Contents lists available at ScienceDirect Applied Ocean Research journal homepage: www.elsevier.com/locate/apor Assessing shipping water vertical loads on a fixed structure by convolution model and wet dam-break tests Jassiel V. Hernández-Fontes 1, ⁎ , Marcelo A. Vitola, Paulo de Tarso T. Esperança, Sergio H. Sphaier LabOceano (Ocean Technology Laboratory), Ocean Engineering Program, COPPE, Federal University of Rio de Janeiro, Parque Tecnológico do Rio, 21941-907, Rio de Janeiro, RJ, Brazil ARTICLE INFO Keywords: Convolution model Force balance Shipping water Systematic experiments Vertical loads Wet dam-break ABSTRACT Estimation of loads derived from shipping water events in naval and offshore structures is of importance to improve their structural design or to predict changes in their dynamics. For the case of vertical loads on deck of a fixed structure, it is possible to estimate analytically their evolution in time by considering the distribution of shipping water elevations. However, the classical approach to estimate this distribution (i.e., dam-break method) tends to overestimate the amount of water on deck and does not follow the generated decay trends observed experimentally. In the present work, the time evolution of the vertical loads due to shipping water events was studied analytically and experimentally. The validation of the use of a convolution model to estimate the time evolution of vertical loads is presented, aiming to improve the results obtained with classical approaches. A systematic experimental study has been conducted using the wet dam-break method to generate isolated ship- ping water events, measuring the slow-varying vertical loads on a rectangular fixed structure. A force balance and a high-speed camera have been used at the same sampling rate to monitor the vertical loads and the shipping water evolution on the deck. Results demonstrated that the use of the convolution model improved the re- presentation of the time series of loads compared with the traditional dam-break approach. With this new method, it was possible to capture the peaks and the decay tendencies observed in the experimental data in an approximated way. 1. Introduction Loading generated on structures due to water interacting with their decks has been of main concern in several research areas, regarding the study of ships [1–4],offshore [5–9] and coastal [10–14] structures. In the naval/offshore field, the analytical estimation of the shipping water vertical loads has relevance for projects that aim to improve the design and performance of structures [8]. Moreover, it is of significant importance in time-domain simulation analyses, including ship-motions [15] and control [16] applications. The vertical loading on deck of a structure due to a shipping water event can be described as an initial slamming (impact) force, followed by a slow-varying force [6]. The former occurs during a very short time because accounts for a sudden transfer of momentum from the incident wave to the structure, whereas the latter occurs during a longer time due to the shipping water propagation (wave inundation) stage. There are several engineering approaches, designed specially for fixed structures, that allow practical estimations of global water-on- deck loads, which consider characteristics of the incident wave that inundates the deck (e.g., water particle velocities) for their assessment [8]. However, when the knowledge of time evolution of vertical loads on deck is required, these approaches may not be useful. Thus, an al- ternative is to use the evolution of the water elevations over the deck to estimate time series of vertical loads analytically. The variation of the momentum of the mass of water over the deck can be used to do it, as proposed by [5,7]. The momentum method allows including the load contributions due to the vertical motion of the structure and to the static water head, being applicable to fixed or moving structures. To apply the momentum method, the knowledge of the shipping water evolution, or time series of water elevations at several positions over the deck, is required. The traditional approach to estimate the shipping water elevations on deck is the use of the analytical dam-break model of Ritter or Stoker [17,18,1,19]. However, this kind of solution tends to over-predict the real amount of water onto the deck [19,20], which may result in the overestimation of the vertical loads. Also, this model does not capture https://doi.org/10.1016/j.apor.2018.10.022 Received 10 April 2018; Received in revised form 15 September 2018; Accepted 29 October 2018 ⁎ Corresponding author. E-mail addresses: jassiel@oceanica.ufrj.br, jassiel.hernandez@gmail.com (J.V. Hernández-Fontes). 1 Currently a Research Associate at the Department of Hydraulics, Engineering Institute (II-UNAM), Universidad Nacional Autónoma de México. Applied Ocean Research 82 (2019) 63–73 0141-1187/ © 2018 Elsevier Ltd. All rights reserved. T