Soil erosion, particularly water erosion and sediment yield, poses significant threats to both human and environmental well-being. This phenomenon, encompassing both surface and subsurface processes, is influenced by a complex interplay of natural factors and human activities. The present study aims to develop models for quantifying runoff and sediment yield as functions of time and slope under simulated scenarios of surface and pipe erosion in silty-loam soil. The laboratory experiments were performed at the slopes of 0 to 20%. The soil profile inside the reservoir consists of two layers, the bottom 5 cm of the soil bed as a water restrictive layer, and 15 cm of topsoil over the first layer. The experiments were performed in three design modes including pipe flow only at 27 \(\:{\text{l}\text{i}\text{t}\:\text{h}\text{r}}^{-1}\) (M1), rainfall intensity only at 30 \(\:{\text{m}\text{m}\:\text{h}\text{r}}^{-1}\) (M2), and a combination scenario of both rainfall and pipe flow (M3) while all of these experiments were repeated three times. Then, an optimization was used to fit a push curve and find the coefficients of the developed equations. Performance metrics including the coefficient of determination (R-squared), Nash–Sutcliffe efficiency, Root Mean Square Error-observed standard deviation Ratio, and Percent Bias were employed to evaluate the equation models. The results revealed a power-law relationship between sediment yield and runoff (independent variables) and slope and time (dependent variables) across all modes. Notably, the calculated RMSE-observation standard deviation ratio and Percent bias values for the runoff and sediment equations in all three modes fall below 0.5 and 15, respectively, indicating very good model performance. Additionally, the simulated runoff and sediment exhibit strong correlations with the observed values. Furthermore, considering the coefficient of determination values and the visual agreement between observed and simulated sediment data, the overall simulation can be considered highly reliable. Experiments of this nature hold significant potential to advance our understanding of piping erosion.
