Stiffness of mooring lines and performance of floating breakwater in three dimensions Eva Loukogeorgaki * , Demos C. Angelides Division of Hydraulics and Environmental Engineering, Department of Civil Engineering, Aristotle University of Thessaloniki, University Campus, Thessaloniki 54124, Greece Received 10 June 2005; received in revised form 1 December 2005; accepted 16 December 2005 Available online 10 March 2006 Abstract In the present paper, the performance of a moored floating breakwater under the action of normal incident waves is investigated in the frequency domain. A three-dimensional hydrodynamic model of the floating body is coupled with a static and dynamic model of the mooring lines, using an iterative procedure. The stiffness coefficients of the mooring lines in six degrees of freedom of the floating breakwater are derived based on the differential changes of mooring lines’ tensions caused by the static motions of the floating body. The model of the moored floating system is compared with experimental and numerical results of other investigators. An extensive parametric study is performed to investigate the effect of different configurations (length of mooring lines and draft) on the performance of the moored floating breakwater. The draft of the floating breakwater is changed through the appropriate modification of mooring lines’ length. Numerical results demonstrate the effects of the wave characteristics and mooring lines’ conditions (slack-taut). The existence of ‘optimum’ configuration of the moored floating breakwater in terms of wave elevation coefficients and mooring lines’ forces is clearly demonstrated, through a decision framework. q 2006 Elsevier Ltd. All rights reserved. Keywords: Coastal engineering; Floating breakwater; Mooring lines; Stiffness; Damping; Effectiveness; Performance; Decision framework 1. Introduction Floating breakwaters present an alternative solution to conventional fixed breakwaters and can be effectively used in coastal areas with mild wave environment conditions. Poor foundation or deep-water conditions as well as environmental requirements, such as phenomena of intense shore erosion, water quality and aesthetic considerations advocate the application of such structures. Floating breakwaters have many advantages compared to the fixed ones, e.g. absence of negative environmental impacts, flexibility of future exten- sions, mobility and relocation ability, lower cost and ability of a short time transportation and installation. As a result of all these positive effects, many types of floating breakwaters have been developed as described by McCartney [17]. However, the most commonly used type of floating breakwaters is the one that consists of rectangular pontoons connected to each other and moored to the sea bottom with cables or chains. A moored floating breakwater should be properly designed in order to ensure effective reduction of the transmitted energy and, therefore, adequate protection of the area behind the floating system. This design objective is subjected to the following constraints: (a) non-failure of the mooring lines and (b) non-failure of the floaters themselves and their inter- connections. The satisfaction of the above design objective and the corresponding constraints represents the overall effective performance of a moored floating breakwater. A brief review of the design process for floating breakwaters and the related design criteria, with respect to wave effects is provided by Isaacson [7]. Isaacson and Baldwin [8] provide a review of the analysis of moored floating structures in currents and waves, with an emphasis on moored floating breakwaters. With regard to the hydrodynamic analysis of the floating body, linear two-dimensional models describing the complete hydrodynamic problem (diffraction and radiation) have been developed by Isaacson and Nwogu [11], Isaacson [6], Isaacson and Bhat [9], Williams and Abul-Azm [23], Bhat and Isaacson [2], Sannasiraj et al. [20], Williams et al. [24] and Lee and Cho [14]. Most of these models are based on the finite element method (FEM) or the boundary integral equation method (BIEM) utilizing Green’s theorem, while Lee and Cho [14] use the element-free Galerkin method. Isaacson and Nwogu [11] Applied Ocean Research 27 (2005) 187–208 www.elsevier.com/locate/apor 0141-1187/$ - see front matter q 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.apor.2005.12.002 * Corresponding author. Tel.: C30 2310 995877; fax: C30 2310 995740. E-mail address: eloukog@civil.auth.gr (E. Loukogeorgaki).