comparative study on breaking wave forces on vertical walls with cantilever surfaces

7/24/2019 COMPARATIVE STUDY ON BREAKING WAVE FORCES ON VERTICAL WALLS WITH CANTILEVER SURFACES

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COMPARATIVE STUDY ON BREAKING WAVE FORCES ON VERTICAL WALLS WITHCANTILEVER SURFACES

Kisa ci k1 Doga n; Van B ogaer t1, Phi li ppe; Tro ch 1, PeterDepartment o f Civil Engineering, Ghent University,

Technologiepark 904, Ghent, 9052, Belgium

ABSTRACT

Physical experiments (at a scale of 1/20) are carried out using twodifferent models: a vertical wall with cantilevering slab and a simplevertical wall. Tests are conducted for a range of values of water depth,wave period and wave height. The largest peak pressures were recordedat the SWL (82 *pghs) on the vertical part and at the fixed corner ofthe cantilever slab (90 * pg hs). Pressure measurements and derivedforce calculations on the simple vertical wall were used to evaluate theexisting prediction formulas. A significant effect of the cantilevering

part is observed on the total horizontal force and overturning momentof a simple vertical wall. This is due to secondary impact occurring onthe overhanging part by a jet climbing on the vertical part.

KEY W ORDS: Wave impact pressure; wave impact force; small

scale tests, regular waves; wave breaking.

INTRODUCTION

Vertical breakwaters and seawalls are frequently used to protect landfrom sea action such as high water levels and waves. To reduce theovertopping, coastal engineers provide the vertical walls with a returncrown wall or even a horizontal cantilever slab. However, waveimpacts on the horizontal structure introduce an important upliftingforce. The lift forces consist of impact loads which one of highmagnitude and short duration. It is reasonably impossible to substitutethese impact effects by a static equivalent. A detailed description of thespace and time distribution of the wave impacts thus becomes

imperative. The Pier of Blankenberge which is located along theBelgian coast is an illustrative example of a vertical wall withcantilever surfaces (Verhaeghe et al., 2006).

The qualitative and quantitative determination of wave loads on verticalwalls has already been examined intensively in the past decades (e.g.Oumeraci et al., 2001; Allsop et al, 1996; Goda, 2000; Cuomo et al.,2009). Uplift loads below horizontal cantilever surfaces are frequentlyexamined in various research projects (McConnell et al., 2003; Cuomoet al., 2007). In opposition to a single vertical or horizontal wall,

structures consisting of both vertical parapets and horizontal cantileveslabs have scarcely been considered. A consensus on the necessaryapproach for the research of this type of structures lacks completely

(Okamura, 1993). Due to the special geometry, involving closed angleswhich do not allow incident waves to dissipate, the wave kinematicdiffer fundamentally from the preceding situations.

In this sense, the main objective of the present research is to bring new design tool to assess violent water wave impacts on a vertical wallincluding an overhanging horizontal cantilever slab, based on thcorrelation between the kinematics of breaking waves. In this particularesearch, model tests with a scale of 1/20 were carried out to fulfill thabove goals and results are compared with the test data of simplvertical case in identical conditions.

Within this paper, an overview of the small scale model tests set up wilbe provided. This will be followed by the comparison of measurehorizontal forces and overturning moments with the results of a simpl

vertical wall and well known theoretical values in the literatur(Minikin, 1963; Goda, 2000; Blackmore & Hewson, 1984; Allsop eal., 1996; Oumeraci et al., 2001; Cuomo et al., 2007). Based on thdiscussion o f the test results, conclusions will be formulated.

LITERATURE REVIEW

Waves attacking vertical structures are usually classified as nobreaking, breaking and broken waves. Breaking waves create shorimpulsive loads on the vertical structures which introduce localizedamages. Coastal structures are bulk structures and most researcherdid not consider these short-duration loads in their design formulasHowever, Oumeraci (1994) emphasise the importance of impulsivloads in the design of vertical structures. Several formulas from designcodes allow calculating impulsive loads on vertical structures.

Minikin (1963) suggests a parabolic pressure distribution for thbreaking waves on vertical walls. The dynam ic pressure pm (Eq. 1) haa maximum value at the SWL and decreases to zero at 0.5Hb below anabove the SWL. The total horizontal force represented by the areunder the dynamic and hydrostatic pressure distribution is shown in Eq2 (SPM, 1984).


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pm = 101P 9 ~ i P + h s) (1)

Fh =1 T P9 ~ i D + hs) + 0.5pgHbhs ( l + f ) (2)

Where Dis the depth at one wavelength in front of the wall, LD is thewavelength in water depthDandHbis the breaker wave height.

Minikin formula is dimensionally inconsistent. Allsop et al. (1996c)show that the horizontal impact force (Fh) predicted by Minikinsformula is incorrect due to the decrease ofFhwith increasingLD. There

are some incompatibilities are found between different versions of theMinikins formula which are mainly due to a unit mistake convertingfrom British to metric units. Therefore, Minikins formula is out offashion in recent years (Bullock, et al., 2004).

Figure 1. Pressure distribution on the vertical wall according to the Minikin

Method.

Goda (1974) suggests his own formula for the wave loads on thevertical walls based on theoretical and laboratory works. He assumes atrapezoidal pressure distribution on the vertical walls with maximum

pressure at the SWT, (Eq.3). His method predicts a static equivalentload instead of short impulsive loads for breaking and non breakingwaves. Takahashi (1996) extends the Goda method for breaking waves

by adding some new term in the max imum pressure (px) at SWL totake into account the effect of berm dimension.

Pi = 0.5(1 + eos)( A1a1 + A2a teos2)pgFImax (3)

Where is the angle o f incidence o f the wave attack with respect to aline perpendicular to the structure, A1} an d A2 are the multiplicationfactors depending on the geometry of the structure. For conventionalvertical wall structures, A = 2 = 1andFlmaxis the highest wave outof the surf zone or is the highest of random breaking waves at adistance of 5Fls seaward of the structure. The total horizontal force iscalculated from the area under the pressure profile shown in Fig. 2.

Blackmore & Hewson (1984) suggest a prediction formula based onfull-scale field measurements (Eq. 4). They consider the effect ofentrained air which results in a reduction in the impact pressure of fieldtests compared to laboratory tests.

Pi = Ap Cl T (4)

Where Cb is the shallow water wave celerity andAis the aeration factorwith dimension [s'1].Ahas a value between 0.1s"1and 0.5s"1at full scaleand between Is"1 and 10s"1 at model scale (Blackmore & Hewson,1984). It is recommended to use value of 0.3s'1for rocky foreshore and0.5s'1 for regular beaches (BS 6349). The total horizontal force iscalculated from the area under the pressure profile shown in Fig. 3.

Figure 2. Pressure distribution on the vertical wall according to the GodMethod.

According to the model tests at HR Wallingford within thPROVERBS project, Allsop & Vicinanza (1996) recommend

prediction formula for horizontal wave impact force on the verticawalls (Eq.5). Data were produced on a slope of 1/50 at 1/250 level fothe range of 0.3


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Figure 4. Pressure distribution on the vertical wall according to the PROVERBS.

Cuomo et al, (2010) recently suggest a prediction formula for thehorizontal impulsive load Fhimpl / 2so 011 the vertical walls on level of1/250 (Eq. 8).

"h.imp,1/250 = pg- Hmo- L hs - ( i - 1 ) (8)

Where Lhs is the wavelength at the toe of the structure for T = Tm, hs

is the water depth at the structure and hbis the water depth at breaking.hb is determined from Miches breaking criteria (Eq. 9) by assuming

hb = - ar ctan h ( Hmo )0 k VO.14-Lft.J

Where kis calculated from, k = 2n/Lhs

(9 )

Eq. 8 is valid in the range of 0.2 m < Hmo < 0.7 m, 0.5 m < hs


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u2.

O 4 8 12 16 20 28 32 36 40 42Time [s]

Figure 6. Time series of the horizon tal force Ff( t) record for the simple verticalmodel (h s=0.135 m, Hi= 0.115 m and T=2.2 s).

Vertical part

2.00

1.75

1.50

* 1.25-C

1.00>

0.75

0.50

0.25

0.00

0 10 20 30 40 50 50 70 80 90

P / PghsFigure 7. Local peak pressure distribution on the vertical part of Model-A for thirty regular waves ( hs=0.135m, T=2.2s, sampling frequency=20kHz and Hi=0.115m). Dashed and solid lines indicate maximum andmean peak pressure values respectively

Horizontal part

Q.

100

0.0 1.0 2.0 3.0 4.0

X / h s

Figure 8. Local peak pressure distribution on the horizontal part ofModel-A for thirty regular waves (hs=0.135m, T=2.2s, samplingfrequency=20 kHz and Hi=0.115m). Dashed and solid lines indicatemaximum and mean peak pressure values respectively

COMPARISION WITH EXISTING PREDICTION METHODS

Fig. 914 shows the comparison o f measured horizontal forces Fh on vertical wall (Model-B) with the existing well known predictioformulas for various values of the wave height (H). Force Fhand H arnormalized by pghs and water depth (hs) respectively. All thesmethods are developed for irregular waves and considered statisticawave height values like Hs or Hrnax to calculate the force. In thi

particular set of data, force and wave height, measured by zero dowcrossing method, are correlated directly rather than showing a statisticarelation. The data set contains results of breaking waves within thrange of waves 0 .6 < /s< 1.1. These are breaking waves changinfrom breaking with small air trapping to well developed breaking witlarge air trapping. The measured data are showing high scatter.

Both Minikin and extended Goda methods are under predicting thhorizontal forces on the vertical walls. In all methods, Hb is consideredas the height of incident waves (Hi) at the location of structure ( hshowever the Goda method is considered incident wave heights 5H

before the structure. The Allsop & Vicinanza formula is undepredicting some of the values but shows a good agreement with thtrend of data. Results from the Blackmore & Hewson method shows aenvelope line for the measurements with an aeration factor 10 which ithe highest value suggested for small scale tests. Proverb methodmainly over estimates the force except for the waves creating very high

impact around H /h s=1 and the Cuomo method shows good agreemenwith our data except for few points in the data cloud. It is a bell shapecurve which considers the reduction at both ends of the data set. Igeneral. Minikin (1963), Goda (ex. Takahashi, 1994) and Allsop &Vicinanza (1996) methods are predicting the measured impulsive forcon the vertical walls. However, PROVERBS (2001), Cuomo et al(2010) and Blackmore & Hewson (1984) prediction methods araccurate for designing according to the results from small the scale testfor regular waves. .

PRESSURE DISTRIBUTION

Fig. 15-18 shows the comparison between the instantaneous pressurdistribution for 5 impacts which creates the highest value force on th

vertical wall and the predicted pressure profile for the envelopfunctions. Instantaneous pressure profile is determined from th

pressure sensor results at the time of peak force calculated from Eq. for each individual impact. Here results are shown for the 5 highesmaximum values. There is a high scattering seen also for the locationand value of peak pressures. Maximum peak pressures were observed

between SWL and 0.5hs above the SWL. Minikin, Blackmore &Hewson and PROVERBS methods (F igl 5, 17 and 18) are fairly gooassuming the upper boundary of the pressure profile. However almethods apparently do not predict the maximum peak pressures afound in the tests. There is a phase difference between the results osensors at the upper corner part and the results of sensors at lower partof the vertical wall. Due to the phase difference, the instantaneou

pressure of upper corner shows negative values which appear jusbefore impact rise. This phenomenon is described by Hattoria et a(1994) as a result o f an extremely high velocity jet shooting up the waface.


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* Measurements

PROVERBS (2001 )30

% 25

20

15

105

0

0.5 0.6 0. 7 0.8 0. 9 1.0 1.1

H/hs

Figure 9. Comparison between the measured horizontal impact force on avertical wall with the predicted horizontal force by PROVERBS formula.(Regular waves, T=2.2 s, hs=0.135 m)

35

x Measurements

Al lsop & V im anz af1996)30

25

20

15

105

0

0. 5 0.6 0. 7 0.8 0. 9 1.0 1.1

H/hs

Figure 12. Comparison between the measured horizontal impact force on vertical wall with the predicted horizontal force by Allsop & Vicinanza formul(Regular waves, T=2.2 s, hs=0.135 m)

35

30

25

20

15

10

5

0

0.5

* Meas jrements

X

# * *

X

*..*...* X * X X /

L f i

X

N

! 5X

* * *tl * 3 $ * ;* Xxx...... V .* .* . . . * ......

* X5 xf XX

X 2 x* Xx x r x , i v p ?

0.6 0. 7 0.8

H / h s

0. 9 1.0 1.1

Figure 10. Comparison between the measured horizontal impact force on avertical wall with the predicted horizontal force by Blackmore & Hewsonformula. (Regular waves, T=2.2 s, hs=0.135 m)

35

x M easuremen ts

* GodafexrTakahashi; 1994)30

25

20

15

10

5

0

0. 5 0.6 0. 7 0.8 0. 9 1.0 1.1

H/hs

Figure 13. Comparison between the measured horizontal impact force on vertical wall with the predicted horizontal force by Goda formula (exTakahashi) (Regular waves, T=2.2 s, hs=0.135 m).

35M e a s u r em e n t s

Cuom o et al. , (2007)30

25

20

15

10

5

0

0.5 0.6 0. 7 0.8 0. 9 1.0 1.1

35

* M easuremen ts

MimkrmSPM(1963)30

25

20

15

10

5

0

0. 5 0.6 0. 7 0.8 0. 9 1.0 1.1

H / h s H/hs

Figure 11. Comparison between the measured horizontal impact force on a Figure 14 Comparison between the measured horizontal impact force on vertical wall with the predicted horizontal force by Cuomo formula. (Regular vertical wall with the predicted horizontal force by Minikin formula (SPMwaves. T=2.2 s. hs=0.135 m) version) (Regular waves. T=2.2 s. hs=0.135 m).


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m ax-pre dicte d Minikin-SPM (1963)

0.30

0.25OJo

OJg 0.20E

E

2 0.15OJcro

0.10

0.05

0.00

-10 0 10 20 30 40 50 60 70 80 90 100

p[k Pa ]

Figure 15. Comparison between the measured vertical pressure profile of 5waves creating the highest impact force with the highest predicted pressure

profile using the Minikin method. (Regular waves, T=2.2 s, hs=0.135 m)

0.30

0.25OJo

OJ-o 0.20

E

E

2 0.15OJcco

0.10

0.05

0.00

-10 o 10 20 30 40 50 60 70 80 90 100

p[k Pa ]

Figure 16. Comparison between the measured vertical pressure profile of 5waves creating the highest impact force with the highest predicted pressure

profile using the Goda (extended) method. (Regular waves, T=2.2 s, hs=0.135m )

COMPARISION BETWEEN TEST RESULTS OF MODEL-AAND MODEL-B

Fig. 19 and Fig. 20 show the comparison between the measurehorizontal force and the overturning moment both on a simple verticawall (Model-B) and a vertical wall with cantilever slab (Model-A)Force and overturning moments are shown on axis of wave height (FInormalized by water depth hs. A significant increases observed on thhorizontal force of Model-A compared to Florizontal force on Model-B(Fig. 19). This is mainly caused by the effect of a second impacoccurring at the corner of the overhanging part fixed to the verticawall. This secondary impact is the result of jets climbing on the verticawall and slamming on the horizontal part. Increase of the horizontaforce is more significant in the zone of breaking wave with small aitrapping (0.6 < Hhs < 0.9). In the zone of breaking with large aitrapping (0.9 < Hhs < 1.1), waves are curving more which results iweak vertical jets and weak pressure on the overhanging part. Theffect of pressure on the overhanging part due to the secondary impac

is more important for the overturning moment (Fig. 20).

)x-pred icted Blackmore & H ewson (1984)

0.30

L 0 .2 5

OJo


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comparative study on breaking wave forces on vertical walls with cantilever surfaces

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