Document Type

Journal Article

Publication Title

Coastal Engineering




School of Engineering




This is an author's accepted manuscript of: Etemad-Shahidi, A., Bali, M., & van Gent, M. R. A. (2021). On the toe stability of rubble mound structures. Coastal Engineering, 164, article 103835.


Toe design is an important task for coastal engineers as it ensures the stability of the main armor layer and prevents scour in front of the armor slope. Several laboratory experiments have been conducted to investigate the toe stability using different testing approaches, i.e. damage due to a single test condition and cumulative damage due to a number of conditions. In addition, the methods of measuring and reporting damage to the toe are not the same as some researchers have counted only stones that were washed away from the toe; while others counted all the stones that have been displaced. Several formulas with different levels of success have been developed based on these studies. However, the scatter in the results is large and effects of some parameters are disregarded. The aims of this study are (a) to briefly review the abovementioned differences and exiting formulas, and (b) to develop a and physically sound formula for common design conditions, which considers the effect of all governing parameters. To achieve this, first a comprehensive data base from existing reliable studies was collected. Then nondimensional parameters which capture effects of governing parameters such as wave height, wave period, water depth, toe depth, toe width and foreshore slopes were deployed to develop a stability formula using physical reasoning and regression analysis. The new formula outperforms existing formulae for toe stability. The coefficient of variation of the formula was also determined to be used for probabilistic design applications. Finally, some design hints are provided for practitioners.



Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.