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SUBMERGED HORIZONTAL PLATE FOR COASTAL RETREATING CONTROL: THE CASE OF POLIGNANO A MARE, ITALY.
SUBMERGED HORIZONTAL PLATE FOR COASTAL RETREATING CONTROL: THE CASE OF POLIGNANO A MARE, ITALY.
SUBMERGED HORIZONTAL PLATE FOR COASTAL RETREATING CONTROL: THE CASE OF POLIGNANO A MARE, ITALY.
SUBMERGED HORIZONTAL PLATE FOR COASTAL RETREATING CONTROL: THE CASE OF POLIGNANO A MARE, ITALY.
SUBMERGED HORIZONTAL PLATE FOR COASTAL RETREATING CONTROL: THE CASE OF POLIGNANO A MARE, ITALY.
SUBMERGED HORIZONTAL PLATE FOR COASTAL RETREATING CONTROL: THE CASE OF POLIGNANO A MARE, ITALY.
SUBMERGED HORIZONTAL PLATE FOR COASTAL RETREATING CONTROL: THE CASE OF POLIGNANO A MARE, ITALY.
SUBMERGED HORIZONTAL PLATE FOR COASTAL RETREATING CONTROL: THE CASE OF POLIGNANO A MARE, ITALY.
SUBMERGED HORIZONTAL PLATE FOR COASTAL RETREATING CONTROL: THE CASE OF POLIGNANO A MARE, ITALY.
SUBMERGED HORIZONTAL PLATE FOR COASTAL RETREATING CONTROL: THE CASE OF POLIGNANO A MARE, ITALY.
SUBMERGED HORIZONTAL PLATE FOR COASTAL RETREATING CONTROL: THE CASE OF POLIGNANO A MARE, ITALY.
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SUBMERGED HORIZONTAL PLATE FOR COASTAL RETREATING CONTROL: THE CASE OF POLIGNANO A MARE, ITALY.

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Many sites along the Apulian coast (SE Italy) are composed of weathered and fractured carbonate rocks, affected by intense erosion and frequent sliding. A detailed research of the University of Bari …

Many sites along the Apulian coast (SE Italy) are composed of weathered and fractured carbonate rocks, affected by intense erosion and frequent sliding. A detailed research of the University of Bari (Andriani and Walsh, 2007) highlighted that from 1997 through 2003, the cliff retreat rate varied from 0.01 to 0.1 myr-1, mostly as a consequence of wave action. In the case of Polignano a Mare, a small town 30 km far from Bari, the erosive process seems to be seriously affecting the stability of buildings. Here, because of the bathymetry, the traditional rubble mound breakwaters are not suited. As an alternative, a rigid horizontal submerged plate on piles is here considered. Since there is no universally accepted theory nor formula to calculate the hydraulic performance of such kind of structure physical models have been constructed at HR Wallingford and subjected to random wave attacks. This paper discusses results of those tests.

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  • 1. SUBMERGED HORIZONTAL PLATE FOR COASTAL RETREATING CONTROL: THE CASE OF POLIGNANO A MARE, ITALY. M. Calabrese1, K. Powell2, M. Marrone3, M. Buccino1Many sites along the Apulian coast (SE Italy) are composed of weathered and fractured carbonaterocks, affected by intense erosion and frequent sliding. A detailed research of the University of Bari(Andriani and Walsh, 2007) highlighted that from 1997 through 2003, the cliff retreat rate variedfrom 0.01 to 0.1 myr-1, mostly as a consequence of wave action. In the case of Polignano a Mare, asmall town 30 km far from Bari, the erosive process seems to be seriously affecting the stability ofbuildings. Here, because of the bathymetry, the traditional rubble mound breakwaters are not suited.As an alternative, a rigid horizontal submerged plate on piles is here considered. Since there is nouniversally accepted theory nor formula to calculate the hydraulic performance of such kind ofstructure physical models have been constructed at HR Wallingford and subjected to random waveattacks. This paper discusses results of those tests.INTRODUCTIONThe main scope of a structural measure for coastal erosion control is indeedreducing the intensity of wave attacks in the nearshore. Yet, in most of casesalso a small intrusion in the landscape is requested. For this reason underwaterbarriers are now becoming rather popular, especially in sites, like the Italiancoasts, where tidal range is small. Submerged barriers are traditionallymultilayered rubble mound breakwaters that force the waves to break and reducetheir power. Generally they are located on a limited depth and may be bothnarrow and wide crested, depending on the degree of wave energy which isconsidered to fit a given design situation.Clearly, as soon as the depth of placement increases, the use of traditionalbreakwaters becomes anti-economical and non conventional solutions have to beconsidered.This may be the case of Polignano a Mare, a small town 30 km far from Bari(Italy), where the erosion process is of such a severity to affect the safety ofbuildings. As many sites along the Apulian coasts, Polignano a Mare is locatedon weathered and fractured carbonate rocks that experienced intense erosionand frequent sliding. Here the sea bottom is 25m depth at a few meters from thecoastline and accordingly the construction of traditional barriers is stronglydiscouraged.As an alternative, a rigid horizontal plate on piles is being considered by HRWallingford. Since no well accepted theory nor empirical formula exists topredict the hydraulic response of such a structure (Patarapanich and Cheong,1989; Yu et al., 2002), ad hoc random wave tests have been conducted.1Hydraulic department, University of Naples “Federico II, Via Claudio, Naples, Italy. Email: calabres@unina.it, buccino@unina.it2HR Wallingford, Howbery park, OX , Wallingford, Email: k.powell@hrwallingford.co.uk3Engineer, Email: marcomarrone83@hotmail.it
  • 2. This paper analyses results of those experiments, with the aim of providingengineers with two simple predictive methods: one permits of estimating the rateof energy that is reflected back by the structure and the other allows ofcalculating the wave height transmitted off the barrier.FACILITIES AND DATA DESCRIPTIONThe models have been tested in the random wave flume of the HR Wallingford’sFlume Hall. The flume was 45 m long, 1 m wide and 1.5 m high.Waves were first calibrated in the model, before the placement of the structure,with the aim of reproducing the same wave conditions as those recorded inPolignano a Mare. With this purpose, a (short) signal sample was first adjustedto ensure the spectral significant wave height, Hm0, was within +/-5% of thetarget value. Then, a long (1000 waves) non-repeating wave sequence was run tosimulate the actual incident sea-state; main wave parameters are reported inTable 1. Table 1 – Results of wave calibration Period H1/10 H1/3 Hm0 Tp Tm of return (m) (m) (m) (s) (s) 1 in 1 4.91 3.95 4.06 8.98 7.44 1 in 10 6.25 5.02 5.18 9.95 8.52 1 in 50 7.20 5.81 6.00 11.60 8.78After the calibration, the plate was built in the flume at a distance of 10m fromthe wave paddle. The width of the structure, B (Figure 1), ranged from 25 and55m (prototype scale); two depths of submergence, d’, have been tested, namely2,5 and 5m. Altogether, 42 tests were run. H HI HT L L LT d B d Fig. 1 – Structure scheme
  • 3. GLOBAL FEATURES OF THE WAVE MOTIONThe coefficient of reflectionThe reflection coefficient, Kr, square root of the reflected to incident spectralareas, has been estimated through the Mansard and Funke’s separationtechnique (1980), which requires the simultaneous acquisition of the waveelevation process at three different positions along the propagation’s direction.From a physical point of view, wave reflection is likely related to the presenceof a pulsating flow driven by the phase shift between the incident and thetransmitted wave. Following Graw (1992), we may reason the momentum fluxof this current to act more or less like a wall that impedes the propagation of thepressure wave below the plate. Thus, a coherent functional form of thecoefficient of reflection might be:  2B  K r  A  sen  (2)  RL in which A represents the maximum of Kr, which is attained at the point of phaseopposition, and R defines the structural condition where such a critical situationoccurs; in this regard previous literature seems to indicate R should not be farfrom 2, so that the maximum reflection would correspond to kB=π. Here thefollowing empirical expressions have been obtained:  H  A  tanh 204 si2  (3)  gT p    0 , 57  d  R  9,5 2  (4)  gT   p Note that Equation (4) gives values of R around 2 only for relatively deep water(d/L0p, from 0.2 to 0.4, being L0p the peak deepwater wavelength), while themaximum reflection would be attained for shorter structures as the depth ofplacement becomes shallow. Fig. 2 shows the comparison with the experimentaldata. Together with the line of perfect agreement, two semi bands correspondingto an error of 15% are reported in the graph.
  • 4. 0,9 Dati Kr, estim.. Perfect match -15% +15% 0,6 0,3 0 0 0,3 0,6 Kr, meas. 0,9 Fig. 2 – Comparison between the formula 2 and the experimental dataHowever, as shown in the previous figure, present data oscillate in a quitenarrow range around the value 0.7; consequently, some further indication on thereliability of the proposed equation has to be achieved using other availabledata. For this purpose experiments by Yu et al. (1995) have been employed,although they have been performed using regular waves. The tests refer to astructure placed on a depth of 20cm, with a submergence of 6cm. Wave heightand period were kept constant (H = 1.8cm, T = 0.8s), while only the plate widthwas varied. The comparison is displayed in Figure 3. The graph shows a fairmatch only in the first cycle of variation of Kr, where the main peak appears tobe correctly estimated. On the other hand data exhibit a progressive damping notpredicted in the model. More experiments are recommended to furtherinvestigate this item. 0,6 Kr Eq. 2 Yu et al. Data 0,4 0,2 0 0 0,4 0,8 1,2 1,6 B/L Fig. 3 – Comparison between the Eq. 2 and the data by Yu et al. (1990) (regular waves)
  • 5. Calculation of the significant transmitted wave heightA predictive model for the transmitted, spectrally defined, wave heights, Hm0,t orHrms,t is of course important to engineering aims, since these waves areproportional, at least for linear waves, to the time averaged wave energy leewardthe structure. Obviously, the latter rules most of the shadow-zonehydrodynamics, including solid transport process, wave run-up as well as thewave power transferred to any structures lying in the protected area.It is well known the spectral wave heights can be generally defined as follows: H m0 H m0  4 m0 ; H rms  8  m0  (5) 2being m0 the area of the power spectrum.The calculation method proposed below might be defined as semi-empirical or“conceptual”; it starts from a quite schematic modeling of main phenomena thatgovern wave transmission process and includes a unique free parameter to beestimated from experimental data. This parameter basically represents the lag ofphase, say ε, between the waves that enter the protected area from above theplate and those passing below. Breaking process is modeled according to Dally,Dean and Dalrymple (1985); moreover, an equivalence between regular and theirregular wave trains is established, by simply substituting the “wave periodaveraging operator” by an averaging “in the ensemble domain ”, that is amongthe different waves which belong to the sea state (Thornton and Guza, 1983).Accordingly, under the hypothesis that the power spectrum is narrow enough toneglect the differences among the single wave periods, we have, for the incidentenergy flux: Pi  g  H 2 f H dH  cg  f p , d   gH rmscg  f p , d  1  1 2 (6) 8 0 8in which f(H) is the probability density function (pdf) of the incident waveheight, Hrms is the root mean square wave height and cg(fp,d) is the linear (peak)group celerity, calculated at the depth of placement d. At the structure, theincident wave power splits into two parts, one propagating below the plate, Piu,and another that overpasses the structure, Pio (Fig. 4). z x d Pio Relection Transmission region region B d Pi Pt Piu Pr Fig. 4 – Scheme of the redistribution of the incident power Pi
  • 6. Regarding the former, we assume it to equal the time averaged energy flux, perunit of span, through a section of height (d – d’). Consistently with the generalapproach above discussed, we first calculate that quantity for a single wave andthen we average the result on the wave ensemble. Consequently we obtain:  Piu   Piu f H dH H (7) 0in which PiuH is the under-passing power for a single wave that is given by: 1 T d Piu  0 dt d pi ui dz H H H (8) Twhere pi represents the (incident) dynamic component of pressure, ui is thehorizontal component of wave velocity and the prime H has been introduced justto highlight that the calculated quantity refers to the single wave. Using linearwave theory one readily gets: 1 1  d  d 2k  senh2k d  d  Piu  gH i2c  H  (9) 8 2 senh2kd  in which c is the incident phase speed and k represents the wave number, k=2π/L(L is the incident wavelength). Finally, by invoking the hypothesis of narrowbanded spectrum, we have: Piu  1 gH rmsi c    1  d  d 2k p  senh 2k p d  d    2 senh2k p d  (10) 8 2  in which the subscript p indicates a “peak quantity” and i stands for “incident”.Note that as a consequence of having adopted the linear wave theory in thecalculations, equation (10) gives no flux below the plate when d’=0. Thishypothesis limits the application of the model to the case of a plate not veryclose to the mean sea level. The power Piu is supposed to undergo no remarkabledissipation, but it will not entirely propagate to the protected area, due toreflection effects. Accordingly the energy flux transmitted below the structurewill be equal to: Ptu  Piu  K r2 Pi (11)It is worth underlining that the coefficient of reflection, Kr, calculated by theformulas (2) – (4), is already a global quantity referred to the ensemble and thenit does not need require any statistical manipulation.Now it is clear that the part of the incident power that overtops the structureequals: Pio  Pi  Piu (12)Obviously this portion of flux is remarkably diminished by wave breaking. Asalready mentioned, here we suppose, in agreement with Dally, Dean andDalrymple (1985), the average power density dissipated by a single breaker tobe proportional to the difference between the local wave energy flux, say PHo,and a stable value, say Ps; moreover dissipation is thought to be inversely
  • 7. proportional to the available depth, d’ (Fig. 4). This leads to the followingexpression: D  l Po H  Ps  (13) din which l is a coefficient of proportionality that Dally, Dean and Dalrymplefixed to the value 0,15. Altogether the energy balance equation above the plate,for the single wave, can be t written as follows: dPoH  l o  P H  Ps  (14) dx dSince Ps does not vary along x, as the plate is horizontal, variables can beseparated. Hence we have:  d PoH  Ps   l dx  Po  Ps H  d (15)Integrating between 0 and B with the initial condition that PoH– Ps=PHio – Ps forx=0 (the suffix “i" indicates the incident value of the flux above the plate), weobtain:    B Pto B   Ps  Pio  Ps exp   0.15  H H (16)  d Moving from the single wave to the whole sea state, we will notice that theenergy flux in the plate’s terminal section will be equal to the Equation (19) onlyfor those waves breaking on the structure; on the other hand the transmitted fluxwill be equal to PioH for the waves that will not break. The mean value of thepower transmitted above the structure will be then equal to:   Pto   Pto B  f b H dH  Pio  f nb H dH H H (17) 0 0in which fb and fnb are the pdf of the breaking and non breaking wavesrespectively. In agreement with Thornton and Guza (1983), the easiest way toestimate such functions is to consider them proportional to the general waveheight pdf, f(H):  f b H dH  Pb f H dH   f nb H dH  1  Pb  f H dH (18)where Pb is the percentage of breaking waves. Finally we have: Pto  Pb  Ptob  1  Pb Ptonb (19)in which Ptob represents the transmitted energy flux for breaking waves:   B Ptob   Pto B  f H dH  Ps  Pio  Ps  exp   0,15  H (20) 0  d while for the energy flux connected to the non-breaking waves, Ptonb, we willsimply set:
  • 8. Ptonb  Pio (21)In the previous integration we considered the stable flux, Ps, as independent ofthe wave height. Basically we set: 1 Ps  gH b2 C gpd (22) 8where Cgpd’ represents the linear peak group speed corresponding to the depth ofsubmergence d’. As far as the incipient breaking wave height, Hb, is concerned,the well known Mc Cowen criterion has been employed: H b  0,78d (23)As regards to the percentage of breaking waves, Pb, it has been assumed it to besimply equal to the exceedance probability of, Hb, under the hypothesis thatoverpassing waves at the seaward edge of the plate are Rayleigh-distributed:  H2  Pb  exp   b   8m  (24)  0o in which m0o is the specific energy of the wave motion above the plate at theleading edge of the structure; it is equal to: Pio m0 o  (25) gc gp,d Now, the wave field at the back of the structure will be composed of twodifferent subsets of waves, respectively coming from above and below the plate.They propagate in the same direction but with different phases owing to the lagof celerity above and below the scaffolding. Thus we may describe the singlewave elevation process as follows: cos  p t   tu cos p t    H to H  t H  t   (26) 2 2in which Htu and Hto represent respectively the underpassing and overpassingtransmitted wave heights, while the symbol ε indicates their difference of phase.Finally to calculate the transmitted wave energy m0t, we introduce thefundamental relation, valid for linear sea states: m0  VAR     2 (27)in which VAR indicates the variance operator and the “overbar” symbolindicates a time average. Following the simplified approach previouslyproposed, the calculation of m0 will be performed in two steps, namely:1. Firstly we calculate the η variance referred to the single wave by an averageover a wave period: T 1 2 H   t2 H   T  t dt (28) o
  • 9. 2. then we estimate the overall sea state energy by averaging t2H  over theensemble of waves, that is among the different wave heights: m0t  t2  E t    2 H (29)    It can be easily shown that aforementioned steps lead to:   m0 t  E  2  H   8 H rms,to  H rms,tu  2H rms,to H rms,tu cos   1 2 2 (30)that holds under the hypothesis that the skewness of the transmitted wave pdf israther small. Hrms,to and Hrms,tu can be simply obtained as Pto H rms,to  8m0,to  8 (31) C gpd Ptu H rms,tu  8m0,tu  8 (32) C gpdIn the Equation (30) ε has been treated as a free parameter and its value has beenoptimized experiment by experiment. Then a multiple regression analysis hasbeen performed in order to relate the optimized values to the main structural andhydraulic parameters. The following final equation has been found:   1,77 exp  0,7011  k p d  k p B  0, 291 (33)where k’p represents the peak frequency wave number calculated at thesubmergence level d’. Note that Equation (33) realistically returns a null phaseshift either for extremely short or deeply submerged structures.The Fig.(8) shows the comparison with the experimental data in terms ofHrms=8m0t. The agreement can be considered reasonable. The maximumdifference between the measured and the calculated values are of about 20% andthe global determination index is 81%.
  • 10. 5 Ht, meas. Data Perfect match -20% 4 +20% 3 2 1 0 0 1 2 3 4 5 Ht, estim. Fig. 8 – Comparison among the measured and the estimated values of the wave heightsSUMMARYThe paper has presented results of hydraulic model tests conducted at HRWallingford on a rigid submerged plate on piles. The structure has beenoriginally thought as a measure for defending the rocky coast of Polignano aMare (Italy) from a structural erosive process. The experiments were run usingrandom sea states representative of the Apulian climate.The data have been used to derive a predictive method for calculating twoleading hydraulic variables, namely the reflection coefficient and the transmitted“energetic” (rms, roughly speaking) wave height. The latter is of course ofinteresting for every engineer as it is strongly related to the entire shadow-zonehydrodynamics. As a conclusion of the work a step by step scheme is hereproposed for application scopes.As far as the reflection coefficient Kr is concerned, Eq. (2)-(4) have to be used.However caution is recommended when applying the formulas to plates widerthan half the incident peak wavelength.Regarding the transmitted wave energy the calculation procedure can besummarized as follows.a) calculate the phase shift  through Eq.(33); b) calculate Ptu by means of (6),(10) and (11); c) calculate Pio through Eq.(12) and then Pb by (24) and (25); d)calculate Ptob and Ptonb by (20),(21) and (22); e) calculate Pto through Eq.(19); f)calculate Hrms,tu and Hrms,to by means of (31) and (32). Finally the transmittedwave energy m0t can be obtained through Eq. (30).REFERENCES: Andriani G., Walsh N. (2007), “Rocky coast geomorphology and erosional processes: a case study along the Murgia coastline south of Bari, Apulia – SE Italy” Geomorphology Vol 87, 224 – 238.
  • 11. Graw, K. (1992) “The submerged plate as a wave filter”, Coastal Eng. J., pp.1153-1160.Mansard, E.P.D. e Funke, E.R., (1980), “The measurement of incident and reflected spectra using a least square method”, Proc. 17th ICCE, Sydney, pp. 154 – 172Marrone M. (2008), Master Thesys: “Indagine sperimentale sulla trasmissione a tergo di una piastra sommersa” Federico II Naples University, Hydraulic geotechnical and environmental engineering department (in Italian)Patarapanich M., Cheong H. (1989), “Reflection and transmission characteristics of regular and random waves from a submerged horizontal plate”, Coastal Eng., Vol. 13, 161 – 182.Yu X., (2002), “Functional Performance of a submerged and essentially horizontal plate for offshore wave control: a review”, Coastal Eng. J., Vol. 44, No. 2, 127 – 144.Yu, X., Isobe, M. and Watanabe, A. (1995), Wave breaking over submerged horizontal plate, J. Waterway Port Coastal Ocean Eng., 121, 2, March/April, pp. 105-113

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