# Numerical approach to the study of coastal boulders: The case of Martigues, Marseille, France

A. Piscitelli, M. Milella, J.C. Hippolyte, M. Shah-Hosseini, C. Morhange, G.

Mastronuzzi

► To cite this version:

A. Piscitelli, M. Milella, J.C. Hippolyte, M. Shah-Hosseini, C. Morhange, et al.. Numerical approach to the study of coastal boulders: The case of Martigues, Marseille, France. Quaternary International, 2017, 439, pp.52 - 64. 10.1016/j.quaint.2016.10.042. hal-01794751

HAL Id: hal-01794751

https://hal.science/hal-01794751v1

Submitted on 23 Jul 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
NUMERICAL APPROACH TO THE STUDY OF COASTAL BOULDERS:
THE CASE OF MARTIGUES, MARSEILLE, FRANCE

5

Piscitelli A.¹, Milella M.¹, Hippolyte J.-C.², Shah-Hosseini M.², Morhange C.², Mastronuzzi G.³*

10

¹ – Spin Off Environmental Surveys s.r.l., Taranto, Italy

² – Aix Marseille Université, CEREGE, UMR 7330,
Technopôle Méditerranéenne l’Arbois, Aix en Provence, France

³– Dipartimento di Scienze della Terra e Geoambientali,
Università degli Studi di Bari “Aldo Moro”, Bari, Italy

15

*Corresponding Author: Dipartimento di Scienze della Terra e Geoambientali,
Università degli Studi di Bari “Aldo Moro”, Campus Universitario, Via E. Orabona 4,
70125 Bari, Italy (email: gimastronuzzi@libero.it)

**Abstract**

20

The coastal strip that extends to the east of the city of Martigues, between the Anse de Bonnieu and that of the Chariot (Provence, South France), is characterized by an alternation of gently rocky coast and 5 m high cliffs shaped in Miocene limestone. The foot of the cliff is marked by a deep notch and a discontinuous wave-cut platform; at its base, the sea bottom has a maximum depth of about 4,5-6m. The emerged area is marked by the presence of boulders weighing up to 35tons, and located up to about 10 m from the coastline and 2 m above the sea level. A geomorphological survey was conducted by means of a Terrestrial Laser Scanner allowing to obtain a breakdown of the boulder sizes. The proposed study has focussed, in particular, to estimate the minimum wave height needed to detach and transport on the surf bench two boulders originally joined in a bigger one about 25 tons heavy placed on the wave cut platform. Hydrodynamic models developed by various authors were used to calculate the minimum wave height necessary to move them. The data obtained from these different hydrodynamic equations were related to wave-climate data collected over the last 15 years by the buoy of Marseille in the Gulf of Lion. This study seems to confirm that a tsunami impact (never recorded in the last 20 years) would not have been necessary to move the two boulders. Hydrodynamic equations suggest that the boulder could have been broken and just after moved as a consequence of the impact of waves generated by an extreme storm occurred before December 2003; this seems to be in agreement with the morphology of the sea bottom, hydrodynamic features and eyewitness.

25

30

35

**Key words:** sea storm, boulders, hydrodynamic equation.

40
# 1. Introduction

In recent years, scientific debate on coastal dynamics has been focused on the effects of the impact of extreme wave on coastal areas and, as consequence, on the awareness that their impact is increasingly risky for all human settlements and the environment has increased in recent years. In fact, examples of the recent impact of hurricanes induced exceptional waves and of devastating tsunamis occurring in the last fifteen years underlines the fact that morphological effects cannot be underrated neither in purely scientific terms nor when applied to the Integrated Coastal Zone Management (ICZM) (i.e.: Mastronuzzi et alii, 2013). In particular, an important part of science that deals with coastal morphodynamics, tries to study large boulder accumulations distributed along the coastline of the Mediterranean basin as an attempt to reconstruct the sequence of the impact of high-energy events that place and distribute them along the coast (i.e.: Mastronuzzi and Sansò, 2000; 2004; Morhange et alii, 2006; Mastronuzzi et alii, 2006; 2007; Scicchitano et alii, 2007; Maouche et alii, 2009; Vött et alii, 2010; Mastronuzzi and Pignatelli, 2012; Shah-Hosseini et alii, 2013; Anzidei et alii, 2014; Biolchi et alii, 2016). The study of extreme waves impacting all along the coasts of the world over the past 25 years has led to assumption that boulder accumulation can be consequence of impacts of both storm surges and tsunamis (Mastronuzzi and Sansò, 2004; Goto et alii, 2007; Barbano et alii, 2010; Bourgeois and MacInnes, 2010; Regnauld et alii, 2010; Paris et alii, 2010; Richmond et alii, 2011; Jaffe et alii, 2011; 2012). Unfortunately, a methodological tool by means of which it is possible to ascribe, with absolute certainty, the origin of the accumulation of boulders or megaboulders to one event or another has not been still identified.

Considering sizes and shape of the boulders surveyed along the coast, many authors have developed hydrodynamic equations from real case studies to build a model that could be applicable to recognize the origin of their deposits (Nott, 2003; Noormets et alii, 2004; Imamura et alii, 2008; Pignatelli et alii, 2009; Nandasena et alii, 2011; Benner et alii, 2010; Engel and May, 2012). These hydrodynamic equations have been widely used by various authors to investigate the origin of past boulder accumulations in many coastal areas of the Mediterranean basin (i.e.: Mastronuzzi and Sansò, 2004; Shah-Hosseini et alii, 2013; Biolchi et alii, 2016).

In particular, the Mediterranean rocky coast of Southern France, in the coastal area of Martigues, near Marseilles (Fig. 1), is characterized by the presence of large boulders at various distances and elevations from the coastline. They testify the impact of exceptional wave(s) that were able to scatter inland boulders coming from the midtidal and subtidal zones (Vella et alii, 2011). The origin of the extreme events responsible for their transport and accumulation is unclear, despite a series of surveys conducted using classic and modern techniques, also digital. Shah-Hosseini et alii, 2013 have attributed them to exceptional storms that occurred during the Little Ice Age (LIA), although
the possibility that it could be a consequence of multiple events, may be also tsunami, cannot be
rule out. Particular attention has been focused on two boulders, "A" and "B", indicated by local
people as derived from an original one, "C".

In a previous paper, Shah-Hosseini et alii (2013) using the wide presence of bio-encrustations as bio-indicators, reconstructed the four phases of the breaking and the transport of the initial boulder ("C" in this paper but M7 in the original one): ì - detachment of the original boulder from its initial intertidal position; ìì - a phase of submersion attested by the development of Vermetids on the *Lithophyllum bissoides* encrustation; ììì - breakdown into boulders, M5 (= "B") and M6 (= "A") followed by the overturning of the latter; ìv - transport of the block to the supratidal zone. To confirm this geomorphological model by means of a digital and mathematical approach, a detailed laser scan survey of the two boulders and of the local topography was carried out jointly to the bathymetric survey of the coastal area immediately near them. This allowed us to: ì - accurately reconstruct the present size of the boulders; ìì - reconstruct their original shape; ììì - apply the wave hydrodynamic equations of various authors to test their validity on a case study of which the impacting wave is known to have been due to a storm; ìv - reconstruct the sequence of events responsible for the breaking, transporting and depositing of the boulders.

## 2. Geographical, geological and wave climate settings

The study described in the following pages has been performed in an area located between the
Bonnieu bay and the Chariot bay, South of Martigues near Marseilles, along the Mediterranean
coast of France (Fig. 1). The coastal area is oriented northwest-southeast; it is characterized by a
gently sloping rocky surface shaped in a highly fractured bioclastic limestone.

This Burdigalian marine limestone (Colomb *et alii*, 1975) is characterized by bioclastic and
conglomeratic pinkish calcarenite with *Chlamys*, *Ostrea* and *Pecten*, about 10 m of thickness
overlying in discordance on Cretaceous (Urgonian) limestone. The outcrop is characterized by a
high density of faults and fractures presenting rough stratigraphic joints separating 50 cm to 2 m
thick layers. Limestone beds gently dip to the southwest (<10°). Despite a lack of apparent finite
deformation this limestone is cut by well-defined sets of fractures (Fig. 2 and Fig.3). The fracture
planes do not exhibit evidence of shear displacement so that they can be referred to as joints. These
joints are predominantly perpendicular to the bedding (Fig. 2A and 2B) and together with the
bedding joints cut the limestone in blocks with planar surfaces. Near the sea shore and under the
water, the joints are largely open as a result of dissolution and abrasion of the limestone (Fig. 2C).

The coastal landscape shaping was conditioned by the presence of these joints and by sea action; the
results is an alternation of surf benches, wave cut platforms and cliffs up to about 5 m high (Fig. 4).

The surf bench (hereinafter SB) generally corresponds to an area directly flooded by broken waves
that have stripped of the soil and the upper strata of the local stratigraphic sequence; inland it is
limited by a step whose height corresponds to the strata thickness (Figs. 4A and 4B). In some
limited areas a wave cut platform (hereinafter WCP) of various extent is shaped in continuity with
the SB from which it is separated by a very low step that it's not higher than 1 m. Locally, a short
WCP corresponding to the strata surface is also present to the base of the cliffs that on their part, are
engraved by the presence of a continuous notch up to about 2 m deep and 1 m high (Figs. 4C and
4D). The emerged area is marked by the presence of hundreds of large boulders with a maximum
size of about 35 tons, positioned up to 10 m from the coastline and at about 2 m above sea level
(Fig. 3 and 4A) (Vella *et alii*, 2011; Shah-Hosseini *et alii*, 2013).

The French Mediterranean basin is considered to have been a moderately active tectonic zone
during the Holocene (Vella *et alii*, 1998; Vella and Provansal, 2000; Jolivet *et alii*, 2008). Tsunami-
generating earthquakes have rarely been reported by the Bureau de Recherches Géologiques et
Minières - BRGM (www.ngdc.noaa.gov). Its archives report the occurrence of 14 tsunamis
since1755, highlighting the occurrence of only one destructive event which occurred on 27 June
1812 (4 on the Sieberg-Ambraseys intensity scale), when boats and infrastructure in the old port of
Marseilles were damaged. The event may have been recorded in the accumulated boulders in the
area of Martigues; in fact 14C ages obtained on some bio-encrustations from different boulders
seem to suggest a sequence of different high-energy wave impacts distributed over the past 700
years (Vella *et alii*, 2011; Shah-Hosseini *et alii*, 2013). Some 14C ages seem to fit in a period that
comprises the 1812 event; on the other hand, the obtained range of ages, from 1660 to1860, in a
period corresponding to the LIA during which it is normal to suppose the occurrence of important
storm events able of scraping and moving boulders inland (i.e.: Kaniewski *et alii*, 2016, for the
Central Mediterranean zone). Minor tsunami events have been recorded in historic and modern
times on the French Riviera coast about 150 km east of Martigues. They were probably triggered by
submarine landslides but no geomorphological evidence have been recognized (Julian and Anthony
1996).

Based on the present knowledge, there is no evidence that leads to correlating the surveyed boulders
to the impact of a tsunami rather than that of a storm. However, it is also possible that storms that
characterize this stretch of coast, since their energy maybe able to move large boulders.

The surveyed coast is exposed to S-NW winds and the fetch is between 400 to about 600 nautical
miles, even if protected by the Balearic Islands. Available wave data sets on the French
Mediterranean coast are of limited durations. These data derive from the buoy placed in the Gulf of
Lion, France (Fig. 5). The data collected, for a total of 1534 events, represent wave heights, period
and direction only for waves with heights > 3m, in the period 1993-2008 (Tab.1). Table 2 shows the
145

highest waves and their provenance direction, recorded by the buoy in the same period for each year.

## 3. Material and methods

150

A geomorphological and structural survey was conducted on the entire coastal area of Carro where boulders have been detected (Vella *et alii*, 2011; Shah-Hosseini *et alii*, 2013). To characterize the structural features of the area, joint planes in four areas have been measured directly in the field (Fig. 3).

155

Particular attention was paid to a limited portion (25m x 25m) of the coastal area, because of the presence of two boulders in the following pages named “A” and “B” The detailed terrestrial laser scan (hereinafter TLS) survey of this area was carried out using the Leica Scan Station 2 that has been operated jointly with a digital ground position system (hereinafter DGPS) Leica 1230 (Fig. 6). The scanner consists of a laser beam generator, a mirror rotating on its horizontal axis and forming a 45° degree angle with the beam direction at the same time rotating around its vertical axis. These features together permit to obtain a scan of an area extending 360°x270°.

160

To obtain a complete coverage of the surveyed area, a scan density of 3 mm was carried out from different positions along horizontal and vertical planes; different surveys have been joined and overlapped using targets to georeference all the points scanned from different positions to make possible a 3D reconstruction of the surveyed objects included in a “point clouds”. So, to obtain a 3D modelspace, it is necessary to overlap numerous scans in which target georeferenced by means of a DGPS were captured from different point of view. The post processing was performed using Cyclone 6.03 software; the point clouds obtained from each scan were linked together through the overlapping of different TLS scans. The next step was to isolate millions of points representing boulders “A” and “B” from the cloud points that comprise all the landscape and to reconstruct the original boulder “C” by matching them along the surface of fracture. The use of TLS techniques permit to reduce significantly the overestimation of the sizes and weight of the surveyed boulders respect to the handmade measurements; obviously this permits to use the hydrodynamic equations with major confidence (Marsico *et alii*, 2009; Hoffmeister *et alii*, 2013).

165

170

For completion of the sub-aerial survey, in the area of the “A” and “B” boulders, a specific bathymetric survey was performed during both ARA and snorkeling dives. They were performed by drawing nine different bathymetric transects starting from the biological mean sea level up to bathymetry 6m; depths and immersion times were recorded by a scuba computer SCUBAPRO Aladin 2G. This methodology allowed to reconstruct a 3D sketch of the morphology of the continuity of emerged coastal area and of the seabed up to about 50 m from the coastline (Fig. 7).

175
180

## 4. Coastal and boulder features

The rose diagram of the 111 measured joints shows that two main trends prevail: NNW-SSE to NNE-SSW and ESE-WNW (Fig. 3b). In detail, seven joints sets can be distinguished from this rose diagram: N160E, N170E, N5E, N20E, N30E, N115E and N130E (Fig. 3b). Taking into account that the Marseilles area underwent N020E and N165E compressions during the Miocene (Hippolyte *et alii*, 1993) the NNW- to NNE-trending joints can be interpreted as tension or shear joints formed during the alpine compressional phases (late Cenozoic). In contrast the ESE-trending joints are filled with Miocene shells and sand suggesting early formation (Burdigalian).

185

Schmidt diagrams of joints (Fig. 3d, e, f) show that the four studied areas are characterized by at least two perpendicular joint sets which allowed the separation of limestone blocks (NNE-SSW and ESE-WNW). We mapped the joint sets in the four areas along the coast using high resolution (15 cm) aerial photos (Fig. 3). Areas 1 to 3 are characterized by closely spaced NNE-trending joints and by numerous transported blocks (Fig. 3d and 3e). In contrast, area 4 is characterized by far fewer NNE-trending joints and transported blocks. The dense joint patterns in areas 1 to 3 probably facilitated the rock detachment.

190

As indicated above, the coastal area shaping has been driven by the sea action on a lithological sequence heavily conditioned by the presence of these joints. Surf benches, wave cut platforms and cliffs alternate between Carro and Bonnieu (Fig. 4). Regarding the sea bottom, its first 50 m has a maximum depth that ranges from 4 to 6 m. In general the surveyed area shows a double trend: starting from the coast line up to a depth of about 1.5 m it has quite a flat surface of varying extension corresponding to the wave-cut platform; a rapid increase of the slope up to 5-6 m deep indicate the passage to a gently sloping surface towards the higher depths.

195

Generally, boulders are distributed on the surf bench; boulders "A" and "B" are 7 meters apart at about 2 m above sea level, placed on the SB, slightly leaning against a step whose height corresponds to the strata thickness (Fig. 4). The details that characterize the geometric features of all three boulders were obtained from the scanned point clouds that permitted to obtain approximation within a few centimeters. The software used also permitted the reconstruction of the boulder "C" as result of the virtual rotation and shift of the boulders "A" and "B" (Fig. 8). All the geometrical parameters of boulders "A", "B" and "C" were obtained by laser scanner software, given the very irregular shape of both blocks. The measures of three axes, the planar *a* (maximum) and *b* (medium) ones, the vertical *c*-axis, the volumes and weights are reported in the synoptic Table 3.

200

Both boulders (Fig. 9) show bio-encrustations that are typical of the base of the midtidal zone represented by the *Lithophyllum byssoides* rim, algae characterizing the lowest limit of the biological sea level (Laborel *et alii*, 1994; Morhange and Marriner, 2015). But mainly, boulder "A" shows a side characterized by the presence of a concavity that seems to correspond to an abrasive

205

210
surface originally placed in the correspondence of the mean sea level. This geomorphological
element confirms the initial position of the boulder "C" in correspondence of the mean sea level.
The cover of the carbonate algae appears partially colonized by *Vermetus triqueter*; this gastropod
develops in the subtidal zone and the upper limit of the population which approximately marks the
biological sea level (Laborel *et alii*, 1994). Its presence with some specimens of *Lithophaga
lithophaga* suggests a lowering of the original position of boulder "C". Finally, the presence of
*Barnacles* sp. can be related to the permanence of the boulder in the surfing area. Boulder "A" is
overturned compared to the original verticality of boulder "C" as confirmed both by the
morphological evidence and by the presence of the *L. byssoides* rim on its lower face. Furthermore,
the rim indicates, with absolute approximation, the boulder's past interface with the mean biological
sea level. On the other hand, boulder "B" is rotated, compared to the supposed original position of
boulder "C"; this is evidenced by the particular aspect of the breaking surface that faces west (Figs.
9A-D), and is in the opposite direction of boulder "A". Boulder "B" is in the natural polarity as
evidenced by the presence of the *L. byssoides* rim on its upper surface corresponding to the ancient
surface below sea level.

The joint geomorphological and laser scan survey of the entire coastal area, emphasized the
presence of two fracture systems (Fig. 2 and Fig. 3). Also considering the general structural
features, and according to them, the first one is oriented NE-SW, almost perpendicular to the
coastline and the second is oriented WNW-ESE, quite parallel to the coastline. These two
alignments and the general one of the coastline, allowed us to hypothesize the original position and
orientation of boulder "C" and the individuation of the detachment zone, located on the WCP about
12 m south of the present position of boulder "B", between two evident fracture lines (Fig. 10).

# 5 - Discussion

## 5.1. Reconstruction of the boulder's movement

The set of morphological and biological data and the bathymetric survey suggest a first
reconstruction of the possible succession of the dynamic events that led the two separated boulders
to the current position on the rocky surface. It was possible also taking into account the virtual
reconstruction of boulder "C" obtained by the TLS survey.

The general shape of the latter and the presence of a quite continuous concavity along one of their
side indicate an original position in correspondence of the mean sea level at the external sea side
border of the surf bench. The extensive presence of *L. bissoides* on the top of boulders "A" - at
present overturned - and "B" suggests that as consequence of numerous and repeated wave impact
the boulders "C" collapsed depositing itself on the WCP, and eventually below sea level. Here it did
not break as there is no evidence of marine organism colonies on its fracture surface. Only at a later
time, after colonization by vermetids, the boulder "C" was broken in two blocks, "A" and "B", without there having been the time to colonize the fracture by marine organisms before a new phase of movement. In fact, the resulting boulders were moved separately inland from the WCP to the current position on the SB just after they have been broken during a following storm impact. Bioindicators and morphological aspects in particular, provide evidence that during the movement, boulder "A" was scattered inland while overturning and, boulder "B" migrated inland, rotating approximately 90° anticlockwise (Fig. 11).

## 5.2 Hydrodynamic calculations

The data set can be analyzed to prove this sequence of morpho-events using also a numerical approach. In this way it is possible to define a morphodynamic sequence recognizable in a morphosequence. The features of the waves responsible for the initial detachment and inland transport of these two boulders can be characterized by applying the Pignatelli et alii (2009) hydrodynamic equations, considering the possible scenarios (Nott, 1997; 2003) that characterized the previous history as: i - boulder "C" was in a Joint Bounded Scenario (JBS) at the external border of the SB facing to the impacting waves; ii- the same boulder was disarticulated and then collapsed on the WCP but it remained here in its integrity; iii-, the two parts in which boulder "C" was broken, moved separately but may be at the same time from the WCP to SB due to waves impacting in a Sub-aerial Boulder Scenario (SBS). Apparently this seems to be a wrong scenario; in effect, after the collapse, during the phase ii and iii, the boulder "C" was below the sea level in condition of wave's absence but alternately in an emerged and submerged position in function of the breaking wave features during the storm. As consequence, due to the low water level of the wave-cut platform, and the behavior of and impacting waves of a strong storm on a WCP, a SBS was considered to explain the movement that split boulder "C" in "A" and "B" and finally deposited both on the surf bench. Assuming these aspects when applying the Pignatelli et alii (2009) equation, possible wave heights (Hs) were estimated:

$$ \text{- JBS for Boulder "C"} \qquad \mathbf{H}_s = (2*c*(\gamma_d-\gamma_w)/\gamma_w)/C_l $$

$$ \text{- SBS for both Blocks "A" and "B"} \qquad \mathbf{H}_s = (2*(b*(\gamma_d-\gamma_w)/\gamma_w-2*(C_i*u_i)/g))/((b/c)*C_l+(c/b)*C_d) $$

where Hs is the storm wave height at breaking point, c is the minor axis, b is the medium axis, γd is the density of boulder, γw is the density of water, C1 is the lift coefficient (Einstein and Samni, 1949), Cd is the drag coefficient (Helley, 1969), Ci is the coefficient of inertia (Noji et alii, 1985), g is the constant of gravity and ui is the instant acceleration wave (Nott, 1997; 2003).

Other hydrodynamic models were tested in order to compare the possible resulting values of wave heights (Tab. 5). We applied formulas by:
285

a - Engel and May (2012) (V is the volume, a is the axis major, α is the slope of the coast and q is a empirical volume coefficient):

- JBS for Boulder C

$$H_s = 2*(\gamma_d - \gamma_w) * V * (\cos\alpha + u_i * \sin\alpha) / (\gamma_w * C_l * a * b * q)$$

- SBS Rampart for both Blocks A and B

$$H_s = 2 * u_f * V * \gamma_d / (\gamma_w * C_d * a * c * q)$$

290

b - Nandasena *et alii* (2011), ($u_s$ is the coefficient of static friction):

- JBS for Boulder C

$$H = [(2*(\gamma_d/\gamma_w - 1) * g * c * (\cos\alpha + u_s * \sin\alpha)) / C_l]$$

- SBS Sliding for Block B

$$H = [(2*(\gamma_d/\gamma_w - 1) * g * c * (u_i * \cos\alpha + \sin\alpha)) / (C_d * (c/b) + u_s C_l)] / \delta g$$

- SBS Overturning for Block A

$$H = [2*(\gamma_d/\gamma_w - 1) * g * c * (\cos\alpha + (c/b) * \sin\alpha)] / [C_d * (c^2/b^2) + C_l] / \delta g$$

295

c - Benner *et alii* (2010) ($C_m$ is the coefficient of inertia):

$$H_s = 2 * b * c * [(\gamma_d - \gamma_w / \gamma_w) * b - (\gamma_d / \gamma_w) * C_m * (u_i / g) * c] / (C_d * c^2 + C_l * b^2)$$

300

The minimum wave heights needed to detach the original boulder “C” from the upper part of wave-cut platform in a JBS, and move boulders “A” and “B” separately from the wave-cut platform to the surf bench in SBS were calculated. The results of all hydrodynamic equations are shown in Tab. 4. Many authors used Nott’s derived equations to determine if sea storm or tsunami were responsible for boulder displacement (i.e. Mastronuzzi and Sansò, 2004; Scicchitano *et alii*, 2007; Maouche *et alii*, 2009); generally, these studies are affected by an overestimation in the calculated wave heights as results of both (i) approximation typical of the techniques of measurement (Marsico *et alii*, 2009; Hoffmeister *et alii*, 2013) and (ii) hydrodynamic equations (i.e. Paris *et alii*, 2009; Goto *et alii*, 2010; Bourgeois and MacInnes, 2010). Different models derived by experiments in flume permit to have a theoretical approach in which morphological and dynamic approximations are adopted at a reduced scale aimed to reproduce the reality of an impacting wave (articulation of coastline, bathymetry and topography; variety of the type of rocky coast, presence of a roughness coefficient, wave direction, etc.) (Imamura *et alii*, 2008; Matsutomi and Okamoto, 2010). On the other hand the use of the Nott’s derived equations is, at present, the only way that permits a deterministic approach which allows the use of “real” data deriving by the observation of a “real” sediment and/or form. Despite this, it is evident that among the considered equations two of them (Benner *et alii*, 2010 and Engel and May, 2012) provide very high values; the other two (Nandasena *et alii*, 2011 and Pignatelli *et alii*, 2009) provide results, although not absolutely fitting surely more compatible, which differ by no more than about 0.40-0.50 m for both considered scenarios.

305

310

315
320

## 5.3 Wave analysis

Having considered the orientation of the coastline and the present position of the boulders, the direction of storm waves needed to move boulders "A" and "B" was evaluated to be approximately 225°N +/- 15°. During the period 1993-2008, the buoy of the Gulf of Lion indicates an occurrence of waves coming from the 150°N-300°N directions, about 1500 of which were over 3,0 m high, and about 340 with the same wave height. Only storm waves with $H > 3$ m and 150°N-300°N directions were considered (Tab. 5).

325

Storm waves that have offshore directions between N150E and N300E, and a 0°-75°incidence range, reach the shoreline with incidence angles ranging 2°-8°(i.e.: A.S.C.E., 1974 and references therein).

330

From its breaking point to the coastline, the wave height first decreases slightly and then greatly increases due to the sea floor trend in the last 3 m. In fact, the sudden slope increasing of the seabed has the effect of amplifying the shoaling process, so that the wave height near the coastline becomes very close to the $H_b$ value (i.e.: Keulegan and Paterson 1940; Sunamura and Horikawa 1974). As shown in Tab. 5, according to the Pignatelli *et alii* hydrodynamic model (2009), a minimum wave height of 5,36 m is required to detach boulder "C" in a JBS; while, to move boulders "A" and "B" from the wave-cut platform inland, minimum wave heights, respectively, of 3,97 and 3,66 m are required in an SBS. Among the recorded waves with $H > 3$ m, at their breaking point, 47 waves present wave heights ($H_b$) $\ge$ 3,66 m (Sunamura, 1992) and water depths ($W_d$) between 4,91 and 6,31 m (Keulegan and Patterson, 1940). While, 26 waves show at their breaking point wave heights ($H_b$) $\ge$3,97 m and water depths ($W_d$) between 5,39 and 6,31 m. The wave direction of all these events is between N152E and N285E. All the hydrodynamic parameters/features of the above-mentioned waves are shown in Tab. 6.

335

340

Analyzing satellite photos available since December 2003, it was already possible to observe and locate the presence of boulders "A" and "B" on the surf bench. Thus, only storm waves occurring before that date can be considered responsible for detaching and subsequently displacing the boulders. The hydrodynamic parameters, in relation to the surveyed sea floor trend and the eyewitness accounts, are absolutely compatible with the minimum $H_s$ values of the Pignatelli *et alii* (2009) and Nandasena *et alii* (2011) models for both Joint Bounded and Sub-aerial Boulder scenarios.

345

350

## 5. Conclusions

The presence on the SB of boulders the position of which, thanks to eyewitness, are ascribed to the impact of a strong storm in the last two decades permits to test the validity of the hydrodynamic model in a real case of which the cause is known: the impact of storm waves. The use of digital

10

10
technologies of survey – TLS and DGPS - coupled with the traditional geomorphological survey and the use of hydrodynamic equation permit to approach the study of boulder movement in coastal scenario using a quantitative–mathematical approach.

The history of the boulders was reconstructed on the basis of the 3D survey and of the presence of bio-encrustations that allow an estimate of the position of future boulder "C" emplaced in JBS at the external limit of the SB, exposed to the impact of waves. The same approach allows to estimate a phase during which the boulder "C" collapsed, completely, in the water on the WCP having a position permanently submerged during calm water. In the JBS, the application of different hydrodynamic equation suggests that a minimum storm wave of about 5,5 m high was required to scrape boulder "C" from the coast according to the Pignatelli *et alii* (2009) and of Nandasena *et alii* (2011) models. The analysis of the wave climate history of the sea in front of the studied area suggests that this value is consistent with the more energetic storms.

In a following phase, which occurred before December 2003, according to the satellite images eventually, the boulder was split into two parts, becoming boulders "A" and "B". Just after this and during the same storm, the two boulders were separately transported inland by storm waves from the wave-cut platform to their present position on the surf bench, as evidenced by the bio-indicators and by the morphological aspects highlighted by the digital survey and by the 3D view. In this case two hydrodynamic models, Pignatelli *et alii* (2009) and Nandasena *et alii* (2011), invocate a wave of 3,5 – 4 m high to move boulders inland towards the remaining models that both require wave height of more than 6,30 m; the first values are in agreement with "the normal more energetic storms" that characterize the studied area.

To conclude, a tsunami impact, which was never recorded in the past 20 years, was not necessary to move inland boulders "A" and "B" which movements occurred before December 2003.

The hydrodynamic parameters of 47 waves (selected in the period between 1993-2008), in relation to the surveyed sea floor trend and eyewitness accounts, confirm the best fitting of the Pignatelli *et alii* (2009) and of Nandasena *et alii* (2011) hydrodynamic models with this reconstructed succession of events.

Acknowledgments

This work has been partially carried out thanks to the support of the Labex OT-Med (ANR-11-LABX-0061) and of the AMIDEX project (n° ANR-11-IDEX-0001-02), funded by the "Investissements d'Avenir" French Government program, managed by the French National Research Agency (ANR) and the Flagship Project RITMARE - The Italian Research for the Sea - coordinated by the Italian National Research Council and funded by the Italian Ministry of Education, University and Research within the National Research Program 2011-2013, and by the
390 PRIN 2010/2011 "Response of morphoclimatic system dynamics to global changes and related geomorphological hazard".

This paper is a French-Italian contribution to the project IGCP 639 – International Geological Correlation Programme “Sea-level change from minutes to millennia” by UNESCO – IUGS (Project Leaders: S. Engelhart, G. Hoffmann, F. Yu and A. Rosentau).

395 We would like to thank Ms. Patricia Salomone for having improved the English form, and two anonymous referees that permitted to heavily improved the entire manuscript.

References

400 Anzidei M., Antonioli F., Furlani S., Lambeck K., Mastronuzzi G., Serpelloni E., Vannucci G. (2014). *Coastal structure, sea level changes and vertical motion of the land in the Mediterranean*. In: Martini, I. P. and Wanless, H. R. (eds) Sedimentary Coastal Zones from High to Low Latitudes: Similarities and Differences. Geological Society, London, Special Publications, 388 pp.

405 Barbano M.S, Pirrotta C., Gerardi F. (2010). *Large boulders along the southeastern Ionian coast of Sicily: storm or tsunami deposits?* Marine Geology, 275, 140–154.

Benner R., Browne T., Brückner H., Kelletat D., Scheffers A. (2010). *Boulder transport by waves: progress in physical modeling*. Zeitschrift für Geomorphologie, 54(3), 127–146.

410 Biolchi S., Furlani S., Antonioli F., Baldassini N., Causon Deguara J., Devoto S., Di Stefano A., Evans J., Gambin T., Gauci R., Mastronuzzi G., Monaco C., Scicchitano G. (2016). *Boulder accumulations related to extreme wave events on the eastern coast of Malta*. Nat. Hazards Earth Syst. Sci., 16, 737–756.

415 Bourgeois J., MacInnes B. (2010). *Tsunami boulder transport and other dramatic effects of the 15 November 2006 central Kuril Islands tsunami on the island of Matua*. Zeitschrift für Geomorphologie, 54, 3, 175–195.

Colomb E, Rouire J., L'Homer A. (1975). *Geological map of the France, map of Istres*. Map 1019, scale 1:50,000, Bur. de Rech. Geol. et Min., Orléans, France.

420 Einstein H.A., El Samni E.A. (1949). *Hydrodynamic forces on a rough wall*. Reviews of Modern Physics, 21-3, 520–524.

425 Engel M., May S.M. (2012). *Bonaire's boulder fields revisited evidence for Holocene tsunami impact on the Leeward Antilles*. Quaternary Science Review, 54, 126–141.

Goto K., Chavanich S.A., Imamura F., Kunthasap P., Matsui T., Minoura K., Sugawara D., Yanagisawa H. (2007). *Distribution, origin and transport process of boulders deposited by the 2004 Indian Ocean tsunami at Pakarang Cape, Thailand*. Sedimentary Geology, 202, 821–837.

425 Goto K., Miyagi K., Kawamata H., Imamura F. (2010). *Discrimination of boulders deposited by tsunamis and storm waves at Ishigaki Island, Japan*. Marine Geology, 269, 34–45.

Helley E.J. (1969). *Field measurement of the initiation of large bed particle motion in blue creek near Klamath, California*. U.S. Geological Survey Professional Paper, 562-G, 19 pp.

430 Hippolyte J-C., Angelier J., Nury D., Bergerat F., Guieu G. (1993). *Tectonic-stratigraphic record of paleostress time changes in the Oligocene basins of the Provence, southern France*. Tectonophysics., 226, 15-35.

435 Hoffmeister D, Ntageretzis K, Aasen H, Curdt C, Hadler H, Willershäuser T, Bareth G, Brückner H, Vött A. (2014) 3D model-based estimations of volume and mass of high-energy dislocated boulders in coastal areas of Greece by terrestrial laser scanning. Zeitschrift für Geomorphologie, 58 (3), 115-35.

Imamura F., Goto K., Ohkubo S. (2008). *A numerical model for the transport of a boulder by tsunami*. Journal Geophysical Research, 113, C01008.
Jaffe B., Buckley M., Richmond B., Strotz L., Etienne S., Clark K., Watt S., Gelfenbaum G., Goff J. (2011). *Flow speed estimated by inverse modeling of sandy sediment deposited by the 29 September 2009 tsunami near Satitoa, east Upolu, Samoa.* *Earth-Science Reviews*, 107, 23–37.

440

Jaffe B.E., Goto K., Sugawara D., Richmond B.M., Fujino S., Nishimura Y. (2012). *Flow speed estimated by inverse modeling of the sandy tsunami deposit: results from 11 March 2011 tsunami on the coastal plain near the Sendai Airport, Honshu, Japan.* *Sedimentary Geology*, 282, 90–109.

445

Jolivet L., Prouteau G., Brun J. P., Meyer B., Rouchy J. M., Scaillet B. (2008). *Géodynamique Méditerranéenne*. Vuibert-SGS, 232 pp.

Julian M., Anthony E. J. (1996). *Aspects of landslide activity in the Mercantour Massif and the French Riviera, south eastern France*. *Geomorphology* **15**, 275 – 289.

Kaniewski N., Marriner N., Morhange C., Faivre S., Otto T., Van Campo E. (2016). *Solar pacing of storm surges, coastal flooding and agricultural losses in the Central Mediterranean*. *Nature Scientific reports*, 6, 25197.

450

Keulegan G., Patterson G.W. (1940). *Mathematical theory of irrotational translation waves*. *Journal of Research of the National Bureau of Standards*, 24, 47-101.

Laborel J., Laborel-Deguen F. (1994). *Biological indicators of relative sea-level variations and of co-seismic displacements in the Mediterranean region*. *Journal of Coastal Research*, 10 (2), 395-415.

455

Maouche S., Morhange C., Meghraoui M. (2009). *Large boulder accumulation on the Algerian coast. Evidence of catastrophic tsunami events in the Western Mediterranean*. *Marine Geology*, 206, 96-104.

Marsico A., Pignatelli C., Piscitelli A., Mastronuzzi G., Pennetta L. (2009). *Ricostruzione digitale di blocchi accumulati da eventi estremi in Italia meridionale*. Atti 13ª Conferenza Nazionale ASITA, 1 – 4 dicembre 2009, 1377-1385.

460

Mastronuzzi G., Brückner H., De Martini P.M., Regnauld H. (2013). *Tsunami: from the open sea to the coastal zone and beyond*. In: Mambretti S. (Ed) *Tsunami: From Fundamentals to Damage Mitigation*. WIT Press, Southampton, 1-36 pp.

465

Mastronuzzi G., Pignatelli C. (2012). *The boulders berm of Punta Saguerra (Taranto, Italy): a morphological imprint of 4th april, 1836 Rossano Calabro tsunami?* *Earth Planets Space*, 64, 10, 829-842.

Mastronuzzi G., Pignatelli C., Sansò P. (2006). *Boulder fields: a valuable morphological indicator of paleotsunami in the Mediterranean Sea*. *Zeitschrift für Geomorphologie*, N.F. Suppl.-Bd., 146, 173–194.

470

Mastronuzzi G., Pignatelli C., Sansò P., Selleri G. (2007). *Boulder accumulations produced by the 20th February 1743 tsunami along the coast of southeastern Salento (Apulia region, Italy)*. *Marine Geology*, 242, 191-205.

Mastronuzzi G., Sansò P. (2000). *Boulders transport by catastrophic waves along the Ionian coast of Apulia (Southern Italy)*. *Marine Geology*, 170, 93-103.

475

Mastronuzzi G., Sansò P. (2004). *Large Boulder Accumulations by Extreme Waves along the Adriatic Coast of southern Apulia (Italy)*. *Quaternary International*, 120, 173-184.

Matsutomi H., Okamoto K. (2010). *Inundation flow velocity of tsunami on land*. *Island Arc*, 19, 443-457.

480

Morhange C., Marriner N. (2015). *Archeological and biological relative sea-level indicators*. In: Shennan I., Long A. J., Horton B. P. (eds) *Handbook of Sea Level Research*, Wiley, pp. 146-156. Morhange C., Marriner N., Pirazzoli A. (2006). *Evidence of late-Holocene tsunami events in Libanon*. *Zeitschrift für Geomorphologie*, 146, 81–95.

Nandasena N.A.K, Paris R., Tanaka N. (2011). Reassessment of hydrodynamic equations: minimum flow velocity to initiate boulder transport by high energy events (storms, tsunamis). *Marine Geology*, 281, 70–84.

485
Noji M., Imamura N., Shuto N. (1985). *Numerical simulation of movement of large rocks transported by tsunami*. Proceedings of the IUGG/IOC International Tsunami Symposium, Wakayama, Japan, 189-197 pp.

490

Noormets R., Crook K.A.W., Felton E.A. (2004). *Sedimentology of rocky shorelines: 3. Hydrodynamics of megaclast emplacement and transport on a shore platform, Oahu, Hawaii*. Sedimentary Geology, 172, 41–65.

Nott J. (1997). *Extremely high wave deposits inside the great barrier reef, Australia; determining the cause tsunami or tropical cyclone*. Marine Geology, 141, 193-207.

495

Nott J.(2003). *Waves, coastal boulders and the importance of the pre-transport setting*. Earth and Planetary Science Letters, 210, 269–276.

Paris R., Wassmer P., Sartohadi J., Lavigne F., Barthomeuf B., Desgages E., Grancher D., Baumert P., Vaultier F., Brunstein D., Gomez C. (2009). *Tsunamis as geomorphic crisis: lessons from the December 26, 2004 tsunami in Lhok Nga, west Banda Aceh (Sumatra, Indonesia)*. *Geomorphology*, 104, 1-2, 59-72.

500

Paris R., Fournier J., Poizot E., Etienne S., Mortin J., Lavigne F., Wassmer P. (2010). *Boulder and fine sediment transport and deposition by the 2004 tsunami in Lhok Nga (western Banda Aceh, Sumatra, Indonesia): a coupled offshore-onshore model*. Marine Geology, 268, 43–54.

Pignatelli C., Sansò P., Mastronuzzi G. (2009). *Evaluation of tsunami flooding using geomorphologic evidence*. Marine Geology, 260, 6-18.

505

Regnauld H., Oszwald J., Planchon O., Pignatelli C., Piscitelli A., Mastronuzzi G., Audevard A. (2010). *Polygenic (tsunami and storm) deposits? A case study from Ushant Island, western France*. Zeitschrift für Geomorphologie, 54(3), 197–217.

Richmond B.M., Watt S., Buckley M., Jaffe B.E., Gelfenbaum G., Morton R.A. (2011). *Recent storm and tsunami coarse-clast deposit characteristics, southeast Hawaii*. Marine Geology, 283, 1–4.

510

Scicchitano G., Monaco C., Tortorici L. (2007). *Large boulder deposits by tsunami waves along the Ionian coast of south-eastern Sicily (Italy)*. Marine Geology, 238, 75-91.

Shah-Hosseini M., Morhange C., De Marco A., Wante J., Anthony E.J., Sabatier F., Mastronuzzi G., Pignatelli C., Piscitelli A. (2013). *Coastal boulders in Martigues, French Mediterranean: evidence for extreme storm waves during the Little Ice Age*. Zeitschrift für Geomorphologie, 57, 181–199.

515

Sunamura T. (1992). *Geomorphology of rocky coasts*. John Wiley and Sons, 302 pp.

Sunamura T., K. Horikawa (1974). *Two dimensional beach transformation due to waves*, Proceedings 14th Coastal Engineering Conference, American Society of Civilian Engineers. 920–938.

520

Vella C., Demory F., Canut V., Dussouillez P., Fleury T.J. (2011). *First evidence of accumulation of mega boulders on the Mediterranean rocky coast of Provence (southern France)*. *Natural Hazards Earth Systems Science*, 11, 905-914.

525

Vella C., Provansal M. (2000). *Relative sea-level rise and neotectonic events during the last 6500 years on the southern eastern Rhône delta, France*. Marine Geology, 170, 27–39.

Vella C., Bourcier M., Provansal M. (1998). *Montée du niveau marin et sédimentation holocène sur la marge orientale du delta du Rhône, Provence, France*. Bulletin de la Société Geologique de France, 169, 403–414.

530

Vött A., Lang F., Brückner H., Gaki-Papanastassiou K., Maroukian H., Papanastassiou D., Giannikos A., Hadler H., Handl M., Ntageretzis K., Willershäuser T., Zander A. (2010). *Sedimentological and geoarchaeological evidence of multiple tsunamigenic imprint on the Bay of Palaios- Pogonia (Akarnania, NW Greece)*. Quaternary International, 242 (1), 213–239.

535
## Captions

540

**Figure 1** – Geographical position of the studied area (from Google Earth).

**Figure 2** – Examples of fracture lines in the study area; for A, B and C see the text.

545

**Figure 3** – Joint patterns along the coast between the Plage de Bonnieu and Carro. Joints have been surveyed and mapped in four areas (Fig. a). b) Rose diagram of the strike of the 111 measured joints. c) dip of the 111 measured joints. d, e, f) aerial photos with mapped joint patterns and boulders of areas 1 to 4. Schmidt nets (lower hemisphere) show the joint planes measured in each area.

550

**Figure 4** – Morphological features of the studied area. A: gently sloping rocky coast characterized by boulders accumulation and soil cover; B: boulders field in the surveyed area; C: cliff about 4 m height; D: notch at the foot of the cliff.

555

**Figure 5** – Position of the buoy in the Gulf of Lion (from Google Earth).

**Figure 6** – Scanned area (above) and point cloud surveyed by TLS Leica Scanstation2 (below).

560

**Figure 7** – Schematic sketch of the surveyed area. w.c.p. = wave cut platform; s.b. = surf bench. The boulder C is located in the probable detachment area.

**Figure 8** – Schematic reconstruction of the reverse procedure adopted to reconstruct the boulder "C" (above): the part "A" has undergone a rollover while the part "B" underwent a rotation. The red dotted lines represent the break's surfaces. Boulders "A", "B" and "C" with their "a" and "b" axes (below) ; the white dotted line represents the break's surface of the boulder "C"..

565

**Figure 9** – Morphological and biological evidence on the blocks "A" and "B". A: the surface indicated by the arrow represents the original face turned upwards; B: the break's surface of block B; C: biological evidence of *Lithophyllum bissoides* rim (white circle) on the block "A" and the break's surface indicated by the arrow; D: biological evidence of *Lithophyllum bissoides*, vermetids and barnacles on the upper surface of block "B".

570

**Figure 10** – Probable original position and detachment zone of boulder "C" on the WCP and positions of the blocks "A" and "B" (from Google Earth, December 2003).

575

**Figure 11** – Reconstruction of the succession of events. Phase 1: boulder "C" is in a Joint Bounded Scenario (JBS); Phase 2: boulder "C" is detached and placed on the WCP; Phase 3: the block "A" moves toward inland while turning in a clockwise direction and overturns; Phase 4: the block "B" moves inward while turning of approximately 90 ° counterclockwise.
<table><caption>**Table 1** – Number of events > 3 m high, per year, recorded by the buoy in the period 1993-2008.</caption><thead><tr><th colspan="5">Number of Waves with HeightH> 3 m</th></tr><tr><th>YEAR</th><th>I Sector</th><th>II Sector</th><th>III Sector</th><th>IV Sector</th><th>Total</th></tr></thead><tbody><tr><td>1993</td><td>21</td><td>9</td><td>0</td><td>31</td><td>61</td></tr><tr><td>1994</td><td>1</td><td>20</td><td>12</td><td>23</td><td>56</td></tr><tr><td>1995</td><td>1</td><td>43</td><td>5</td><td>43</td><td>92</td></tr><tr><td>1996</td><td>16</td><td>93</td><td>12</td><td>15</td><td>136</td></tr><tr><td>1997</td><td>6</td><td>39</td><td>10</td><td>7</td><td>62</td></tr><tr><td>1998</td><td>8</td><td>6</td><td>1</td><td>20</td><td>35</td></tr><tr><td>1999</td><td>0</td><td>19</td><td>17</td><td>33</td><td>69</td></tr><tr><td>2000</td><td>14</td><td>27</td><td>13</td><td>14</td><td>68</td></tr><tr><td>2001</td><td>22</td><td>15</td><td>15</td><td>9</td><td>61</td></tr><tr><td>2002</td><td>12</td><td>49</td><td>10</td><td>7</td><td>78</td></tr><tr><td>2003</td><td>7</td><td>78</td><td>8</td><td>29</td><td>122</td></tr><tr><td>2004</td><td>3</td><td>50</td><td>6</td><td>29</td><td>88</td></tr><tr><td>2005</td><td>27</td><td>33</td><td>7</td><td>81</td><td>148</td></tr><tr><td>2006</td><td>10</td><td>30</td><td>18</td><td>21</td><td>79</td></tr><tr><td>2007</td><td>48</td><td>41</td><td>0</td><td>108</td><td>197</td></tr><tr><td>2008</td><td>14</td><td>58</td><td>21</td><td>89</td><td>182</td></tr></tbody><tfoot><tr><th>TOTAL</th><td>210</td><td>610</td><td>155</td><td>559</td><td>1534</td></tr></tfoot></table>

585

<table><caption>**Table 2** – Highest waves recorded by the buoy, for each year, in the period 1993-2008. H: height of wave in m; °N: wave direction.</caption><thead><tr><th colspan="5">Highest Wave (m) per Directions</th></tr><tr><th>YEAR</th><th>I Sector<br>H - °N</th><th>II Sector<br>H - °N</th><th>III Sector<br>H - °N</th><th>IV Sector<br>H - °N</th></tr></thead><tbody><tr><td>1993</td><td>4,16 – 88°</td><td>3,57 – 91°</td><td>//</td><td>4,19 – 318°</td></tr><tr><td>1994</td><td>3,22 – 88°</td><td>4,29 – 98°</td><td>4,87 – 188°</td><td>3,94 – 320°</td></tr><tr><td>1995</td><td>4,32 – 90°</td><td>4,34 – 91°</td><td>3,77 – 187°</td><td>4,02 – 303°</td></tr><tr><td>1996</td><td>3,99 – 86°</td><td>4,57 – 146°</td><td>5,16 – 190°</td><td>4,26 – 307°</td></tr><tr><td>1997</td><td>3,98 – 89°</td><td>6,08 – 96°</td><td>5,07 – 187°</td><td>3,30 – 325°</td></tr><tr><td>1998</td><td>3,95 – 90°</td><td>3,72 – 126°</td><td>3,13 – 189°</td><td>3,78 – 314°</td></tr><tr><td>1999</td><td>//</td><td>5,24 – 97°</td><td>4,03 – 199°</td><td>4,07 – 294°</td></tr><tr><td>2000</td><td>3,83 – 90°</td><td>4,97 – 108°</td><td>4,07 – 198°</td><td>3,62 – 343°</td></tr><tr><td>2001</td><td>4,62 – 88°</td><td>4,60 – 91°</td><td>4,66 – 203°</td><td>3,50 – 323°</td></tr><tr><td>2002</td><td>4,33 – 87°</td><td>4,89 – 96°</td><td>3,55 – 195°</td><td>3,80 – 317°</td></tr><tr><td>2003</td><td>3,86 – 90°</td><td>6,47 – 107°</td><td>5,25 – 202°</td><td>3,77 – 352°</td></tr><tr><td>2004</td><td>3,79 – 1°</td><td>5,41 – 95°</td><td>3,26 – 191°</td><td>4,17 – 357°</td></tr><tr><td>2005</td><td>3,85 – 4°</td><td>3,54 – 105°</td><td>5,15 – 200°</td><td>4,20 – 314°</td></tr><tr><td>2006</td><td>3,74 – 14°</td><td>5,66 – 115°</td><td>4,30 – 197°</td><td>4,13 – 330°</td></tr><tr><td>2007</td><td>4,31 – 3°</td><td>4,95 – 97°</td><td>//</td><td>4,34 – 296°</td></tr><tr><td>2008</td><td>5,17 – 90°</td><td>6,85 – 97°</td><td>4,51 – 195°</td><td>4,19 – 300°</td></tr></tbody></table>

590

<table><caption>**Table 3** – Dimensional parameters of the boulders.*The boulders volume was calculated by means of the laser scanner software.</caption><thead><tr><th></th><th>a axis (m)</th><th>b axis (m)</th><th>c axis (m)</th><th>Volume* (m³)</th><th>γd (g/cm³)</th><th>Weight (t)</th></tr></thead><tbody><tr><th>Boulder A</th><td>3,60</td><td>2,60</td><td>0,38</td><td>6,90</td><td>2,3</td><td>15,87</td></tr><tr><th>Boulder B</th><td>2,60</td><td>2,10</td><td>1,10</td><td>3,85</td><td>2,3</td><td>8,86</td></tr><tr><th>Boulder C</th><td>6,20</td><td>2,60</td><td>0,38</td><td>10,75</td><td>2,3</td><td>24,73</td></tr></tbody></table>
<table><caption>**Table 4** –Storm wave Hs obtained by different hydrodynamic equations for boulders A, B and C.</caption><thead><tr><th></th><th>Engel and May<br>(2012)</th><th>Nandasenaet alii<br>(2011)</th><th>Benner et alii<br>(2010)</th><th>Pignatellietalii<br>(2009)</th></tr><tr><th></th><th>Hs (m)</th><th>H (m)</th><th>Hs (m)</th><th>Hs (m)</th></tr></thead><tbody><tr><th>Boulder A (SBS)</th><td>6,35</td><td>4,58</td><td>6,25</td><td>3,97</td></tr><tr><th>Boulder B (SBS)</th><td>4,89</td><td>3,10</td><td>5,53</td><td>3,66</td></tr><tr><th>Boulder C (JBS)</th><td>5,72</td><td>5,61</td><td>6,25</td><td>5,36</td></tr></tbody></table>

<table><caption>**Table 5** –Number of events with height > 3 m and the highest waves selected per 10° range direction recorded in the period 1993-2008.</caption><thead><tr><th rowspan="2">Wave Range Direction</th><th colspan="2">Observed Period 1993 - 2008</th></tr><tr><th>N. events with H > 3 m</th><th>Highest Wave in m</th></tr></thead><tbody><tr><td>150-160 °N</td><td>14</td><td>4,38</td></tr><tr><td>160-170 °N</td><td>11</td><td>4,35</td></tr><tr><td>170-180 °N</td><td>18</td><td>5,48</td></tr><tr><td>180-190 °N</td><td>45</td><td>5,16</td></tr><tr><td>190-200 °N</td><td>90</td><td>5,15</td></tr><tr><td>200-210 °N</td><td>19</td><td>5,25</td></tr><tr><td>210-220 °N</td><td>0</td><td>//</td></tr><tr><td>220-230 °N</td><td>0</td><td>//</td></tr><tr><td>230-240 °N</td><td>0</td><td>//</td></tr><tr><td>240-250 °N</td><td>0</td><td>//</td></tr><tr><td>250-260 °N</td><td>0</td><td>//</td></tr><tr><td>260-270 °N</td><td>1</td><td>3,23</td></tr><tr><td>270-280 °N</td><td>17</td><td>4,15</td></tr><tr><td>280-290 °N</td><td>38</td><td>4,17</td></tr><tr><td>290-300 °N</td><td>83</td><td>4,34</td></tr></tbody><tfoot><tr><th>TOTAL</th><td>336</td><td></td></tr></tfoot></table>

<table><thead><tr><th>Date</th><th>Wave Height H (m)</th><th>Wave Direction (°N)</th><th>Period (s)</th><th>Length Wave L<sub>0</sub>(m)</th><th>Breaking Water Depth W<sub>d</sub> (m)</th><th>Breaking Wave Height H<sub>b</sub>(m)</th></tr></thead><tbody><tr><td>06/01/1994</td><td>3,85</td><td>193</td><td>8,36</td><td>109,06</td><td>4,61</td><td>3,44</td></tr><tr><td>06/01/1994</td><td>4,24</td><td>193</td><td>8,49</td><td>112,48</td><td>5,00</td><td>3,73</td></tr><tr><td>06/01/1994</td><td>4,62</td><td>192</td><td>8,95</td><td>125,00</td><td>5,47</td><td>4,08</td></tr><tr><td>06/01/1994</td><td>4,73</td><td>193</td><td>8,68</td><td>117,57</td><td>5,49</td><td>4,09</td></tr><tr><td>06/01/1994</td><td>4,70</td><td>190</td><td>8,97</td><td>125,56</td><td>5,55</td><td>4,14</td></tr><tr><td>06/01/1994</td><td>4,87</td><td>188</td><td>8,96</td><td>125,28</td><td>5,70</td><td>4,25</td></tr><tr><td>07/01/1994</td><td>3,71</td><td>197</td><td>9,11</td><td>129,51</td><td>4,68</td><td>3,49</td></tr><tr><td>07/01/1994</td><td>4,47</td><td>197</td><td>9,12</td><td>129,79</td><td>5,39</td><td>4,02</td></tr><tr><td>07/01/1994</td><td>4,66</td><td>193</td><td>9,05</td><td>127,81</td><td>5,54</td><td>4,13</td></tr><tr><td>23/01/1996</td><td>4,04</td><td>159</td><td>7,97</td><td>99,12</td><td>4,67</td><td>3,48</td></tr><tr><td>23/01/1996</td><td>4,38</td><td>152</td><td>8,23</td><td>105,70</td><td>5,04</td><td>3,76</td></tr><tr><td>11/11/1996</td><td>4,17</td><td>182</td><td>7,77</td><td>94,21</td><td>4,72</td><td>3,52</td></tr><tr><td>11/11/1996</td><td>4,46</td><td>185</td><td>8,25</td><td>106,21</td><td>5,12</td><td>3,82</td></tr><tr><td>11/11/1996</td><td>4,77</td><td>187</td><td>8,43</td><td>110,90</td><td>5,44</td><td>4,06</td></tr><tr><td>12/11/1996</td><td>3,66</td><td>185</td><td>8,29</td><td>107,24</td><td>4,42</td><td>3,30</td></tr><tr><td>12/11/1996</td><td>3,98</td><td>186</td><td>8,41</td><td>110,37</td><td>4,74</td><td>3,54</td></tr><tr><td>12/11/1996</td><td>4,33</td><td>186</td><td>8,58</td><td>114,88</td><td>5,10</td><td>3,81</td></tr><tr><td>12/11/1996</td><td>4,66</td><td>190</td><td>8,86</td><td>122,50</td><td>5,48</td><td>4,09</td></tr><tr><td>12/11/1996</td><td>4,95</td><td>190</td><td>8,99</td><td>126,12</td><td>5,78</td><td>4,31</td></tr><tr><td>12/11/1996</td><td>5,11</td><td>188</td><td>8,63</td><td>116,22</td><td>5,80</td><td>4,32</td></tr><tr><td>12/11/1996</td><td>5,16</td><td>190</td><td>8,98</td><td>125,84</td><td>5,96</td><td>4,44</td></tr><tr><td>03/01/1997</td><td>4,25</td><td>178</td><td>7,86</td><td>96,41</td><td>4,82</td><td>3,59</td></tr><tr><td>03/01/1997</td><td>4,35</td><td>190</td><td>8,38</td><td>109,59</td><td>5,06</td><td>3,78</td></tr></tbody></table>
<table><tr><td>04/01/1997</td><td>3,76</td><td>196</td><td>8,91</td><td>123,89</td><td>4,68</td><td>3,49</td></tr><tr><td>04/01/1997</td><td>4,19</td><td>195</td><td>8,55</td><td>114,08</td><td>4,97</td><td>3,71</td></tr><tr><td>06/11/1997</td><td>4,55</td><td>176</td><td>7,98</td><td>99,37</td><td>5,11</td><td>3,81</td></tr><tr><td>06/11/1997</td><td>5,19</td><td>174</td><td>8,51</td><td>113,01</td><td>5,82</td><td>4,34</td></tr><tr><td>06/11/1997</td><td>5,48</td><td>173</td><td>9,17</td><td>131,22</td><td>6,30</td><td>4,70</td></tr><tr><td>06/11/1997</td><td>5,43</td><td>180</td><td>9,34</td><td>136,13</td><td>6,31</td><td>4,71</td></tr><tr><td>07/11/1997</td><td>3,47</td><td>191</td><td>9,4</td><td>137,89</td><td>4,53</td><td>3,37</td></tr><tr><td>07/11/1997</td><td>4,32</td><td>189</td><td>9,64</td><td>145,02</td><td>5,40</td><td>4,03</td></tr><tr><td>07/11/1997</td><td>5,07</td><td>187</td><td>9,54</td><td>142,04</td><td>6,06</td><td>4,52</td></tr><tr><td>18/12/1997</td><td>3,91</td><td>165</td><td>7,53</td><td>88,48</td><td>4,43</td><td>3,30</td></tr><tr><td>18/12/1997</td><td>4,07</td><td>159</td><td>7,57</td><td>89,42</td><td>4,58</td><td>3,41</td></tr><tr><td>18/12/1997</td><td>4,16</td><td>156</td><td>7,59</td><td>89,90</td><td>4,66</td><td>3,47</td></tr><tr><td>18/12/1997</td><td>4,24</td><td>155</td><td>7,63</td><td>90,85</td><td>4,74</td><td>3,53</td></tr><tr><td>18/12/1997</td><td>4,41</td><td>156</td><td>7,75</td><td>93,73</td><td>4,92</td><td>3,67</td></tr><tr><td>18/12/1997</td><td>4,35</td><td>161</td><td>7,96</td><td>98,88</td><td>4,93</td><td>3,68</td></tr><tr><td>24/10/1999</td><td>3,84</td><td>200</td><td>8,23</td><td>105,70</td><td>4,57</td><td>3,41</td></tr><tr><td>24/10/1999</td><td>4,03</td><td>199</td><td>8,33</td><td>108,28</td><td>4,77</td><td>3,55</td></tr><tr><td>24/10/1999</td><td>4,01</td><td>198</td><td>8,38</td><td>109,59</td><td>4,76</td><td>3,55</td></tr><tr><td>25/10/1999</td><td>3,69</td><td>198</td><td>8,35</td><td>108,80</td><td>4,47</td><td>3,33</td></tr><tr><td>28/12/1999</td><td>4,07</td><td>294</td><td>7,07</td><td>78,00</td><td>4,42</td><td>3,30</td></tr><tr><td>06/11/2000</td><td>3,91</td><td>198</td><td>7,63</td><td>90,85</td><td>4,46</td><td>3,33</td></tr><tr><td>06/11/2000</td><td>3,74</td><td>199</td><td>8,45</td><td>111,42</td><td>4,54</td><td>3,38</td></tr><tr><td>06/11/2000</td><td>4,07</td><td>198</td><td>8,13</td><td>103,14</td><td>4,74</td><td>3,54</td></tr><tr><td>02/03/2001</td><td>4,37</td><td>203</td><td>8,52</td><td>113,28</td><td>5,12</td><td>3,82</td></tr><tr><td>03/03/2001</td><td>3,52</td><td>201</td><td>9,33</td><td>135,84</td><td>4,56</td><td>3,40</td></tr><tr><td>03/03/2001</td><td>4,11</td><td>201</td><td>9,30</td><td>134,97</td><td>5,11</td><td>3,81</td></tr><tr><td>03/03/2001</td><td>4,66</td><td>203</td><td>9,19</td><td>131,79</td><td>5,58</td><td>4,16</td></tr><tr><td>31/10/2003</td><td>4,35</td><td>199</td><td>8,35</td><td>108,80</td><td>5,05</td><td>3,77</td></tr><tr><td>31/10/2003</td><td>4,58</td><td>201</td><td>9,42</td><td>138,47</td><td>5,58</td><td>4,16</td></tr><tr><td>31/10/2003</td><td>5,00</td><td>202</td><td>8,73</td><td>118,93</td><td>5,74</td><td>4,28</td></tr><tr><td>31/10/2003</td><td>5,05</td><td>201</td><td>9,32</td><td>135,55</td><td>5,97</td><td>4,45</td></tr><tr><td>31/10/2003</td><td>5,25</td><td>202</td><td>9,22</td><td>132,66</td><td>6,12</td><td>4,56</td></tr><tr><td>01/11/2003</td><td>3,94</td><td>198</td><td>9,54</td><td>142,02</td><td>5,02</td><td>3,74</td></tr><tr><td>18/01/2005</td><td>3,90</td><td>298</td><td>7,70</td><td>92,52</td><td>4,47</td><td>3,33</td></tr><tr><td>19/01/2005</td><td>4,05</td><td>299</td><td>8,20</td><td>104,93</td><td>4,75</td><td>3,54</td></tr><tr><td>02/12/2005</td><td>3,77</td><td>194</td><td>10,30</td><td>165,55</td><td>5,05</td><td>3,76</td></tr><tr><td>02/12/2005</td><td>4,52</td><td>197</td><td>9,00</td><td>126,40</td><td>5,40</td><td>4,03</td></tr><tr><td>02/12/2005</td><td>4,53</td><td>195</td><td>10,10</td><td>159,19</td><td>5,73</td><td>4,27</td></tr><tr><td>02/12/2005</td><td>5,15</td><td>200</td><td>9,60</td><td>143,82</td><td>6,15</td><td>4,59</td></tr><tr><td>02/12/2005</td><td>5,03</td><td>196</td><td>10,10</td><td>159,19</td><td>6,20</td><td>4,62</td></tr><tr><td>19/02/2006</td><td>3,67</td><td>198</td><td>9,20</td><td>132,08</td><td>4,67</td><td>3,48</td></tr><tr><td>19/02/2006</td><td>3,95</td><td>196</td><td>8,50</td><td>112,75</td><td>4,74</td><td>3,54</td></tr><tr><td>19/02/2006</td><td>4,09</td><td>198</td><td>9,10</td><td>129,23</td><td>5,04</td><td>3,76</td></tr><tr><td>19/02/2006</td><td>4,30</td><td>197</td><td>9,00</td><td>126,40</td><td>5,20</td><td>3,88</td></tr><tr><td>04/03/2006</td><td>3,56</td><td>206</td><td>8,90</td><td>123,61</td><td>4,49</td><td>3,35</td></tr><tr><td>04/03/2006</td><td>3,60</td><td>200</td><td>9,30</td><td>134,97</td><td>4,63</td><td>3,45</td></tr><tr><td>23/01/2007</td><td>4,08</td><td>281</td><td>8,30</td><td>107,50</td><td>4,80</td><td>3,58</td></tr><tr><td>23/01/2007</td><td>4,17</td><td>285</td><td>8,40</td><td>110,11</td><td>4,91</td><td>3,66</td></tr><tr><td>24/01/2007</td><td>3,84</td><td>291</td><td>8,20</td><td>104,93</td><td>4,56</td><td>3,40</td></tr><tr><td>24/01/2007</td><td>3,86</td><td>291</td><td>8,30</td><td>107,50</td><td>4,61</td><td>3,43</td></tr><tr><td>24/01/2007</td><td>3,91</td><td>290</td><td>8,20</td><td>104,93</td><td>4,62</td><td>3,45</td></tr><tr><td>24/01/2007</td><td>4,13</td><td>288</td><td>8,30</td><td>107,50</td><td>4,85</td><td>3,61</td></tr><tr><td>24/01/2007</td><td>4,09</td><td>290</td><td>8,40</td><td>110,11</td><td>4,84</td><td>3,61</td></tr><tr><td>28/05/2007</td><td>4,00</td><td>287</td><td>8,20</td><td>104,93</td><td>4,70</td><td>3,50</td></tr><tr><td>28/05/2007</td><td>4,16</td><td>300</td><td>8,30</td><td>107,50</td><td>4,87</td><td>3,63</td></tr><tr><td>28/05/2007</td><td>4,34</td><td>296</td><td>8,30</td><td>107,50</td><td>5,03</td><td>3,75</td></tr><tr><td>29/05/2007</td><td>3,93</td><td>297</td><td>8,10</td><td>112,39</td><td>4,61</td><td>3,44</td></tr><tr><td>09/12/2007</td><td>3,99</td><td>279</td><td>8,20</td><td>104,93</td><td>4,69</td><td>3,50</td></tr><tr><td>10/12/2007</td><td>3,75</td><td>283</td><td>8,20</td><td>104,93</td><td>4,48</td><td>3,34</td></tr><tr><td>10/12/2007</td><td>3,93</td><td>282</td><td>8,30</td><td>107,50</td><td>4,67</td><td>3,48</td></tr></table>
<table><caption>**Table 6** – Hydrodynamic parameters of the events with a H<sub>b</sub>prox to the minimum value (H<sub>b</sub>>3,66m) useful to move boulders A and B. H<sub>0</sub> = Wave Height offshore; L<sub>0</sub> = Wave Length offshore; W<sub>d</sub> = Water Depth at breaking point; H<sub>b</sub> = Wave Height at breaking point.</caption><tr><td>10/12/2007</td><td>4,01</td><td>279</td><td>8,30</td><td>107,50</td><td>4,74</td><td>3,53</td></tr><tr><td>10/12/2007</td><td>4,15</td><td>280</td><td>8,40</td><td>110,11</td><td>4,89</td><td>3,65</td></tr><tr><td>10/12/2007</td><td>4,17</td><td>281</td><td>8,40</td><td>110,11</td><td>4,91</td><td>3,66</td></tr><tr><td>11/01/2008</td><td>3,87</td><td>202</td><td>8,30</td><td>107,50</td><td>4,61</td><td>3,44</td></tr><tr><td>21/03/2008</td><td>3,97</td><td>277</td><td>7,80</td><td>94,94</td><td>4,56</td><td>3,40</td></tr><tr><td>20/04/2008</td><td>3,83</td><td>168</td><td>8,30</td><td>107,50</td><td>4,63</td><td>3,45</td></tr><tr><td>21/11/2008</td><td>4,04</td><td>300</td><td>8,20</td><td>104,93</td><td>4,74</td><td>3,53</td></tr><tr><td>21/11/2008</td><td>4,19</td><td>300</td><td>8,40</td><td>110,11</td><td>4,93</td><td>3,67</td></tr><tr><td>29/11/2008</td><td>4,13</td><td>196</td><td>9,50</td><td>140,84</td><td>5,18</td><td>3,87</td></tr><tr><td>29/11/2008</td><td>4,51</td><td>195</td><td>9,00</td><td>126,40</td><td>5,39</td><td>4,02</td></tr></table>
<figure><img src="image_2.png" /></figure>

Image © 2015 Aerostat International Surveys
Image © 2015 DigitalGlobe
Data: SIO, NOAA, U.S. Navy, NSA, GEBCO
Image © 2015 TerraMetrics
<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /></figure>
<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /></figure>
<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /></figure>
<figure><img src="image_15.png" /></figure>

Martigues

Plage de
Bonnieu

Marseille

Google earth
<figure><img src="image_16.png" /></figure>

<figure><img src="image_17.png" /></figure>
<figure><img src="image_18.png" /></figure>

↑N
<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>
<figure><img src="image_21.png" /></figure>

A

<figure><img src="image_22.png" /></figure>

B

<figure><img src="image_23.png" /></figure>

C

<figure><img src="image_24.png" /></figure>

D
Boulder B

<figure><img src="image_25.png" /></figure>

Original
position
of
Boulder C

<figure><img src="image_26.png" /></figure>

Boulder A

<figure><img src="image_27.png" /></figure>
<figure><img src="image_28.png" /></figure>

<figure><img src="image_29.png" /></figure>

<figure><img src="image_30.png" /></figure>

<figure><img src="image_31.png" /></figure>