Revista de Gestão Costeira Integrada
Volume 10, Número 4, Dezembro 2010, Páginas 397-417

DOI: 10.5894/rgci227
* Submissão – 5 Agosto 2010; Avaliação – 20 Outubro 2010; Recepção da versão revista – 12 Novembro 2010; Disponibilização on-line – 6 Janeiro 2011

Estudo do Galgamento de Estruturas Marítimas utilizando um Modelo Numérico baseado na Teoria da Onda em Condições de Água pouco Profunda *

Numerical Modelling of Wave Overtopping of Maritime Structures using a NLSW Equation Model

Maria Teresa Reis ^{@, 1}, Maria da Graça Neves ¹

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@ Autor correspondente
1 LNEC – Laboratório Nacional de Engenharia Civil, Av. do Brasil 101, 1700-066, Lisboa. E-mails: Teresa Reis - [email protected]; Graça Neves - [email protected]

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RESUMO
Apresenta-se neste artigo o modelo numérico AMAZON, baseado na teoria da onda em condições de água pouco profunda. Na sua versão original, o modelo estava essencialmente desenvolvido para estruturas impermeáveis. Desde 2007, o Laboratório Nacional de Engenharia Civil (LNEC), em colaboração com o Dr. Keming Hu (Royal Haskoning, UK), tem vindo a desenvolver o modelo de forma a permitir modelar explicitamente o escoamento em meios porosos e a proceder à sua validação sistemática para o estudo do galgamento de estruturas marítimas porosas. Os modelos deste tipo existentes têm sido validados essencialmente para estruturas impermeáveis e para praias permeáveis. Para simular o escoamento em meios porosos, foram implementadas no modelo as equações de Darcy e de Forchheimer.
São apresentados dois casos de aplicação do modelo, utilizando a equação de Darcy, para o estudo do galgamento de estruturas de protecção portuária e a validação dos seus resultados por comparação com dados de ensaios em modelo físico reduzido bidimensional realizados no LNEC. O primeiro caso de estudo corresponde a uma solução alternativa proposta para a reabilitação do enraizamento do molhe Sul do porto de pesca da Póvoa de Varzim, trecho sobre o qual recai a maior exigência de eficácia relativamente aos galgamentos. O perfil-tipo proposto consiste num quebra-mar de estrutura mista com manto de enrocamento. O segundo caso de estudo corresponde a duas soluções alternativas propostas para a reabilitação final do molhe Oeste do Porto de Sines, que em 1978/79 sofreu estragos muito avultados. Dos três postos de acostagem existentes neste molhe, apenas dois se encontram em funcionamento actualmente (postos 2 e 3). A reabilitação final visa reactivar o posto 1 e melhorar as condições de abrigo e a operacionalidade do porto. Os perfis-tipo propostos para esta reabilitação consistem num quebra-mar de taludes com manto composto por cubos Antifer.
Os resultados obtidos são bastante satisfatórios, embora o modelo apresente uma ligeira tendência para prever por excesso os caudais obtidos nos ensaios: os valores do cociente entre os caudais médios de galgamento obtidos com a nova versão do AMAZON, qAM, e com o modelo físico, qMF, variam entre 0.9 e 1.4 para o quebra-mar com manto de enrocamento e entre 1.0 e 1.76 para o quebra-mar com manto composto por blocos artificiais. Os resultados mostram ainda que os valores de qAM são mais sensíveis ao valor da velocidade máxima que o escoamento de água pode ter durante a transferência entre a camada porosa e a camada superficial, do que à escolha da condutividade hidráulica e da porosidade.
Com o objectivo de se dispor no futuro duma ferramenta numérica eficiente para estudos de engenharia costeira e portuária, é necessário ainda: validar o modelo para diferentes geometrias de estruturas marítimas, diferentes características do seu meio poroso e diferentes escalas do modelo; investir na optimização da discretização da malha de cálculo; e implementar alguns desenvolvimentos que incluem, entre outros, o acoplamento entre o AMAZON e um modelo de propagação da agitação marítima desde o largo até à estrutura galgada e a paralelização do código.

Palavras-chave: Estruturas marítimas; galgamentos; modelos numéricos; teoria da onda em condições de água pouco profunda; escoamento em meios porosos.

ABSTRACT
This paper presents the numerical model AMAZON, based on the nonlinear shallow water (NLSW) equations. The original version of AMAZON did not explicitly account for porous flow; it was developed basically for impermeable structures. Since 2007, the National Civil Engineering Laboratory (LNEC), Portugal, in collaboration with Dr. Keming Hu (Royal Haskoning, UK), has been developing the porous flow model to allow the numerical simulation of wave overtopping of porous maritime structures and its systematic validation for these structures. The existing NLSW models have mainly been validated for impermeable structures and for permeable beaches. The development includes the addition of one porous layer to the original model design and the porosity is taken as constant for the whole porous element. To govern the water exchange between the porous cells, both the Darcy equation (valid for laminar stationary flows) and the Forchheimer equation (valid for turbulent stationary flows) are implemented in AMAZON. Unlike some other NLSW models, the maximum velocity that the flow can have during the exchange of water between the porous and the free-flow layers has been included as an input to AMAZON.
The paper illustrates AMAZON’s application, using Darcy’s equation, to study the mean wave overtopping discharge at two porous breakwaters that protect Portuguese harbours and the validation of its results by comparison with two-dimensional physical model data collected at LNEC. The first case study is of a proposed cross-section for the rehabilitation of the root of the South breakwater of Póvoa de Varzim harbour. The root of this breakwater directly protects the local Nautical Club building and, therefore, it is the stretch for which overtopping should be minimal. The proposed cross-section is basically a composite structure, with double layer rock armour. The second case study refers to two proposed solutions for the final rehabilitation of the West breakwater of Sines harbour, which suffered serious damage to the armour layer and superstructure in 1978/79. At present, only two of the three oil tanker berths are in operation: berth 2 and berth 3. The final rehabilitation has the primary objective of reactivating berth 1 (for reception, loading and unloading of oil tankers) but it also aims to generally improve the shelter and operating conditions within the port. The cross-sections proposed for this rehabilitation are basically rubble-mound breakwaters protected by Antifer cubes.
The AMAZON results are quite satisfactory, although the model tends to slightly over-predict the discharges: the ratio between the mean overtopping discharges obtained with the new version of AMAZON, qAM, and with the physical model, qMF, varies between 0.9 and 1.4 for the rock structure and between 1.0 and 1.76 for the Antifer structure. The results also show that the values of qAM are more sensitive to the value of the maximum velocity that the flow can have during the exchange of water between the porous and the free-flow layers than to the choice of the hydraulic conductivity and of the constant porosity.
The results are rather promising, given the different approximations made for modelling the porous breakwaters (such as using the Darcy equation instead of the Forchheimer equation to govern the internal flow and employing only one porous layer to represent multi-layered structures) and AMAZON’s inherent restrictions (mainly relating to the shallow water assumptions and the simulation of wave breaking). Nevertheless, to develop a user-friendly numerical model that may be used in real case studies of overtopping of porous structures and that provides a good compromise between computational effort and accuracy in terms of overtopping results, it is necessary to: further test the model, employing different structural configurations, different arrangements of rock or concrete armour blocks and different scales (to consider the implications of using two different governing equations for flow within the porous layer); analyse the grid optimization; and implement some developments of AMAZON, which are expected to include coupling AMAZON with a wave transformation model to propagate the waves to the AMAZON seaward boundary and code parallelization.

Keywords: Maritime structures; wave overtopping; numerical models; non-linear shallow water (NLSW) equations; porous flow.

 

Besley, P. (1999) - Overtopping of Seawalls: Design and Assessment Manual. 130p., Environment Agency, R&D Technical Report W178, Bristol, UKReino Unido. (ISBN: 1-85705-069-X).

CIRIA/CUR/CETMEF (2007) - The Rock Manual: The Use of Rock in Hydraulic Engineering (2nd edition). 1304p., CIRIA C683, Londres, Reino Unido. (ISBN: 978-0-86017-683-1)

Clarke, S.; Dodd, N., Damgaard, J. (2004) - Modelling flow in and above a porous beach. Journal of Waterway, Port, Coastal, and Ocean Engineering, 130(5):223-233. (ISSN: 0733-950X).
http://dx.doi.org/10.1061/(ASCE)0733-950X(2004)130:5(223)

CONSULMAR (2008) - Reconstrução e Activação do Posto 1 do Porto de Sines. Reabilitação do Molhe Oeste. Projecto de Execução. 124p., Lisboa, Portugal. (não publicado).

CONSULMAR (2006) - Reconstrução e Activação do Posto 1 do Molhe Oeste do Porto de Sines. Estudo Prévio. 86p., Lisboa, Portugal. (não publicado)

Dalrymple, R.A.; Rogers, B.D. (2006) - Numerical modeling of water waves with the SPH method. Coastal Engineering, 53(2-3): 141-147. (ISSN: 0378-3839). http://dx.doi.org/10.1016/j.coastaleng.2005.10.004

Didier, E.; Neves, M.G. (2009) - Wave overtopping of a typical coastal structure of the Portuguese coast using a SPH model. Journal of Coastal Research, Special Issue 56:496-500. (ISSN: 0749-0208)

Dodd, N. (1998) - Numerical model of wave run-up, overtopping and regeneration. Journal of Waterway, Port, Coastal, and Ocean Engineering, 124(2):73-81. (ISSN: 0733-950X). http://dx.doi.org/
10.1061/(ASCE)0733-950X(1998)124:2(73)

García, R.G. (2007) - Análisis de la Funcionalidad y Estabilidad de Obras Marítimas Mediante un Modelo Numérico Basado en las Ecuaciones de Reynolds. 266p., Ph.D. thesis, University of Cantabria, Espanha.

Harten, A.; Lax, P.D.; Van Leer, B. (1983) - On upstream differencing and Godunov type schemes for hyperbolic conservation laws. SIAM
Review, 25(1):35-61. (ISSN: 0036-1445). http://dx.doi.org/
10.1137/1025002

Hu, K. (2000) - High-Resolution Finite Volume Methods for Hydraulic Flow Modelling. 194p., PhD Thesis, Centre for Mathematical Modelling and Flow Analysis, Manchester Metropolitan University, Manchester, Reino Unido.

Hu, K.; Meyer, D. (2005) - The validity of the non-linear shallow water equations for modelling wave runup and reflection. Proc. ICE Coastlines, Structures & Breakwaters ‘05, 195-206, Thomas Telford, Londres, Reino Unido.

Hu, K.; Mingham, C.G.; Causon, D.M. (2000) - Numerical simulation of wave overtopping of coastal structures using the non-linear shallow water equations. Coastal Engineering, 41(4):433-465. (ISSN: 0378-3839). http://dx.doi.org/10.1016/S0378-3839(00)00040-5

Ingram, D.; Causon, D.; Mingham, C.; Zhou, J.G. (2002) - Numerical simulation of violent wave overtopping. In: J.M. Smith (ed.), Proc. 28th International Conference on Coastal Engineering (ICCE), 2286-2298, World Scientific, Singapore.

Ingram, D.M.; Causon, D.M.; Gao, F.; Mingham, C.G.; Troch, P.; Li, T.; De Rouck, J. (2004) - Free Surface Numerical Modelling of Wave Interactions with Coastal Structures. 53p., CLASH WP5 Report, Manchester Metropolitan University and University of Gent, Manchester, Reino Unido.
http://www.clash.ugent.be/results/D27numericalmodelling.pdf

Lemos, R.; Reis, M.T.; Silva, L.G. (2006) - Scale Model Tests of the South Breakwater Root of Póvoa de Varzim Harbour: Overtopping Two-Dimensional Tests. 70p., Relatório 05/06-NPE, LNEC, Lisboa, Portugal. (não publicado)

Lemos, R.; Silva, L.G. (2008) - Ensaios em Modelo Reduzido da Reconstrução do Molhe Oeste do Porto de Sines. 91p., Relatório 141/2008-NPE, LNEC, Lisboa, Portugal. (não publicado)

Lin, P.; Liu, P.L.-F. (1998) - A numerical study of breaking waves in the surf zone. Journal of Fluid Mechanics, 359:239-264. (ISSN: 0022-1120).
http://dx.doi.org/10.1017/S002211209700846X

Losada, I.J.; Lara, J.L.; Guanche, R.; Gonzalez-Ondina, J.M. (2008) - Numerical analysis of wave overtopping of rubble mound breakwaters. Coastal Engineering, 55(1):47-62. (ISSN: 0378-3839).
http://dx.doi.org/10.1016/j.coastaleng.2007.06.003

Mansard, E.P.D.; Funke, E.R. (1980) - The measurement of incident and reflected spectra using a least squares method. In: B.L. Edge (ed.), Proc. 17th International Conference on Coastal Engineering (ICCE), 154-172, ASCE, Nova Iorque, Estados Unidos da América. 1981

Neves, M.G.; Reis, M.T.; Didier, E. (2010) - Comparisons of wave overtopping at coastal structures calculated with AMAZON, COBRAS-UC and SPHYSICS. Proc. ECCOMAS CFD 2010, V European Conference on Computational Fluid Dynamics, 14 a 17 de Junho, LNEC, Lisboa, Portugal. (CD-Rom).

Neves, M.G.; Reis, M.T.; Losada, I.; Hu, K. (2008) - Wave overtopping of Póvoa de Varzim breakwater: physical and numerical simulations. Journal of Waterway, Port, Coastal, and Ocean Engineering, 134(4):226-236. (ISSN: 0733-950X). http://dx.doi.org/10.1061/
(ASCE)0733-950X(2008)134:4(226)

Pullen, T.; Allsop, N.W.H. (2003) - Use of Numerical Models of Wave Overtopping: A Summary of Current Understanding. http://www.hrwallingford.co.uk/downloads/ projects/overtopping/
num_model _guidance.pdf.

Reis, M.T.; Hu, K.; Hedges, T.S.; Mase, H. (2008a) - A comparison of empirical, semi-empirical and numerical wave overtopping models. Journal of Coastal Research, 24(2B):250-262. (ISSN: 0749-0208). http://dx.doi.org/10.2112/05-0592.1

Reis, M.T.; Hu, K.; Neves, M.G.; Hedges, T.S. (2008b) - Numerical modelling of breakwater overtopping using a NLSW equation model with a porous layer. Proc. 31st International Conference on Coastal Engineering (ICCE), 3097-3109, World Scientific, Singapore.

Reis, M.T.; Neves, M.G.; Hedges, T.S. (2008c) - Investigating the lengths of scale model tests to determine mean wave overtopping discharges. Coastal Engineering Journal, 50(4):441-462. (ISSN: 0578-5634). http://dx.doi.org/10.1142/S057856340800182X

Reis, M.T.; Neves, M.G.; Hu, K. (2009a) - Wave overtopping of a porous structure: numerical and physical modeling. Journal of Coastal Research,
SI 56(II):539-543. (ISSN: 0749-0208)

Reis, M.T.; Neves, M.G.; Hu, K.; Lopes, M.R.; Silva, L.G. (2009b) - Final rehabilitation of Sines west breakwater: physical and numerical modelling of overtopping. In: W. Allsop (ed.), Proc. ICE Coasts, Marine Structures and Breakwaters 2009, 636-647, Thomas Telford, Londres, Reino Unido. (ISBN: 978-0-7277-4131-8)

Van Albada, G.D., Van Leer, B. & Roberts, W.W. Jr. (1982) - A comparative study of computational methods in cosmic gas dynamics. Astronomy and Astrophysics, 108:76-84. (ISSN: 0004-6361).

Van Gent, M.R.A. (1994) - The modelling of wave action on and in coastal structures. Coastal Engineering, 22:311-339. (ISSN: 0378-3839)
http://dx.doi.org/10.1016/0378-3839(94)90041-8

Van Gent, M.R.A. (1996) - Numerical modeling of wave interaction with dynamically stable structures. Proc. 25th International Conference on Coastal Engineering (ICCE), 1930-1943, Orlando, Florida, Estados Unidos da América.

Van Gent, M.R.A.; Pozueta, B.; Van den Boogaard, H.F.P.; Medina, J.R. (2005) - D42 Final Report on Generic Prediction Method. 33p.,
CLASH WP8 Report. Delft, Holanda. http://www.clash.ugent.be/results/
D42finalreportgenericpredictionmethod.pdf

Van Leer, B. (1979) - Towards the ultimate conservative difference scheme. V. A second order sequel to Godunov’s method. Journal of Computational Physics, 32(1):101-136. (ISSN: 0021-9991). http://dx.doi.org/10.1016/0021-9991(79)90145-1

 

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