OPTIMISING A BREAKWATER LAYOUT USING AN ITERATIVE ALGORITHM

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1 OPTIMISING A BREAKWATER LAYOUT USING AN ITERATIVE ALGORITM Michael Rutell R Wallingford / Univerity of Surrey Due to the remote and expoed coatal location of mot liquefied natural ga (LNG) exportation terminal, a breakwater i often required to reduce the wave energy at the veel berth. Bet practice and reearch technique for developing the cro-ection and izing armour tone are well etablihed however, little reearch exit for developing economical breakwater layout. Thi paper decribe the methodology behind a new piece of oftware which can be ued to quickly develop breakwater layout that imultaneouly minimie berth downtime and capital cot. Thi i achieved on the premie that for a given level downtime, there exit a correponding breakwater length. Thi allow the berth availability to be conidered a a function of the breakwater layout, which can therefore be olved through an iterative approach. A random wave tranformation model i ued to tranform the wave to, through and around the breakwater. The diffracted and tranmitted wave energie are ummed uing the root mean quare (RMS) approach before the effective wave i ued to determine whether the veel mooring threhold i exceeded. Performing thi for a time erie of wave give an indication of the percentage of downtime that will be incurred with thi breakwater layout. An Iterative earch i performed uing Brent algorithm to find the layout which offer the deired level of berth availability. Thi methodology i applied to a detached rubble-mound breakwater, though could eaily be tranpoed to a berm, caion or breakwater connecting to the hore. A cae tudy comparing thi approach to the reult of a front end engineering deign i ued to demontrate the effectivene of thi methodology in developing accurate breakwater layout in a very hort time-frame, highlighting that a imple approach can deliver accurate concept deign quickly. A lit of the notation ued in thi paper i included on page 11. Keyword: Breakwater, Concept Deign, Optimiation, Root-Finding, Wave Tranformation, Berthing 1. Introduction A more countrie are looking to capitalie on national ga reource through exportation, many new Liquefied Natural Ga (LNG) terminal are in development. LNG exportation terminal are often ituated in location where adequate natural protection i unavailable, therefore requiring an artificial breakwater to reduce wave condition at the berth to within acceptable limit (figure 1). The mot common type of breakwater ued in an LNG terminal i the rubble mound breakwater armoured with rock or concrete armour unit. Caion breakwater are ometime ued, although they only uually become cot effective in depth > 15m. Figure 1 - Breakwater Protecting two berthed LNG veel The breakwater i primarily ued to reduce wave energy tranmitting through the core, diffracting around the breakwater and overtopping the breakwater. In typical circumtance, overtopping only occur when wave condition approach deign condition, although wave 1

2 energy will be tranmitted through the core and around the breakwater on a continual bai and i therefore of paramount importance when developing a layout. Rubble mound breakwater are flexible tructure. Their deign i baed on the concept of tolerable damage and acceptable diplacement of armour tone. Careful conideration mut be given to frequent and extreme event a the former affect the wave climate behind the tructure and the latter affect afety (BSI, 1999). A wave diffract around the breakwater, they loe a ignificant amount of energy. owever, wave energy reaching the berth may till be above acceptable limit. In a typical berthing tudy, a target level of downtime may be 5% which give a berth availability of 95%. The percentage of time that the wave climate in the breakwater hadow i below acceptable limit i ued a the criteria to find a uitable length of the breakwater Concept Deign of a Breakwater The conceptual deign tage of any engineering project i arguably the mot important a up to 80% of the project reource are committed and a time progree, change become harder and more expenive to implement (Kicinger et al., 2005) (figure 2). It i eential that good deciion are made in the early deign tage a thee have great influence on the final deign. Regarding the deign of a breakwater, there are two major apect. The firt i the deign of the croection, and the econd i deigning the hape of it footprint. Deign of the cro-ection (figure 3) i a welletablihed field of practice, the foundation of which involve calculating the cret height which i uually deigned to limit the volume of overtopping dicharge; electing the front and rear lope angle and (uually a teep a poible to minimie material volume) and determining the cret width which i largely determined by uage factor uch a whether the pipe tretle will be built on the cret or vehicular acce i required. A common approach to determining the armour ize of a breakwater i to ue the deign wave which i a ingle value wave height (often or 1/10 ) which ha a low probability of exceedence during the deign life (BSI, 1999; Goda, 2010). Wave period, direction, pectral energy and whether the wave are breaking i alo important; longer period wave tranmit more energy through the breakwater (CIRIA and CUR, 2007) which may require wider core to reduce tranmitted energy. The rock armour ize i typically calculated uing van der Meer lope tability formulae for rock armour (van der Meer, 1988), or uing udon tability formula (udon, 1958) for concrete armour unit uch a Accropode. The ize of the armour ha only a minimal effect on the berthing condition, more important are the cro-ectional dimenion. B R c front rear Figure 3 Breakwater cro-ection howing main variable Figure 2 - Cot and Eae of Change over Time Initial breakwater layout concept are often baed on engineering judgement in order to obtain an 2

3 approximate breakwater layout, length and ultimately cot. Figure 4 how two breakwater layout with wave diffracting around the breakwater roundhead to a pecified location (the veel berth). The breakwater on the left provide a higher level of protection a the angle of diffraction i maller than that of the one on the right, although it will alo cot more to contruct. Judging the right length i a primary concern for the engineer. an equation. Thi allow a breakwater layout to be generated, wave condition to be tranformed to the berth imulating the effect of hoaling, refraction, diffraction and tranmiion where the veel mooring threhold i teted. Performing thi for a time erie allow an etimation of the percentage of berth availability to be made and the breakwater length i either increaed or decreaed until the breakwater layout providing the deired level of berth availability i found. Thi method i fat and more accurate than uing judgement alone and can be automated to tet multiple berth location and layout. Figure 4 Two breakwater offering more (left) and le protection (right) to the pecified point. Numerical and phyical modelling i often ued during the latter deign tage to optimie a deign, although thee technique are not appropriate for the conceptual deign tage a everal concept may be in development a thee modelling technique are expenive and timeconuming. When performing a concept layout dek tudy, common practice i to review wave table of the propoed location and create a deign wave which i often ued in conjunction with tool uch a Goda random wave diffraction diagram (Goda and Takayama et al., 1978). Through thi approach, an indication of the length of breakwater can be calculated, although thi i baed on a ingle or few wave which ummarie potentially decade of wave data and i therefore le accurate than conidering the entire time erie. 1.2 Aim of thi Paper Thi paper outline a method for developing detached breakwater layout concept uing a imple oftware model. The model integrate random wave tranformation and veel mooring imulation model within a mathematical algorithm ued to find the root of Note: Root-finding in thi context i a mathematical term where an iterative algorithm i ued to olve f(x) = y, not the root of the breakwater where the breakwater meet the hore. 2. Wave Tranformation In mot cae, wave data will not exit exactly where the engineering work i propoed; wind or wave data i often only available from offhore urvey buoy. Thi mean that the procee of wave refraction, hoaling and diffraction mut be imulated to provide wave condition at the breakwater. Refraction i the bending of water wave due to variation in celerity acro the wave cret; hoaling i the increae in wave height proportional to the decreae in wave celerity occurring a the wave enter hallower water and diffraction i the bending of wave a they pa an object. Although the random nature of ea wave wa undertood by ome engineer in the early 20 th century, it wan t until the 1950, that theorie tarted to emerge. Sea wave can be analyed a an infinite pectrum of maller wave of varying height, frequencie and direction, mot pronounced around the peak value (Goda, 2010). Thi i often repreented a a directional wave pectrum when deigning for wave. 3

4 2.1. Refraction Fat and accurate wave height prediction conidering the wave pectrum can be made with Goda and Suzuki method (Goda and Suzuki, 1975) where: ( ) ( ) ( ) ( ) In which: i the repreentative value of total wave energy, ( ) ( ) ( ) and i the combined directional pectral denity function and directional preading function Shoaling A nonlinear, random wave nearhore hoaling theory wa publihed by Shuto (1974) uing the Bretchneider- Mituyau pectrum and ha been expreed in term of the hoaling coefficient by Goda (1975) which i ued in thi tudy to imulate hoaling of random wave employing the following equation: 3. Optimiation Technique Many optimiation routine make ue of evolutionary baed algorithm uch a genetic algorithm (GA ). Elchahal et al. (2013) ued a genetic algorithm to optimie the hape of a detached breakwater within a port. Thi i an intereting approach though the algorithm took over 13 hour to run and optimal deign were often quite unrealitic and would likely have been redeigned by the contractor for a more cot optimal olution highlighting the importance of olid concept deign Root-Finding Algorithm Root-finder are a cla of algorithm which iteratively etimate a value of x until ( ) i found. Figure 5 how a function y=f(x) where the root can clearly be een a y = 0. Root-finder are imple to implement and have been ued uccefully for millennia. K K i h L L ' Diffraction Penney and Price (1952) publihed a eminal trancript on a methodology for calculating the diffraction coefficient for monochromatic wave due to interaction with a emi-infinite breakwater. In 1962, Weigel publihed the o-called Weigel Diagram for calculating wave diffraction. Goda et al. (1978) developed random wave diffraction diagram uing the Bretchneider-Mituyau pectrum. Krau (1984) publihed an approximation for random wave diffraction baed on Goda method which can be calculated without integral; thi i implemented in thi tudy: ( ) [ ] Where: and i in radian. Figure 5 - Graph of f(x) = 0 The firt root-finding algorithm i thought of to be the Secant Method ~2300BC which ue a ucceion of root of ecant line to find an approximation of ( ). The Secant Method only work in elect circumtance which limit it generic applicability. The Newton- Rhapon Method i a Method for approximating ( ) where the function i iteratively divided by it derivative until an acceptably accurate root i found. Though the algorithm i fat, the Newton-Rhapon Method occaionally fail to converge making it le uitable. A more robut method i the Biection Method where a 4

5 poitive ( ) and negative ( ) etimate of ( ) i made and the error i computed. The interval between a Create breakwater contour ( ) and ( ) i then halved iteratively until the approximation i found. Though robut, the Biection Firt ide Method i often low to converge, epecially in comparion to the Newton-Rhapon Method. Another Length etimate important method i the Invere Quadratic Interpolation algorithm. Thi algorithm i generally fat to converge if the current approximation i cloe to the actual root though low in other circumtance. In repone to b Tranform wave to coordinate of end of breakwater thee hortcoming, Brent developed Brent Method (Brent, 1973) which implement the Biection Method, the Secant Method and Invere Quadratic Interpolation, c Diffract and tranmit wave No electing which i mot appropriate for the current No iteration. It ha the robutne of the Biect Method and the peed of the Newton-Rhapon Method making it a d Tet berth operability ueful and appropriate tool for thi tudy. 4. Methodology In order to find the breakwater layout which offer the Target operability reached? required level of berth protection, the model require a Ye bathymetric data et, a wind and wave time erie and the tidal range a well a the coordinate of the deired e Second ide teted? berth location a hown in figure 6. Ye f Retet firt ide g Approximate line of bet fit for each ide h Calculate breakwater volume Figure 6 - igh Level Flow Diagram Figure 7 give an overview of the oftware algorithm that i ued to calculate the layout of the breakwater. The following ection will briefly dicu each of the procee labelled in Figure 7 from a to h. End Figure 7 Flow diagram of the breakwater layout algorithm 5

6 27 Apr May May May May May May 11 Michael Rutell a. Creating the Breakwater Outline With the berth location elected, the centre point of the breakwater found by extruding in the direction of the eabed lope (which hould align with the direction of the tranformed ignificant wave due to millennia of wave-eabed interaction). From thi point, two line are extruded at + 90 and -90 which give the potential breakwater layout a hown in Figure 8 where the black circle repreent the berth location, the yellow line i the direction of the contour, red X i the mid-point of the breakwater and the dark red line are the potential length of each ide of the breakwater. 5m 10m 15m 20m Figure 8 Topographical view of potential breakwater layout Now that a potential breakwater layout ha been found, Brent Algorithm can be ued to find the length which correpond to the layout which offer the deired level of berth operability. b. Tranforming the Wave to the Breakwater The wave height at the berth i a product of the three major wave component and can be approximated a the root mean quared (RMS) of their total wave energy: Where the value of i the refracted, hoaled and diffracted wave travelling around the L ide of the X breakwater, i the refracted, hoaled and tranmitted wave coming through the breakwater core and i the refracted, hoaled and diffracted wave travelling around the R ide of the breakwater a hown in figure 9. Figure 9 - Simplified Diagram of the Major Wave Energy Component The water level i calculated from the oberved tidal level dataet which i inputted into the model. Figure 10 how ea level variation baed on tidal motion. In abence of uch data, approximation can be made if the highet and lowet atronomical tide are known uing baic trigonometric function to imulate the gravitational pull of the un and moon imultaneouly Figure 10 Sea level variation through tidal motion The offhore wave time erie i refracted and hoaled to the mid-point of the breakwater and the tranformed wave data i tored in an array. Only one breakwater ide length can be found at a time uing a root-finder o each ide of the breakwater mut be conidered independently at firt. A the effect of the diffracted wave emerging from the other ide are unknown a a length ha not been etimated for that ide yet, the effective wave height equation reduce to: 6

7 . For the firt ide, Brent algorithm i ued to elect a breakwater length from which the correponding coordinate are eaily found. The offhore wave time erie i tranformed to the coordinate correponding to the length which ha been choen by the algorithm, taking into account the water level variation due to tidal motion. c. Diffract and tranmit wave to the berth The diffraction angle i calculated for each of the tranformed wave from which the diffraction coefficient can be found uing Krau Method for. The following equation i ued to calculate the coefficient of wave energy tranmitted through and over the breakwater cro-ection for : period Tp to the ignificant wave height are ued, a graphical repreentation of which i hown in figure 12: Figure 12 - Mooring Threhold Curve Thee equation are baed on full dynamic mooring imulation that have been conducted at R Wallingford. Equation for 75,000m 3, 138,000m 3 and 210,000m 3 capacity veel for wave which are headon, quartering, and beam-on have been developed (figure 13). C C t t Rc 0.4 Rc B B exp 0.5 m 1 exp 0.41 m : B 10 : B 10 The total wave height at the berth i now computed a a product of the diffracted and tranmitted wave height a hown in figure 11. Figure 13 Relative wave direction to the veel Figure 11 - Diffracted Wave Angle d. Tet berth operability To tet whether the mooring threhold of the berthed veel ha been exceeded, equation, linking the peak The diffracted wave i the larget contributor to o the direction of thi component relative to the veel i ued to elect the correct equation. The wave period from the current tep in the time erie i ued in combination with. If the combination i below the threhold then a pa i given for that tep. The operability for the berth ( ) i then calculated a the percentage of wave which were given a pa. The error in ( ) i ued to etimate a cloer value of. Thi proce continue until a uitably accurate value ha been found for. Generally peaking, maller veel are more uceptible to mall period wave and large veel 7

8 are more uceptible to longer period wave a the peak frequencie are cloer to their natural frequencie. Larger wave height and longer wave period carry more energy o there i a trade-off between thee which can be approximated with the threhold curve. e. Calculate Length of Other Side Step b-d are now repeated for the econd ide. A the length of the firt ide i now known, wave emerging from both ide can be conidered a hown in figure 9 uing the equation from ection 4.b. f. Recalculate firt ide Once the econd ide ha been calculated, the procedure i performed on the firt ide once more, thi time conidering the wave emerging from the econd ide alo. Thi proce could go on for everal more iteration, though it ha been found that after thi iteration, the percentage of length change i negligible. h. Calculate Breakwater Volume Now that the cro-ection and length have been found, the volume of each layer i eaily found from which a cot etimate can be developed. In thi model, coting i automated baed on unit rate inputted by the engineer which provide a metric for comparion. 5. Cae Study A cae tudy ha been ued to demontrate the effectivene of thi algorithm in etimating the conceptual layout of a breakwater. Figure 16 how a breakwater protecting two berthed LNG veel. Thi layout i the product of a everal month FEED tudy. g. Approximate line of bet fit In location where wave are large, the model at thi tage may produce a breakwater length that eem too large a hown in figure 14. Figure 16 - FEED Deign of a Breakwater Protecting Two Berthed LNG Veel Figure 14 Non-optimied breakwater layout A routine ha been included that reduce the length of the breakwater if thi i the cae. By enuring that the line of the wave travelling from the roundhead i intercepted, the breakwater length can be reduced coniderably (figure 15). Figure 15 Optimied breakwater layout The ignificant wave direction i 178, the breakwater face 180, i 700m long cret centre-point to cret centre-point and the end of the bae are 755m apart. Uing the ame bathymetric and wave dataet, the root-finding algorithm i ued to develop a concept deign. The wind/wave time erie ha 20 year of data. To account for the two veel, the algorithm i run independently for a 75,000m 3 veel cloe to the breakwater and a 210,000m 3 veel in the more ditant poition. The deign breakwater length i then wort cae for each ide a hown in figure 17. 8

9 breakwater did have a lightly different alignment to the Figure 17 - Superimpoition of Two Breakwater Optimiation Overlaying the FEED tudy with the newly created deign (figure 18) how that a imilar breakwater layout ha been found. The exact percentage of difference in length i difficult to determine a the point from which diffraction occur are omewhere beneath the water level making the effective length of the FEED breakwater omewhere between 700m and 750m. Figure 18 - Comparion of Breakwater Layout 6. Reult and Dicuion The algorithm performed well on thi tudy. It wa able to produce an anwer imilar to that which took everal month and ignificant project cot to create uing the conventional approach. Thi tudy took an hour to prepare the data and et up the model and le than 10 econd to run. The length of breakwater produced wa 773m in total which i within the error range of 2~10% which i acceptable conidering that the FEED deign ha been through a full dynamic mooring aement a well a numerical and phyical modelling during a everal month deign period and other tudie uch a current and ediment modelling have alo been undertaken. The one from the FEED tudy, though other apect which are currently outide of the cope of thi tool had an effect on the actual deign. The algorithm developed a concept that wa a traight breakwater a the total length wa le than the threhold at which tep 4.g reduce the layout by creating a convex hape. Brent algorithm wa capable of finding the value of which gave ( ) in around 6 iteration for each ide for each time. The implicity of the rootfinding concept mean that it can be followed and undertood by any engineer without having to delve into advanced computer method which offer a level of comfort through tranparency. Though the algorithm wa able to create a imilar ized layout, it doe ue implified procee and relationhip to enure a fat running time. An example of thi i the dynamic mooring aement which i only able to conider the wave height, period and direction. In a full dynamic mooring imulation, current, wind, line trength and the full range of veel movement would alo be conidered. The wave tranformation model i accurate though not a accurate a a 2D or 3D SWAN model, however it i fat and computationally inexpenive to run which i important in thi project. Improvement in the accuracy of the algorithm may be poible through developing a more accurate dynamic mooring aement model though a a proof of concept and foundation for further development in thi tool, thi tudy ha proved ueful. Conidering that in the wort cae, the algorithm wa within 10% accuracy, the potential for uing thi at a erie of location to find the mot optimal i realitic. Thi algorithm i capable of being ued in concept tudie to develop reaonably accurate layout from which a better undertanding of the likely cot of a breakwater can be obtained before committing ignificant um of money to the project. 9

10 The model can be et up to tet a range of direction in different depth to find which i mot optimal, offering a ueful earch tool to help develop economic layout concept during the initial tage of a project. Thi methodology ha been applied to a detached rubble mound breakwater, though could eaily be implemented for caion, concrete armour or berm breakwater concept or adapted for breakwater that meet the hore. 7. Concluion The algorithm performed well in thi tudy and wa able to develop a imilar layout to that which wa developed through a everal month FEED tudy. It benefit are quite obviou, though uch a tool hould only be ued to augment the judgement of an experienced deigner and hould only be ued for producing potential concept deign. A a tool to gain an undertanding of the likely configuration, ize and ultimately, cot of a breakwater, thi tool ha proven to be ucceful. Reference Beley (1991). Overtopping of Seawall, Deign and Aement Manual. Environment Agency, Britol. Wallingford, R Wallingford Ltd. Brent, R. P. (1973). Chapter 4. Algorithm for Minimization without Derivative. Englewood Cliff, NJ, Prentice all. BSI (1999). Britih Standard Code of Practice for Maritime Structure. Part 1: General Criteria. BS 6349: Part 1: (and Amendment 5488 and 5942), Serie, Editor London, Britih Standard Intitution. CIRIA and CUR (2007). The Rock Manual. The Ue of Rock in ydraulic Engineering. Serie, Editor London, CIRIA. Elchahal, G., R. Youne, et al. (2013). "Optimization of Coatal Structure: Application on Detached Breakwater in Port." Ocean Engineering 63(0): udon, R. Y. (1958). "Deign of Quarry Stone Cover Layer for Previou Term Rubble-Mound Breakwater " Reearch Report No. 2 2, Waterway Experiment Station, Coatal Engineering Reearch Centre, Vickburg, MS. Goda, Y. (1975). "Deformation of Irregular Wave Due to Depth Controlled Wave Breaking." Report for the Port and arbour Reearch Intitute 14(3): Goda, Y., T. Takayama, et al. (1978). "Diffraction Diagram for Directional Random Wave. ASCE Proceeding of the 16th Coatal Engineering Conference 1: Goda, Y. (2010). Random Sea and Deign of Maritime Structure. Advanced Serie on Ocean Engineering - Volume 33, Serie, Editor London, World Scientific Publihing Co. Pte. Ltd. Goda, Y. and Y. Suzuki (1975). "Computation of Refraction and Diffraction of Sea Wave with Mituyau' Directional Spectrum." Technical note of Port and arbour Reearch Intitute 230: 45. Britih Standard Intitution (1999). Maritime Structure. Part 7: Guide to the deign and contruction of breakwater, Britih Standard Intitute. BS :1991. Kicinger, R., Arcizewki, T. & Jong, K. D. (2005) Evolutionary computation and tructural deign: A urvey of the tate-of-the-art. Computer & Structure, 83, Krau, N. (1984). "Etimate of Breaking Wave eight Behind Structure." Journal of Waterway, Port, Coatal and Ocean Engineering 110(2):

11 Owen, M. W. (1980). "Deign of Seawall Allowing for Wave Overtopping." R Wallingford, Report EX 924. Penney, W. G. and A. T. Price (1952). "The Diffraction Theory of Sea Wave and the Shelter Afforded by Breakwater." Philo. Tran. Roy. Soc. A 244(882): Pullen, T., W. Allop, et al. (2007). Eurotop Wave Overtopping of Sea Defence and Related Structure: Aement Manual., Serie, Environmental Agency, UK Expertie Netwerk Waterkeren (NL) Kuratorium fr Forchung im Kteningenieurween (DE),. Shuto, N. (1974). "Nonlinear Long Wave in a Channel of Variable Section." Coatal Engineering in Japan 17: TAW (2002). "Technical Report Wave Run-up and Wave Overtopping at Dike." TAW, Technical Adviory Committee on Flood Defence. Author: J.W. van der Meer. van der Meer, J. W. (1988b). Rock Slope and Gravel Beache under Random Wave Attack. PhD-thei,, Delft Univerity of Technology. h Water depth (m) 1,2,3... Wave height component (m) eff Effective tranformed wave height (m) 0' K d K r K K i L 0 Q Q * R c T m T p Effective offhore wave height (m) Significant wave height (m) Diffraction coefficient Refraction coefficient Shoaling coefficient (monochromatic) Non-linear hoaling coefficient Offhore wave length (m) Mean overtopping dicharge (m 3 /m/) Non-dimenional overtopping Cret freeboard (m) Mean period of wave () Peak period of wave () W L Water level (m) m Iribarren number Weigel, R. L. (1962). "Diffraction of Wave around a Semi-Infinite Breakwater." Journal of ydraulic Diviion, ASCE 88(Y1): Notation A A c Slope coefficient for Owen overtopping method Armour freeboard (m) A * Dimenionle armour freeboard B B c C t g Slope coefficient for Owen overtopping method Cret width of breakwater (m) Tranmitted wave coefficient Acceleration due to gravity About the Author Michael Rutell i in the third year of an Engineering Doctorate in deigning LNG terminal layout uing artificial intelligence. e conduct hi reearch at R Wallingford and i a tudent of the Univerity of Surrey. i reearch i funded by R Wallingford and the EPSRC. 11