Wave impacts on vertical breakwaters are among the most severe and dangerous loads this type of structure can suffer. Whilst many design procedures for these structures are well established worldwide recent research in Europe has shown that some of those design methods are limited in their application and may over or underpredict the loading under important conditions. This will then lead to overdesigned and very expensive structures or, even more dangerous, 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. Furthermore, data available from different hyraulic model tests, field surveys and experience from numerical modelling were collected and analysed to overcome the aforementioned limitations. Engineers from both universities and companies were working together to derive new methods for calculating forces and pressures under severe impact conditions taking into account the influence of salt water and aeration of the water. This new approach was then further optimized by taking into account the dynamic properties of the structure itself and the foundation of the breakwater (see Volume I, Chapter 3.4). The multidirectionality of the waves approaching 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 loadings under 2D conditions and to give references to more detailed work on the different aspects of the steps described in here. For sake of completeness and easier understanding of the whole method some parts had to be repeated from other sections within Vol. II of the PROVERBS report. This was considered to be more useful rather than giving too many references to other sections. Geometric dimensions and a sketch of a typical caisson breakwater are given in Fig. 1
See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/2460541 Wave Impact Loads - Pressures And Forces Article · February 2001 Source: CiteSeer CITATIONS READS 3,049 8 authors, including: William Allsop Mario Calabrese HR Wallingford University of Naples Federico II 162 PUBLICATIONS 1,060 CITATIONS 55 PUBLICATIONS 278 CITATIONS SEE PROFILE SEE PROFILE Diego Vicinanza Università degli Studi della Campania "Luigi … 153 PUBLICATIONS 945 CITATIONS SEE PROFILE Some of the authors of this publication are also working on these related projects: Wave overtopping performance of steep low-crested structures View project CFD MODELING OF WAVE LOADINGS ON WAVE ENERGY CONVERTERS View project All content following this page was uploaded by Diego Vicinanza on 06 February 2013 The user has requested enhancement of the downloaded file 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-38106 Braunschweig, 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 Netherlands 4) University of Plymouth, School of Civil and Structural Engineering, Palace Street, GB-Plymouth PL1 2DE, U.K 5) Queens University of Belfast, Department of Civil Engineering, Stranmills Road, GB-Belfast BT7 1NN, Northern Ireland 6) 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 and Kortenhaus (1997) have been brought together and amended by many partners in PROVERBS This paper proposes a procedure to calculate time-dependent pressures, forces and lever arms of the forces on the front face and the bottom of a vertical breakwater For this purpose, (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 background and data information Suggestions for estimating the forces on a caisson in feasibility studies are also given -1- LWI / HR / DUT / UE / UoN / UoP / QUB A KORTENHAUS ET AL INTRODUCTION Wave impacts on vertical breakwaters are among the most severe and dangerous loads this type of structure can suffer Whilst many design procedures for these structures are well established worldwide recent research in Europe has shown that some of those design methods are limited in their application and may over- or underpredict the loading under important conditions This will then lead to overdesigned and very expensive structures or, even more dangerous, 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 Furthermore, data available from different hyraulic model tests, field surveys and experience from numerical modelling were collected and analysed to overcome the aforementioned limitations Engineers from both universities and companies were working together to derive new methods for calculating forces and pressures under severe impact conditions taking into account the influence of salt water and aeration of the water This new approach was then further optimized by taking into account the dynamic properties of the structure itself and the foundation of the breakwater (see Volume I, Chapter 3.4) The multidirectionality of the waves approaching 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 loadings under 2D conditions and to give references to more detailed work on the different aspects of the steps described in here For sake of completeness and easier understanding of the whole method some parts had to be repeated from other sections within Vol II of the PROVERBS report This was considered to be more useful rather than giving too many references to other sections Geometric dimensions and a sketch of a typical caisson breakwater are given in Fig -2- CHAPTER 5.1 WAVE IMPACT LOADS: FORCES AND PRESSURES OVERVIEW OF RECENT WORK There are a number of formulae available for different types of waves breaking at the structure These formulae generally include magnitudes of maximum pressures, their distributions and forces In some cases, uplift pressures are given as well All formulae are fully empirical or semi-empirical as the process of wave breaking at the structure is still not fully explained Tab summarizes the most important methods in a chronological order, details are given in the respective references Tab 1: Overview of design methods for wave loading Author Year Pressures Forces Uplift Comments Quasi-Static Waves Sainflou 1928 yes yes, but difficult no vertical wall, no berm Miche-Rundgren 1944 yes 1958 yes no design curves from SPM, 1984 Goda 1985 yes yes yes most-widely used design method Impact Waves Hiroi 1919 yes yes no vertical wall Bagnold 1939 - - - conceptual model only Minikin 1963 yes yes no sometimes incorrect dimensions! Ito 1971 yes yes yes Blackmore & Hewson 1984 yes yes no Partenscky 1988 yes not given no air content of wave needed Kirkgöz 1990 yes 1995 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! -3- LWI / HR / DUT / UE / UoN / UoP / QUB Author Year McConnell Pressures A KORTENHAUS ET AL Forces Uplift Comments 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 under impact conditions Furthermore, the dynamic characteristics of impact forces were considered essential for the behaviour of the structure subject to this type of loading The design procedure is therefore based on the approach by Oumeraci and Kortenhaus, 1997 which was derived from solitary wave theory but amendments were made to many details like the statistical distributions of impact and uplift pressures, the vertical pressure distribution at the front face, and the relation between rise time and duration of impact forces OVERVIEW OF DATA SETS Different hydraulic model tests have been carried out and analysed to obtain the design method proposed in this paper These tests are summarized in Tab where the most important information is given Furthermore, references are added where more detailed information on these tests is available -4- CHAPTER 5.1 Tab 2: Overview of hydraulic model tests (random waves) Tests Year Co fsam No n- Scale Waves Slope Imp.2) Upl.2) References [Hz] tests fig.1) Oumeraci et al., 1995 WKS 1993 1:15 600 90 1:50 121 10 GWK 1993/94 1:5 100 100 1:50 62 10 HR94 1994 10 1:20 400 500 1:50 217 PIV 1:50 400 1:20 77 - Oumeraci et al., 1995 1000 1:50 1:20 1:10 1:7 - McConnell & Allsop, 1998 Kortenhaus & Löffler, 1998 1994 HR97 1997 QUB 1997 1) WAVE IMPACT LOADS: FORCES AND PRESSURES 1:20 1:30 1000 1000 800 1:50 12 McConnell & Kortenhaus, 1996 number of configurations tested; 2) number of transducers It may be assumed from the differences in the number of waves per test and the acquisition rate 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 other which will be explained in more details in the successive sections PREPARATORY STEPS -5- LWI / HR / DUT / UE / UoN / UoP / QUB A KORTENHAUS ET AL 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, Chapter 2.4.1) without any account for load duration can be used (Fig 2a); Fh Hb Fh Fh 3.0 Fh D·g·H b 1.0 0.0 2.0 2.0 1.0 1.0 0.0 0.5 1.0 t/T (a) Standing wave 0.0 0.2 0.4 t/T (b) Slightly Breaking wave "Pulsating load" (d) (f) (h) 0.1 0.2 t/T (c) Plunging breaker Impact load (Goda-formula applicable) Fig 1: T=wave period (Goda-formula not applicable) Pulsating and impact load - problem definition slightly breaking wave loads which already consist of some breaking waves but not significantly exceeding the Goda loads (Fig 2b); an impact load for which new formulae including impact duration are to be used (Fig 2c); and 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 more detail described in Chapter 2.2 of Volume IIa Input for this map are geometric and wave parameters which in combination yield an indication of a certain probability that one of the aforementioned breaker types will occur -6- CHAPTER 5.1 WAVE IMPACT LOADS: FORCES AND PRESSURES "Vertical" Breakwater h*b < 0.3 Crown Walls Rubble Mound Breakwater h*b > 0.9 Composite Breakwater 0.3 < h *b< 0.9 L Low Mound Breakwater 0.3 < h *b< 0.6 SWL d hs Large waves Small waves H *s< 0.35 0.35 < H Small waves 0.1 < H s*< 0.2 * s Quasi-standing wave hs B eq hb Large waves Small waves Large waves 0.1 < H s*< 0.2 0.25 < H *s< 0.6 8.0 8.0 8.0 6.0 6.0 6.0 4.0 4.0 0.0 with h*b= 0.2 Moderate berm w Wide berm 0.12 < B *< 0.4 B* > 0.4 Impact loads Fh* 0.0 Narrow berm * 0.12 0.08 < B < Slightly breaking wave Fhq 0.4 t/T 0.0 Hs B eq Fh * hb ; H *s= ; B* = ; F= h D·g·H hs L hs Broken waves Fh* Fhmax 8.0 6.0 4.0 Fhmax Fhq 2.0 0.0 SWL 0.2 < H *s< 0.6 Fh* Fhmax High Mound Breakwater 0.6 < h *b< 0.9 d Fh 2.0 Fig 2: Hsi 0.1 4.0 Fhq 2.0 0.2 t/T 0.0 0.0 0.1 Fhmax Fhq 2.0 0.2 t/T 0.0 0.0 0.1 0.2 t/T b PROVERBS parameter map 8.4 Breaker height at the structure A breaking criterion which accounts for the reflection properties of the structure has been suggested by Calabrese (1997) (see Chapter 2.3 of Volume IIa) based on extensive random wave tests in hydraulic model tests and previous theoretical works (Oumeraci et al., 1993): Hbc ' Lpi @ 0.1025 % 0.0217 @ & Cr % Cr (1) where Lpi is the wave length in the water depth hs for the peak period Tp which can be calculated iteratively by: Lpi ' L0 @ B @ hs (2) Lpi -7- LWI / HR / DUT / UE / UoN / UoP / QUB A KORTENHAUS ET AL where L0 is the wave length in deep water which can be taken as: L0 ' g @T2 2B p (3) or can be approximated using the method given in Fenton (1990): Lpi ' L0 @ B @ hs 3/4 2/3 (4) L0 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 crest Cr = 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: kb ' 0.0076 @ Beq / d & 0.1402 @ B eq / (5) where Beq is the equivalent berm width which is defined as: Beq ' Bb % hb (6) tan " and Bb is the berm width in front of the structure Further details on this approach are given in Section 2.3 of Volume IIa -8- CHAPTER 5.1 WAVE IMPACT LOADS: FORCES AND PRESSURES 8.6 Probability of occurrence of impacts The parameter map as given in Fig results in different branches where the probability of the respective breaker type is not known in advance The branch of 'impact breakers' proposes to use an impact loading formulae which generally yields much higher forces than any other approach for quasi-standing waves, slightly breaking waves or broken waves Hence, it is necessary 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 non impulsive Goda forces) The aforementioned method by Calabrese and Allsop (1998) described in Chapter 2.3 of Volume IIa also gives a simple formula for the probability of broken waves Pb based on the idea that every wave with a higher wave height than the breaking wave height Hbc (as calculated in Section 4.2) is already broken or will break as an impact breaker at the wall The probability of occurrence of breaking and broken waves can therefore be calculated as follows: Pb ' exp & @ Hbc / Hsi @ 100% (7) The maximum wave height Hbs which describes the transition from impact breakers to already broken waves can be described by Eq (1) where Beq/d and Cr are set to zero which then yields: Hbs ' 0.1242 @ Lpi @ B hs Lpi (8) The proportion of impacts can then be derived from: Pi ' exp & @ Hbc / Hsi & exp & @ H (9) The magnitude of the horizontal force itself is strongly related to the type of breakers at the wall which are essentially depth limited It can be expected that the magnitude is related to the relative 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 low percentages of impacts (smaller than 1%) the problem can be reduced to the quasi-static problem and the Goda method can be used to calculate pressures and forces (see Chapter 4.1 of Volume IIa) In all other cases the method as described in the successive sections has to be used -9- CHAPTER 5.1 12.2.4 b) WAVE IMPACT LOADS: FORCES AND PRESSURES Total duration tdu Deterministic approach The triangular total duration of the uplift force tdu can be obtained from the rise time tru by using the following relationship similar to Eq (22) for horizontal forces: tdu ' tru @ 2.0 % 8.0 @ exp & 18 @ t ru / Tp (44) 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 Random waves GWK 1993/94 WKS 1993 HR 1994 10.0 No of tests = 239 5.0 Eq (44) t d = 2*t r 0.00 0.05 0.10 0.15 0.20 Relative rise time t Fig 15: d) 0.25 ru /T p [-] Relative triangular total duration versus relative triangular rise time (GWK data) Probabilistic approach - 31 - LWI / HR / DUT / UE / UoN / UoP / QUB A KORTENHAUS ET AL Again, Van Gelder (1998) has proposed the same formula than for impact duration and rise time (see Eq (23)) tdu ' & cu (45) ln ( t ru ) where cu is again normally distributed with a mean value of 1.88 for large-scale tests and a standard deviation of 0.99 Given the rise time of the uplift force and the total duration, the force history can be calculated for each time step by interpolating the times between t0 and the uplift force maximum at the time tru and the total duration tdu (Fig 17) 12.4 Pressure distributions Uplift pressures underneath vertical breakwaters should generally be calculated using the approach described in Section 3.5.3 where the instantaneous pore pressure development underneath the breakwater is described However, a very simple approach was derived empirically from the data available and is based on hydraulic model test data using 'upper bound' envelopes which may lead to conservative estimates Therefore, all results should be compared to the pressures derived by using the Goda model (see Vol I, Section 2.4.1) and are expected to be larger than those It was observed from hydraulic model tests that the uplift pressure distribution (Fig 17) should at least 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 maximum of the uplift force was observed to occur when the shock wave traveling underneath the structure has reached this point) - 32 - CHAPTER 5.1 WAVE IMPACT LOADS: FORCES AND PRESSURES Fu(t) DWL = Design Water Level F u,max Bc R c = Freeboard Rc DWL d F (t) u dc t tru t p t du p u p mu 0.25@B c Fig 16: ru l Fu Fu Approximate pressure distribution for temporal development of pressure distribution For impact forces the pressures were given as functions of the impact force itself and the pressure distribution was assumed to remain constant in itself A similar principle will be followed here but the number of points to form the pressure distribution is reduced to only two for simplicity reasons Furthermore, the pressure underneath the landward side of the structure will be calculated using relative wave parameters The pressure distribution is assumed to be constant 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 from model tests and prototype conditions in PROVERBS where many times pressures up to the same magnitude than at the seaward side were measured (rectangular pressure distribution) Explanation of the processes involved have been provided by Van Hoven (1997), Hölscher et al (1998), and Peregrine (1997) which indicates that the most relevant parameters responsible for non zero pressures are the exit area, the foundation material and the water depth behind the structure However, most of these parameters were kept constant over the tests so that analysis of the data did not take this into account - 33 - LWI / HR / DUT / UE / UoN / UoP / QUB A KORTENHAUS ET AL The inital analysis of available data for pressures underneath the shoreward edge of the breakwater related these pressures to the wave parameters by applying an upper envelope to the data for the time of the maximum uplift force (Fig 18) From this the following empirical formula was achieved: pru ' D @ g @ Hb Hb hs & 0.1 (46) GWK 0.90 0.72 0.54 0.36 0.18 0.00 0.16 0.32 0.48 0.64 0.80 H b/h s [-] Fig 17: Uplift pressure underneath the shoreward edge of the breakwaters in GWK and WKS which can easily be transformed to: pru ' D @ g @ Hb @ Hb hs & 0.1 (47) For all times # tru # tdu the respective values may be interpolated from the above following the same principle than already used for the uplift force history (Fig 17) - 34 - CHAPTER 5.1 12.4.4 WAVE IMPACT LOADS: FORCES AND PRESSURES Pressure at the seaward edge of the structure pu Since the pressure at the shoreward side of the structure is known the pressure underneath the seaward edge pu can be calculated as follows: pu ' @ Fu,max Bc & pru (48) where Bc is the structure width, Fumax is the maximum uplift force and pru is the pressure at the shoreward 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 distribution underneath the structure for each time step as follows: lFu ( t ) ' Bc2 @ pru % @ p u (49) @ Fu,max 14 AERATION OF IMPACT WAVES All results discussed so far have been achieved from model tests at different scale using fresh water These results are very difficult to directly apply to prototype conditions as there are a lot of additional factors which should be taken into account One of these phenomena which is most 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 both fresh and sea water The different behaviour of air bubbles in the breaking process of waves hitting 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 generally very little aeration was observed in the reflected waves; @ for impacting waves, field measurements have shown that high aeration levels coincide with long rise times and lower pressures whereas short duration high peaked pressures were also observed, but occur at lower aeration levels; @ comparing results with fresh and sea water under laboratory conditions has shown that pressures are generally higher with longer rise times and vice versa, thus following the observations made in the field; - 35 - LWI / HR / DUT / UE / UoN / UoP / QUB A KORTENHAUS ET AL These results have led to some simple guidance on estimating the aeration of impact waves and its influence on the impact force (Hewson et al., 1998) which might be adopted for design purposes The aeration in impact waves can be calculated to: Pa ' 2.0 % 5.3 @ Ni (50) where Ni is the number of breaking waves per minute and Pa is the percentage of aeration in the breaking wave given in percent The number of breaking waves per minute, however, is not known in advance but may be estimated for model tests using the percentage of breaking waves in a test Pi (Eq (7)): Ni ' Pi @ NW (51) ttot where NW is the number of waves in a test, and ttot is the total length of the test given in minutes Under prototype conditions NW may be replaced by the number of the waves in a storm whereas ttot is the duration of the design storm From the aeration percentage obtained by Eq (50) a force reduction factor kfa according to Hewson et al (1998) can be calculated as follows: kfa ' 7.726 2.5 % P a 97.5 & P a 0.372 (52) It has also been shown that the total force impulses seemed to remain independent from the aeration level of the breaking wave Assuming this impulse to be more or less equal to the triangular impulse as given by Eq (24) longer rise times due to aeration can be calculated as the inverse of the force reduction factor: kta ' k fa (53) Since uplift and impact loading are strongly coupled it can be expected that the uplift force will be dependent on the aeration in the same way though no data supporting this are yet available The working assumption therefore is to use Eqs (50) to (53) for uplift forces as well - 36 - CHAPTER 5.1 WAVE IMPACT LOADS: FORCES AND PRESSURES 16 CONCLUDING REMARKS The extremely complex phenomena of wave breaking at a vertical wall has been investigated in PROVERBS Hydraulic model tests, numerical modelling, field measurements and desk studies 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 to improved design procedures for impact loading which are summarized in this and other sections of Chapter in Volume IIa ('Breaking Wave Loads') The calculation process within this section is graphically summarized in Fig 19 - 37 - LWI / HR / DUT / UE / UoN / UoP / QUB A KORTENHAUS ET AL - 38 - CHAPTER 5.1 WAVE IMPACT LOADS: FORCES AND PRESSURES Geometric Conditions Wave Conditions Fig Vol IIa, Chapter Parameter Map H bc Eq (1) Fig Impact Filter Pi Section 4.3 Eq (9) Quasi-Static Loading Volume IIa Chapter 4.1 Impact Loading Horiz Force Uplift Force @ initial force calc (Eq (10)) @ statistics of rel force (Fig 5, Eq (14)) @ statistics of rel force (Fig 11, Eq (43)) @ calc of force history (Eqs (21), (23)) @ calc of force history (Eqs (21), (45)) @ reduction by aeration (Eqs (50) to (53)) @ reduction by aeration (Eqs (50) to (53)) Press Distr Vert Wall Press Distr Breakwater Press Distr Uplift (Eqs (26) to (30)) (Eqs (32) to (36)) (Eqs (46) to (48)) Parameter Output p1(t) to p (t) Fig 18: , p u(t), p (t) (t), M (t)u , l Fh , l Fu ru , F h(t), F (t) u ,M h Overview of calculation scheme for impact loading (probabilistic approach) - 39 - LWI / HR / DUT / UE / UoN / UoP / QUB A KORTENHAUS ET AL This section therefore summarizes and updates two tentative procedures for calculating timedependent pressures and forces at the front face and underneath vertical breakwaters subject to impact breakers The performed improvements as compared to previous versions of this method (Oumeraci and Kortenhaus, 1997) are as follows: @ updated method to calculate the breaking wave height in front of vertical breakwaters following the formulae proposed by Calabrese and Allsop (1997); @ new procedure to calculate the percentage of impacts for given geometric and wave conditions following the same method as described above; @ simple calculation method to estimate relative wave impact forces for feasibility and preliminary design studies (Allsop et al., 1996); @ use of updated relative wave impact and uplift forces to be used for statistical distributions; @ new distribution type to present the statistics of both impact and uplift forces (Generalized Extreme Value (GEV) Distribution); @ new results of k-values to estimate the part of the water mass involved in the impact taken from analysis of PIV-measurements (Vicinanza, 1998); @ application of method to different bed slopes and improvement of statistical parameters used for calculating the relative forces (McConnell and Allsop, 1998); @ implementation of new results regarding aeration of impact waves as reported by Crawford et al (1996) and Hewson et al (1998); @ new statistical relation between total duration of wave forces and rise times for both impact 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-static loading as described in Section 4.1 of Volume IIa To allow for any comparison the - 40 - CHAPTER 5.1 WAVE IMPACT LOADS: FORCES AND PRESSURES dynamic loading has to be transformed into a quasi-static loading which has the same effect to the structure than the dynamic loading This can principally be done by using the dynamic load factor concept which is in more detail described in Chapter of Volume IIb The 3D character of waves in nature has been ignored in describing the methods to calculate the loading However, it is believed that especially for impact breakers there is a very significant difference between 2D and 3D cases as impacts occur very locally A detailed description of model tests performed within PROVERBS and results to reduce the magnitude of 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-CT95-0041 and 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 REFERENCES ALLSOP, 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 Workshop, MAST III, PROVERBS-Project: Probabilistic Design Tools for Vertical Breakwaters, Edinburgh, U.K., Annex 1.0.4 CALABRESE, M.; ALLSOP, N.W.H (1997): Impact loadings on vertical walls in directional seas Proceedings 2nd Task Workshop, MAST III, PROVERBS-Project: Probabilistic Design 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 vertical walls Proceedings International Conference Coastal Engineering (ICCE), ASCE, Copenhagen, Denmark, no 26, pp COOKER, M.J.; PEREGRINE, D.H (1990): A model for breaking wave impact pressures Proceedings International Conference Coastal Engineering (ICCE), ASCE, Delft, The Netherlands, no 22, Volume 2, pp 1473-1486 - 41 - LWI / HR / DUT / UE / UoN / UoP / QUB A KORTENHAUS ET AL CRAWFORD, A.R.; BULLOCK, G.N.; HEWSON, P.J.; BIRD, P.A (1997): Wave impact pressures 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 Coastal Engineering, 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 wave impact forces Proceedings 2nd Overall Project Workshop, MAST III, PROVERBSProject: Probabilistic Design Tools for Vertical Breakwaters, Naples, Italy, Chapter 1.5a), pp HÖLSCHER, P.; ZWANENBURG, C.; DE GROOT, M.B.; LUGER, H.J (1998): Hindcast Hannover 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 impact pressures 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 Proceedings 2nd Task Workshop, MAST III, PROVERBS-Project: Probabilistic Design Tools for Vertical Breakwaters, Edinburgh, U.K., Annex 1.0.3, 14 pp.; 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.; Annex KORTENHAUS, A.; LÖFFLER, A (1998): Analysis of new model experiments on uplift underneath vertical breakwaters Research Report MAST III, PROVERBS-Project: Probabilistic Design Tools for Vertical Breakwaters, Braunschweig, Germany, 51 pp., Annexes 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 from hydraulic model tests and prototype measurements - discussion note Proceedings Task Workshop Belfast, MAST III, PROVERBS-Project: Probabilistic Design Tools for Vertical Breakwaters, 2nd Draft, Annex 19, Belfast, Northern Ireland, 13 pp., Annexes MCCONNELL, K.J.; KORTENHAUS, A (1997): Analysis of pressure measurements from hydraulic model tests and prototype measurements Proceedings 1st Overall Project Workshop, MAST III, PROVERBS-Project: Probabilistic Design Tools for Vertical Breakwaters, Las Palmas, Gran Canaria, Annex C3, 14 pp., Annex - 42 - CHAPTER 5.1 WAVE IMPACT LOADS: FORCES AND PRESSURES MCCONNELL, K.J.; ALLSOP, N.W.H (1998a): Prediction of wave impact forces and durations: further considerations and discussion Proceedings 2nd Overall Project Workshop, MAST III, PROVERBS-Project: Probabilistic Design Tools for Vertical Breakwaters, Naples, Italy, Class Report, Chapter 1.5a), pp MCCONNELL, K.J.; ALLSOP, N.W.H (1998b): Wave forces on vertical and composite breakwaters Strategic Research Report Hydraulic Research Wallingford, SR 509, Wallingford, U.K OUMERACI, H.; KLAMMER, P.; PARTENSCKY, H.-W (1993): Classification of breaking wave loads on vertical structures Journal of Waterway, Port, Coastal and Ocean Engineering, 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 Reliable Coastal Structures", Bologna, Italy, 16 pp OUMERACI, H.; BRUCE, T.; KLAMMER, P.; EASSON, W.J (1995): PIV measurement of breaking wave kinematics and impact loading of caisson breakwaters Proceedings International 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 and suggestions for the development of final formulae Proceedings 2nd Task Workshop, MAST III, PROVERBS-Project: Probabilistic Design Tools for Vertical Breakwaters, Edinburgh, U.K., Annex 1.0.2, 13 pp; Annexes PEREGRINE, D.H (1997): Pressure at the back of a caisson on a permeable foundation Proceedings 2nd Task Workshop, MAST III, PROVERBS-Project: Probabilistic Design Tools for Vertical Breakwaters, Edinburgh, U.K., Annex 1.3.1c, pp VAN GELDER, P.H.A.J.M (1998): Analysis of task force data Discussion Note, MAST III, PROVERBS-Project: Probabilistic Design Tools for Vertical Breakwaters, Delft, The Netherlands VAN HOVEN, A (1997): Hindcast of pore pressures underneath Porto Torres breakwater Proceedings 2nd Task Workshop, MAST III, PROVERBS-Project: Probabilistic Design Tools for Vertical Breakwaters, Edinburgh, U.K., 1st Draft, Annex 2.2, 19 pp.; Annexes VICINANZA, D (1998): Azioni impulsive di un' onda frangente su una diga a paramento verticale di tipo composto XXVI Convegno di Idraulica e Construzioni Idrauliche, Catania, Italy, 12 pp In Italian - 43 - LWI / HR / DUT / UE / UoN / UoP / QUB A KORTENHAUS ET AL File MAST_III\FIN_REP\IMPACT\impact.wp5 (last changes: 15 January 2001) - 44 - ABSTRACT 1 INTRODUCTION 2 OVERVIEW OF RECENT WORK 3 OVERVIEW OF DATA SETS 4 PREPARATORY STEPS 4.1 Identification of wave impact loading 4.2 Breaker height at the structure 4.3 Probability of occurrence of impacts 5 WAVE IMPACT LOADING 5.1 Initial calculation of impact forces 5.2 Statistics of relative wave forces 5.3 Calculation of impact force history 5.3.1 Rise time tr 5.3.2 Total duration td 5.3.3 Force impulses Ihr and Ihd 5.4 Pressure distributions at the wall 5.4.1 Distributions from vertical wall tests 5.4.2 Pressure distributions from breakwater tests 5.5 Lever arm of horizontal force 9 11 13 14 18 19 20 20 22 25 WAVE UPLIFT LOADING 6.1 Calculation of uplift force history 6.1.1 Rise time tru 6.1.2 Total duration tdu 6.2 Pressure distributions 6.2.1 Pressure at the shoreward edge of the structure pru 6.2.2 Pressure at the seaward edge of the structure pu 6.3 Lever arm of uplift force 26 27 27 28 30 31 33 33 AERATION OF IMPACT WAVES 33 CONCLUDING REMARKS 35 ACKNOWLEDGEMENTS 37 REFERENCES 37 View publication stats