CHAPTER 5.1: WAVE IMPACT LOADS - PRESSURES AND FORCES faculteit/Afdelingen... · (h) broken wave...

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CHAPTER 5.1: WAVE IMPACT LOADS- PRESSURES AND FORCES -

A. KORTENHAUS1); H. OUMERACI1); N.W.H. ALLSOP2); K.J. MCCONNELL2);P.H.A.J.M. VAN GELDER3); P.J. HEWSON4); M.WALKDEN4); G. MÜLLER5);

M. CALABRESE6); D. VICINANZA6)

1) Leichtweiß-Institut, Technical University of Braunschweig, Beethovenstr. 51a, DE-38106Braunschweig, Germany

2) HR Wallingford, Howbery Park, GB-Wallingford OX10 8BA, U.K.3) Delft University of Technology, Faculty of Civil Engineering, Stevinweg 1, NL-2628 CN

Delft, The Netherlands4) University of Plymouth, School of Civil and Structural Engineering, Palace Street, GB-Ply-

mouth PL1 2DE, U.K.5) Queens University of Belfast, Department of Civil Engineering, Stranmills Road, GB-Bel-

fast BT7 1NN, Northern Ireland6) Università degli Studi di Napoli 'Frederico II', Dipartimento di Idraulica, Via Claudio n. 21,

IT-80125 Naples, Italy

ABSTRACT

The tentative procedures for both impact and uplift loading proposed by Oumeraci andKortenhaus (1997) have been brought together and amended by many partners in PROV-ERBS. This paper proposes a procedure to calculate time-dependent pressures, forces and le-ver arms of the forces on the front face and the bottom of a vertical breakwater. For this pur-pose, (i) the data sets on which this method is based are briefly described or referred to; and(ii) a stepwise procedure is introduced to calculate the wave loading supported by some back-ground and data information. Suggestions for estimating the forces on a caisson in feasibilitystudies are also given.

LWI / HR / DUT / UE / UoN / UoP / QUB A. KORTENHAUS ET AL.

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2. INTRODUCTION

Wave impacts on vertical breakwaters are among the most severe and dangerous loads thistype of structure can suffer. Whilst many design procedures for these structures are well estab-lished worldwide recent research in Europe has shown that some of those design methods arelimited in their application and may over- or underpredict the loading under important condi-tions. This will then lead to overdesigned and very expensive structures or, even more danger-ous, to underdesign and consequently to danger to personnel and properties.

Within PROVERBS engineering experience from various fields (hydrodynamic, foundation,structural aspects) concerned with vertical breakwaters has been brought together. Further-more, data available from different hyraulic model tests, field surveys and experience fromnumerical modelling were collected and analysed to overcome the aforementioned limitations.Engineers from both universities and companies were working together to derive new meth-ods for calculating forces and pressures under severe impact conditions taking into accountthe influence of salt water and aeration of the water. This new approach was then furtheroptimized by taking into account the dynamic properties of the structure itself and the founda-tion of the breakwater (see Volume I, Chapter 3.4). The multidirectionality of the waves ap-proaching the structure (Vol. I, Chapter 2.5.3) has also been considered.

The intention of this paper is to describe a procedure to calculate both impact and uplift load-ings under 2D conditions and to give references to more detailed work on the different aspectsof the steps described in here. For sake of completeness and easier understanding of the wholemethod some parts had to be repeated from other sections within Vol. II of the PROVERBSreport. This was considered to be more useful rather than giving too many references to othersections.

Geometric dimensions and a sketch of a typical caisson breakwater are given in Fig. 1.

CHAPTER 5.1 WAVE IMPACT LOADS: FORCES AND PRESSURES

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Tab. 1: Overview of design methods for wave loading

4. OVERVIEW OF RECENT WORK

There are a number of formulae available for different types of waves breaking at the struc-ture. These formulae generally include magnitudes of maximum pressures, their distributionsand forces. In some cases, uplift pressures are given as well. All formulae are fully empiricalor semi-empirical as the process of wave breaking at the structure is still not fully explained.Tab. 1 summarizes the most important methods in a chronological order, details are given inthe respective references.

Author YearPres-sures

Forces Uplift Comments

Quasi-Static Waves

Sainflou 1928 yesyes, butdifficult

no vertical wall, no berm

Miche-Rundgren19441958

yes yes no design curves from SPM, 1984

Goda 1985 yes yes yesmost-widely used designmethod

Impact Waves

Hiroi 1919 yes yes no vertical wall

Bagnold 1939 - - - conceptual model only

Minikin 1963 yes yes nosometimes incorrect dimen-sions!

Ito 1971 yes yes yes

Blackmore &Hewson

1984 yes yes no

Partenscky 1988 yes not given no air content of wave needed

Kirkgöz19901995

yes yes no vertical wall only

Takahashi 1994 yes yes yes extension of Goda model

Allsop et al. 1996 no yes yes

Walkden et al. 1996 no yes no relation of forces and rise time

Oumeraci &Kortenhaus

1997 yes yes yes time-dependent approach!


Author YearPres-sures

Forces Uplift Comments

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McConnell 1998 no yes no amendment of O&K, 1997

Hull & Müller 1998 yes yes no amendment of O&K, 1997

Vicinanza 1998 yes yes no amendment of O&K, 1997

Broken Waves

SPM 1984 yes yes no vertical walls only

Camfield 1991 yes yes no amendment of SPM, 1984

Jensen 1984 yes yes yes Crown walls

Bradbury &Allsop

1988 yes yes yes Crown walls

Pedersen 1997 yes yes yes Crown walls

Martín et al. 1997 yes yes yes Crown walls

This paper is concentrated on calculation of pressure distribution and related forces underimpact conditions. Furthermore, the dynamic characteristics of impact forces were consideredessential for the behaviour of the structure subject to this type of loading. The designprocedure is therefore based on the approach by Oumeraci and Kortenhaus, 1997 which wasderived from solitary wave theory but amendments were made to many details like thestatistical distributions of impact and uplift pressures, the vertical pressure distribution at thefront face, and the relation between rise time and duration of impact forces.

6. OVERVIEW OF DATA SETS

Different hydraulic model tests have been carried out and analysed to obtain the designmethod proposed in this paper. These tests are summarized in Tab. 2 where the mostimportant information is given. Furthermore, references are added where more detailedinformation on these tests is available.


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Tab. 2: Overview of hydraulic model tests (random waves)

Tests YearCon-

fig.1)

Scalefsam

[Hz]Waves Slope

No.tests

Imp.2) Upl.2) References

WKS 1993 1 1:15 600 90 1:50 121 10 6Oumeraci etal., 1995

GWK 1993/94 1 1:5 100 100 1:50 62 10 5 McConnell& Korten-haus, 1996HR94 1994 10 1:20 400 500 1:50 217 8 4

PIV 1994 1 1:50 400 1 1:20 77 7 -Oumeraci etal., 1995

HR97 1997 1 1:20 1000 1000

1:501:201:101:7

9 -McConnell& Allsop,1998

QUB 1997 3 1:30 1000 800 1:50 12 1 4Kortenhaus& Löffler,1998

1) number of configurations tested; 2) number of transducers

It may be assumed from the differences in the number of waves per test and the acquisitionrate that results of pressure distributions and forces might also differ significantly.Nevertheless, data analysis has confirmed that most of the data sets fit well to each otherwhich will be explained in more details in the successive sections.

8. PREPARATORY STEPS


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Impact load

(Goda-formula not applicable)(Goda-formula applicable)

"Pulsating load"

t/T t/T t/T

(a) Standing wave (b) Slightly Breaking wave (c) Plunging breaker

F

D·g·Hb2

h

1.0

2.0

3.0

1.0

2.0

0.1 0.20.2 0.40.5 1.0

1.0

0.00.00.0

Hb F hF hF h

T=wave period

Fig. 1: Pulsating and impact load - problem definition

8.2. Identification of wave impact loading

A simple method is needed to distinguish between:(b) quasi-standing loads for which available formulae (e.g. Goda, see Vol. I, Chap-

ter 2.4.1) without any account for load duration can be used (Fig. 2a);

(d) slightly breaking wave loads which already consist of some breaking waves but notsignificantly exceeding the Goda loads (Fig. 2b);

(f) an impact load for which new formulae including impact duration are to be used(Fig. 2c); and

(h) broken wave loads, i.e. the waves already broke before reaching the structure.

For this purpose the PROVERBS parameter map (Fig. 3) was developed which is in moredetail described in Chapter 2.2 of Volume IIa. Input for this map are geometric and waveparameters which in combination yield an indication of a certain probability that one of theaforementioned breaker types will occur.


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"Vertical"Breakwaterh < 0.3b

*

dh

bBeq

sh

L

Hsi

CompositeBreakwater

0.3 < h < 0.9b*

Crown WallsRubble Mound Breakwater

h > 0.9b*

Low MoundBreakwater

0.3 < h < 0.6b*

High MoundBreakwater

0.6 < h < 0.9b*

Large waves

0.2 < H < 0.6s*

Small waves

0.1 < H < 0.2s*

Large waves

0.25 < H < 0.6s*

Small waves

0.1 < H < 0.2s*

Narrow berm

0.08 < B < 0.12*

Moderate berm w.

0.12 < B < 0.4*

Wide berm

B > 0.4*

dhs

SWL SWL

with

Small waves

H < 0.35s*

Large waves

0.35 < H s*

F =F

hh

D·g·H 2b

*

hb* h b

sh = s

*

h s

HsH = *

L

B eqB =; ; ;

t/T

2.0

6.0

8.0

0.1 0.20.0

0.0

4.0

Fhmax

Fhq

Fh*

t/T

2.0

6.0

8.0

0.1 0.20.0

0.0

4.0 Fhmax Fhq

Fh*

t/T

2.0

6.0

8.0

0.1 0.20.0

0.0

4.0 Fhmax Fhq

Fh*

Slightly breaking wave Impact loads Broken waves

t/T

2.0

6.0

8.0

0.2 0.40.0

0.0

4.0Fhmax Fhq

Fh

Quasi-standing wave

Fig. 2: PROVERBS parameter map

Hbc ' Lpi @ 0.1025 % 0.0217 @1 & Cr1 % Cr

(1)

Lpi ' L0 @ tanh 2 B @hsLpi

(2)

8.4. Breaker height at the structure

A breaking criterion which accounts for the reflection properties of the structure has been sug-gested by Calabrese (1997) (see Chapter 2.3 of Volume IIa) based on extensive random wavetests in hydraulic model tests and previous theoretical works (Oumeraci et al., 1993):

where Lpi is the wave length in the water depth hs for the peak period Tp which can be calcu-lated iteratively by:


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L0 'g2 B

@ T 2p (3)

Lpi ' L0 @ tanh 2 B @hsL0

3 / 4 2 / 3

(4)

kb ' 0.0076 @ Beq / d2 & 0.1402 @ Beq / (5)

Beq ' Bb %hb

2 tan "(6)

where L0 is the wave length in deep water which can be taken as:

or can be approximated using the method given in Fenton (1990):

The reflection coefficient Cr in Eq. (1) may be estimated as follows (Calabrese and Allsop,1998):

Cr = 0.95 for simple vertical walls and small mounds, high crestCr = 0.8 + 0.1@Rc / Hsi for low crest walls (0.5 < Rc / Hsi < 1.0)Cr = 0.5 to 0.7 for composite walls, large mounds, and heavy breaking

The empirical correction factor kb can be estimated as follows:

where Beq is the equivalent berm width which is defined as:

and Bb is the berm width in front of the structure. Further details on this approach are given inSection 2.3 of Volume IIa.


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Pb ' exp & 2 @ Hbc / Hsi2 @ 100% (7)

Hbs ' 0.1242 @ Lpi @ tanh 2 BhsLpi

(8)

Pi ' exp & 2 @ Hbc / Hsi2 & exp & 2 @ H (9)

8.6. Probability of occurrence of impacts

The parameter map as given in Fig. 3 results in different branches where the probability of therespective breaker type is not known in advance. The branch of 'impact breakers' proposes touse an impact loading formulae which generally yields much higher forces than any otherapproach for quasi-standing waves, slightly breaking waves or broken waves. Hence, it isnecessary to know how many of the waves approaching the structure will break at the wall(thus causing impulsive forces) and how many will not break at the wall (inducing nonimpulsive Goda forces).

The aforementioned method by Calabrese and Allsop (1998) described in Chapter 2.3 of Vol-ume IIa also gives a simple formula for the probability of broken waves Pb based on the ideathat every wave with a higher wave height than the breaking wave height Hbc (as calculated inSection 4.2) is already broken or will break as an impact breaker at the wall. The probabilityof occurrence of breaking and broken waves can therefore be calculated as follows:

The maximum wave height Hbs which describes the transition from impact breakers to alreadybroken waves can be described by Eq. (1) where Beq/d and Cr are set to zero which then yields:

The proportion of impacts can then be derived from:

The magnitude of the horizontal force itself is strongly related to the type of breakers at thewall which are essentially depth limited. It can be expected that the magnitude is related to therelative wave height at the wall Hsi/hs.

Eq. (9) can be regarded as a filter in the 'impact' domain of the parameter map. For very lowpercentages of impacts (smaller than 1%) the problem can be reduced to the quasi-staticproblem and the Goda method can be used to calculate pressures and forces (see Chapter 4.1of Volume IIa). In all other cases the method as described in the successive sections has to beused.


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Fh, 1/250 ' 15 @ DW g d2 @ Hsi / d

3.134 (10)

0.0 0.5 1.0 1.5

15.0

30.0

45.0

Hsi/d [-]

Random waves

A&V prediction

GWK 1993/94 WKS 1993 HR 1994

Fig. 3: Relative wave force Fh,max/(Dgd2) plotted vs. relative wave height Hsi/d andcomparison to calculation method given by Eq. (10)

10. WAVE IMPACT LOADING

10.2. Initial calculation of impact forces

Allsop et al. (1996) have investigated a large data set (10 different structure geometries, seeTab. 2) to predict horizontal wave forces on vertical breakwaters. The relative waveheight Hsi/d has been found to most significantly influence the wave forces nondimensionalized by the water depth over the berm. All forces were given at a 1/250 level thustaking the mean out of the highest two waves (500 waves per test were measured). Themagnitude of the horizontal impact force can then be estimated from:

This formula has been derived from data sets with a 1:50 foreshore slope and checked againstother slopes where it also seems to fit the data reasonably well. In Fig. 4 data from three dif-ferent model tests have been plotted and compared to the prediction method given in Eq. (10).

It can be seen from the graph that Eq. (10) gives an upper bound to the data and is onlyexceeded by some data points. Allsop et al. (1996) give the validity range of the method asHsi/d in between 0.35 and 0.6 whereas here the graph in Fig. 4 shows that it can be used up to


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F ( x̃ ) '

exp & 1 & ( @ x̃1(

with

or

exp & exp & x̃ with

(11)

relative wave heights Hsi/d = 1.3. It is not possible to take into account the structural response(dynamic load factor) as rise time and duration of the force is not calculated. Hence, Eq. (10)provides a quick estimation of the expected horizontal force to the structure but cannot predictthe length of its duration.

Furthermore, problems occur when tests were performed with a low water depth over theberm resulting in unreasonably high relative values for the forces and wave heights. For anyoccurrence probabilities of impacts higher than 1% it is therefore recommended to also usethe method described in the sucessive section.

10.4. Statistics of relative wave forces

A statistical distribution of the relative impact forces F*h,max is needed in order to allow for a

choice of exceedance or non exceedance values for the relative impact forces. Following dis-cussions and exchange of data within PROVERBS, a Generalized Extreme Value distribution(GEV) is proposed (see example for small-scale data in Fig. 5). The cumulative distributionfunction (cdf) of the GEV distribution can be written in its standard form as follows (Johnsonand Kotz, 1995):


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0.1 10.0 50.0 80.0 90.0 95.0 97.5 99.0 99.5 99.9 99.99

4.0

8.0

12.0

16.0

20.0

24.0

28.0

Non exceedance probability

GEV

Parameter (ME): n = 260 " = 3.7816 ß = 8.7819 ( = 0.0381 *)

s = 0.0917

Kolm.-Sm. Test: Dn = 0.000 " = 0.01 (%) " = 0.025 (%) " = 0.05 (%)*) scales x-axis

Fig. 4: Statistical distribution of relative impact forces observed in the WKS for randomwaves

x̃ 'x & $

"(12)

f ( x̃ ) '1 & ( @ x̃

1(

& 1@ exp & 1 & (

exp & x̃ @ exp & exp & x̃

(13)

In Eq. (11) the standardized x-parameter x̃ can be written as follows:

The probability density function (pdf) of the GEV in its standardized form can be given as:

where parameters ", $ and ( can be taken from model tests similar to the structure to bedesigned or can generally be estimated as " = 3.97; $ = 7.86; and ( = -0.32. The latter valueswere derived from large-scale tests with a 1:50 foreshore slope and almost non-overtoppingconditions (GWK, 1994) and are used in PROVERBS for all probabilistic calculations ofstructures where impact waves are considered. Further advice for different bed slopes havebeen given by McConnell and Allsop (1998) so that the following parameters for further usecan be suggested:


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Tab. 3: Values of ", $, and ( for GEV distribution of relative horizontal force

F (

h, max '"(

1 & & ln P F̂ (

h, max

(% ß (14)

Fh, max ' F (

h, max @ D g H2b (15)

Bed slope no. waves scale "" $$ ((

1:7 116 .1:20 / HR97 2.896 6.976 -0.526

1:10 159 .1:20 / HR97 10.209 12.761 -0.063

1:20 538 .1:20 / HR97 3.745 7.604 -0.295

1:50 3321 .1:20 / HR94 1.910 3.268 -0.232

For details on HR94 and HR97 tests see Tab. 2

In Kortenhaus (1998) the influence of the number of waves on statistical parameters of thevarious distributions available has shown that the number of data points should be not lessthan about 250. The values given in Tab. 3 for bed slopes of 1:7 and 1:10 should therefore beconsidered carefully. More details on the influence of geometric and wave parameters onstatistics of wave impact forces can also be found in Kortenhaus (1998).

Furthermore, Eq. (11) has been used to plot data from other wave flumes where significantdifferences were observed resulting in much higher relative forces (McConnell and Allsop,1998). These differences are assumed to be mainly due to the differences in logging fre-quencies (GWK: 100 Hz; WKS: 600 Hz; HR94: 400; HR97: 1000 Hz), the different numberof waves per test (GWK: 100; WKS: 100; HR94: 500; HR97: 1000) and the different totalnumber of impacts as given in Tab. 3.

Eq. (11) can be transformed using Eq. (12), yielding the force as a function of the probabilityof the horizontal impact force:

where P(F*h,max) is the probability of non exceedance of relative impact forces which generally

may be taken as 90% and F*h,max is the relative horizontal force at the front face of the structure

non dimensionalised by DgHb2. The maximum horizontal force can then be calculated by :


1) The triangular shape is derived from the actual force history based on the equivalence ofbreaking wave momentum and force impulse.

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trFh ' k @ 8.94deff / g

F (

h, max

(16)

deff ' d % Brel @ mrel @ hs & d (17)

where Hb is the wave height at breaking (Eq. (1)) and D is the density of the water.

10.6. Calculation of impact force history

A full impact force history is needed to account for the temporal variation of the forces andpressures induced by the breaking wave. For practical reasons the typical impact force historymay be reduced to a triangle1) (Fig. 6) which is described by the rise time tr and the total dur-ation of the force td as discussed below.

10.6.2. Rise time tr

Following considerations derived from solitary wave theory (Oumeraci and Kortenhaus,1997) a relationship between relative impact force peak F*

h,max = Fh,max/DgHb2 and the rise time

trFh can be derived. It is proposed to use the following equation for trFh:

The effective water depth in front of the structure deff can be assumed to be identical to thewater depth in which the wave breaks and may be calculated as follows:


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t

tdFh

t rFh t

F h,max

rFhIrFhI

dFhI

dFhI

F hF h

t d

t r

Fig. 5: Substitution of actual force history by an equivalent triangular load

Brel '

1 for smaller

1 & 0.5 ·BbL

for larger(18)

mrel '

1 for steeper slopes1

mfor flatter slopes (19)

where Brel is the part of the berm width which influences the effective water depth (Brel = 1 forno berm width):

and mrel is the part of the berm slope influencing the effective water depth (mrel = 0 for simplevertical wall):


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k 'MimpMtot

'IrFhIdFh

(20)

b) Deterministic approach

The k-factor used in Eq. (16) is dependent on the breaker type and the fluid mass directlyinvolved in the impact process and can be expressed as follows:

where Mimp is the mass part involved in the impact; Mtot is the total mass of the breaking wavemoving towards the structure and IrFh and IdFh are the corresponding force impulses. Thisapproach is based on solitary wave theory again and thus is regarded as preliminary forrandom waves. Detailed investigations on pressure impulses on vertical walls and breakwatershave been performed by Bristol University and references are given in Vol. I, Section 2.5.5.Specific details on the most relevant parameters involved can be found in Cooker andPeregrine (1990).

Preliminary analysis by early PIV measurements in 1994 (Oumeraci et al., 1995) and moredetailed analyses of breaker types at University of Naples (Vicinanza, 1998) together withUniversity of Edinburgh derived from random wave trains have shown that

@ even though there is some scatter the k-parameters for waves breaking over low andhigh berms are in the same range;

@ a mean value of k = 0.205 ± 20% (standard deviation of 11%) can be assumed for allplunging breakers regardless the relative height of the berm.

Eq. (16) is compared to random wave data from three different model tests in Fig. 7. All datasets have been re-analysed where the following filters were applied:

@ the highest 10 waves of each test;@ only breaking waves of the highest 10 waves (following the criteria as given by

Kortenhaus and Oumeraci, 1997);@ the total duration td is shorter than 6 times the rise time tr (to avoid unreasonable results)

These filters reduce the scatter considerably and will lead to some other formulae thanindicated by previous papers (Oumeraci and Kortenhaus, 1997). Fig. 7 shows that theproposed formula represents a curve fitted to most of the random data sets whereas an evenbetter fit is obtained for solitary waves (Oumeraci and Kortenhaus, 1997). Data fromMcConnell and Allsop (1998) have not yet been plotted using the aforementioned filters but itis assumed that the high values found in these data are reduced considerably as well.


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0.0 0.5 1.0 1.5 2.0 2.5

15.0

30.0

45.0

Relative rise time t rFh /%(d eff /g) [-]

Random waves GWK 1993/94 WKS 1993 HR 1994

No. of tests = 239

McConnell & Allsop, 1998

Eq. (16), k = 0.205

Fig. 6: Comparison of prediction formula to large-scale measurements (random waves)

The equivalent 'triangular' rise time tr (see Fig. 6) is assumed to be much shorter for breakingwaves, especially when rise times are very short. For longer rise times it is expected that trian-gular rise time tr and measured rise time trFh are in the same range. For non breaking waves itmay be expected that the rise time is no longer than a 1/4 of the wave period whereas forbreaking waves much shorter relative rise times can be assumed. It is, however, extremelydifficult to derive a clear relationship between both values so that the ratio trFh/tr was derivedfor the GWK, WKS and some of the HR94 data and a statistical distribution was plotted(Fig. 8).


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Fig. 7: Probability distribution for triangular rise time ratio for horizontal forces

This best fit was achieved by a log-Normal distribution with a mean value of 1.487 and a stan-dard deviation of 0.667. The mean value is higher than what was found in Oumeraci andKortenhaus (1997) which is most probably due to that only breaking waves are included in thepresent analysis.

d) Probabilistic approach

For probabilistic calculations the aforementioned uncertainties in the relations of rise time totriangular rise time and triangular rise time to relative impact force were considered together.This was achieved by defining a factor k' which summarizes k*8.94 (right side of Eq. (16))and the relation of the measured rise time trFh (left side) and the 'triangular' rise time tr (assum-ing a constant relationship). Eq. (16) will then read:


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tr ' k ) @deff / g

F (

h, max

(21)

From statistical analysis of the unfiltered data the factor k' can best be described by aLogNormal distribution with a mean value of 0.086 and a standard deviation of 0.084 (Van


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td ' tr @ 2.0 % 8.0 @ exp &18 @ tr / Tp (22)

0.00 0.05 0.10 0.15 0.20 0.25

5.0

10.0

Relative rise time t r/T p [-]

Random waves

GWK 1993/94 WKS 1993 HR 1994

No. of tests = 239

t = 2*t rd

Eq. (22)

Fig. 8: Triangular impact duration td vs. relative triangular rise time tr for random waves

Gelder, 1998). These values are again based on results from large-scale hydraulic model testswhich are believed to best represent the situation under prototype conditions.

10.6.4. Total duration td


The relationship between rise time and total duration of the impact is dependent on thebreaker type. The aforementioned filter which was applied to the data sets has led to a newapproach describing the total duration of impact forces:

In Fig. 9 this relation is examplarily plotted for random wave tests. According to what wasexpected the total duration is rarely smaller than 2.0, i.e. the decay time of the impact isusually longer than the rise time. For longer relative rise times the total duration is close to 2.0whereas for shorter rise times the factor can increase significantly. When ignoring very sharppeaks (and thus very high ratios of td/tr) Eq. (22) gives a good estimate of the upper bound ofthese data.


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td '&c

ln ( tr )(23)

Ihr '12@ Fh,max @ tr (24)

Ihd '12@ Fh,max @ td (25)


Upper bound approaches as given in the previous section are not applicable for probabilisticdesign. Therefore, a relation of rise time and total duration was derived by Van Gelder (1998)where td can be calculated from tr by:

Eq. (23) is dimensionally incorrect but has given the best correlation of the data. In Eq. (23) cis a random variable (dimension: [-s@ln(s)]) with a Gaussian distribution which can be givenby its mean value (c = 2.17) and its standard deviation (F = 1.08). Again, these valuescorrespond to large-scale measurements without any filtering of the data. Different parameterswere found from other (small-scale) tests which indicates that filtering of the data as indicatedabove would be useful for this statistical approach as well.

10.6.6. Force impulses Ihr and Ihd

Force impulses are more relevant to the response of the overall structure than the impactforces and should therefore be calculated and probably used for the selection of the worstdesign situation of the brakwater. Since rise time (or total duration, respectively) and themaximum force are known (Eqs. (21) and (23)), the force impulse over the rise time Ihr can beobtained from:

and the horizontal force impulse over the total duration Ihd can be calculated as follows:


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t

Fh(t)

t d

t r

DWL

d

Fh,max

p3 = 0.45 p

1

t

Fh (t)

p1

Fh,maxl Fh

p4

DWL = Design Water Level

dc

0 = 0.8@ H b*

cR

cR = Freeboard

Fig. 9: Simplified Pressure Distribution at a Vertical Wall

10.8. Pressure distributions at the wall

Two types of pressure distributions were proposed and discussed within PROVERBS one ofwhich is based on extensive large-scale testing of waves breaking at a vertical wall whereasthe other is derived from small-scale tests of a composite breakwater with extensive variationof geometric and wave conditions. Both distributions start with the maximum force at the wallas the dominant input parameter so that the overall loading of the structure is identical in bothcases. It should be noted that results from these pressure distributions are not used forprobabilistic calculations. Both approaches are described in the following.

10.8.2. Distributions from vertical wall tests

Based on the analysis of almost 1000 breakers of different types hitting a vertical wall, thesimplified distribution of impact pressure just at the time where the maximum impact forceoccurs, can tentatively be determinated according to Fig. 10. Three or four parameters need tobe calculated in order to describe the pressure distribution: (a) the elevation of the pressuredistribution 0* above design water level; (b) the bottom pressure p3; (c) the maximum impactpressure p1 which is considered to occur at the design water level; and (d) the pressure at thecrest of the structure if overtopping occurs.


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0( ' 0.8 Hb (26)

p3 ' 0.45 p1 (27)

Fh( t ) '12p1 ( t ) @ 0.8 @ Hb % d % dc (28)

p1 ( t ) 'Fh ( t )

0.4 @ Hb % 0.7 @ d % dc(29)

p4 '

0 für 0(< Rc

0(& Rc0(

p1 für 0($ Rc

(30)

b) Elevation of pressure distribution 0*

The elevation of pressure distribution 0* may be calculated from the following tentativeformula (see Fig. 10):

d) Bottom pressure p3

The bottom pressure p3 may be derived as a function of the maximum pressure at the height ofthe still water level as follows (see Fig. 10):

f) Maximum pressure p1

The maximum impact pressure p1 can be calculated directly from the equivalent force history(Fig. 10), since Fh(t) represents the area of the pressure figure at any time of the history(assuming an infinitely high wall):

Substituting Eq. (27) in Eq. (28) yields:

h) Pressure at the crest of the structure p4

If the waves in front of the structure are high enough, overtopping is expected to occur. Thiswill reduce the total impact force as parts of the energy of the wave will get lost. This effectcan be taken into account by cutting off the pressure distribution at the top of the structure(Fig. 10) so that the pressure at the crest of the structure can be described as follows:


1) Consequently, the statistical distribution given in Fig. 5 is no longer valid for thisreduced force as the statistical distribution was determined for relatively high caissonstructures and almost no overtopping.

- 24 -

Fh,max,ov ' Fh,max &12@ 0

(& Rc @ p4 (31)

0.0 25.0 50.0 75.0 100.0 125.0

0.0

0.5

1.0

0.0

-0.5

P / Pmax [%]

Wave run-up

PulsatingImpact

(0 / -0.9)

(40 / -0.25)

(100 / 0)(40 / 0.17)

(8 / 0.4)

(0 / 1.2)

DWL

Fig. 10: Vertical pressure distribution after Hullet al. (1998)

z 'y @ hbh 2s

(32)

The horizontal impact force1) is then reduced to:

10.8.4. Pressure distributions from breakwater tests

Very recently, Hull et al. (1998) proposed a different pressure distribution based on the HR94data set (see Tab. 2). This distribution is given in a non dimensionalized form only dependenton the maximum pressure observed at still water level, pmax, the height of the berm, hb, and theheight of still water level at the toe of the foundation, hs. Fig. 11 shows this pressuredistribution which is separated into three areas: pulsating, impact, and wave runup.

This distribution has been derivedfrom all composite type breakwaterstested (10 different configurations)and can therefore be used for anystructural configuration. The z-coordinate at the wall is obtained for avery high wall (no overtopping) asfollows:

where hb is the height of the berm, hs is the water depth at the toe of the foundation, and y isthe vertical distance above or below still water level (positive upwards). All points of the dis-tribution may be calculated using the coordinates given in the graph. The relative pressures inthis graph are only dependent on the maximum pressure pmax, and the vertical coordinate isonly dependent on two known variables. Hence, the integration of this distribution is straight-forward for a very high wall with no overtopping and relatively deep water over the berm. Thesummation of areas of the relative pressure distribution then yields:


- 25 -

Fh,max ' 0.5112 @ pmax @h 2s

hbif R (

c > (33)

Fig. 11: Relative maximum pressure at SWL andlever arm of forces as a function ofrelative water depth at the structure (Hullet al., 1998)

where Rc* is defined as relative crest

height (= Rc@hb/hs2) and d* is the

relative water depth at the structure(= d'@hb/hs

2), d' being the distance fromthe bottom of the caisson to the stillwater level. The maximumpressure pmax and the lever arm of theresultant force z can graphically beestimated from Fig. 12 using as inputthe relative water depth at the wall.

For calculation, a distinction of caseswill be necessary, if all types of wallshall be considered. The maximumpressure at the wall, pmax, has to becalculated from Fhmax to obtain the fullpressure distribution. Therefore, thefollowing steps are needed:

2) find equations to describe the integration of pressure distribution to give the maxi-mum horizontal force dependent on

@ crest height Rc, and @ water depth d';

4) rearrange these equations such that the maximum pressures can be derived from themaximum horizontal force.

Regarding the first point Eq. (33) can be expanded to three equations where the first gives areduction due to low crest level (still assuming that d* > 0.9):


- 26 -

pmax @h 2s

hb@ 0.5112

Fh,Rc ' pmax @h 2s

hb@ 0.4632 % 0.04 R (

c

pmax @h 2s

hb@ 0.3832 % 0.24 R (

c

(34)

pmax @h 2s

hb@ 0.3312 % 0.2 d (

Fh,d ) ' pmax @h 2s

hb@ 0.2832 % 0.04 R (

c %

pmax @h 2s

hb@ 0.2032 % 0.24 R (

c %

(35)

pmax @h 2s

hb@ 0.2062 % 0.7 d (

Fh,d ) ' pmax @h 2s

hb@ 0.1582 % 0.04 R (

c %

pmax @h 2s

hb@ 0.0782 % 0.24 R (

c %

(36)

The second equation calculates a further reduction due to lower relative water depths 0.25 <d* # 0.9:

and the third gives the force for low water levels over the berm (d* < 0.25):

The case where Rc* is smaller than 0.17 is not considered here as this is very unlikely to hap-

pen. For this case it can be assumed that no impacts will occur as the crest height is too low(waves will heavily overtop the structure).

From Eqs. (34) to (36) the maximum pressure can be easily calculated by solving these equa-tions for pmax. For all cases the pressure distribution can then be calculated using the relativecoordinates of Fig. 11 and considering the relative crest height and the relative water depth,respectively.


- 27 -

lFh(t) 'p1@0

2ov % 3@p1@d

)@0ov% 3@p4@0ov@d)

6 @Fh ((37)

0ov ' min 0(; Rc (38)

d ) ' d % dc (39)

10.10. Lever arm of horizontal force

Finally, the lever arm for the horizontal impact force can be calculated from the pressure dis-tribution as given in Fig. 10 at the wall as follows:

In Eq. (37) 0ov is defined in relation to the height of the wave crest to the wall (see Fig. 10):

and d' is defined as:

In case of the second pressure distribution described under Section 5.4.2 the analytic calcu-lation of the lever arm of the horizontal force is rather complicated and very much dependenton the relative water depth and crest height. For simplicity reasons it may be either assumedthat the force attacks at the height of the still water level or the height may be taken fromFig. 12.

12. WAVE UPLIFT LOADING

The procedure for calculating the uplift pressures and forces is similar to the procedure forcalculation of horizontal components in Section 5. A Generalized Extreme Value (GEV)distribution was also found to fit the data and is consistent to the method used for impactforces (see example for small-scale test in Fig. 12). The GEV distribution function has alreadybeen defined in Eqs. (11) and (13).

Parameters for application of the GEV to relative uplift forces can be taken from large-scaletests (for quasi-non overtopping conditions " = 2.17; $ = 4.384; ( = -0.11). The sameprocedure as already used for horizontal forces can be applied to derive the relative upliftforce resulting in:


- 28 -

F (

u, max '"(

1 & & ln P F̂ (

u, max

(% ß (40)

0.1 10.0 50.0 80.0 90.0 95.0 97.5 99.0 99.5 99.9 99.99

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

Non exceedance probability

GEV

Parameter (ME): n = 255 " = 2.5100 ß = 5.6278 ( = 0.0457 *)

s = 0.0784

Kolm.-Sm. Test: Dn = 0.000 " = 0.01 (%) " = 0.025 (%) " = 0.05 (%)*) scales x-axis

Fig. 12: Statistical distribution of relative uplift forces observed in the WKS for randomwaves

dtFu ' trFu & tr (41)

12.2. Calculation of uplift force history

Similar parameters are needed to describe the uplift force history than already used for theimpact forces (see Figs. 6 and 17):

(b) tru = triangular rise time;(d) tdu = triangular total duration of maximum uplift force;

It should be stressed that the times listed above are not necessarily identical to the times forthe impact loads. If it is assumed that t0 is identical for both impact and uplift loading the timedifference between the peaks can be calculated as follows (McConnell and Kortenhaus,1997):


- 29 -

trFu ' ku @ 8.94deff / g

F (

u, max

(42)

0.0 0.5 1.0 1.5 2.0 2.5

15.0

30.0

45.0

Relative rise time t rFu /%(d eff /g) [-]

Random waves

No. of tests = 239 GWK 1993/94 WKS 1993 HR 1994

Eq. (42), k = 0.205

Fig. 13: Relative uplift force versus relative rise time (GWK data)

trFu ' 1.83 @deff / g

Fu, max@ D @ g @ H 2

b (43)

12.2.2. Rise time tru


The following relationship between relative uplift force peak F*u,max = Fu,max/(DgHb

2) and risetime tr was derived from Fig. 14 following the procedure for impact loads:

The effective water depth deff can be assumed to be identical to the water depth in which thewave breaks and may be estimated by the procedure described for impact loads (Eq. (17)).The ku-factor used here is dependent on the breaker type and the part of the mass taking part inthe impact process, and will be set to ku = k = 0.205 ± 20% identical than for the impactforces. From Eq. (42) the total duration trFu can then be calculated as follows:


- 30 -

Fig. 14: Probability distribution for triangular rise time ratio for uplift forces

The relation between tru and trFu was derived as a probability distribution again (see sec-tion 5.3.1 for horizontal forces). For uplift forces, however, the distribution is no longer a log-Normal distribution but better described by a Generalized Extreme Value distribution(Fig. 15). The mean value of this ratio is 1.11, thus again larger than the value proposed byOumeraci and Kortenhaus (1997). This is again due to the filtered values where only breakingwaves are taken into account.


For probabilistic design the same equation than for horizontal forces (Eq. (21)) was used foruplift forces as well. The k'u parameter (for uplift forces) corresponds to k' (for impact forces)and has a mean of 0.16 and a standard deviation of 0.17.


- 31 -

tdu ' tru @ 2.0 % 8.0 @ exp &18 @ tru / Tp (44)

0.00 0.05 0.10 0.15 0.20 0.25

5.0

10.0

Relative rise time t ru/T p [-]

Random waves

Eq. (44)

GWK 1993/94 WKS 1993 HR 1994

No. of tests = 239

td = 2*t r

Fig. 15: Relative triangular total duration versus relative triangular rise time (GWK data)

12.2.4. Total duration tdu


The triangular total duration of the uplift force tdu can be obtained from the rise time tru byusing the following relationship similar to Eq. (22) for horizontal forces:

This relation was obtained from all data sets again (Fig. 16) and shows a large scatter. Eq. (44)gives the upper bound of this relation which might be used as a conservative approach.



- 32 -

tdu '&cu

ln ( tru )(45)

Again, Van Gelder (1998) has proposed the same formula than for impact duration and risetime (see Eq. (23)).

where cu is again normally distributed with a mean value of 1.88 for large-scale tests and astandard deviation of 0.99.

Given the rise time of the uplift force and the total duration, the force history can be calculatedfor each time step by interpolating the times between t0 and the uplift force maximum at thetime tru and the total duration tdu (Fig. 17).

12.4. Pressure distributions

Uplift pressures underneath vertical breakwaters should generally be calculated using theapproach described in Section 3.5.3 where the instantaneous pore pressure developmentunderneath the breakwater is described.

However, a very simple approach was derived empirically from the data available and is basedon hydraulic model test data using 'upper bound' envelopes which may lead to conservativeestimates. Therefore, all results should be compared to the pressures derived by using theGoda model (see Vol. I, Section 2.4.1) and are expected to be larger than those. It wasobserved from hydraulic model tests that the uplift pressure distribution (Fig. 17) should atleast be digitized in three points (Kortenhaus and Oumeraci, 1997):

@ pressure at the seaward edge of the structure pu;@ pressure at the shoreward edge of the structure pru (as it is not necessarily zero); and@ pressure at about 25% of the structure width from the seaward edge pmu (as the maxi-

mum of the uplift force was observed to occur when the shock wave traveling under-neath the structure has reached this point).


- 33 -

t

Fu(t)

t du

t ru

DWL

d

Fu,max

t

Fu (t)

DWL = Design Water Level

pu

pru

Fu

l Fu

cBR = Freeboardc

cR

pmu

c0.25@B

dc

Fig. 16: Approximate pressure distribution for temporal development of pressure distribu-tion

For impact forces the pressures were given as functions of the impact force itself and the pres-sure distribution was assumed to remain constant in itself. A similar principle will be followedhere but the number of points to form the pressure distribution is reduced to only two for sim-plicity reasons. Furthermore, the pressure underneath the landward side of the structure willbe calculated using relative wave parameters. The pressure distribution is assumed to be con-stant in itself over the time.

12.4.2. Pressure at the shoreward edge of the structure pru

Different pressure heads underneath the shoreward edge of the structure were reported frommodel tests and prototype conditions in PROVERBS where many times pressures up to thesame magnitude than at the seaward side were measured (rectangular pressure distribution).Explanation of the processes involved have been provided by Van Hoven (1997), Hölscher etal. (1998), and Peregrine (1997) which indicates that the most relevant parameters responsiblefor non zero pressures are the exit area, the foundation material and the water depth behind thestructure. However, most of these parameters were kept constant over the tests so that analysisof the data did not take this into account.


- 34 -

pruD @ g @ Hb

'Hbhs

& 0.1 (46)

0.00 0.16 0.32 0.48 0.64 0.80

0.18

0.36

0.54

0.72

0.90

Hb/hs [-]

GWK

Fig. 17: Uplift pressure underneath the shoreward edge of the breakwaters in GWK andWKS

pru ' D @ g @ Hb @Hbhs

& 0.1 (47)

The inital analysis of available data for pressures underneath the shoreward edge of the break-water related these pressures to the wave parameters by applying an upper envelope to thedata for the time of the maximum uplift force (Fig. 18). From this the following empiricalformula was achieved:

which can easily be transformed to:

For all times 0 # tru # tdu the respective values may be interpolated from the above followingthe same principle than already used for the uplift force history (Fig. 17).


- 35 -

pu '2 @ Fu,max

Bc& pru (48)

lFu ( t ) 'B 2c @ pru % 2 @ pu

6 @ Fu,max(49)

12.4.4. Pressure at the seaward edge of the structure pu

Since the pressure at the shoreward side of the structure is known the pressure underneath theseaward edge pu can be calculated as follows:

where Bc is the structure width, Fumax is the maximum uplift force and pru is the pressure at theshoreward side of the structure.

12.6. Lever arm of uplift force

Finally, the lever arm for the uplift force can be calculated from the pressure distributionunderneath the structure for each time step as follows:

14. AERATION OF IMPACT WAVES

All results discussed so far have been achieved from model tests at different scale using freshwater. These results are very difficult to directly apply to prototype conditions as there are alot of additional factors which should be taken into account. One of these phenomena which ismost difficult to account for is the aeration of both non breaking and impact waves.

Crawford et al. (1997) have reported field and model measurements performed with bothfresh and sea water. The different behaviour of air bubbles in the breaking process of waveshitting a (almost) vertical breakwater is described, as well as effects of this behaviour:

@ for non breaking waves, similar results were obtained for fresh and sea water when gen-erally very little aeration was observed in the reflected waves;

@ for impacting waves, field measurements have shown that high aeration levels coincidewith long rise times and lower pressures whereas short duration high peaked pressureswere also observed, but do occur at lower aeration levels;

@ comparing results with fresh and sea water under laboratory conditions has shown thatpressures are generally higher with longer rise times and vice versa, thus following theobservations made in the field;


- 36 -

Pa ' 2.0 % 5.3 @ Ni (50)

Ni ' Pi @NWttot

(51)

kfa '7.726

2.5 % Pa 97.5 & Pa0.372 (52)

kta '1kfa

(53)

These results have led to some simple guidance on estimating the aeration of impact wavesand its influence on the impact force (Hewson et al., 1998) which might be adopted for designpurposes. The aeration in impact waves can be calculated to:

where Ni is the number of breaking waves per minute and Pa is the percentage of aeration inthe breaking wave given in percent. The number of breaking waves per minute, however, isnot known in advance but may be estimated for model tests using the percentage of breakingwaves in a test Pi (Eq. (7)):

where NW is the number of waves in a test, and ttot is the total length of the test given in min-utes. Under prototype conditions NW may be replaced by the number of the waves in a stormwhereas ttot is the duration of the design storm.

From the aeration percentage obtained by Eq. (50) a force reduction factor kfa according toHewson et al. (1998) can be calculated as follows:

It has also been shown that the total force impulses seemed to remain independent from theaeration level of the breaking wave. Assuming this impulse to be more or less equal to the tri-angular impulse as given by Eq. (24) longer rise times due to aeration can be calculated as theinverse of the force reduction factor:

Since uplift and impact loading are strongly coupled it can be expected that the uplift forcewill be dependent on the aeration in the same way though no data supporting this are yetavailable. The working assumption therefore is to use Eqs. (50) to (53) for uplift forces aswell.


- 37 -

16. CONCLUDING REMARKS

The extremely complex phenomena of wave breaking at a vertical wall has been investigatedin PROVERBS. Hydraulic model tests, numerical modelling, field measurements and deskstudies have been performed to improve the physical knowledge of the phenomena involved.Significant progress has been achieved related to this problem and eventually have led toimproved design procedures for impact loading which are summarized in this and othersections of Chapter 5 in Volume IIa ('Breaking Wave Loads'). The calculation process withinthis section is graphically summarized in Fig. 19.


- 38 -


- 39 -

Geometric ConditionsFig. 1

Wave ConditionsVol. IIa, Chapter 2

Parameter MapFig. 3

Impact FilterSection 4.3

Quasi-StaticLoading

ImpactLoading

Volume IIaChapter 4.1

Parameter Outputp (t) to p (t)1 4 u ru h u h u Fh Fu, p (t), p (t) , F (t), F (t) , M (t), M (t) , l , l

HbcEq. (1)

PiEq. (9)

Horiz. Force

@ initial force calc.(Eq. (10))

@ statistics of rel. force(Fig. 5, Eq. (14))

@ calc. of force history(Eqs. (21), (23))

@ reduction by aeration(Eqs. (50) to (53))

Uplift Force

@ statistics of rel. force(Fig. 11, Eq. (43))

@ calc. of force history(Eqs. (21), (45))

@ reduction by aeration(Eqs. (50) to (53))

Press. Distr.Vert. Wall(Eqs. (26) to (30))

Press. Distr.Breakwater(Eqs. (32) to (36))

Press. Distr.Uplift

(Eqs. (46) to (48))

Fig. 18: Overview of calculation scheme for impact loading (probabilistic approach)


- 40 -

This section therefore summarizes and updates two tentative procedures for calculating time-dependent pressures and forces at the front face and underneath vertical breakwaters subject toimpact breakers. The performed improvements as compared to previous versions of thismethod (Oumeraci and Kortenhaus, 1997) are as follows:

@ updated method to calculate the breaking wave height in front of vertical breakwatersfollowing the formulae proposed by Calabrese and Allsop (1997);

@ new procedure to calculate the percentage of impacts for given geometric and waveconditions following the same method as described above;

@ simple calculation method to estimate relative wave impact forces for feasibility andpreliminary design studies (Allsop et al., 1996);

@ use of updated relative wave impact and uplift forces to be used for statistical dis-tributions;

@ new distribution type to present the statistics of both impact and uplift forces (Gener-alized Extreme Value (GEV) Distribution);

@ new results of k-values to estimate the part of the water mass involved in the impacttaken from analysis of PIV-measurements (Vicinanza, 1998);

@ application of method to different bed slopes and improvement of statistical parametersused for calculating the relative forces (McConnell and Allsop, 1998);

@ implementation of new results regarding aeration of impact waves as reported byCrawford et al. (1996) and Hewson et al. (1998);

@ new statistical relation between total duration of wave forces and rise times for bothimpact and uplift loadings (Van Gelder, 1998);

@ new vertical pressure distribution as proposed by Hull et al. (1998).

The dynamic loading described in this section cannot be directly compared to a quasi-staticloading as described in Section 4.1 of Volume IIa. To allow for any comparison the


- 41 -

dynamic loading has to be transformed into a quasi-static loading which has the same effect tothe structure than the dynamic loading. This can principally be done by using the dynamicload factor concept which is in more detail described in Chapter 3 of Volume IIb.

The 3D character of waves in nature has been ignored in describing the methods to calculatethe loading. However, it is believed that especially for impact breakers there is a verysignificant difference between 2D and 3D cases as impacts do occur very locally. A detaileddescription of model tests performed within PROVERBS and results to reduce the magnitudeof the loading due to these effects are described in Section 5.3 of this volume.

ACKNOWLEDGEMENTS

This work has been compiled under the European Union funded PROVERBS project(Probabilistic Design Tools for Vertical Breakwaters) under contract no. MAS3-CT95-0041and other additional national funding sources.

Many partner institutions have contributed to this section by performing the model tests,analysing and providing the data, and giving comments and proposals for improving the work.All these contributions are gratefully acknowledged.

REFERENCESALLSOP, N.W.H.; VICINANZA, D.; MCKENNA; J.E. (1996): Wave forces on vertical and

composite breakwaters. Strategic Research Report. Hydraulic Research Wallingford,SR 443, Wallingford, U.K., 94 pp.

CALABRESE, M. (1997): Onset of breaking in front of vertical and composite breakwaters.Proceedings 2nd Task 1 Workshop, MAST III, PROVERBS-Project: ProbabilisticDesign Tools for Vertical Breakwaters, Edinburgh, U.K., Annex 1.0.4.

CALABRESE, M.; ALLSOP, N.W.H. (1997): Impact loadings on vertical walls in directionalseas. Proceedings 2nd Task 1 Workshop, MAST III, PROVERBS-Project: ProbabilisticDesign Tools for Vertical Breakwaters, Edinburgh, U.K., Annex 1.2.7, 16 pp.

CALABRESE, M.; ALLSOP, N.W.H. (1998): Effects of obliquity on wave loads on verticalwalls. Proceedings International Conference Coastal Engineering (ICCE), ASCE,Copenhagen, Denmark, no. 26, 2 pp.

COOKER, M.J.; PEREGRINE, D.H. (1990): A model for breaking wave impact pressures.Proceedings International Conference Coastal Engineering (ICCE), ASCE, Delft, TheNetherlands, no. 22, Volume 2, pp. 1473-1486.


- 42 -

CRAWFORD, A.R.; BULLOCK, G.N.; HEWSON, P.J.; BIRD, P.A. (1997): Wave impactpressures and aeration at a breakwater. Ocean Wave Measurement and Analysis, Waves'97 Proceedings of International Symposium, Virginia, USA, no. 3, 14 pp.

FENTON, J.D.; MCKEE, W.D. (1990): On calculating the length of water waves. CoastalEngineering, Amsterdam, The Netherlands: Elsevier Science Publishers B.V., vol. 14,pp. 499-513.

HEWSON, P.J.; CRAWFORD, A.R.; WALKDEN, M.J.A. (1998): Effect of aeration on waveimpact forces. Proceedings 2nd Overall Project Workshop, MAST III, PROVERBS-Project: Probabilistic Design Tools for Vertical Breakwaters, Naples, Italy, Chapter1.5a), 5 pp.

HÖLSCHER, P.; ZWANENBURG, C.; DE GROOT, M.B.; LUGER, H.J. (1998): HindcastHannover breakwater. Research Report, Delft Geotechnics, Part IV: Evaluation,CO-364920/103, Delft, The Netherlands, 64 pp., Annexes.

HULL, P.; MÜLLER, G.; ALLSOP, N.W.H. (1998): A vertical distribution of wave impactpressures for design purposes. Research Report, MAST III, PROVERBS-Project:Probabilistic Design Tools for Vertical Breakwaters, Belfast, Northern Ireland, 16 pp.

JOHNSON, N.L.; KOTZ, S.; BALAKRISHNAN; N. (1995): Distributions in statistics. II.Continouus univariate distributions, New York: Wiley, 2nd edition, 719 pp.

KORTENHAUS, A.; OUMERACI, H. (1997): Wave uplift loading for impact breakers -tentative formulae and suggestions for the development of final formulae. Proceedings2nd Task 1 Workshop, MAST III, PROVERBS-Project: Probabilistic Design Tools forVertical Breakwaters, Edinburgh, U.K., Annex 1.0.3, 14 pp.; 2 Annexes.

KORTENHAUS, A. (1998): Statistics of impact and non impact waves. Discussion Note,MAST III, PROVERBS-Project: Probabilistic Design Tools for Vertical Breakwaters,Braunschweig, Germany, 13 pp.; 1 Annex.

KORTENHAUS, A.; LÖFFLER, A. (1998): Analysis of new model experiments on upliftunderneath vertical breakwaters. Research Report. MAST III, PROVERBS-Project:Probabilistic Design Tools for Vertical Breakwaters, Braunschweig, Germany, 51 pp., 4Annexes.

MCCONNELL, K. (1998): Revetment systems against wave attack - a design manual.London, U.K.: Thomas Telford, 168 pp.

MCCONNELL, K.J.; KORTENHAUS, A. (1996): Analysis of pressure measurements fromhydraulic model tests and prototype measurements - discussion note. ProceedingsTask 1 Workshop Belfast, MAST III, PROVERBS-Project: Probabilistic Design Toolsfor Vertical Breakwaters, 2nd Draft, Annex 19, Belfast, Northern Ireland, 13 pp., 5Annexes.

MCCONNELL, K.J.; KORTENHAUS, A. (1997): Analysis of pressure measurements fromhydraulic model tests and prototype measurements. Proceedings 1st Overall ProjectWorkshop, MAST III, PROVERBS-Project: Probabilistic Design Tools for VerticalBreakwaters, Las Palmas, Gran Canaria, Annex C3, 14 pp., 1 Annex.


- 43 -

MCCONNELL, K.J.; ALLSOP, N.W.H. (1998a): Prediction of wave impact forces anddurations: further considerations and discussion. Proceedings 2nd Overall ProjectWorkshop, MAST III, PROVERBS-Project: Probabilistic Design Tools for VerticalBreakwaters, Naples, Italy, Class 2 Report, Chapter 1.5a), 8 pp.

MCCONNELL, K.J.; ALLSOP, N.W.H. (1998b): Wave forces on vertical and compositebreakwaters. Strategic Research Report. Hydraulic Research Wallingford, SR 509,Wallingford, U.K.

OUMERACI, H.; KLAMMER, P.; PARTENSCKY, H.-W. (1993): Classification of breakingwave loads on vertical structures. Journal of Waterway, Port, Coastal and OceanEngineering, ASCE, vol. 119, no. 4, pp. 381-397.

OUMERACI, H. (1994): Classification of breaking wave loads on vertical structures. In:MAST Advanced Study Course "Probabilistic Approach to the Design of ReliableCoastal Structures", Bologna, Italy, 16 pp.

OUMERACI, H.; BRUCE, T.; KLAMMER, P.; EASSON, W.J. (1995): PIV measurement ofbreaking wave kinematics and impact loading of caisson breakwaters. ProceedingsInternational Conference on Coastal and Port Engineering in Developing Countries(COPEDEC), Rio de Janeiro, Brazil, no. 4, Volume 3, pp. 2394-2410.

OUMERACI, H.; KORTENHAUS, A. (1997): Wave impact loading - tentative formulae andsuggestions for the development of final formulae. Proceedings 2nd Task 1 Workshop,MAST III, PROVERBS-Project: Probabilistic Design Tools for Vertical Breakwaters,Edinburgh, U.K., Annex 1.0.2, 13 pp; 3 Annexes.

PEREGRINE, D.H. (1997): Pressure at the back of a caisson on a permeable foundation. Pro-ceedings 2nd Task 1 Workshop, MAST III, PROVERBS-Project: Probabilistic DesignTools for Vertical Breakwaters, Edinburgh, U.K., Annex 1.3.1c, 3 pp.

VAN GELDER, P.H.A.J.M. (1998): Analysis of task 1 force data. Discussion Note, MAST III,PROVERBS-Project: Probabilistic Design Tools for Vertical Breakwaters, Delft, TheNetherlands.

VAN HOVEN, A. (1997): Hindcast of pore pressures underneath Porto Torres breakwater.Proceedings 2nd Task 1 Workshop, MAST III, PROVERBS-Project: ProbabilisticDesign Tools for Vertical Breakwaters, Edinburgh, U.K., 1st Draft, Annex 2.2, 19 pp.; 8Annexes.

VICINANZA, D. (1998): Azioni impulsive di un' onda frangente su una diga a paramentoverticale di tipo composto. XXVI Convegno di Idraulica e Construzioni Idrauliche,Catania, Italy, 12 pp. In Italian.


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File MAST_III\FIN_REP\IMPACT\impact.wp5 (last changes: 15. January 2001)

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2. OVERVIEW OF RECENT WORK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3. OVERVIEW OF DATA SETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

4. PREPARATORY STEPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54.1. Identification of wave impact loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54.2. Breaker height at the structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64.3. Probability of occurrence of impacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

5. WAVE IMPACT LOADING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95.1. Initial calculation of impact forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95.2. Statistics of relative wave forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115.3. Calculation of impact force history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

5.3.1. Rise time tr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145.3.2. Total duration td . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185.3.3. Force impulses Ihr and Ihd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

5.4. Pressure distributions at the wall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205.4.1. Distributions from vertical wall tests . . . . . . . . . . . . . . . . . . . . . . . . 205.4.2. Pressure distributions from breakwater tests . . . . . . . . . . . . . . . . . . 22

5.5. Lever arm of horizontal force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

6. WAVE UPLIFT LOADING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266.1. Calculation of uplift force history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

6.1.1. Rise time tru . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276.1.2. Total duration tdu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

6.2. Pressure distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306.2.1. Pressure at the shoreward edge of the structure pru . . . . . . . . . . . . . 316.2.2. Pressure at the seaward edge of the structure pu . . . . . . . . . . . . . . . . 33

6.3. Lever arm of uplift force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

7. AERATION OF IMPACT WAVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

8. CONCLUDING REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

CHAPTER 5.1: WAVE IMPACT LOADS - PRESSURES AND FORCES faculteit/Afdelingen... · (h) broken wave...

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Transcript of CHAPTER 5.1: WAVE IMPACT LOADS - PRESSURES AND FORCES faculteit/Afdelingen... · (h) broken wave...