Ferréol Salomon
email: ferreol.salomon@live-cnrs.unistra.fr

Kristian Strutt
email: k.d.strutt@soton.ac.uk

Dragana Mladenović
email: mladenovicd@yahoo.com

Jean-Philippe Goiran
email: jean-philippe.goiran@mom.fr

Simon Keay

Management of fluvio-coastal dynamics in the Tiber delta during the Roman period: using an integrated waterways system to cope with environmental challenges at Ostia and Portus

Keywords: geoarchaeology, watercourse management, Roman canals, Roman harbours, Ostia and Portus, Tiber delta

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Located at the mouth of the River Tiber (Figure 1), Ostia and Portus were essential for the economic and transport connectivity of Rome, linking the city with the Mediterranean Sea.

Ostia was initially a fortified colonial settlement built on the left bank of the river mouth of the River Tiber, and eventually became a significant port-city over time [START_REF] Calza | Scavi di Ostia, Topografia generale. Libreria dello Stato, Roma Cherkauer D[END_REF][START_REF] Zevi | Origini di Ostia[END_REF][START_REF] Heinzelmann | Ostia I. Forma Urbis Ostiae: Untersuchungen Zur Entwicklung Der Hafenstadt Roms Von Der Zeit Der Republik Bis Ins Frühe Mittelalter[END_REF]. By contrast, Portus was built ex novo with the aim of creating an Imperial harbour installation [START_REF] Lugli | Il porto di Roma imperiale e l'agro portuense[END_REF][START_REF] Keay | Portus : An Archaeological Survey Of The Portus Of Imperial Rome[END_REF][START_REF] Keay | The Port System of Imperial Rome[END_REF]). Both provided harbour facilities for ships to load and unload different kinds of goods. Both, however, faced significant environmental risks and constraints. River mouths are geomorphologically unstable environments. Riverbanks and coastlines can be modified by single events (floods/storms) and on a seasonal basis. This is particularly true during high frequency changes and exceptional events [START_REF] Noli | La Sapienza" di Roma, Regione Lazio Assessorato opere e reti di servizi e mobilità[END_REF][START_REF] Bencivenga | Piene storiche del Tevere a Roma[END_REF]. Generally, coastal risks during the Roman period are expressed in terms of coastline mobility (Vella et al. 2000;[START_REF] Brückner | Rapid Delta Growth in Historical Times at Ephesus and Miletus-The Examples of the Küçük and the Büyük Menderes Rivers[END_REF]), storms [START_REF] Sabatier | Clay minerals and geochemistry record from northwest Mediterranean coastal lagoon sequence: Implications for paleostorm reconstruction[END_REF][START_REF] Sabatier | 7000 years of paleostorm activity in the NW Mediterranean Sea in response to Holocene climate events[END_REF] or tsunamis [START_REF] Luque | Sedimentary record of a tsunami during Roman times, Bay of Cadiz, Spain[END_REF][START_REF] Dey | Tsunamis and the port of Caesarea Maritima over the longue durée: a geoarchaeological perspective[END_REF]. Studies considering fluvial risks during the Roman period focus mainly on flood intensity and frequency, their extent (Le [START_REF] Gall | Le Tibre, fleuve de Rome dans l'antiquité. Presses Universitaires de France, Paris Le Gall J[END_REF][START_REF] Berger | Origin of fluvial fluctuations of the River Vidourle and their effect on the organisation ans evolution of the site of Ambrussum (Hérault, Fr.) between the Iron Age and lat Antiquity. E Fouache (éd)[END_REF][START_REF] Ollive | Rhine flood deposits recorded in the Gallo-Roman site of Oedenburg (Haut-Rhin, France)[END_REF][START_REF] Arnaud-Fassetta | Fluvial geomorphology and flood-risk management[END_REF][START_REF] Arnaud-Fassetta | Fluvial geomorphology and flood-risk management[END_REF], and adjustment to water levels [START_REF] Bravard | Le site de Vienne (38), Saint-Romain-en-Gal (69) et Sainte-Colombe (69): l'évolution de la plaine alluviale du Rhône de l'âge du Fer à la fin de l'Antiquité, proposition d'interprétation[END_REF][START_REF] Allinne | Les villes romaines face aux inondations. La place des données archéologiques dans l'étude des risques fluviaux[END_REF][START_REF] Allinne | La place des sources archéologiques dans la construction de modéles de gestion des risques naturels dans l'Empire Romain: l'exemple du risque d'inondation[END_REF][START_REF] Leveau | Environmental risk in the Lower Rhône valley: high water levels and floods[END_REF]. Many studies focus on the 1 st c. BCE -2 nd c. CE, when a hydro-sedimentary crisis can be observed (Cherkauer 1976;[START_REF] Bravard | Le climat d'après les informations fournies par les enregistrements sédimentaires fluviatiles étudiés sur des sites archéologiques[END_REF][START_REF] Brown | People, climate and alluviation: theory, research design and new sedimentological and stratigraphic data from Etruria[END_REF][START_REF] Arnaud-Fassetta | Hydroclimatic hazards, vulnerability of societies and fluvial risk in the Rhone Delta (Mediterranean France) from the Greek period to the Early Middle Ages[END_REF][START_REF] Ollive | Rhine flood deposits recorded in the Gallo-Roman site of Oedenburg (Haut-Rhin, France)[END_REF][START_REF] Berger | Le développement économique romain face à la crise environnementale : le cas de la Gaule narbonnaise[END_REF]. The construction of Portus has also been studied in relation to this specific palaeoclimatic context [START_REF] Salomon | Géoarchéologie du delta du Tibre : Evolution géomorphologique holocène et contraintes hydrosédimentaires dans le système Ostie -Portus[END_REF], also called the Roman Climate Optimum [START_REF] Harper | Reconstructing the Roman climate[END_REF][START_REF] Strutt | Contexte géomorphologique de trois ports antiques provençaux : Fos, Les Laurons[END_REF]. By contrast, fewer studies have considered the consequence of fluvial lateral mobility on Roman cities [START_REF] Bravard | Dynamique du paysage : entretiens de géoarchéologie[END_REF][START_REF] Franc | Chapitre X. Trente ans d'études géomorphologiques au service de l'archéologie préventive lyonnaise (France) : Méthodes et résultats d'une démarche géo-archéologique[END_REF][START_REF] Salomon | Geoarchaeology of the Roman port-city of Ostia: Fluviocoastal mobility, urban development and resilience[END_REF].

Ostia and Portus offer an interesting case study for observing structural adjustments to fluvio-coastal dynamics. In this paper, we propose a hypothesis that the port-city of Ostia and the port complex at Portus formed an integrated water management system in the delta of the Tiber, developed over time to combat specific environmental challenges. The first source of evidence that we draw on are the physical remains of structures and archaeological features at Ostia and Portus concentrating on their planning and orientation. We contextualize this evidence with data from geoarchaeological cores collected from the study area, discussing the sedimentological (sediment deposition-erosion) and geomorphological (lateral mobility 1 aspects of the Tiber channels, canals, and sedimentation/erosion of the river mouth bars) issues related to the Tiber in Ostia and the canals of Portus. Hydrological 1 Lateral mobility of a channel or a canal is a specialist term relating to a displacement of the riverbanks in a planimetric view.

constraints (e.g. floods) will not be directly discussed in this paper, but they remain of primary importance during the Roman period [START_REF] Gall | Le Tibre, fleuve de Rome dans l'antiquité. Presses Universitaires de France, Paris Le Gall J[END_REF][START_REF] Salomon | Géoarchéologie du delta du Tibre : Evolution géomorphologique holocène et contraintes hydrosédimentaires dans le système Ostie -Portus[END_REF].

MATERIAL AND METHODS

Two sets of data are considered in this paper. First, the urban fabric of Ostia and Portus will be analysed and compared, seeking tangible evidence of incorporation of harbour infrastructure and river water management into the planning of the sites. A synthesis of the geoarchaeological cores drilled in the palaeochannels and harbour of Ostia is then presented and compared to the cores drilled in the canals of Portus, allowing us to assess this evidence and elaborate on the interactions between the Tiber, the canals, the harbours and the layout of Ostia and Portus.

Urban fabric

The urban morphology of Ostia reveals an existence of districts within the city (Fluvial, Coastal, River mouth) and possible adjustments of the urban fabric to the mobility of the riverbanks has already been observed [START_REF] Salomon | Geoarchaeology of the Roman port-city of Ostia: Fluviocoastal mobility, urban development and resilience[END_REF]. In this paper, we apply the same type of GIS analysis of the orientation of the archaeological features to Portus, while using the existing case study of Ostia as a comparandum aimed at comparing and contrasting the observed patterns (Figure 2 and 3).

The shapefile of Ostia has been drawn based on excavated archaeological structures (roads, walls, etc.). By contrast, Portus has not been extensively and continuously excavated.

The dataset from Portus is based on the map from [START_REF] Keay | Portus : An Archaeological Survey Of The Portus Of Imperial Rome[END_REF]. It represents a mix of visible excavated archaeological structures [START_REF] Lanciani | Ricerche topografiche sulla città di Porto. Tipografia Tiberina[END_REF][START_REF] Lugli | Il porto di Roma imperiale e l'agro portuense[END_REF]Testaguzza 1970;[START_REF] Paroli | Il porto di Roma nella tarda antichità[END_REF][START_REF] Keay | Portus : An Archaeological Survey Of The Portus Of Imperial Rome[END_REF] and archaeological features identified from geophysical survey [START_REF] Keay | Portus : An Archaeological Survey Of The Portus Of Imperial Rome[END_REF]. Archaeological features are interpretations of magnetic anomalies and may or may not be actual archaeological structures from the Roman period. However, the quality of the magnetic signal from archaeological structures in and around Portus is of particularly good quality [START_REF] Keay | Portus : An Archaeological Survey Of The Portus Of Imperial Rome[END_REF](Keay et al. , 2020)). The interpretations from 2005 were also largely confirmed by later excavations conducted by the University of Southampton in the area of the Palazzo Imperiale between the Claudian and Trajanic basins (particularly the extent and the orientation of the main buildings) (Keay et al. 2011, in press).

The GIS database includes the shapefiles for Ostia and Portus in the coordinate system WGS 84 / UTM 33N (EPSG: 32633). Transverse Mercator projection is conformal since it preserves angles. The preservation of the angles is essential for the analysis. Orientations of archaeological structures and features were calculated in the QGIS software within the range 0° to 179°. In order to compare Ostia and Portus, classes of orientations were defined every 10° and assigned different colour values. The maps containing orientation analysis of the two sites are presented in Figure 2. Figure 3 presents the orientation of the structures and features to a degree. We can observe that the dataset of Ostia (96915 lines distributed according to the Y-axis on the right) is more detailed than the one available for Portus (3594 lines distributed according to the Y-axis on the left). The dataset from Portus will in future be made more complete by research currently being conducted by the Parco Archeologico di Ostia Antica, the University of Southampton (Keay et al. 2011, in press), the École Française de Rome [START_REF] Bukowiecki | Portus. Chronique des activités archéologiques de l'École française de Rome[END_REF][START_REF] Bukowiecki | Portus. Le môle nord-sud -Première campagne de fouilles[END_REF], and the Universidad Huelva [START_REF] Bermejo | Il molo est-ovest a Portus. Un'analisi preliminare dalla archeologia della archittetura[END_REF]), but the overall orientation of the main features of the site will not change.

Geoarchaeological cores

For the last 20 years, much geoarchaeological fieldwork involving sedimentary drillings has been conducted at Ostia [START_REF] Goiran | Geoarchaeology confirms location of the ancient harbour basin of Ostia (Italy)[END_REF][START_REF] Hadler | Temple-complex post-dates tsunami deposits found in the ancient harbour basin of Ostia (Rome, Italy)[END_REF][START_REF] Salomon | Geoarchaeology of the Roman port-city of Ostia: Fluviocoastal mobility, urban development and resilience[END_REF]Portus (Arnoldus-Huyzendveld 2005;[START_REF] Bellotti | Geoarchaeological investigations in the area of the imperial harbours of Rome[END_REF][START_REF] Giraudi | Late Holocene evolution of Tiber river delta and geoarchaeology of Claudius and Trajan Harbor, Rome[END_REF][START_REF] Goiran | Palaeoenvironmental reconstruction of the ancient harbors of Rome: Claudius and Trajan's marine harbors on the Tiber delta[END_REF]). These cores were studied using a large range of palaeoenvironmental analyses (e.g. Pollens: [START_REF] Sadori | The plant landscape of the imperial harbour of Rome[END_REF][START_REF] Pepe | Late Holocene pollen record from Fiume Morto (Dead River), a palaeomeander of Tiber River near Ancient Ostia (central Italy)[END_REF]Ostracods: Mazzini et al. 2011;Geochemistry: Delile et al. 2014;Foraminifers: Bella et al. 2011[START_REF] Hadler | Temple-complex post-dates tsunami deposits found in the ancient harbour basin of Ostia (Rome, Italy)[END_REF].

In this paper, we use a selection of cores drilled in the fluvial environments around Ostia and in the canals around Portus (Figure 1). For Ostia we chose two cores drilled in the palaeomeander, immediately upstream of the Porta Romana (Cores MO-3 and MO-1 from [START_REF] Salomon | Long-Term Interactions between the Roman City of Ostia and Its Paleomeander, Tiber Delta, Italy[END_REF], and two cores drilled downstream of the city near the river mouth, and in the fluvial harbour of Ostia next to the Palazzo Imperiale (Core PO-2 from [START_REF] Goiran | Geoarchaeology confirms location of the ancient harbour basin of Ostia (Italy)[END_REF] Core ISF-1 from [START_REF] Salomon | Geoarchaeology of the Roman port-city of Ostia: Fluviocoastal mobility, urban development and resilience[END_REF]. For Portus, we chose, on the one side, cores drilled in the Canale Romano (Core CN-1 from [START_REF] Salomon | A harbour-canal at Portus: a geoarchaeological approach to the Canale Romano: Tiber delta, Italy[END_REF], the Canale Traverso (Core CT-1 from [START_REF] Salomon | The Canale di Comunicazione Traverso in Portus: the Roman sea harbour under river influence (Tiber delta, Italy). Géomorphologie : relief, processus[END_REF], and the harbour pool of Portus (TR-14 from [START_REF] Goiran | Palaeoenvironmental reconstruction of the ancient harbors of Rome: Claudius and Trajan's marine harbors on the Tiber delta[END_REF][START_REF] Delile | Geochemical investigation of a sediment core from the Trajan basin at Portus, the harbor of ancient Rome[END_REF], and on the other side, cores drilled in the Portus to Ostia Canal (Cores CPO-2 and 3 from [START_REF] Salomon | The Portus to Ostia Canal. In: The Isola Sacra Survey: Ostia, Portus and the port system of Imperial Rome[END_REF]. These cores will provide evidence of the lateral stability or mobility of the palaeochannels/canals, but also the hydrodynamic conditions during their periods of activities and their periods of abandonment.

Only a few of the palaeoenvironmental analyses are reported in Figures 4 (Ostia) and 5 (Portus). For the aims of this paper we focus on the stratigraphic logs, a short description of the facies, the texture (coarse fraction > 2 mm; 2 mm > sand > 63 µm ; and silts and clays < 63 µm), and the radiocarbon dates recalibrated according to [START_REF] Reimer | The IntCal20 Northern Hemisphere radiocarbon age calibration curve (0-55 cal kBP)[END_REF]. These essential data provide chronostratigraphical evidence and a basic proxy of the hydrodynamic conditions during the deposition of the sediments.

RESULTS OF THE GIS AND PALAEOENVIRONMENTAL ANALYSES

Orientations of archaeological structures and features at Ostia and Portus

Ostia is generally considered to have grown organically from a fortified early settlement (Castrum) built between the 4 th and the 3 rd c. BCE [START_REF] Zevi | Origini di Ostia[END_REF]. Initially, the Castrum was built not far from the left riverbank of the Tiber [START_REF] Constans | Ostie primitive[END_REF][START_REF] Salomon | Geoarchaeology of the Roman port-city of Ostia: Fluviocoastal mobility, urban development and resilience[END_REF]. The last section of the via Ostiensis coming from Rome towards the sea corresponds to the decumanus of the Castrum that the city was built around. Interestingly, the decumanus displays slightly different orientations within Ostia [START_REF] Sclavi | The orientation of the Mithraea in Ostia Antica[END_REF]. The alignment of the eastern and western gates of the Castrum probably best represent the initial orientation of the decumanus [START_REF] Calza | Scavi di Ostia, Topografia generale. Libreria dello Stato, Roma Cherkauer D[END_REF], while the sections of the decumanus leading to Porta Romana could have been modified through time in response to urban dynamics along the street. [START_REF] Sclavi | The orientation of the Mithraea in Ostia Antica[END_REF], put the orientation azimuth of the decumanus within the Castrum at 58.14° (238.14°) and the section of the decumanus the closest to Porta Romana at 60.48° (240.48°), measured on the ground with a professional GPS (averaging 100 measures per point with ± 0.5° uncertainty). According to georeferenced maps we collected, the orientation of the Castrum from the eastern to the western gate measures 61°±1° (241°±1°). A large part of the urban fabric of Ostia that grew out of the Castrum conforms to the orientations of the decumanus and the cardo; e.g. the orientation of streets within the Fluvial district ranges between 61° and 63°. The coastal and river mouth areas do not follow the same pattern and might follow other features, such as the Via Laurentina, Via della Foce, Via del Mare, and possibly palaeocoastlines and palaeoriverbanks.

At Portus, the main excavated sections of Claudian moles are oriented at 62° ± 1° (242°± 1°) (Figure 2). Similar orientations are recorded in the area of the Darsena. Trajan's architects used this orientation for sides II and V of the new hexagonal basin. Following geometric rules, sides III and VI are at 32° ± 1° (112°± 1°) and sides I and IV are at 92° ± 1° (272°± 1°). The eastern part of the Canale Romano (upstream) is aligned with the structures located east of Portus (the via Portuensis and the aqueduct). Upstream, the canal is oriented at 77° ± 1° and downstream it conforms to the side III of the hexagonal basin. The northern canal is out of the main grid of planned features of Portus with 104° ± 1° on the left riverbank and 106° ± 1° on the right riverbank. The actual orientation of the Fossa Traiana -Fiumicino is difficult to characterise due to small curves in its outline. It was probably related to the orientation of the side IV of the hexagon. The Canale Traverso conforms to the Claudian orientations. The left riverbank of the Portus to Ostia canal is a straight line oriented at 152°/ 332° ± 1°, while interestingly, the right riverbank is irregular and its orientation cannot be measured.

Evidence of fluvial lateral mobility at Ostia and Portus

The two cross-sections of cores selected for Ostia demonstrate fluvial lateral mobility during the Roman period (Figure 4). All cores are characterised at their base (Units A) by yellow layered sands corresponding to shoreface deposits from the 1 st part of the 1 st millennium BCE (Unit A in Core PO-2) or before [START_REF] Salomon | Les origines d'Ostie : quelles interactions avec la dynamique d'embouchure ? (Delta du Tibre, Italie)[END_REF].

Coarse sands and small pebbles are the bedload-derived facies of the deltaic Tiber [START_REF] Salomon | Long-Term Interactions between the Roman City of Ostia and Its Paleomeander, Tiber Delta, Italy[END_REF]. They are observed in most of the stratigraphy of Core MO-3 and correspond to the point bar deposits of the palaeochannel of Ostia. Similar point bar successions are observed in Core TEV-4A [START_REF] Hadler | River channel evolution and tsunami impacts recorded in local sedimentary archives -the 'Fiume Morto' at Ostia Antica (Tiber River, Italy)[END_REF]. Core MO-1 demonstrates a decrease of the grain-size from Units B and C (composed of coarse sands and pebbles) to Unit D (composed of sand) and Unit E (composed of silts and clays). This decrease in grain-size is a typical stratigraphic succession from a cut-off palaeochannel. Similar stratigraphies of cut-off palaeochannels are also observed in Cores TEV-1, TEV-3A, possibly TEV-2 in the neck of the Fiume Morto [START_REF] Hadler | River channel evolution and tsunami impacts recorded in local sedimentary archives -the 'Fiume Morto' at Ostia Antica (Tiber River, Italy)[END_REF], and possibly below the cardo of Ostia (Core CAT-3 in [START_REF] Salomon | Geoarchaeology of the Roman port-city of Ostia: Fluviocoastal mobility, urban development and resilience[END_REF].

At the mouth of the Tiber, Units B, C, and D, from Core ISF-1, contain many layers of different grain-size and facies, from silts and clays to coarse sands. Quick-changing depositional conditions characterise river mouth environments affected by both fluvial and coastal processes. The sedimentation in Core ISF-1 could be related to a migration of the river mouth channel to the south or a contraction of the channel width. The two hypotheses relate to riverbank mobility. On the left side of the Tiber, a harbour was excavated between the 4 th and the 2 nd c. BCE [START_REF] Goiran | Geoarchaeology confirms location of the ancient harbour basin of Ostia (Italy)[END_REF]. The harbour muds are sealed by coarse fluvial deposits with sediments presenting a bedload-derived facies [START_REF] Goiran | Geoarchaeology confirms location of the ancient harbour basin of Ostia (Italy)[END_REF][START_REF] Delile | Palaeotsunami deposits at the Tiber River mouth (Ostia Antica, Italy): Do they really exist?[END_REF]. A large part of the fluvial harbour was filled up in the 1 st c. CE [START_REF] Goiran | Geoarchaeology confirms location of the ancient harbour basin of Ostia (Italy)[END_REF].

Interestingly, all evidence of riverbank mobility in the palaeomeander of Ostia [START_REF] Salomon | Long-Term Interactions between the Roman City of Ostia and Its Paleomeander, Tiber Delta, Italy[END_REF][START_REF] Hadler | River channel evolution and tsunami impacts recorded in local sedimentary archives -the 'Fiume Morto' at Ostia Antica (Tiber River, Italy)[END_REF], north of the Castrum [START_REF] Salomon | Geoarchaeology of the Roman port-city of Ostia: Fluviocoastal mobility, urban development and resilience[END_REF]), or at the river mouth [START_REF] Goiran | Geoarchaeology confirms location of the ancient harbour basin of Ostia (Italy)[END_REF][START_REF] Salomon | Geoarchaeology of the Roman port-city of Ostia: Fluviocoastal mobility, urban development and resilience[END_REF]) is dated to the 1 st c. CE at the latest. Most of the evidence of fluvial lateral mobility dates to the second part of the 1 st millennium BCE, during the Republican period of Ostia. Morphogenetic activities of the river started again much later in the 10 th -13 th c. CE [START_REF] Hadler | Temple-complex post-dates tsunami deposits found in the ancient harbour basin of Ostia (Rome, Italy)[END_REF][START_REF] Delile | Palaeotsunami deposits at the Tiber River mouth (Ostia Antica, Italy): Do they really exist?[END_REF] and after 1557 CE.

The sedimentary cores drilled in the canals around Portus reveal different types of stratigraphical successions (Figure 5). Three canals will be presented: the Canale Romano, the Canale Traverso, and the Portus to Ostia Canal. The first cross-section shows the Canale Traverso leading to Fiumicino (Fossa Traiana), and then the Canale Traverso and the Portus pool between the harbours of Claudius and Trajan. Similar to the area of Ostia, all cores reach a Unit A composed of yellow layered sand corresponding to shoreface deposits. These deposits date back to the first part of the 1 st millennium BCE or earlier [START_REF] Giraudi | Evoluzione tardo-olocenica del delta del Tevere[END_REF][START_REF] Bellotti | Late Quaternary landscape evolution of the Tiber River delta plain (Central Italy): new evidence from pollen data, biostratigraphy and 14C dating[END_REF][START_REF] Salomon | Les origines d'Ostie : quelles interactions avec la dynamique d'embouchure ? (Delta du Tibre, Italie)[END_REF].

Core CN-1 from the Canale Romano reveals the typical stratigraphy of a cut-off channel [START_REF] Salomon | A harbour-canal at Portus: a geoarchaeological approach to the Canale Romano: Tiber delta, Italy[END_REF]. Units B and C are composed of medium-to-coarse sands, suggesting bedload-derived facies. A sharp limit marks the change from the coarse deposits in Unit C to the fine deposits in Unit D characteristic of sediment deposited after a cut-off. Finally, the canal is covered by fine floodplain deposits (Unit E). No core is available yet from the Fiumicino (Fossa Traiana) since the canal is still in activity.

Core CT-1 drilled in the Canale Traverso has more in common with a protected harbour stratigraphy (Core TR-14) than that of a fluvial canal (Core CN-1). No bedload-derived facies are observed at the bottom of the canal. Muds from Unit B were found directly lying on shoreface sands (Unit A). Coarse material is observed in Unit D relating to the second phase of use of the canal. The sedimentation in the canal was likely controlled by dredging [START_REF] Salomon | The Canale di Comunicazione Traverso in Portus: the Roman sea harbour under river influence (Tiber delta, Italy). Géomorphologie : relief, processus[END_REF]) and possibly also by a sluice-gate (Testaguzza 1970;[START_REF] Lisé-Pronovost | Dredging and canal gate technologies in Portus, the ancient harbour of Rome, reconstructed from event stratigraphy and multi-proxy sediment analysis[END_REF].

No lateral mobility is observed in the magnetometer survey around Portus for the Canale Romano and the Canale Traverso [START_REF] Keay | Portus : An Archaeological Survey Of The Portus Of Imperial Rome[END_REF]. However, along the two canals high local magnetic fields are observed [START_REF] Keay | Portus : An Archaeological Survey Of The Portus Of Imperial Rome[END_REF]. These certainly indicate structures along the canals rather than lateral mobility. The two canals were probably articulated by built riverbanks or quays similar to the Fiumicino -Fossa Traiana (Testaguzza 1970).

Palaeoenvironmental analyses of the cores from the Northern Canal are currently in process of being studied. Magnetometer survey revealed no lateral mobility of the canal, nor any features that could be associated with a built riverbank.

The lower part of Figure 5 shows a cross section of the Portus to Ostia Canal. The two cores CPO-2 and 3 can be compared to the cores from the palaeomeander of Ostia (MO-1 and MO-3). Core CPO-3 shows bedload-derived facies up to the Roman sea level in units B and C, similar to point bar deposits. However, Core CPO-2 demonstrates first a Unit B composed of coarse sands and gravels and then fine deposits (Unit C). These two stratigraphic successions led us to consider a lateral mobility of the Portus to Ostia canal [START_REF] Salomon | The Portus to Ostia Canal. In: The Isola Sacra Survey: Ostia, Portus and the port system of Imperial Rome[END_REF]). In the area of the cross section, magnetometry revealed lateral mobility, but no features relating to built riverbanks.

DISCUSSION

Ostia, a port-city affected by rapid fluvial sediment deposition and lateral mobility of the river channel

The Castrum at Ostia was originally built in the 4 th -3 rd c. BCE to control access to the Tiber channel from the sea (Vaglieri 1911;[START_REF] Calza | Scavi di Ostia, Topografia generale. Libreria dello Stato, Roma Cherkauer D[END_REF]. By the end of the Republican period, Ostia's close association with the river [START_REF] Heinzelmann | River port, navalia, and harbour temple at Ostia: new results of a DAI-AAR Project[END_REF][START_REF] Goiran | Geoarchaeology confirms location of the ancient harbour basin of Ostia (Italy)[END_REF]) and the coastlines (Strabo V, 3, 5) was shaping the urban fabric through harbour interfaces and their mobility [START_REF] Salomon | Geoarchaeology of the Roman port-city of Ostia: Fluviocoastal mobility, urban development and resilience[END_REF], turning Ostia into a port-city [START_REF] Zevi | Ostie sous la République[END_REF][START_REF] Zevi | Origini di Ostia[END_REF]. Along the shore, possible harbour structures were built between the end of the 1 st c. BCE/1 st c. CE and the beginning of the 3 rd c. CE [START_REF] Raddi | Indagini Archeologiche -Preliminari alla realizzazione del progetto del nuovo "Ponte della Scafa" -Relazione tecnica[END_REF]. Little is, however, known about the coastal interface management for earlier periods.

With the urbanisation of the two sides of the river [START_REF] Germoni | Ostia beyond the Tiber : recent archaeological discoveries in the Isola Sacra[END_REF]Keay et al. 2020), the harbour within Ostia took a linear form along the banks of the Tiber. Along the left bank of the Tiber, one or several small harbours indented the riverbanks. Geoarchaeological evidence confirmed the existence of one of these small harbours at the mouth of the Tiber (Goiran et al. 2014). Meanwhile, a thick layer of fine deposits observed north of the Castrum could suggest the existence of similar harbour deposits (Core CAT-3 Unit C in [START_REF] Salomon | Geoarchaeology of the Roman port-city of Ostia: Fluviocoastal mobility, urban development and resilience[END_REF]; the molo repubblicano in the palaeomeander of Ostia could also be interpreted as a harbour structure [START_REF] Pannuzi | Ostia Antica, Località Fiume Morto: Una Rilettura Della Problematica Archeologica Alla Luce Delle Nuove Indagini Geofisiche E Geomorfologiche[END_REF].

The linear harbour of Ostia indented by small basins was clearly exposed to fluvial and coastal risks. The main problem reported by ancient authors is related to the Tiber access for maritime ships due to the formation of river mouth bars. This frequent problem was notably reported in 205-204 BCE (Livy, Ab Urbe Condita, 29.14.11; Ovid, Fasti 4.291-304), and at the end of the 1 st c. BCE-beginning of the 1c. CE (Dionysius of Halicarnassus, Antiquitates Romanae 3. 44; Strabo 5.3.5). Though these bars appear to have formed regularly at the river mouth, such unsteady morphologies are not easy to identity using sedimentary cores.

The channel of the Tiber conveyed water and sediment through the city of Ostia.

Consequently, small harbour basins along the river were exposed to quick sedimentation.

Unfortunately, the estimation of the sedimentation rate in the harbour at the river mouth is particularly difficult to ascertain. The calibrations of the radiocarbon dates performed in the harbour muds (Core PO-2, Unit B in Figure 4) offer dates ranging from the 4 th to the 2 nd c. BCE [START_REF] Goiran | Geoarchaeology confirms location of the ancient harbour basin of Ostia (Italy)[END_REF]. During this first phase, the harbour was maybe prone to quick fine sedimentation, but coarse material derived from the bedload did not reach the harbour. However, during the second phase, the harbour was sealed by 2.5m of coarse material deposited during flood events (Core PO-2, Unit C - [START_REF] Goiran | Geoarchaeology confirms location of the ancient harbour basin of Ostia (Italy)[END_REF][START_REF] Delile | Palaeotsunami deposits at the Tiber River mouth (Ostia Antica, Italy): Do they really exist?[END_REF]. Additionally, the regular modification of the profile of the river channel at the entrance to the harbour might have affected access [START_REF] Goiran | High chrono-stratigraphical resolution of the harbour sequence of Ostia: palaeo-depth of the basin, ship drought and dredging[END_REF].

Regarding the river channel itself, fluvial mobility possibly eroded infrastructure, like the via Ostiensis to the north-east of Ostia [START_REF] Bertacchi | Elementi per una revisione della topografia ostiense[END_REF][START_REF] Arnoldus-Huyzendveld | Alcune considerazioni sullo sviluppo storico dell'ansa dell Tevere presso Ostia e sul porto-canale[END_REF][START_REF] Salomon | Long-Term Interactions between the Roman City of Ostia and Its Paleomeander, Tiber Delta, Italy[END_REF], or moved the riverbanks away from the city, such as those north of the Castrum [START_REF] Constans | Ostie primitive[END_REF][START_REF] Salomon | Geoarchaeology of the Roman port-city of Ostia: Fluviocoastal mobility, urban development and resilience[END_REF]).

Portus, a harbour complex planned to reduce river mouth risks

Portus is the result of two main phases of planning. Founded during the reign of the emperor Claudius (mid 1 st c. CE), it was reorganised at the beginning of the 2 nd c. CE by the emperor Trajan [START_REF] Lugli | Il porto di Roma imperiale e l'agro portuense[END_REF][START_REF] Keay | Portus : An Archaeological Survey Of The Portus Of Imperial Rome[END_REF]. Due to this Trajanic intervention some of the details of the initial Claudian plan are not fully known. Other phases of construction have also been identified, notably during the reigns of Nero and Hadrian, but these interventions did not significantly affect the plan established by their predecessors [START_REF] Keay | Portus : An Archaeological Survey Of The Portus Of Imperial Rome[END_REF].

While Ostia may be understood as a port city, we suggest that Portus ought to be considered as a harbour complex. In terms of planning, while there is a fort at the centre of Ostia, Portus is organised around its harbour basins. No residential occupation has been attested at the site (Keay et al. 2020, p. 159), and it is only at the beginning of the fourth century CE that Portus became an urban settlement with municipal status (cf. CIL XIV 4449, dated to CE 337-345 or 334-341 [START_REF] Keay | Portus : An Archaeological Survey Of The Portus Of Imperial Rome[END_REF].

The configuration of Portus suggests that the harbour system was conceived to reduce the fluvial inputs in the harbour basins (Figure 1 and6). The harbour basins and the Tiber channel were not directly connected by waterways [START_REF] Salomon | The Canale di Comunicazione Traverso in Portus: the Roman sea harbour under river influence (Tiber delta, Italy). Géomorphologie : relief, processus[END_REF][START_REF] Salomon | Géoarchéologie du delta du Tibre : Evolution géomorphologique holocène et contraintes hydrosédimentaires dans le système Ostie -Portus[END_REF]. The Northern canal and the Fiumicino (Fossa Traiana) are connected upstream to the Tiber with outlets in the sea north and south of Portus. The canal mouth bars would thus form away from Portus and the harbour basins. In between these two channels, the Canale Romano is also connected upstream to the Tiber, and instead of flowing straight, with the attendant risk of flowing into a harbour basin, the canal curves towards the south, follows one side of the hexagonal basin of Trajan, and empties into the Fiumicino (Fossa Traiana). The Canale Romano was thus a harbour canal [START_REF] Salomon | A harbour-canal at Portus: a geoarchaeological approach to the Canale Romano: Tiber delta, Italy[END_REF] only indirectly connected to the Trajanic harbour via the side III of the Hexagonal basin, possibly to facilitate transhipment.

Nevertheless, connections existed between the fluvial waterways and the harbour basins.

The northern entrance to the Claudian basin [START_REF] Goiran | Caracteristiques sedimentaires du bassin portuaire de Claude: nouvelles donnees pour la localisation des ouvertures[END_REF]) and the Canale Traverso [START_REF] Salomon | The Canale di Comunicazione Traverso in Portus: the Roman sea harbour under river influence (Tiber delta, Italy). Géomorphologie : relief, processus[END_REF][START_REF] Lisé-Pronovost | Dredging and canal gate technologies in Portus, the ancient harbour of Rome, reconstructed from event stratigraphy and multi-proxy sediment analysis[END_REF]) are indirectly connected to the Tiber through the Northern canal and the Fiumicino (Fossa Traiana) respectively (Figure 1). This layout reveals a complex flow and sediment routing management planned by Roman engineers.

Additionally, the Northern entrance to the Claudian basin and the Canale Traverso could have contributed to reduce sediment deposition in the harbour. Models demonstrate that stronger currents induced by winds in the north-eastern channel and the Canale Traverso could have reduced rapid sediment infilling in the harbour basin system [START_REF] Millet | Hydrodynamic Modeling of the Roman Harbor of Portus in the Tiber Delta: The Impact of the North-Eastern Channel on Current and Sediment Dynamics[END_REF]. In this context, these stronger currents in the north-eastern channel could have possibly removed sediments deposited at the mouth of the Northern canal. In addition, sluice gates were possibly built in the narrow Canale Traverso to better control sediment inputs in the harbours during river floods by blocking both water and sediment discharge towards the harbour basins [START_REF] Lisé-Pronovost | Dredging and canal gate technologies in Portus, the ancient harbour of Rome, reconstructed from event stratigraphy and multi-proxy sediment analysis[END_REF].

Roman engineers working in Portus had to deal with fluvial inputs in the harbour basin, but also with riverbank mobility prevention. It should be noted that fluvial erosion affects natural channels as much as canals. Lateral canal mobility is observed on images produced by the magnetometer survey of the Portus to Ostia Canal [START_REF] Keay | Portus and its Hinterland: Recent Archaeological Research[END_REF]Keay et al. 2020) and has been confirmed by sedimentary drillings (Figure 5, lower part) [START_REF] Salomon | The Portus to Ostia Canal. In: The Isola Sacra Survey: Ostia, Portus and the port system of Imperial Rome[END_REF]).

The Canale Romano, the Fiumicino (Fossa Traiana), and the Canale Traverso, however, show evidence of built riverbanks. Archaeological evidence revealed riverbanks along the Fiumicino, at least along the reach south of Portus, and the northern part of the Canale Traverso (Testaguzza 1970). Results from geophysical survey identified high magnetic features along the Canale Romano and the Canale Traverso suggesting built riverbanks and no lateral mobility in the canals. Surprisingly, magnetic surveys revealed no riverbanks and no lateral mobility for the Northern canal. Analyses in progress on cores drilled in the Northern canal will probably shed new light on this feature. A clear pattern emerges: the closer the canal to Portus, the better channelised it was. The channelisation of the canals next to Portus and their shorter width (<50m) compared to the Tiber channel (> 100m) would have made them easier to maintain by dredging.

The study of the canal system of Portus thus reveals engineering solutions to sedimentological, geomorphological, and possibly hydrological constraints first faced at Ostia.

From Ostia to the Ostia-Portus system

Portus was clearly not conceived independently from Ostia [START_REF] Keay | The Port System of Imperial Rome[END_REF], and the two sites present an integrated system of complementary units.

In this respect, it is interesting to observe the matching orientation of the original structures at the two sites: the Castrum at Ostia and the Claudian structures at Portus. Alignments of the mentioned structures (marked in blue on Figure 2) follow the original axis of the Castrum at Ostia (decumanus = 62°/ 238° ± 6° and cardo = 152° / 332° ± 6° -Le Gall 1975; [START_REF] Sclavi | The orientation of the Mithraea in Ostia Antica[END_REF][START_REF] Sparavigna | The Hexagon of Portus Traiani and Its Link to the Solar Arc and the Ancient Wind Rose[END_REF]). Ostia's original orthogonal grid orientation of c.

238° is solar and corresponds to the Winter Solstice Sunset at the time of the town's foundation [START_REF] Sclavi | The orientation of the Mithraea in Ostia Antica[END_REF]. Solar orientation was not uncommon among Roman colonies in Italy or in towns founded across the Roman Empire [START_REF] Magli | On the orientation of Roman towns in Italy[END_REF], though note that the orientation value for Ostia used in Table 1 is off by 10°), and though Roman town foundation ritual incorporated a symbolic dimension, in practice the laying out of the new town grid was predominantly governed by local topography [START_REF] González-García | Roman city planning and spatial organization[END_REF]Orfilia Pons et al. 2017). At Ostia, local factors included the positions of the coastline and the riverbanks, limitations imposed by the salt lagoon of Stagno di Ostia, the prevailing winds, and any preexisting land division and road infrastructure.

Winds have been given particular consideration in Vitruvius, the only surviving Roman architecture treatise that deals explicitly with city foundation. The Castrum of Ostia conforms fully to the advice given (Vitruvius,De Architectura,1.6.8): the predominant NE and SE winds would indeed break upon the walls of the fortress, as recommended (cf. Figure 1). The Castrum thus positioned was also aligned with the riverbank (Figure 2), the continued importance of which is reflected in the orientation of the Fluvial district, which although representing a later organic growth of the town still respects the first alignment. At Portus, harbour engineers repeated the same alignment, matching that of Ostia, time and time again -in the original layout of Claudius, the enlargement of Trajan, and the large warehouse block added in the Severan period. Bearing in mind that land division on the Isola Sacra is most probably late 1 st century CE in date (Keay et al. 2020: 151), and there is no evidence yet for any land division on either the Isola Sacra or at Portus predating the construction of the Claudian Harbour, it is clear that the orientation of structures and features at Portus was not dictated by a pre-existing land grid, but that it was either copied from Ostia or decided upon based on the same environmental considerations.

Wind and water swell direction would have been even more important in designing a harbour environment than a town, and the orientation that offered protection from the prevailing winds must have been seen as advantageous. Preliminary modelling does in fact suggest that the alignment and height of the structures surrounding the Trajanic basin was effective in protecting it from wind, and the same is most likely the case for the Darsena (Keay et al. 2021a, pp. 390-391). Unfortunately, we cannot tell how successfully the harbour design combatted the destructive force of water swells, as we currently cannot reconstruct the position of the original Portus harbour entrance with absolute certainty.

While some canals display orientation independent of either Portus or Ostia (the upstream reach of the Canale Romano, the Northern Canal), most likely for hydrological reasons, other elements of the canal network align with the Trajanic layout of Portus (the downstream reach of the Canale Romano follows side III of the Trajanic hexagonal basin, Canale Traverso that of the district of the Darsena). The Portus to Ostia canal, on the other hand, seems to conform to the original orientation of Ostia and later of Portus (the left/eastern bank not affected by lateral erosion). This alignment of the navigable link between Ostia and Portus adds to the evidence of the existence of a general plan regulating the River Tiber mouths in the Imperial period.

Lateral mobility of the Tiber in Ostia seems to stop between the end of the 1 st c. BCE and the beginning of the 3 rd c. CE [START_REF] Salomon | Long-Term Interactions between the Roman City of Ostia and Its Paleomeander, Tiber Delta, Italy[END_REF][START_REF] Salomon | Geoarchaeology of the Roman port-city of Ostia: Fluviocoastal mobility, urban development and resilience[END_REF]. It restarts in the 10 th -13 th c. CE at least with fluvial coarse deposits observed in the river mouth harbour of Ostia [START_REF] Hadler | Temple-complex post-dates tsunami deposits found in the ancient harbour basin of Ostia (Rome, Italy)[END_REF][START_REF] Delile | Palaeotsunami deposits at the Tiber River mouth (Ostia Antica, Italy): Do they really exist?[END_REF]. Several hypotheses can be proposed to explain the end of the lateral mobility of the Tiber in Ostia during the Imperial period and for a millennium. Climatic variations could have reduced the intensity and the frequency of the Tiber floods during this period; palaeoclimatic data, however, do not confirm this hypothesis for the long period under consideration (e.g. hydroclimatic crisis in the 8 th c. CE -Le [START_REF] Gall | Le Tibre, fleuve de Rome dans l'antiquité. Presses Universitaires de France, Paris Le Gall J[END_REF][START_REF] Berger | Le développement économique romain face à la crise environnementale : le cas de la Gaule narbonnaise[END_REF][START_REF] Mccormick | Climate Change during and after the Roman Empire: Reconstructing the Past from Scientific and Historical Evidence[END_REF] -is yet to be observed in the sediments of Ostia). Alternatively, the creation of large canals at Portus would have locally diverted large amounts of water and the flow competence of the river could have been largely reduced at Ostia, notably limiting the lateral erosion. It should be noted that while all the dates related to the coarse fluvial deposits at Ostia indicate periods before the 1 st c. CE [START_REF] Goiran | Geoarchaeology confirms location of the ancient harbour basin of Ostia (Italy)[END_REF][START_REF] Hadler | Temple-complex post-dates tsunami deposits found in the ancient harbour basin of Ostia (Rome, Italy)[END_REF][START_REF] Hadler | River channel evolution and tsunami impacts recorded in local sedimentary archives -the 'Fiume Morto' at Ostia Antica (Tiber River, Italy)[END_REF][START_REF] Salomon | Long-Term Interactions between the Roman City of Ostia and Its Paleomeander, Tiber Delta, Italy[END_REF][START_REF] Salomon | Geoarchaeology of the Roman port-city of Ostia: Fluviocoastal mobility, urban development and resilience[END_REF]Vött et al. 2020;[START_REF] Delile | Palaeotsunami deposits at the Tiber River mouth (Ostia Antica, Italy): Do they really exist?[END_REF], the radiocarbon dates from the canals of Portus fit in a timespan ranging from the middle of the 1 st to the 7 th c. CE.

It is also possible that some of the solutions applied to the canals of Portus would have also been adopted for the natural channel of the Tiber at Ostia, with built riverbanks facilitating its channelization. In this case, Portus was not the sole solution to the problems at Ostia, but Ostia itself also adapted against fluvial hazards.

Additional studies would be necessary to reconstruct precisely the mobility of the downstream reach of the Tiber and the management of the riverbanks of Ostia between the Republican and the Imperial period. The long history of Ostia would offer the possibility of detailing the temporal trajectory and the different phases of fluvial management during the Roman period.

CONCLUSION

The main hazards recorded by ancient texts for the port-city of Ostia were the large amount of sediment deposited at the river mouth affecting the harbour and the presence of river mouth bars constraining the access to large maritime ships. Geoarchaeological sedimentary drillings confirmed the important sedimentation at the river mouth [START_REF] Goiran | Geoarchaeology confirms location of the ancient harbour basin of Ostia (Italy)[END_REF][START_REF] Salomon | Geoarchaeology of the Roman port-city of Ostia: Fluviocoastal mobility, urban development and resilience[END_REF][START_REF] Salomon | The Portus to Ostia Canal. In: The Isola Sacra Survey: Ostia, Portus and the port system of Imperial Rome[END_REF] and revealed the importance of the lateral mobility of the Tiber in Ostia [START_REF] Salomon | Long-Term Interactions between the Roman City of Ostia and Its Paleomeander, Tiber Delta, Italy[END_REF][START_REF] Salomon | Geoarchaeology of the Roman port-city of Ostia: Fluviocoastal mobility, urban development and resilience[END_REF]. This study demonstrates how a city like Ostia tried to manage dynamic river mouth environments through time, and how the Imperial harbour facility at Portus was planned from its foundation with these problems in mind (Figure 6).

Fluvial mobility.

During the Republican period, Ostia was founded along the natural channel of the Tiber. The city expanded and eventually urbanised the two banks of river mouth [START_REF] Germoni | Ostia beyond the Tiber : recent archaeological discoveries in the Isola Sacra[END_REF]Keay et al. 2020). During the Republican period, the river moved laterally and Ostia adjusted to these changes by rebuilding riverine infrastructures [START_REF] Salomon | Long-Term Interactions between the Roman City of Ostia and Its Paleomeander, Tiber Delta, Italy[END_REF][START_REF] Salomon | Geoarchaeology of the Roman port-city of Ostia: Fluviocoastal mobility, urban development and resilience[END_REF]. A few kilometres to the north, in the middle of the 1 st c. CE, the maritime harbour at Portus was conceived away from the Tiber and its direct erosion. Nevertheless, canals had to be excavated to connect Portus to the Tiber and allow direct transhipment via the river to Rome. Built riverbanks were used in the canals close to Portus in order to limit their lateral mobility (Fiumicino -Fossa Traiana, Canale Romano, Canale Traverso and possibly some parts of the Portus to Ostia canal). These riverbanks are currently known via geophysical survey alone [START_REF] Keay | Portus : An Archaeological Survey Of The Portus Of Imperial Rome[END_REF](Keay et al. , 2020)).

Water and sediment routing. In Ostia, the Tiber flowed through the city with a high sediment discharge during floods. Consequently, the harbours excavated along the Tiber were more prone to be filled by sediments. In Portus, the canal system dispatched the main water and sediment discharges of the Tiber to the south and north of Portus. Additionally, the connection between the river flow and the harbour basins was indirect (e.g. a secondary connection via channels/canals, transhipping between the Trajanic harbour and the Canale Romano). While the river channel and the harbours are joint or closely interconnected in Ostia, the river system (including canals) and the harbour basins are separated at Portus (Figure 6).

Finally, the corresponding orientation of archaeological structures observed at Ostia, the harbour of Claudius and Trajan, and the Portus to Ostia canal that aimed at reducing the adverse impact of wind and likely also waves, further supports the existence of a common planning logic. The management of sediment and water discharge was, furthermore, conceived in considering the possibility of navigation between the different harbour units of Ostia and Portus (the Tiber channel, canals, harbour basins of Ostia and Portus), indicating the existence of a single integrated water management and harbour system.

Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013/ERC grant agreement n° 339123). The project also leading to this publication has received funding from Excellence Initiative of Aix-Marseille Université -A*MIDEX, a French "Investissements d'Avenir" programme, AMX-18-MED-018.

Figure 1 .Figure 2 .

 12 Figure 1. -Site location -Two archaeological sites at the mouth of the River Tiber during the Roman period Figure 2. -Map of the orientation of the structure/features in Ostia and Portus Figure 3. -Diagram of the orientation of the archaeological structures/features in Ostia and Portus Figure 4. -Fluvial mobility and harbour construction along the River Tiber -Synthesis of chronostratigraphical data Figure 5. -From the canals to the harbours of Portus -Synthesis of chronostratigraphical data

Acknowledgments

We gratefully acknowledge the financial and logistical support of the École Française de Rome and the British School at Rome, as well as the financial support from ANR-Poltevere (ANR-11-JSH3-0002). The research leading to these results has also received funding from the European


Abhishek Palchoudhary

Vincent Maurel

Cristian Ovalle

Pierre A Kerfriden

Fast Neuber-Type

A fast Neuber-type finite element simulator

Keywords: Model Reduction, Neuber's rule, Finite Element Method, Accelerated Calculations

Evry, France abhishek.palchoudhary@minesparis.psl.eu, pierre.kerfriden@minesparis.psl.eu

Résumé :

Cet article aborde les aspects numériques d'une nouvelle méthode développée pour accélérer les calculs sur des structures poreuses à comportement non linéaire. L'hypothèse de proportionnalité est utilisée en conjonction avec une méthode de Neuber modifiée afin de réduire la complexité dimensionnelle typique des méthodes de Neuber multiaxiales. Cette méthode est utilisée afin d'intégrer numériquement les lois matérielles non linéaires en fonction de la réponse élastique EF de la structure, pour obtenir la dissipation intrinsèque en champ complet via les composantes déviatoriques élasto-plastiques approchées de contrainte et de déformation. Les erreurs generés en utilisant de cette méthode sont illustrées. Cette méthode permet la génération rapide de grands ensembles de données de la réponse thermique des structures avec des populations de pores variables ayant un comportement non linéaire. Des approches d'apprentissage automatique basées sur ces données pour lier la réponse thermique des structures à leur durée de vie en fatigue sont donc rendues possibles.

Abstract :

This paper addresses the numerical aspects of a new method developed to accelerate calculations on porous structures with non-linear material behavior. The hypothesis of proportionality is used in conjuction with a modified Neuber method in order to reduce the dimensional complexity that the multi-axial Neuber methods intrinsically have. This method is used in order to numerically integrate the non-linear material laws as a function of the FE elastic response of the structure, to obtain the full-field intrinsic dissipation via the approximated elasto-plastic deviatoric components of stress and strain. The errors generated by using this method are illustrated. This method enables rapid generation of large data-sets of the thermal response of structures with varying pore populations having a non-linear behavior. Datadriven deep-learning approaches for linking the thermal response of structures to their fatigue life are therefore made possible. Proportionality ratio of the approximated total deviatoric stress tensor to the elastic deviatoric stress tensor at the last peak of cyclic loading

Introduction

Fatigue life characterization of industrial components has traditionally required a large number of experiments, in depth investigation by SEM and more recently tomographic analysis to understand the mechanisms of damage especially in presence of defects, to identify a fatigue lifetime law based on a criterion and to describe the scatter in lifetimes [START_REF] El Khoukhi Driss | Experimental Investigation of the Size Effect in High Cycle Fatigue : Role of the Defect Population in Cast Aluminium Alloys[END_REF], [START_REF] Dezecot | 3D characterization and modeling of low cycle fatigue damage mechanisms at high temperature in a cast aluminum alloy[END_REF]. This approach is both costly and time consuming, therefore, a new method of fatigue lifetime characterization is to be developed, consisting of a threefold approach, including experiments, simulations and machine learning. The main objective is to reach a real-time criterion from measurements to assess residual lifetime of a material subjected to fatigue loading in presence of defects.

A deep-learning based tool will be developed that can be used in real-time to aid in the decision making regarding the service life of structures bearing fatigue loading in presence of a population of defects.

The fatigue lifetime will be predicted based on image data that can be easily and inexpensively acquired via non contact measurement techniques. The study is based around laboratory specimens made from cast aluminium alloys, manufactured by the lost foam method, that is commonly used in the automotive industry. The manufacturing method causes formation of pores and defects in the material, which adds to the uncertainty in the fatigue lifetime characterization [START_REF] El Khoukhi Driss | Experimental Investigation of the Size Effect in High Cycle Fatigue : Role of the Defect Population in Cast Aluminium Alloys[END_REF], [START_REF] Le | Investigation of the effect of porosity on the high cycle fatigue behaviour of cast Al-Si alloy by X-ray micro-tomography[END_REF]. The proposed approach aims to exploit the thermal response of these porous specimens under cyclic mechanical solicitation in order to predict their fatigue lifetime. The thermal response includes thermoelastic coupling as well as intrinsic dissipation in the structures, which causes a temperature change in the structures identifiable via IR thermography that reduces the ill-posedness of the inverse problem to be solved.

Deep-learning approaches require a large and representative data-set for learning the parameters responsible for failure. As experiments remain scarce, simulations will form a large part of the data-set. A Monte-Carlo approach is adopted to simulate varying pore populations. Nevertheless, nonlinear FE calculations on structures with pores remain computationally expensive and highly time consuming and are not feasible in large quantities. Thus, a method of acceleration is needed.

In this paper, a modified Neuber type method is developed and solved in conjunction with an elastoplastic model [START_REF] Chaboche | Constitutive equations for cyclic plasticity and cyclic viscoplasticity[END_REF] to accelerate the calculation by using inexpensive elastic finite element calculations. This permits fast calculation of internal plastic variables like the intrinsic dissipation for a range of structures with varying pore populations.

2 Literature

Neuber-Type methods

Neuber [START_REF] Neuber | Theory of stress concentration for shear-strained prismatic bodies with arbitrary nonlinear stress-strain law[END_REF] originally derived a way to approximate the unidimensional plastic stress and strain at a notch root under monotonic loading from an elastic calculation. The Neuber rule states that the Hookian or elastic stress concentration factor k t is the geometric mean of the plastic stress and strain concentration factors k σ and k ϵ , i.e.

k t = (k σ k ϵ ) 1 2 (1)
which can also be written as

σϵ = σ e ϵ e (2)
where σ e and ϵ e are the elastic stress and strain at the notch and σ and ϵ are the approximated real stress and strain at the notch. This equation represents the equality of the total work at the notch tip.

This concept was extended for cyclic uni-axial loading by assuming a zero mean stress at the notch root and relating the elastic local stress and strain ranges ∆σ e and ∆ϵ e to the real local stress and strain ranges ∆σ and ∆ϵ [START_REF] Topper | Neuber's rule applied to fatigue of notched specimens[END_REF] :

∆σ∆ϵ = ∆σ e ∆ϵ e (3)
The authors in [START_REF] Chaudonneret | Adaptation of Neuber's theory to stress concentration in viscoplasticity[END_REF] suggest taking into account the mean stress by including a change of origin every time a peak in the uni-axial cycling loading is reached :

(σ -σ o ) : (ϵ -ϵ o ) = (σ e -σe o ) : (ε e -εe o ) (4)
The Neuber method has been generalized for proportional multi-axial loadings, with the extension being [START_REF] Moftakhar | Calculation of Elasto-Plastic Strains and Stresses in Notches under Multiaxial Loading[END_REF] :

σ ij ϵ ij = σ e ij ϵ e ij (5)
Where i,j = 1,2,3 and summation of the components is applied. The authors note that this formulation applies when the deviatoric stresses of the notch tip are proportional during loading. The authors also assume that the fractional contribution of the largest principal notch tip stress and strain to the total notch tip strain energy density is virtually equal to the corresponding fraction calculated elastically. Together with the material constitutive equations, the stresses and strains at the notch tip are thereby calculated.

The investigations in [START_REF] Chu | Incremental Multiaxial Neuber Correction for Fatigue Analysis[END_REF] report that the estimated elastic-plastic solution seems insensitive to the assumed path for proportional nominal loadings, but becomes very sensitive to the assumed path for nonproportional nominal loadings. Thus, an incremental version of the Neuber method has been developed to account for non-proportional cyclic loading via the application of incremental plasticity. The authors in [START_REF] Buczynski | An analysis of elasto-plastic strains and stresses in notched bodies subjected to cyclic non-proportional loading paths[END_REF] suggest that in order to formulate the set of necessary equations for a multiaxial non-proportional analysis of elastic-plastic stresses and strains at the notch tip, increments of the total distortional strain energy density contributed by each pair of stress and strain components are equal :

σ d ij ∆ϵ d ij + ∆σ d ij ϵ d ij = σ e d ij ∆ϵ e d ij + ∆σ e d ij ϵ e d ij (6)
Therefore, the incremental deviatoric elastoplastic stress and strain components at the notch tip are therefore calculated via increments of the hypothetical linear elastic stresses and strains due to nonproportional loading and the material constitutive equations (the authors use the Prandtl-Reuss flow rule).

Methodology

Modified Neuber hypothesis

The Neuber-type hypothesis used for our case considers the deviatoric parts of the stress and strain tensors :

(σ d -σ d,o ) : (ε d -ε d,o ) = (σ e d -σ e d,o ) : (ε e d -ε e d,o ) (7)
Where σ d , ε d stand for the approximated total deviatoric stress and strain tensors and σ d,o , ε d,o stand for the approximated total deviatoric stress and strain tensors at the last peak. Similarly, σ e d , ε e d stand for the hypothetical elastic deviatoric stress and strain tensors and σ e d,o , σ e d,o stand for the hypothetical elastic deviatoric stress and strain tensors at the last peak. The hydrostatic part of the total stress and strain tensors is assumed to be directly equal to the elastic hydrostatic stress and strain.

It is important to note that stresses and strains in a structure depend on its geometry, the material behavior and the external loading applied. When there is a change in the direction or ratio of the stresses developed in the material, these local stresses are said to be non-proportional. If there is plastic flow anywhere in the structure, local non-proportionality can appear even if the external loading is proportional.

We assume a hypothesis of proportionality, that is, while the local evolution of the actual deviatoric stress and strain tensors at a point can be arbitrarily complex, it stays in the direction of the elastic deviatoric stress and strain, i.e. there is no shift in the direction in which plasticity develops. All the components of the total deviatoric stress have the same ratio s with the respective components of the elastic deviatoric stress that does not change in direction or magnitude over the loading history. Similarly, the ratio between the total and elastic components of the deviatoric strain is defined as e. According to this hypothesis :

σ d = sσ d (8)
ε d = eε d (9)
where s and e are scalar functions of time.

The elastic tensors vary linearly with respect to the loading, and therefore, if an elastic calculation via the finite-element method for a point at a fixed global loading is denoted by σ and ε , then the following holds true :

σ e d = f σ d (10)
ε e d = f ε d (11)
where the loading function f is chosen to be a sawtooth function to represent cyclic loading.

The main advantage of this hypothesis allows for a reduction in the number of dimensions that the Neuber equation needs to be solved in, i.e. the number of equations is reduced from six to one :

(sσ d -s o σ d ) : (eε d -e o ε d ) = (f σ d -f o σ d ) : (f ε d -f o ε d ) (12)
σ d : ε d (s -s o )(e -e o ) = σ d : ε d (f -f o )(f -f o ) (13)
(s -s o )(e -e o ) = (f -f o ) 2 (14)
This equation is now scalar as there is only one component to solve for. The evolution of this component is shown in Figure 1.

Material law

While any model of plasticity can be used to solve the modified Neuber equations, the following elastoplastic Chaboche model with kinematic and isotropic hardening [START_REF] Chaboche | Constitutive equations for cyclic plasticity and cyclic viscoplasticity[END_REF] is used in our case : The total strain tensor is the sum of the elastic and plastic strain tensors :

ϵ = ϵ e + ϵ p (15)
The stress tensor is given by :

σ = 2µ(ϵ -ϵ p ) + λtr(ϵ -ϵ p ) (16)
The total stress tensor can be split into its deviatoric and hydrostatic parts :

σ = σ d + σ h ( 17
)
The deviatoric stress tensor is given by :

σ d = 2µ(ϵ d -ϵ p d ) (18)
The total hydrostatic stress tensor is assumed to be equal to the elastic hydrostatic stress, as they are close [START_REF] Lemaitre | Mécanique des matériaux solides[END_REF] :

σ h = 1 3 tr(σ e ) (19)
The Von-Mises stress is :

σ VM = 3 2 σ d : σ d ( 20
)
Kinematic hardening :

Ẋ = 2 3 C ε p -DX ṗ (21) Isotropic hardening : R = Q(1 -e -bp ) (22)
The accumulated plastic strain depends only on the deviator of the plastic strain :

ṗ = 2 3 ε p d : ε p d (23)
where ε p d is the time derivative of the deviatoric plastic strain tensor. The yield surface is defined by : f (σ; X, p) = σ eq (σ; X) -σ y -R where f (σ; X, p) <= 0 (24)

With the hypothesis of proportionality, these equations change accordingly from six components to one component. The system of equations can thus be solved for the scalar functions s and e. Together with the modified equations describing the material behavior and the modified Neuber equation, s and e are calculated, which result in a full approximate mechanical solution of the non-linear structural problem. This can be used to calculate the intrinsic dissipation over a cycle [START_REF] Besson | Non-Linear Mechanics of Materials[END_REF] :

ϕ 1 = (f (σ; X, p) + σ y + R 2 2Q + D 2C J 2 (X )) ṗ ( 25
)
This equation is suitably simplified to a variant containing scalar functions that arise from the hypothesis of proportionality. The parameters chosen for this study are summarized in table 1.

Finite Element simulator and interpretability

The previous section focused on obtaining the intrinsic dissipation, a value that depends heavily on the form of the non-linear stress-strain curves, from elastic calculations at a cyclically loaded point undergoing multi-axial stress. It is desired to apply this approach to not just a point, but all points within a larger domain of interest, for example, all points within a geometry with an explicitly modelled distribution of defects, while also keeping the calculation time short.

To make interpretation of developing plasticity easier in the reduced dimensions, some steps are needed : A structure without pores with elastic behavior is modelled, and the global loading is chosen such that the Von-Mises stress at all the points in the region of interest is equal to the yield stress of the material.

Next, this global loading is applied to the same geometry, with the same elastic behavior, but this time with explicitly modelled spherical pores. Due to the elastic behavior, the points near the pores develop a Von-Mises stress higher than the yield stress, and are therefore hypothetically elastic. The plasticity at these points will be approximated via the modified Neuber method. The quantities σ and ε are therefore obtained for all the points in the material, and the quantity σ : ε captures the elastic information for all the points in the structure, including hypothetically elastic points near the pores.

The loading function f defined earlier captures the extent of loading of the structure. As σ and ε represent a calculation at the yield limit, the function f will vary between 0 and 1 for a load that is below the yield limit of the material, and be exactly 1 when the yield limit of the material is reached. Therefore, choosing the amplitude of f to be 0.8 would be equivalent to loading the material to 80% of its yield limit. Locally, due to explicitly modelled pores, some points would cross the yield limit due to localized stresses, i.e. plasticity occurs when σ V M > σ y .

Information about these variably stressed local points is extracted in the form of σ : ε from the elastic FE calculation. This quantity, which captures the elastic stress and strain values at these points, are used Next, a 1-D Gaussian process is fitted on this range of variably stressed points and their corresponding intrinsic dissipation. This allows for rapid sampling -the entirety of the elastic field of the porous structure is given as an input, the full-field intrinsic dissipation is directly sampled as the output. Instead of doing a lengthy cyclic non-linear FE calculation on a structure to obtain the dissipation, the FE simulator thus created needs only a call to an elastic FE calculation of the structure to predict the full-field intrinsic dissipation in a cycle for a given loading sequence (illustrated in Figure 2).

Results

Full-field intrinsic dissipation

Part of the full-field dissipation obtained by the modified Neuber approach and the reference dissipation obtained by a full elasto-plastic FE calculation is shown in Figure 3(a). A comparison of all the points is shown in Figure 4(c). A good overall match is found in the values of the dissipation obtained by the modified Neuber method and the reference dissipation. However, there exists some scatter, which is expected due to the cumulative errors of the assumptions of the modified Neuber method. The next section aims to go in depth of the nature of these errors.

Errors due to the hypothesis of proportionality

The relative error ξ rel between the approximated deviatoric stress tensor using the hypothesis of proportionality and the reference deviatoric stress tensor, calculated via a full non-linear FE calculation can be calculated :

Error, ξ = σ d -σ d (26)
ξ rel = ∥ξ∥ F ∥σ d ∥ F (30)
The relative error ξ rel is calculated for all the loading history. Figure 5(a) shows the evolution of the relative error of an element near a pore (shown in Figure 3), alongside the accumulated plastic strain. The load reversal naturally causes the error due to the hypothesis of proportionality to skyrocket, but due to elasticity during reversal, the accumulated plastic strain is zero and thereby there is no accumulated dissipation during load reversal. In other words, the error during load reversal does not contribute to the error in plasticity or dissipation calculations.

Conclusion

Neuber's rule was modified to obtain the full-field intrinsic dissipation of structures with non-linear behavior subjected to cyclic loading. The modifications to the Neuber method consist of :

⋄ Equivalency between the deviatoric stress-strain tensors ⋄ Incorporation of full load reversal, and ⋄ A hypothesis of proportionality These assumptions lead to certain errors, which are non-negligible during load reversal due to the hypothesis of proportionality. However, as demonstrated, the bulk of the errors occur when there is no accumulating plasticity, therefore the dissipation is reasonably well estimated. While the overall match between the dissipation calculated via this method and the reference dissipation from a complete nonlinear FE calculation is rather good, certain points remain over and under-estimated. The main advantage in using this method is in its speed : the calculation time is accelerated manifold by using this method, as the modified Neuber method relies on cheap elastic calculations at a fixed global loading. Thus, the developed finite element simulator allows generation of big data-sets within a reasonable time.

A

  fast Neuber-type finite element simulator to enable deep-learning-based fatigue life predictions from thermographic data A. Palchoudhary, C. Ovalle, V. Maurel, P. Kerfriden MINES ParisTech, PSL University, Centre des Matériaux (CMAT), CNRS UMR 7633, BP 87 91003

Figure 1 -

 1 Figure 1 -An illustration of the modified Neuber method during the (a) first branch of loading (b) second branch of loading, with s o and e o updated to their respective values at the last peak

Figure 2 -

 2 Figure 2 -(a) Elastic FE calculation at the yield limit without pores, with σ V M = σ y (b) Loading function as a proportion of the yield limit (c) The Von-Mises stress obtained by applying the loading function to the elastic FE calculation, shown for a peak (d) The Gaussian process to predict the dissipation given by the modified Neuber method for the chosen load cycle (e) Full-field dissipation calculated via the modified Neuber method, sampled from the Gaussian process for all the points in the structure

Figure 3 -Figure 4 -

 34 Figure 3 -(a) Full-field dissipation using the modified Neuber approach, with the highlighted purple cell showing the point of comparison of the curves (b) Full-field reference dissipation as a result of a complete nonlinear FE calculation in the Z-Set [17] software (c) The evolution of the proportionality ratios evaluated by the modified Neuber method at the highlighted cell (d) Comparison between the cumulative dissipation obtained by the two methods at the same point, showing an under-estimation of the dissipation at this cell via the modified Neuber method

Figure 5 -

 5 Figure 5 -(a) Relative error and cumulated plastic strain of an element near a pore, over time (b) Percentage of elements in the FE calculation below 15% relative error, over time, alongside the loading history

σ d = sσ d ( 27 )

 27 (σ d : σ d ) -s(σ d : σ d ) = 0(28)Combining equations 26 and 28 :ξ = σ d -[(σ d : σ d )/(σ d : σ d )]σ d(29)

  Nomenclature σ d , ε d Approximated total deviatoric stress and strain tensors σ d,o , ε d,o Approximated total deviatoric stress and strain tensors at the last peak of cyclic loading

	σ d , ε d	Finite-Element elastic stress and strain deviatoric tensors for a point at a fixed global
		loading
	σ e d , ε e d	Elastic deviatoric stress and strain tensors
	σ e d,o , ε e d,o	Elastic deviatoric stress and strain tensors at the last peak of cyclic loading
	σ d , ϵ d	Reference total deviatoric stress and strain tensors
	e	Proportionality ratio of the approximated total deviatoric strain tensor to the elastic
		deviatoric strain tensor
	e

o Proportionality ratio of the approximated total deviatoric strain tensor to the elastic deviatoric strain tensor at the last peak of cyclic loading f Loading function f o Loading function at the last peak of cyclic loading s Proportionality ratio of the approximated total deviatoric stress tensor to the elastic deviatoric stress tensor s o

Table 1 -

 1 Parameters of the elasto-plastic model

	Parameter E	σ y	b	Q	C	D
		MPa	MPa		MPa MPa	MPa
	Value	200000 100 10 100 40000 400


Mai Lan Nguyen
email: mai-lan.nguyen@ifsttar.fr

Pierre Hornych

Minh Tan Do

Duc Thierry Sedran

Tung Dao
email: ductung.dao@lafargeholcim.com

Tung Duc

Dao

Accelerated pavement testing for the evaluations of structural design and safety performance of an innovative road coating

Keywords: Pervious concrete, APT, Pavement design, Interface bonding, Dynamic friction test, Innovative Road Coating

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Road maintenance budgets have a strong economic impact. In general, developed countries are spending in maintenance yearly amounts between 0.2 % and 0.4 % of their GDP. With bitumen price rising, concrete pavements become competitive with asphalt pavements, with lower maintenance costs during their service life. Indeed, maintenance cost, including the economic loss caused by traffic disruption due to maintenance works, represent an important budget (FEHRL, 2008).

However, the riding comfort (evenness, noise) of concrete pavements is still a big issue. Many studies were carried out to improve the riding comfort of rigid pavements but the results are still far from expectations. Recently, LafargeHolcim Research Center (LRC) has developed an innovative coating as wearing course for concrete pavements, to offer: a durable solution with concrete structural capacity; expected standards in terms of comfort and safety; technical innovations such as color choices and easy placing.

This new wearing course with a thickness of 3-4 cm, which is placed "fresh on fresh" on conventional concrete, aims to offer an interface between the structural function and the user perception. It is designed to have equivalent costs at construction level as classical concrete pavements, and no structural maintenance over the lifetime, (only surface maintenance, to be assessed). To validate this innovative concept, a full-scale accelerated test was carried out, with the FABAC traffic simulator of IFSTTAR.

Material properties

The properties of the ultra-thin pervious concrete, based on polymer modified cement, were studied in the first stage by laboratory mechanical tests, including 3point flexural strength, compressive strength and durability (scaling resistance).

The strength of concrete containing different types of polymers was measured by 3-point flexural tests and compressive tests on 4 cm x 4 cm x 16 cm size prisms. Figure 1 shows that the mechanical strength of concretes, at a constant rheology, is significantly different, depending on the type and dosage of polymer. In general, polymer improves the flexural strength of concrete (up to 40 % compared to the control concrete without polymer). The influence of polymer on the compressive strength needs to be studied further, as it can enhance or reduce the latter.

The influence of polymer on the resistance to scaling of concrete was also studied with 2 different families: an acrylic acid ester copolymer which proved very efficient to improve the flexural strength and classically recommended polymer for concrete, Styrene Butadiene emulsion. The scaling test used the most severe method, developed by LRC, in which the pervious concrete is submerged in salty water containing 3% of NaCl and is submitted to freeze-thaw cycles (cf. figure 2) until complete failure. The polymer pervious concrete performance was compared to that of classical pervious concrete tested simultaneously. The classical pervious concrete used a 6/10 mm crushed aggregate within cement paste volume of 160 liters for a Water/Cement ratio of 0.34. The results, presented on figure 2 show that polymer can improve significantly the scaling resistance of pervious concrete.

FABAC traffic simulator and APT pavement structure

The FABAC machine is a small linear traffic simulator, capable of applying heavy vehicle loads on small pavement sections. The machine has a total length of 10m, and is equipped with four wheel modules, driven by a chain and electric motor (see figures 3 and 4). Each wheel module can be equipped with single or dual wheels, and apply loads varying between 30 and 75 kN. The length of the loaded section is 2 m. The loading speed can vary between 1 and 5 km/h. A classical road concrete, of class BC5, was used for the base course. A wooden formwork was installed on the granular subbase, for the construction of the concrete structure (figure 5). The BC5 concrete was placed in the formwork, leveled and vibrated. Then, the pervious concrete was laid on top of the base layer immediately (fresh on fresh). A 4 cm thick layer was put in place. The concrete was first vibrated with a striker roller (figure 5), but the compaction was not very efficient. Therefore, it was decided to modify the compaction method: a wooden board was placed on the porous concrete, and the compaction was carried out using a vibrating plate, placed on the board (figure 5).

24 hours after the construction, two joints were created, by sawing the pavement structure up to a depth of 9 cm. One joint was created in the middle of the structure, and the second one 50 cm apart. The surface texture of the porous concrete and the joint are shown on figure 7. The experimental pavement was also instrumented with 8 temperature probes, measuring the air temperature, and the temperatures at different depths in the structure.

Test program

The experimental pavement section was subjected to 5 million load cycles with the FABAC machine, using dual wheels, loaded at 65 kN (French standard equivalent axle load), and a loading speed of 3,6 km/h. The test was performed between November 2016 and June 2017. The monitoring of the pavement included:  Visual inspections, to assess pavement deterioration;  Transverse profile measurements, carried out with a profilometer equipped with a laser displacement sensor, with a vertical resolution of 1 mm;  Air temperature and pavement temperature measurements (8 sensors).  Mean texture depth measurements, using the sand patch method;  Skid resistance measurements, using the Skid Resistance Tester (SRT) and the Dynamic Friction Tester (DFT);  Coring, outside the loaded area, to perform pull-off tests, to evaluate the bonding strength between the porous concrete and the base layer.

Commenté [NM1]:

Car l'équipe de construction ne savait pas comment utilizer ce striker roller compactor. Maintenant, seul ce mode de compactage suffira.

Tung, pourrais-tu confirmer cela ? Pour l'article, est-ce tu d'accord de laisser cette description ?

Results

Bonding strength

To verify the bonding strength at 28 days of the 2 layers, pull off tests (NF EN 1542 standard) were carried out on the slab at different positions. The results are shown in table 1. The National Concrete Pavement Technology Center (USA) recommends a bonding strength from 0.5 MPa to 2.5 MPa for a durable two-lift concrete pavement.

APT structure analysis

Temperature measurements and visual inspections

Figure 7 presents the surface temperature variations recorded during the whole test period. On the surface, the temperatures varied between 0°C in the winter and 40°C in the summer. These conditions are representative of the Nantes climate. Visual inspections were performed at different stages of the test, to detect surface damage (cracking, surface wear). As practically no evolution was observed, only the results obtained at the end of the test are presented. Figure 9 shows the aspect of the surface of the porous concrete, and of the joints, after 5 million load cycles. The marks on the surface correspond to rubber deposited by the tyres, and to grease coming from the FABAC machine. No cracking or deterioration of the surface was detected at the end of the test. The joints also presented no significant damage (no wear or breaking of the edges of the joints -figure 8).

V Fig. 8 View of the porous concrete surface, and of one transverse joint at the end of the test

Transverse profile measurements

Transverse profile measurements were made at 4 different positions on the experimental pavement, at different stages of the test, using a profilometer with a non contact laser displacement transducer. An example of transverse profiles measured after construction and at the end of the test, near the center of the test section is shown on figure 9. The measurements indicate absolutely no permanent deformation of the concrete. The same results were obtained for the other transverse profiles.

Service life of the evaluated structure

Calculations were performed with the French pavement design method, to evaluate the design life of the tested structure. These calculations were performed considering different traffic classes, (and design hypotheses for structuring road networks (VRS)). The results are summarized on Figure 10: for each traffic class, the figure indicates the design life (in number of years), and compares it with the applied traffic (also converted to number of years). The tested structure has a design life of 23 years, for a traffic class T1 (500 heavy vehicles/day), which is validated by the results of the FABAC test (no significant deterioration after this level of traffic). Naturally, this type of structure could be designed for a heavier traffic, by increasing its thickness.

Skid resistance evolution

To evaluate the evolution of the surface characteristics of the porous concrete, three types of tests were performed:  Mean texture depth measurements (MTD), by the volumetric patch test (standard NF EN 13036-1);  Skid resistance measurements, using the Skid Resistance Tester (SRT, standard NF EN 13036-4) and the Dynamic Friction Tester (DFT, ASTM E 1911 standard). The DFT measures the friction force between the surface and three rubber pads attached to a rotating disc. A water supply unit provides a water depth of 1 mm on the surface. A friction-speed curve is recorded from 80 km/h to complete stop. Generally, values of friction coefficient, at 20, 40 and 60 km/h (DFT20, DFT40 and DFT60) respectively, are extracted for analyses. The mean texture depth and friction measurements were performed before loading, and after 1, 3 and 5 million load cycles at 4 different points on the pavement. The results (mean values) of the different tests are summarized in table 2. The mean texture depth of the porous concrete is relatively high, and remained practically constant throughout the test. The lower value obtained at 1 million loads is probably due to the particular test conditions (humid weather and wet pavement). Figure 11 presents the evolution of the SRT and DFT measurements with the number of load applications. The SRT tests indicated a high initial friction coefficient (0.74), followed by a decrease after 3 million loads, and then a stabilization. After 5 million loads, (which represents a high level of traffic), the friction coefficient is equal to 0.54, which remains satisfactory, according to French practice. The DFT tests show a similar trend to the SRT, with a decrease of the friction coefficient in the first part of the experiment, followed by a stabilization. For this test developed in the USA, there are no specified values in France. However, the final value of DFT20 of 0.41 meets the requirements of the state of Louisiana for a conventional mix with a life of 15 years.

Conclusions

In the APT test, the Innovative Road Coating was submitted to 5 million loads, without presenting significant damage. The macrotexture did not evolve after 5 million cycles. The microtexture has decreased as expected, but still presented a satisfactory level after 5 million cycles. The SRT test gave relatively stable results between 3 and 5 million cycles, while the DFT friction test showed a continuous wear of the microtexture, with still acceptable values at the end of the test.

Measurements of cross-sectional profiles showed no significant deformation after 5 million passages, and no evolution of the joints.

The design calculations confirmed the durability of the structure tested here, which can support 20 years of traffic, with 500 trucks per day per lane, without any maintenance due to safety or structural requirements. The new material could then represent an excellent alternative as wearing course for concrete pavements for upcoming projects.

Fig. 1

 1 Fig. 1 Influence of polymer type on the mechanical strength of concrete (a) (b)

Fig. 3

 3 Fig. 3 Principle of the FABAC machine

Fig. 5

 5 Fig. 5 Compaction of the porous concrete layer with a striker roller, and then a vibrating plate

Fig. 6

 6 Fig. 6 Surface texture of the porous concrete, sawed joint, and sealing of the joint (Sikaflex resin)

Fig. 7

 7 Fig. 7 Temperature variations at the surface of the pavement structure

Fig. 9

 9 Fig. 9 Transverse profiles in the center of the experimental section, after construction and after 5 million load cycles

Fig. 10

 10 Fig. 10 Comparison of design life and observed service life (in years) for different levels of traffic.

Fig. 11

 11 Fig. 11 Evolution of the SRT and DFT friction coefficients during the experiment

Table 1

 1 Bonding strength of porous concrete versus base course concrete

	Mean	Standard	Coeff of	Min. value	Max. value
		deviation	variation
	Direct tensile strength 2.00 MPa 0.49 MPa	24.5 %	1.09 MPa	2.82 MPa

Table 2

 2 Mean texture depth and friction coefficient measurements

	Number	Initial	1 million	3 million	5 million
	of cycles	(0 loads)	load cycles	load cycles	load cycles
	MTD (mm)	0.85	0.75	0.85	0.91
	SRT (friction coefficient ) 0.74	0.75	0.52	0.54
	DFT20 ()	0.60	0.55	0.46	0.41
	DFT40 ()	0.59	0.52	0.45	0.41
	DFT60 ()	0.55	0.48	0.43	0.40

  FEHRL (2008). New road construction concepts. NCPTC. (May 2014). Guide to Concrete Overlays: Sustainable Solutions for Resurfacing and Rehabilitating Existing Pavements (3rd edition). National Concrete Pavement Technology Center. NF EN 1542. July 1999. Products and systems for the repair and protection of concrete structures. Test methods. Measurement of bond strength by pull-off. NF EN 13036-1. September 2010. Road and airfield surface characteristics -Test methods -Part 1 : measurement of pavement surface macrotexture depth using a volumetric patch technique. NF EN 13036-4. March 2012. Road and airfield surface characteristics -Test methods -Part 4 : method for measurement of slip/skid resistance of a surface : the pendulum test. ASTM E 1911. Standard Test Method for Measuring Surface Frictional Properties Using the Dynamic Friction Tester.