Backward erosion piping is an internal erosion process, which compromises the stability of water retaining structures such as dams and levees. In this paper, we propose a numerical solution that combines a 2D Darcy groundwater solution with Exner's 1D sediment transport mass conservation equation. As an estimate of sediment transport, we tested four different empirical transport equations for laminar flow. The model performance was evaluated based on the results of the real-scale IJkdijk experiment. Through this, we were able to demonstrate the applicability of existing sediment transport equations to the description of particle motion during piping erosion. The proposed transient piping model not only predicts the pipe progression in time, it also allows for an identification of pore pressure transitions due to the erosion process. A major conclusion of the study is that from the four different modeling approaches for laminar flow, it is recommended to follow the approach of Yalin et al. regarding the simulation of backward erosion piping for dike configurations similar to those of the IJkdijk experiment.