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Coastal management sourcebooks 2

Wave propagation and sedimentation at the Pharos site

J.-M. MENON and
  Laboratoire National d’Hydraulique
Électricité de France


The present study lies within the scope of the corporate patronage of Électricité de France (EDF). Dr. Jean-Yves Empereur, the French archaelogist in charge of the Pharos submarine excavations in Alexandria (Egypt), asked the EDF Foundation for a technical assessment of the coastal engineering problems linked to the displacement of a submerged wall. This submerged concrete wall corresponds to the first phase of an uncompleted project on the construction of a large breakwater, and was built in 1994 to protect the Mamelouk fortress at Qait Bey, itself established on the old Pharos foundations. The wall partly covers the submarine excavation site, consequently inhibiting completion of the archaeological work. The archaeologists would like to displace this wall, keeping in mind that the displaced structure would have to meet the following requirements:

  1. protection of the Qait Bey fortress against prevailing waves,
  2. enabling the continuation of the Pharos excavations and
  3. protection of the archaeological site from wave agitation and sedimentation, with a view to creating a ‘submarine museum’ which could be visited by divers or by observers in glass-bottomed boats.

These constraints, which apply to archaeological preservation and coastal management preoccupations, may not be fully compatible. The objective of the present study is to provide some preliminary results, particularly regarding wave agitation and possible sedimentation, useful for the global understanding of the local hydrodynamic system. Impacts in terms of wave agitation have been studied with the help of numerical modelling using the ARTEMIS software developed at EDF-LNH (Laboratoire National d’Hydraulique); sedimentological aspects have been investigated during a short mission to Alexandria, although with only a limited field-data set, and a comparison was made with similar situations already studied.

The first part of this report is an overview of the present situation. It is followed by the results on wave agitation from four different schematic configurations describing present or possible future maritime works. The limited sediment data set available just allows a few conclusions on the sedimentological impact to be expected from the installation of new marine structures.

Present context

Alexandria is on the Mediterranean coast of Egypt, and stretches more than 50 km along the shore from Abu Qir Bay to Sidi Krir. The Alexandrian coast is oriented along a SW–NE axis and is characterized by the presence of the Pharos peninsula which separates the Western and Eastern Harbours. A Mamelouk fortress is located at Qait Bey, on the north-eastern part of the Pharos peninsula, and stands on the foundations of the famous old Pharos whose remains have been found near the fortress, 6–8m under water (Fig. 1). In 1994, the first concrete blocks of a breakwater were laid on the site of the archaeological remains and compromised their preservation. An emergency programme was then decided, to undertake systematic archaeological investigations. Since this date, Dr. J-Y. Empereur, Director of the Centre d’Études Alexandrines, has been in charge of this task. More than 2,000 archaeological remains have been located, and it is assumed that the present submerged concrete wall may cover some other remains.

Figure 1. Map showing the site of the archaeological remains of Fort
Qait Bey and the modern submerged wall intended to
protect the foundation of the fort.
Qait Bey fort

Wave-propagation modelling

The objective of this section is to describe a model of the propagation of waves in a localized area around the Pharos excavations. The method is based upon the following steps:

  1. definition of the wave conditions offshore in deep water
  2. estimation or computation of the wave deformation when approaching the shore line (wave refraction controlled by the bathymetry)
  3. specification of the wave conditions at the boundaries of the local computational domain
  4. digitizing of the bathymetric and shore contours
  5. numerical computations in the local domain using the ARTEMIS software.

Offshore wave conditions

The objective here is to define boundary conditions to be imposed on the local computational domain around the Pharos excavations. Offshore wave climate and the effect of bottom refraction have then to be considered. No criteria have been specified regarding, for instance, the maximum allowable significant wave height in the area of interest. We then focussed our study on wave agitation for annual conditions; i.e., for which a statistical probability of occurrence is about once a year.

The wave climate in the deep water off Alexandria is relatively well known and has been determined in a previous LNH study of the Sidi-Krir Power Plant project.[1] Hindcasting of the wind-induced wave regime and statistical analysis of swell observations by ships provide the following results:

  1. 75% of the waves reaching the coast come from the WNW–NNW sector;
  2. statistically significant wave heights (Hs0 ) for statistical return periods of 1 year and 100 years are about 4.0 m and 8.0 m, respectively;
  3. 60% of the time, wave periods are in the range 6–9 seconds for NW waves and 5–8 seconds for NE waves.

Refraction by the near-shore sea floor (depths < 100 m) modifies the wave propagation. We have assessed its effect analytically and finally chose the following ‘annual’ conditions:

  1. NW waves: Hs0 = 4.0 m; Tp = 8.0 s
  2. WNW waves: Hs0 = 4.0 m; Tp = 8.0 s
  3. NE waves: Hs0 = 3.0 m; Tp = 7.0 s

where Hs0 = significant wave height; Tp = peak period of the wave-energy spectrum.

The ARTEMIS numerical model

ARTEMIS is a piece of scientific software developed by LNH and commercialized within the TELEMAC system.[2] ARTEMIS deals with wave propagation towards the coast and into harbours. It is based on the Berkhoff, or Mild-Slope, equation (refraction-diffraction equation [3]), including dissipation through depth-induced wave breaking and bottom friction in shallow and very shallow water.[4] ARTEMIS uses a finite-element formulation and then enables accurate and reliable results in coastal areas of complex geometry to be obtained. ARTEMIS computes wave parameters such as significant wave height, wave incidence, breaking rate, etc.

In this study, bottom-friction dissipation has been neglected, given the short distance covered by the computational domain, whereas wave breaking is taken into account. We used ARTEMIS in random mode to represent the frequency distribution of the wave energy, defined through a typical Joint North Sea Wave Project (JONSWAP) spectrum by the parameters Hs and Tp defined above.[5]

Configuration of the marine structures

The local computational mesh comprises 2233 nodes defining 4236 triangular elements. It covers an area of about 400 m x 500 m around the excavations (Fig. 2). Direction Y is parallel to the North direction. Borders B1, B2, B3 and B5 are liquid limits across which, waves can enter or leave the domain. Border B4 corresponds to a solid boundary made of concrete blocks. A reflexion coefficient R = 0.3 is assigned to this limit.

Figure 2. ARTEMIS: computational mesh for wave simulations, comprising 2,233 nodes and 4,236 elements.
ARTEMIS compotational mesh for wave simulations

With the help of the Centre d’Études Alexandrines, we set up a bathymetric map of the site and assumed it to be constant in time for the numerical simulations. There are no significant sea-level or tidal variations: a free surface at rest is fixed at the elevation 0 m, referred to as the Chart Datum. Four topographic/structural configurations have been studied:

C1: The present situation, including the submerged concrete wall next to the fortress (Fig. 3). The wall is represented as a bathymetric artefact, roughly adding the height of two concrete-block layers (+ 4.0 m) to the estimated natural bottom level, and clipping the maximum water depth above the top of the wall at 1.25 m.

C2: The ‘natural’ topography assuming that the concrete wall is removed. Notice the presence of Diamond Rock in the north-eastern part of the domain (Fig. 4).

C3: The installation of an emerged breakwater, located along the north-western limit of the computational domain (see Fig. 5; the mesh presented in Fig. 2 was designed for this purpose). One length only has been considered: 100 m.

C4: The installation of a submerged breakwater, located along the north-western limit of the computational domain (Fig. 6). Three different lengths have been considered: 100, 125 and 150 m. It is assumed that the water depth over the top of this structure is 3.0 m, on average, considering that the submerged breakwater corresponds to the displacement of the two-layer block structure in configuration C1.

Figure 3. Bathymetry of configuration C1.
  Figure 4. Bathymetry of configuration C2.
Bathymetry C1
Bathymetry C2
Figure 5. Bathymetry of configuration C3.
  Figure 6. Bathymetry of configuration C4.
Bathymetry C3
Bathymetry C4
For configurations C1 and C4, submerged breakwaters have been integrated into the bathymetry. However, Booij[6] has shown that Berkhoff’s equation, used by ARTEMIS, can integrate the bottom slope up to 1/3. It is not therefore possible to represent the vertical slope of the concrete blocks directly, so we connect the water depths above the natural sea floor and above the top of the submerged wall with a ‘numerical’ bottom slope of 1/3.
'Numerical' sea bottom

Wave-simulation results

Refraction-diffraction patterns

Figures 7a to 7d show the wave phase field computed for each topographic configuration and each set of wave conditions. This depicts the refraction-diffraction patterns of the wave propagation and shows how the wave length and wave direction are modified in the various configurations and offshore wave conditions used: diffraction behind detached breakwater for NW waves, behind Diamond Rock for NE waves, etc.

Figure 7a. Wave refraction-diffraction patterns resulting from model configuration C1. PRESENT SITUATION
Wave conditions: NW - 8s - 4 m
Wave conditions C1 NW
Wave conditions: WNW - 8s - 4 m
Wave conditions C1 WNW
Wave conditions: NE - 7s - 3 m
Wave conditions C1 NE
Figure 7b. Wave refraction-diffraction patterns resulting from model configuration C2.
Wave conditions: NW - 8s - 4 m
Wave conditions C2 NW
Wave conditions: WNW - 8s - 4 m
Wave conditions C2 WNW
Wave conditions: NE - 7s - 3 m
Wave conditions C2 NE
Figure 7c. Wave refraction-diffraction patterns resulting from model configuration C3 (breakwater length = 100 m).
Wave conditions: NW - 8s - 4 m
Wave conditions C3 NW
Wave conditions: WNW - 8s - 4 m
Wave conditions C3 WNW
Wave conditions: NE - 7s - 3 m
Wave conditions C3 NE
Figure 7d. Wave refraction-diffraction patterns resulting from model configuration C4 (breakwater length = 125 m; depth over breakwater top = 3 m). SUBMERGED DISPLACED BREAKWATER
Wave conditions: NW - 8s - 4 m
Wave conditions C4 NW
Wave conditions: WNW - 8s - 4 m
Wave conditions C4 WNW
Wave conditions: NE - 7s - 3 m
Wave conditions C4 NE

Significant-wave-height field

Hs values have been computed for the four configurations and the various wave conditions. For example, Figures 8 to 11 show the results for configurations C1–C4, respectively, for NW wave conditions. Hs profiles along P1 and P2 are also given on the same figures. All the results are summarized in Table 1.

CONFIGURATION C1 P1: 75% / 25% (FIG. 9)
P2: 35% / 75%
P1: 75% / 20%
P2: 20% / 75%
P1: 45% / 65%
P2: 70% / 90%
CONFIGURATION C2 P1: 80% / 55% (FIG. 10)
P2: 65% / 70%
P1: 80% / 30%
P2: 35% / 75%
P1: 50% / 80%
P2: 85% / 100%
LENGTH = 100 m
P1: 30% / 25% (FIG. 11)
P2: 25% / 50%
P1: 35% / 20%
P2: 25% / 30%
P1: 50% / 80%
P2: 80% / 100%
LENGTH =100 m
P1: 75% / 25% (FIG. 12)
P2 : 35% / 75%
P1: 45% / 20%
P2: 25% / 50%
P1: 30% / 80%
P2 : 85% / 100%
Notes: For each simulation, results are given in terms of relative significant wave height Hs/Hs 0 along profiles P1 and P2; the lefthand value, in each case, is for the first part of the profile, and the righthand value is for the second part. NW and WNW wave simulations were run using an incident Hs 0 of 4.0 m; NE wave simulations used an incident Hs 0 of 3.0 m.

Analysis of wave-simulation results

WNW and NW waves (prevailing conditions): The results observed for incoming NW and WNW waves are similar, even if the last part of profile P1 is more protected against WNW waves than against NW waves. This is why we do not give herein the figures related to WNW wave conditions. In the configuration C1, the NW waves propagate almost parallel to the axis of the submerged wall. Strong wave breaking occurs over the top of this wall, as shown in Figure 12 (for example, Qb = 50% roughly means that 50% of the waves break). This may generate a strong residual current, induced by breaking and driven along the corridor between the submerged wall and the fortress seawall. This may emphasize the undermining of the fortress’s foundations through direct erosion and/or transport of bottom sediment material suspended by oscillatory wave currents.

Conversely, when the submerged wall is removed (configuration C2), the degree of wave agitation obviously increases (Fig. 9) relative to configuration C1 (Fig. 8): the risk of sea-bed scouring may increase, because wave agitation and wave reflection are stronger, and wave overtopping is also emphasized, even if waves propagate along the fortress wall.

It is not possible in this preliminary study to quantify precisely which of the two previously mentioned processes is prevailing. But this shows that: (a) special attention has to be given to the protection of Qait Bey fortress, considering the damage observable on the site; and (b) the present situation may be dangerous for the foundation’s stability.

The installation of an emerged breakwater along a SW–NE axis (configuration C3) notably decreases the level of wave agitation (Fig. 10). However, agitation behind such a detached breakwater depends on the length of the structure and is not zero, owing to diffraction.

The wave agitation behind the submerged displaced breakwater (configuration C4) is not reduced in the same range as for configuration C3, owing to wave transmission over the maritime structure (Fig. 11). It is interesting here to refer to experimental flume results obtained by Elkamhawy [7] for the transmission of waves through 2-dimensional submerged obstacles, to estimate the transmitted wave height for any other water depth over the breakwater. In our case, we observed a transmitted wave height of about 2.5 m, which is consistent with the experimental observations of Elkamhawy.[7] But here, the finite length of the breakwater induces 3-dimensional processes that slightly modify the expected results, according to Elkamhawy’s experimental results. And again, the ‘shadow’ area (in terms of wave agitation) behind the detached breakwater depends on the length of the structure.

We observe no difference between C1 and C4 in terms of agitation for NW waves. This means that a smaller water depth over the top of the breakwater would be necessary to improve the protection of the area of interest from wave agitation, if the present 2-layer concrete block wall were displaced as shown in Figure 6. If a criterion of wave agitation is imposed in the excavation area, it is possible, using [7], to estimate firstly the depth over the submerged wall required roughly to meet the adopted criterion, after which, a numerical simulation might be used to compute the wave agitation in the whole area, to estimate the horizontal wave energy distribution.

All computations for WNW and NW waves showed wave-breaking over Diamond Rock (see as an example Figure 12 for NW waves). During our second visit to Alexandria, a NW-wave climate was present over the area, with an estimated significant wave height of 2.5 to 3.0 m. Wave-breaking was clearly observable over Diamond Rock. This is directly comparable to the computational results shown in Figure 12.

Figure 8. Distribution of significant wave heights resulting from model configuration C1 (for NW waves only).
Wave height distribution C1
Wave height profiles C1
Figure 9. Distribution of significant wave heights resulting from model configuration C2 (for NW waves only).
Wave height distribution C2
Wave height profiles C2
Figure 10. Distribution of significant wave heights from model configuration C3 (breakwater length = 100 m; for NW waves only).
Wave height distribution C3
Wave height profiles C3
Figure 11. Distribution of significant wave heights resulting from model configuration C4 (breakwater length = 125 m; depth over breakwater top = 3 m; for NW waves only).
Wave height distribution C4
Wave height profiles C4
Figure 12. Distribution of breaking rate resulting from model configuration C1 (for NW waves only).
Wave breaking rate distribution C1
Wave breaking rate profiles C1

NE waves: None of the proposed configurations offers satisfactory protection against NE waves. We can see the impact of Diamond Rock on wave propagation: it diffracts waves around the rocky point. For annual conditions, configurations C1 and C2 do not show any quantitative differences. If stronger incident wave heights occurred for the NE direction, the effect of the present submerged wall may be positive with respect to the risk of overtopping the fortress seawall; but again, the presence of the corridor may emphasize the risk of undermining the fortress seawall foundations.

Once criteria can be specified for prescribed priorities, the design of an emerged/submerged breakwater is possible; it would have to guarantee the stability of the structures against extreme events using relevant design methodology [8], but keeping in mind that the installation of such marine structures may have an impact on the sedimentological environment in a way not compatible with intended touristic or archaeological objectives.

Sedimentological aspects


Even if we are here concerned with a very limited area, sedimentological preoccupations require us to view the matter on a large scale, in time and in space. Alexandria was founded on a coastal barrier. Its coasts are formed by: a sandy shoreline from Sidi-Krir to El Agami; a mixed shore with rocky zones and sandy beaches in Alexandria Bay; and, on the eastern side of the Eastern Harbour, as far as Abu Qir; and Abu Qir Bay itself.

Information from the evolution of coastal morphology

A previous study of the site of Sidi-Krir [1] showed that the estimated mean longshore transport of sand is about 100,000 m3/yr from west to east. This seems to be in agreement with the shape of the shoreline in the vicinity of the large rocky area of Abu Qir. Obviously, the large number of human activities along the coast over many centuries depicted in the maps available in the Centre d’Études Alexandrines does not allow clear conclusions about the natural trends in the large-scale sedimentological regime. It seems that recent activities linked to tourism in the western part of the Egyptian coast showed sand accretion on the western side and erosion on the eastern side of groynes. Some sandy beaches on the eastern side of the Eastern Harbour are subject to strong erosion. Some of them are periodically renourished with fine desert sand, which rapidly disappears under wave and current action.

This incomplete analysis of the large-scale sedimentological evolution of the Alexandrian coast suggests, however, the existence of significant longshore sand transport from west to east, which can be locally interrupted by the construction of obstacles.

Local sedimentological data

Non-cohesive sediments: No precise and quantitative data on the sediments in the area of interest could be collected during our missions. The only information available comes from observations by archaeologists diving in the submarine excavations. It seems that the bottom in the area is rocky and partly covered with sand 20 cm to 50 cm thick. Farther offshore, the sand thickness could be greater. The sand in the excavation area seems to be coarse (D50 ~ 0.5 mm; that is, the mesh size through which 50%, by weight, of the sand grains pass). This is consistent with constant wave agitation which imposes resuspension of fine sediment which can be transported by currents and redeposited in calmer areas, the coarse sand staying in place.

The French nautical instructions manual [9] for 1981 indicates that the Eastern Harbour of Alexandria is no longer frequented, being partly filled by high inner sand banks. This evolution is probably due to the dikes and the detached breakwater built to protect the Eastern Harbour.

Cohesive sediments: The site of interest is surrounded by a lot of industrial, agricultural, and domestic sewage outfalls: 3 in the Western Harbour (Mahmoudia Canal, East Noubaria Canal, and the Umoum outfall), and 3 domestic sewage outfalls in the western part of the Qait Bey fortress, in the Eastern Harbour, and along the eastern part of the Silsila promontory. (See figure 3, chapter on human impacts Alexandrias marine environment). Divers have pointed out the fact that, in certain wind conditions, the water turbidity in the archaeological area becomes much too high for them to pursue their excavation. Mud deposition is also observable in the Eastern Harbour. It is clear that such conditions would compromise visits by tourist divers.

Sedimentological risk

In the present case, it seems that:

  1. no significant non-cohesive (sand) sedimentation occurs in the archaeological area at present, owing to the frequently high level of wave agitation
  2. there may be a potential stock of sand seawards to be moved and displaced through cross-shore and along-shore transport if structures are displaced
  3. no precise quantitative data (grain-size distribution {D50, D90}, sand-layer thickness, etc.) are available
  4. cohesive sediments are often in suspension in the water column.

The protection solution consisting of a displaced emerged/submerged breakwater has to be carefully considered; here, we must focus on the possible use of such marine structures to increase sedimentation on the wave-protected side of the breakwater (formation of tombolos: sand accretions on the wave-protected side of a detached breakwater), to improve the nourishment of the beaches and the shore by sand, for instance. This potential effect would be completely opposite to that required for the creation of a submarine museum.

The rate of sand accretion in the lee of such a detached breakwater depends on the incident-wave characteristics, the distance from the shore, the water depth, and the sand’s characteristics and availability. For instance, a small wave length brings less wave energy (i.e., less agitation) in the lee of the breakwater than a larger wave length for a given Hs value, and thus promotes sand accretion.

Numerical modelling of such processes is in progress, but requires a consistent linking between wave regime, wave-induced currents, and sediment-transport modelling. We performed such modelling within a recent European research programme dealing with tombolo formation behind a hypothetical detached breakwater on a sandy beach (D50 = 0.25 mm). [10]

For the estimation of long-term sedimentary impacts, laboratory studies on reduced scales are generally used to check and finalize the options that could be indicated by numerical modelling. Physical modelling of sedimentary impacts due to the installation of marine structures facilitates reproduction of the long-term morphological evolution to be expected when exposing the site to a representative wave climate. Such an approach has already been applied in our laboratory for instance to assess the sedimentary impacts around the new Olympic harbour in Barcelona (Spain). [11]


Localized numerical wave-agitation simulations in the vicinity of the Pharos excavation site in Alexandria (Egypt) have been carried out for annual wave-climate conditions. They show how WNW, NW and NE waves propagate towards the site. Depending on criteria that have not yet been specified and on the priorities to be fixed by Egyptian authorities, it is possible to assess the wave-agitation level in the case of emerged or submerged detached breakwaters.

A rapid investigation of the Qait Bey fortress area, reinforced by local information, has shown the necessity of looking carefully at the present protection system. The presence of a corridor between the submerged concrete wall and the fortress is favourable to high wave-driven currents during extreme events. The present submerged concrete blocks may therefore be unuseful, at best, or harmful, at worst.

Suspended materials from a large number of adjacent industrial and domestic outfalls in the vicinity of the archaeological site caused high water turbidity which can compromise the visit to the site by divers.

Local sedimentological data are not readily available. Nevertheless, previous experience at LNH suggests that the creation of a submarine museum, protected from wave agitation by a detached breakwater, could be considered, but with much caution. Morphological evolution observed along the Alexandrian coasts shows that the risk of sedimentation by sand or mud, associated with the installation of detached marine structures, is appreciable.

EDF-LNH has been asked questions that relate to a more global problem. A solution therefore has to take into account all the sources of complexity in the problem. A durable solution may be reached through a few temporary actions consistent with the priorities to be fixed.

No definitive solution for durable marine structures can be proposed at the moment without an extensive and integrated study, which must include:

  1. complete field-data collection; (particularly regarding sediments)
  2. complete diagnosis of the efficiency of the present Qait Bey fortress protection;
  3. refined numerical modelling of wave-induced currents and sediment transport; and
  4. validation of a physical model of the projected configurations.
[1] Teisson, C. and Bouchard, J-P. (1987). Étude de faisabilité pour la centrale thermique de Sidi Krir (Égypte). Phase I. EDF-LNH Reports, HE-42/87.10 and HE-43/87.21.
[2] Hervouet, J-M. (1996). Introduction to the TELEMAC System. EDF-LNH Report, HE-43/ 96/073/A.
[3] Berkhoff, J. C. W. (1976). Mathematical models for simple harmonic linear water waves – wave diffraction and refraction. Delft Hydraulics Laboratory Publication, 163 (April).
[4] Aelbrecht, D. (1997). Logiciel ARTEMIS – version 3.0. Notice théorique. EDF-LNH Report, HE-42/97/002.
[5] Hasselmann, K. et al. (1973). Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP). Deutschen Hydrographischen Zeitschrift, Reihe A (8°), no. 12.
[6] Booij, N. (1981). Gravity Waves on Water with Non-uniform Depth and Current. (PhD thesis) Technical University of Delft, The Netherlands.
[7] Elkamhawy, H. (1995). Submerged Rubble-mound Breakwater. (PhD thesis) University of Windsor, Canada.
[8] Feuillet, J., Coeffe, Y., Bernier, J. and Chaloin, B. (1987). Le dimensionnement des digues à talus. Collection EDF-DER, no.64. Éditions Eyrolles.
[9] Service Hydrographique et Océanographique de la Marine. (1981). Instructions nautiques : Afrique - Côte Nord, entre la Mer Egée et le canal de Suez. Série D, vol. 6.
[10] Pechon, P. et al. (1997). Intercomparison of wave-driven current models. Coastal Engineering, 31:199–215.
[11] Pechon, P., Leymarie, J-C., Caillat, M. and Rabeau, J. (1991). Étude sédimentologique sur modèle réduit du Port Olympique de Barcelone. EDF-LNH Report, HE-42/91.33.
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