Stability of cube armoured roundheads exposed to long crested and short crested waves Enrique G. Maciñeira a, ⁎, Hans F. Burcharth b a Water and Environment Research Group, University of A Coruña, Campus de Elviña s/n, 15071 A Coruña, Spain b Department of Civil Engineering, Aalborg University, Sofiendalsvej 11, 9000 Aalborg, Denmark abstract article info Article history: Received 4 September 2015 Received in revised form 18 February 2016 Accepted 7 March 2016 Available online 11 April 2016 The paper presents an update of the stability formulae by Maciñeira and Burcharth (2007) for cube armoured roundheads exposed to long- and short-crested waves. Reanalysis of former model test results and supplemen- tary new model tests leads to a more precise set of formulae covering long-crested and short-crested waves. The formulae are valid for two layers of randomly placed cubes, ranges of head diameter, slope, cube mass density and wave steepness. © 2016 Elsevier B.V. All rights reserved. Keywords: Breakwater Roundhead Armour stability Cube Model test 1. Introduction Based on model tests with two layers of randomly placed concrete cubes exposed to long- and short-crested waves, Aalborg University (2003, 2004), two formulae for armour stability covering “large” and “small” radii were presented by Maciñeira and Burcharth (2007). How- ever, general criteria for the separation in large and small radii were not established. Since then more model tests were carried out at Aalborg University (2008) as part of the final design of the roundhead for the Langosteira main breakwater at La Coruña, Spain, see Burcharth et al. (2014). This made an update of the 2007 formulae possible. The updated formula predicts the cube armour stability in the most critical 45° sector of the roundhead. However, information of the armour stability in the other 45° sectors is given as well. The 2007 formulae were defined for two sizes of roundheads, termed “large” and “small”. The only parameter used to characterize the size of the roundhead was R n = R/D n , R being the head radius at SWL, and D n the side length of the cubes. This parameter signifies the number of armour units within a given sector, i.e. a 45° sector, and is rel- evant for the damage level in terms of the relative number of displaced units, D % . In the updated formula this parameter is supplemented by the following two physically relevant parameters R/L and R/H s representing the relative size of the head related to local wave conditions. L is the local wave length corresponding the wave peak period, and H s is the sig- nificant wave height of the local incident waves. The influence of R/L was already demonstrated by Vidal et al. (1989), Matsumi et al. (1994, 1996, 1998, 2000) and Comola et al. (2014). The influence of R/H s is demonstrated in the present paper. The performance of the new formulae was checked against addition- al model test data obtained in the laboratory at University of A Coruña (2014) in relation to a study of the stability in long-crested waves of the secondary breakwater for the Langosteira Port, model test data ob- tained in the laboratory at University of Cantabria presented by Lomónaco et al. (2009), and model test data obtained in the laboratory of the Spanish Department of Public Works (CEPYC) presented by Berenguer and Baonza (1999). Maciñeira and Burcharth (2008) demonstrated, as was concluded by Matsumi et al. (1994, 1996, 1998, 2000), that short-crested waves cause more damage than long-crested waves. However, the quantitative influ- ence of this parameter was not given. In the present research the influ- ence on armour stability of the short-crestedness combined with the other relevant parameters was studied and included in the updated formulae. More detailed information and results related to the various model test programmes on which the present analyses are based can be found in Aalborg University (2000, 2003, 2004, 2008), Maciñeira and Burcharth (2007, 2008), University of A Coruña (2014), Lomónaco et al. (2009), and Berenguer and Baonza (1999). Coastal Engineering 112 (2016) 99–112 ⁎ Corresponding author. E-mail addresses: emacine@puertocoruna.com, enrique.macineira@udc.com (E.G. Maciñeira), hansburcharth@gmail.com (H.F. Burcharth). http://dx.doi.org/10.1016/j.coastaleng.2016.03.002 0378-3839/© 2016 Elsevier B.V. All rights reserved. Contents lists available at ScienceDirect Coastal Engineering journal homepage: www.elsevier.com/locate/coastaleng