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The long-term failure of rubble mound breakwaters

Destruction des brise-lames à talus sur le long terme
Arthur de Graauw

Abstracts

Rubble mound breakwaters have probably existed for around 3000 years and modern coastal engineers still build them to create harbours sheltered from wave action. Some ancient breakwaters are still well preserved today, while many others are now eroded and submerged as a consequence of thousands of years of storms and wave activity.
The present study aims to find a simple relationship between the governing parameters (water depth, structure height, stone size) and the equilibrium position of the crest of rubble mound breakwaters subject to repeated wave attack in breaking wave conditions over many centuries.
It is concluded that an initially undersized emerging rubble mound breakwater will be eroded by the waves and finally reduced to a submerged breakwater whose height above the sea bed depends on its stone size and on the water depth.

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Author's notes

I am deeply grateful to Nic Flemming for having challenged me on this subject and for his support and thoughtful comments. I am also very thankful to the reviewers for their help in improving this paper.

Full text

1 - Rubble mound breakwaters

Figure 1

Figure 1

The Kissamos breakwater (Crete) is a typical example of a rubble mound breakwater. This particular structure has been preserved from wave attack due to tectonic uplift (Flemming, 1981). However, most ancient breakwaters were destroyed by wave action and their remains are found under water as “submerged breakwaters”.

Picture from Hariclia Hampsa’s PhD thesis, 2006.

1In addition to vertical breakwaters made of ashlar blocks or concrete poured into wooden caissons, many rubble mound breakwaters were built in Antiquity to provide better shelter for ships (Haggi, 2005). Rubble-mound breakwaters consist of piles of stones more or less sorted according to their unit weight : smaller stones for the core and larger stones for an armour layer protecting the core from wave action.

2This kind of structure has probably existed for around 3000 years (e.g. the Phoenician breakwater at Athlit in Israel is dated to the 9th or early 8th century BC, Haggi, 2005) and modern coastal engineers still build them to create harbours sheltered from wave action. Ancient breakwaters may have been over- or undersized with the result that some are still well-preserved today while many others are now submerged as a consequence of thousands of years of storms and wave action. Without going into the details of breakwater design (e.g. Rock Manual, 2007), the stability of a structure made of stones depends primarily on their size in relation to wave strength : breakwaters in open waters exposed to storms acting on large areas and therefore producing high waves must be built with larger stones than breakwaters located in sheltered areas.

3The present analysis can be seen as a follow-up to work done previously by Foster (1977), Ahrens (1987), Vidal (1995) and Burcharth (2003). Some of van der Meer's tests (1992) and Ota's test reported by Kobayashi (2013), and other scale model tests, are also taken into account in the present analysis.

4The goal of this study was to find a simple relationship between the governing parameters (water depth, structure height, stone size) and the equilibrium position of the rubble crest of mound breakwaters subject to long-term wave attack in breaking wave conditions.

Figure 2

Figure 2

Klazomenae (Liman Tepe near Izmir, Turkey) is a major Bronze Age harbour settlement and an example of a submerged breakwater dated to the 6th century BC. The remains are 140 m long and 45 m wide in a water depth of around 4 m at its seaward roundhead. The crest of the structure is 1 to 1.5 m below present sea level (NB: the ancient water level was 0.30 to 0.50 m lower, see Morhange, 2014). It should be noted that the location of this structure inside the Bay of Izmir is relatively sheltered from offshore waves and this may explain why it has survived so well over time. This ancient harbour has been intensively studied by Vasif Sahoglu and his colleagues from the Ankara University Research Centre for Maritime Archaeology.

5Careful examination of Google Earth images enables us to see quite a number of breakwaters in shallow waters. Some remarkable ancient rubble mound breakwaters can be listed as follows :

  • Thapsus (Bekalta, Tunisia, Lat : 35.624299°N, Long : 11.051314°E) : about 870 m long, submerged in open water (Younès, 2013) ;

  • Leukas/Ligia (Lefkada island, Greece, Lat : 38.845037 °N, Long : 20.718422 °E) : about 540 m long, submerged in sheltered water,

  • Tieion (Filyos, Turkey, Lat : 41.571794 °N, Long : 32.0247°E) : over 350 m long, submerged in open water ;

  • Mytilini (Lesbos island, Greece, Lat : 39.113145 °N, Long : 26.55641 °E) : about 350 m long, submerged in sheltered water ;

  • Sabratha (Libya, Lat : 32.810859 °N, Long : 12.477982 °E) : about 320 m long, submerged in open water ;

  • Leptis Magna (Lebda, Libya, Lat : 32.637865 °N, Long : 14.300074 °E) : about 300 m long, berm breakwater in open water ;

  • Methone (Modon, Greece, Lat : 36.813244 °N, Long : 21.709883 °E) : about 250 m long, submerged in fairly open water ;

  • Neftina (Lemnos island, Greece, Lat : 39.98768 °N, Long : 25.351852 °E) : about 200 m long, submerged in open water ;

6Others such breakwaters are referenced in a more comprehensive publication (de Graauw, 2014).

7Obviously, questions remain regarding many of these structures, e.g. was the Thapsus structure a rubble mound breakwater or a vertical breakwater ? Is the feature in Kainopolis (60 km West of Apollonia, Libya) a breakwater or just beach rock ?

2 - Process of breakwater destruction by long-term wave action

8Different types of rubble mound breakwater can be distinguished (see Rock Manual, 2007).
Emerging breakwaters, which are stable if :

  • a) they are not overtopped, i.e. they are high enough, for instance twice the water depth, if waves are breaking at their toe,

  • b) they have a stable front armour layer, i.e. the stone size is large enough, at least around 20 % of the water depth, if waves are breaking at their toe (see definition of parameters below).

As an example of these (conservative) rules of thumb, consider a breakwater in water 5 m deep : the front armour layer stones should have a diameter of 1 m in order to be stable under wave action, and the crest should be 5 m above Still Water Level (SWL) so as not to be overtopped by waves … this was probably not a common feature of ancient breakwaters, and they therefore suffered damage over time, were eroded and eventually became submerged.

Submerged breakwaters have their crest at or below SWL and have a narrow crest (say 3 to 5 Dn) ; they are stable if made of large stones (Burcharth's rule : Dn > 0.3 d) and are eroded by offshore movement of front slope stones combined with onshore movement of crest stones falling behind the structure, the result being a lowering of the crest.

If they have a wide crest (say 50 Dn and more) the eroded stones remain there, the result being a rise in the crest similar to the reconstruction of an S-shaped beach.

9Hydraulic scale models are used intensively to study the stability of breakwaters.

3 - Hydraulic studies using scale models

10Many researchers, hydraulics specialists and engineers have used scale models for over a century, in particular in towing tanks. Scale models allow a design to be tested prior to construction, and in many cases are a critical step in the development process. Dimensional analysis is used to express the system with as few independent variables and as many dimensionless parameters as possible. The values of the dimensionless parameters are held to be the same for both the scale model and reality. This can be done because they are dimensionless and will ensure dynamic similitude between the model and reality. The resulting equations are used to derive scaling laws which dictate model testing conditions. It is often impossible to achieve strict similitude during a model test. The greater the departure from the application's operating conditions, the more difficult it is to achieve similitude. In these cases some aspects of similitude may be neglected, focusing on only the most important parameters (Heller, 2011).

11Coastal engineers have chosen to apply the similitude law of William Froude (1810-1879) for their hydraulic models of coastal structures. This means that gravity is considered to be preponderant over the other forces acting on the structure (viscosity, capillarity, cavitation, compressibility, etc.).

12The speed (V) is in agreement with Froude's law and the velocity scale is therefore the square root of the length scale, e.g. for a model with a length scale of 49 :

S(V) = S1/2(L) = sqrt(49) = 7 (times slower than in real life)

13As time (T) is a distance (L) over speed (V), the time scale is :

S(T) = S(L) / S(V) = S1/2(L) = sqrt(49) = 7 (times faster than in real life)

14The present analysis of long-term stability of breakwaters concentrates on cases with waves breaking between the toe and the crest of the submerged structure. These are the worst possible wave conditions and they are used in this study on the assumption that they will eventually occur in the long term. Hence, the local wave climate must include waves large enough to break in the water in front of the submerged structure ; breakwaters in very sheltered areas are therefore not considered in this analysis.

15Further details on designs for coastal structures in the Mediterranean area can be found on : http://www.ancientportsantiques.com/​ancient-port-structures/​design-waves/​.

Figure 3 – Process of reshaping of a low crested breakwater consisting of relatively small rubble on a scale model at Sogreah's Laboratory in 2006.

Figure 3 – Process of reshaping of a low crested breakwater consisting of relatively small rubble on a scale model at Sogreah's Laboratory in 2006.

Fig. 3a shows the initial structure at the beginning of the test. Stone size on the model is Dn = 7 mm. The structure is 545 mm high and placed in a water depth h = 450 and 480 mm.
Fig. 3b shows the structure after a sequence of around 1700 waves with significant height Hs = 60 mm and peak period Tp = 1.15 s. Waves were obviously not breaking before the seaward toe of the mound as Hs/h = 0.13 only, but broke on the front slope of the structure. This led to erosion of the front slope, moving material from the crest down to the seaward toe, producing an “S‑shaped” profile.
Fig. 3c shows the structure after a sequence of around 1500 waves with Hs = 80 mm and period Tp = 1.35 s. Waves were still breaking on the front slope. This resulted in further erosion of the crest, moving material from the crest to the rear side.The main limitation of the tests shown in Fig. 3 is that they were performed with non-breaking waves. Hence, wave attack on the structure was not the worst case scenario.

16This structure was nevertheless changed from an emerging breakwater into a submerged breakwater.

17Some unpublished scale model tests were performed in a wave flume at Sogreah's Laboratory in April 1993 by the author.

Figure 4 – Scale model tests on a submerged rubble mound structure.

Figure 4 – Scale model tests on a submerged rubble mound structure.

Fig. 4a - The initial structure at the beginning of the test was given a very simple trapezoidal shape with 1:1.5 slopes, a height of 40 mm and a crest 100 mm long. It was built with one single type of stone defined by its nominal Dn = 5 mm for the smallest size tested. The water depth h was 250 mm for most tests; hence, the 40 mm high structure was largely submerged.
Fig. 4b - The wave height was increased step by step during the test until full wave breaking occurred and no further increase in significant wave height could be obtained. The wave period was set at Tp = 1.75 s for most tests. Wave breaking was of the "spilling" type in all the tests.
Fig. 4c - The structure was reshaped by wave attack and finally stabilised in a rounded shape featuring a steeper front slope and a milder rear slope. The crest was lowered somewhat (2 to 3 Dn) and the rear toe moved backwards (about 18 Dn).

4 - Results

18The tests shown in Fig. 4 are of course very limited and modest, but they confirm and extrapolate Kramer & Burcharth’s results (2003), offering a much wider perspective on the processes involved. It is concluded that undersized emerging rubble mound breakwaters which are eroded by wave action can erode and submerge breakwaters and that the crest below SWL can be located as follows after long-term wave action :

Rc/h = 3.45 Dn/h – 1

Figure 5

Figure 5

For a given stone size, submerged breakwaters stabilize to the predicted crest level after long-term wave attack in breaking wave conditions; e.g. rock with diameter Dn = 1 m in water 5 m deep will yield a crest level at 30% of the water depth h below the water surface SWL.

19This result is obviously very useful for defining breakwater construction phases, when the core of the structure may be exposed to breaking waves produced by storms, and for near-bed rubble mounds protecting pipelines.
It is also useful to determine the long-term equilibrium level of the crest of undersized breakwaters.

5 - Conclusion

20It was concluded that initially undersized emerging rubble mound breakwaters reduce to submerged breakwaters and that, for a given stone size, submerged breakwaters stabilise to a predictable crest level after multi-secular long-term attack in breaking wave conditions.

21For ancient rubble mound breakwaters, this means that :

  • We may find ancient breakwaters still in good condition : they were emerging structures fulfilling modern design conditions (they may also have been uplifted by tectonic action, as at Kissamos, or have been somewhat oversized !) ;

  • If they were slightly undersized, we may find ancient breakwaters that were reshaped into an S‑shape by 2000 years of storms : the seaward side is lowered to below SWL and the landward side may reach SWL, as on Fig. 3b ;

  • If they were much smaller, ancient breakwaters have been eroded by wave action and eventually been submerged, with their crest located below SWL, as on Fig. 5.

22We must also remember that, in tectonically stable areas, the SWL has risen about 0.3 to 0.5 m since Antiquity (Morhange, 2014), so that breakwaters that were stable at that time in shallow water (a few metres water depth) may no longer be stable because larger waves can reach them nowadays. These impacts can be alleviated or accentuated by additional positive or negative tectonic movements.

23In tidal areas, the worst conditions for stability occur when the largest waves occur together with the highest water level. The probability of this happening is lower than for a fixed water level, but that may not change the final result in terms of long-term stability.

6 - Parameters

  • Hs : significant wave height in front of breakwater (m)

  • Tp : peak wave period (s)

  • h : water depth in front of breakwater (m)

  • Rc : crest elevation of breakwater above water level (Rc < 0 if under water) (m)

  • d : height of breakwater above sea-bed (m)

  • Dn : nominal diameter of rock (m) = (M50/ρ)1/3

  • ρ : specific mass of rock (kg/m3)

  • M50 : median mass of rock (kg)

  • SWL : Still Water Level

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Bibliography

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CIRIA, CUR, CETMEF, (2007), Rock Manual - The use of rock in hydraulic engineering, (2nd edition), Published by C683, CIRIA, London, 1304 p.

DE GRAAUW, A., (2014), Ancient Ports and Harbours, The Catalogue, 4th ed., Port Revel, 233 p. [Ancient Ports - Ports Antiques],[Remains of ancient breakwaters].

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FOSTER, D., (1977), Model simulation of damage to Rosslyn Bay breakwater during cyclone "David", 6th Australian Hydraulics and Fluid Mechanics Conference, Adelaide, p. 344-347.

GODA, Y., (2010), Reanalysis of regular and random breaking wave statistics, Coastal Engineering Journal, vol. 52, N° 1, p. 71‑106.

HAGGI, A., (2005), Underwater excavation at the Phoenician harbor at Athlit, 2002 season, RIMS newsletter No 31, Leon Recanati Institute for Maritime Studies, Univ. Haifa, p. 12‑14.

HAMPSA, H., (2006), Tesi Dottorato, I porti antichi di Creta, Università degli Studi di Salerno, 341 p.

HELLER, V., (2011), Scale Effects in Physical Hydraulic Engineering Models, Journal of Hydraulic Research, vol. 49, N° 3, p. 293‑306. [JHR 49:3]

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KRAMER, M. & BURCHARTH, H., (2003), Stability of low-crested breakwaters in shallow water short crested waves, ASCE, 4th Int. Coastal Structures Conf., Portland, OR, p. 137‑149.

LARONDE, A., (1983), Kainopolis de Cyrénaïque et la géographie historique, in : Comptes rendus des séances de l'Académie des Inscriptions et Belles-Lettres, 127e année, No 1, p. 67‑85.

MORHANGE, C., (2014), Ports antiques et variations relatives du niveau marin, Géochronique N° 130, p. 21‑24.

SAHOGLU, V., (2010), Ankara University Research Center for Maritime Archeology and its role in the protection of Turkey’s underwater cultural heritage, Proceedings of the World Universities Congress, Canakkale, October 2010, p. 1572‑1590.

VAN DER MEER, J., (1992), Stability of the seaward slope of berm breakwaters, Coastal Engineering, 16, p. 205‑234.

VIDAL, C., LOSADA, M., & MANSARD, E., (1995), Stability of Low-Crested Rubble-Mound Breakwater Heads, ASCE J. Waterway, Port, Coastal, Ocean Eng., 121(2), p. 114‑122.

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List of illustrations

Title Figure 1
Caption The Kissamos breakwater (Crete) is a typical example of a rubble mound breakwater. This particular structure has been preserved from wave attack due to tectonic uplift (Flemming, 1981). However, most ancient breakwaters were destroyed by wave action and their remains are found under water as “submerged breakwaters”.
Credits Picture from Hariclia Hampsa’s PhD thesis, 2006.
URL http://mediterranee.revues.org/docannexe/image/7078/img-1.png
File image/png, 340k
Title Figure 2
Caption Klazomenae (Liman Tepe near Izmir, Turkey) is a major Bronze Age harbour settlement and an example of a submerged breakwater dated to the 6th century BC. The remains are 140 m long and 45 m wide in a water depth of around 4 m at its seaward roundhead. The crest of the structure is 1 to 1.5 m below present sea level (NB: the ancient water level was 0.30 to 0.50 m lower, see Morhange, 2014). It should be noted that the location of this structure inside the Bay of Izmir is relatively sheltered from offshore waves and this may explain why it has survived so well over time. This ancient harbour has been intensively studied by Vasif Sahoglu and his colleagues from the Ankara University Research Centre for Maritime Archaeology.
URL http://mediterranee.revues.org/docannexe/image/7078/img-2.png
File image/png, 410k
Title Figure 3 – Process of reshaping of a low crested breakwater consisting of relatively small rubble on a scale model at Sogreah's Laboratory in 2006.
Caption Fig. 3a shows the initial structure at the beginning of the test. Stone size on the model is Dn = 7 mm. The structure is 545 mm high and placed in a water depth h = 450 and 480 mm. Fig. 3b shows the structure after a sequence of around 1700 waves with significant height Hs = 60 mm and peak period Tp = 1.15 s. Waves were obviously not breaking before the seaward toe of the mound as Hs/h = 0.13 only, but broke on the front slope of the structure. This led to erosion of the front slope, moving material from the crest down to the seaward toe, producing an “S‑shaped” profile. Fig. 3c shows the structure after a sequence of around 1500 waves with Hs = 80 mm and period Tp = 1.35 s. Waves were still breaking on the front slope. This resulted in further erosion of the crest, moving material from the crest to the rear side.The main limitation of the tests shown in Fig. 3 is that they were performed with non-breaking waves. Hence, wave attack on the structure was not the worst case scenario.
URL http://mediterranee.revues.org/docannexe/image/7078/img-3.png
File image/png, 3.9M
Title Figure 4 – Scale model tests on a submerged rubble mound structure.
Caption Fig. 4a - The initial structure at the beginning of the test was given a very simple trapezoidal shape with 1:1.5 slopes, a height of 40 mm and a crest 100 mm long. It was built with one single type of stone defined by its nominal Dn = 5 mm for the smallest size tested. The water depth h was 250 mm for most tests; hence, the 40 mm high structure was largely submerged. Fig. 4b - The wave height was increased step by step during the test until full wave breaking occurred and no further increase in significant wave height could be obtained. The wave period was set at Tp = 1.75 s for most tests. Wave breaking was of the "spilling" type in all the tests. Fig. 4c - The structure was reshaped by wave attack and finally stabilised in a rounded shape featuring a steeper front slope and a milder rear slope. The crest was lowered somewhat (2 to 3 Dn) and the rear toe moved backwards (about 18 Dn).
URL http://mediterranee.revues.org/docannexe/image/7078/img-4.png
File image/png, 350k
Title Figure 5
Caption For a given stone size, submerged breakwaters stabilize to the predicted crest level after long-term wave attack in breaking wave conditions; e.g. rock with diameter Dn = 1 m in water 5 m deep will yield a crest level at 30% of the water depth h below the water surface SWL.
URL http://mediterranee.revues.org/docannexe/image/7078/img-5.jpg
File image/jpeg, 64k
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References

Electronic reference

Arthur de Graauw, « The long-term failure of rubble mound breakwaters », Méditerranée [Online], Varia, Online since 11 December 2014, connection on 27 July 2017. URL : http://mediterranee.revues.org/7078

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About the author

Arthur de Graauw

ARTELIA, Director Port Revel Shiphandling

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Copyright

Tous droits réservés

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