Laboratory investigation of beach scarp and dune recession due to notching and subsequent failure

Analytical models to calculate notch development and subsequent mass failure of dunes are presented. The notch evolution model is based on a transport equation for sediment from the dune and the sediment volume conservation equation, whereas the models of mass failure are derived using elementary engineering statics and soil mechanics. An empirical transport coefficient in the model describing the notch growth rate is found to be related to the hydrodynamic forcing at the dune normalized by geotechnical parameters describing the resistive strength of the dune. Two modes of mass failure are modeled whereby the overhang generated by the removal of material from the dune foot (notching) slides downward or topples over following the development of a tensile crack some distance shoreward of the maximum notch depth. The accuracy of the notch evolution and mass failure models are assessed by comparing calculated recession distances against measurements from a small-scale laboratory experiment.