The recent advances of numerical beach profile models allowed the simulation of on/offshore sandbar migrations on timescales of weeks to months with fair success. These models were systematically applied to natural, persistently evolving, beaches. In this contribution, we apply our model to small-scale laboratory experiments for which coarse and lightweight sediment is used to satisfy the laws of similitude in the flume. Such experiments can result in equilibrium beach profiles and provide detailed information on the respective role of undertow and wave nonlinearities on sediment transport and the resulting cross-shore sandbar migration. Here we first apply the coupled, wave-averaged, cross-shore waves-currents-bathymetric evolution model 1DBeach to an equilibrium beach profile. The model simulates an equilibrium beach profile with reasonable success. Yet, when applying the best fit parameters to a subsequent rapid onshore sandbar migration, the model fails in reproducing the overall beach profile evolution. Further model calibration on the evolving beach profile sequence shows that the model can actually reproduce the rapid onshore sandbar migration with a significant contribution of acceleration skewness. This suggests that a number of misspecifications of the physics remain in coupled, wave-averaged, cross-shore waves-currents-bathymetric evolution model. In addition, given that best-fit model free parameters are of the same order of magnitude of those found on natural beaches, our study suggests that small-scale experiments with coarse and lightweight sediment can be used to further explore the respective contribution of wave nonlinearities and undertow to sediment transport and the overall beach profile evolution