A physics-based approach for predicting time-dependent progression length of backward erosion piping

The progression length at various stages of backward erosion piping (BEP) in levee systems can serve as a key engineering demand parameter for reliability and risk assessments. The main goal of this study is to put forward a reliable and computationally efficient technique for predicting the progression length during BEP. Many existing modeling approaches for predicting progression lengths of BEP are either computationally expensive or consider a constant, time-independent amplification factor for the permeability coefficient. In contrast, the model developed here considers the underlying physical phenomena to properly capture the amplification of the permeability coefficient during the progression of BEP. The proposed model is derived considering the rolling threshold condition, which is obtained from the moment equilibrium of erodible particles. This modeling approach with time-varying permeability coefficients has been implemented in FLAC3D, and the derived BEP paths are validated for three flume experiments. The impact of material properties including porosity, tortuosity, and coefficient of uniformity on the amplification factor are investigated. These analyses show that the permeability amplification factor and the progression length increase with low rates at the initial stages of piping. Following the formation of the piping path, they both increase at a generally greater rate over time.