On the stability of rock armored rubble mound structures

Document Type

Journal Article

Publication Title

Coastal Engineering


Elsevier B.V.


School of Engineering




Etemad-Shahidi, A., Bali, M., & van Gent, M. R. (2020). On the stability of rock armored rubble mound structures. Coastal Engineering, 158, Article 103655. https://doi.org/10.1016/j.coastaleng.2020.103655


Estimation of the required armor size is a major task in the design of coastal structures under wave loading such as breakwaters and revetments. Several semi-empirical formulas have been developed for this purpose. However, these formulas are often either limited to certain water depth conditions or do not incorporate the permeability of the structure in an appropriate way. The main objectives of this study are to (a) develop a unified physically sound formula for the estimation of the required rock size in all relevant water depth conditions and (b) to relate the effects of the permeability of the structure directly to physical parameters. To achieve these, first a comprehensive data base of deep and shallow water experiments within the design conditions was built. Then physical reasoning along with a robust data mining approach, i.e. M5 model tree, were used to develop formulas for armor stability. In the stability formula, wave characteristics such as the significant wave height and spectral energy mean period (Tm-1,0) are invoked while the permeability is incorporated using the ratio between the size of the core material and the armor stones. Accuracy metrics such as discrepancy ratio and scatter index indicated high performance of the model in different conditions. Finally, a probabilistic formula and some guidelines are provided for practicing engineers. © 2020 Elsevier B.V.



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