocity increased as a power function with increasing slope gradients. Slope gradient was a good predictor of flow velocity for different rainfall intensities with NSE from 0.91 to 0.93 and MSE from 0.01 to 0.015 and R2 from 0.95 to 0.98. The runoff rate increased as a power function with increasing slope gradients. Slope gradient was a good predictor of runoff rate for different rainfall intensities with NSE from 0.90 to 0.95 and MSE from 0.000000024 to 0.000000044 and R2 from 0.94 to 0.97. The interrill erosion rate increased as a power function with increasing slope gradients. Slope gradient was a good predictor of interrill erosion rate for different rainfall intensities with NSE from 0.98 to 0.99 and MSE from 0.00022 to 0.00055 and R2 from 0.98 to 0.99. By performing the controlled simulated rainfall experiments, this study showed that slopes strongly influenced interrill erosion processes for different rainfall intensities.

Additional file 1: Figure S1. Results of plasma protein indexes and blood ion levels during the administration. Compared with vehicle control group ***: P < 0.001; **: P < 0.01; *: P < 0.05. Figure S2. Results of blood chemistry after the oral administration of TAZF. Compared with vehicle control group, ***: P < 0.001; **: P < 0.01; *: P < 0.05. Figure S3. Microphotographs of liver, kidney and lung in control group and high-dose group. No obvious toxic change was found. Each figure is a representative photomicrograph from a rat in each group. Figure S4. Microphotographs of brain and digestive tract in control group and high-dose group. No obvious toxic change was found. Each figure is a representative photomicrograph from a rat in each group. Figure S5. Mean plasma concentration profiles of components in rat plasma after 1-day and 28-day oral administration of TAZF. Table S1. OCs of lung, spleen and heart in male rats during (n = 10) and after (n = 6) administration. Table S2. OCs of lung, spleen and heart in female rats during (n = 10) and after (n = 6) administration. Table S3. Results of hematological examination in male rats during (n = 10) and after (n = 6) administration. Table S4. Results of haematological examination in female rats during (n = 10) and after (n = 6) administration. Table S5. Linearity and linear range of the components. Table S6. Results of sensitivity and recovery. Table S7. Pharmacokinetic parameters of 6 components on the first and 28th day treated day in male rats. Table S8. Pharmacokinetic parameters of 6 components on the first and 28th day treated day in female rats.