Cassandre Rey-Thibault

Youenn Gourain Valérie

Does a multi-risk approach help in understanding urban networks

Reflections on entangled dynamics based on two French cities and a Turkish metropolis

IntroductIon

The Covid-19 global pandemic powerfully demonstrated the key role networks play during disasters, as both vectors for the propagation of outbreaks and as support for prevention measures. Airports are an emblematic example of this. From the start of the pandemic to date, airports have been the object of numerous measures (the closure of air borders, limits on access, prevention measures such as compulsory mask wearing, thermal cameras, health "passes," manual temperature taking, etc.). However, these new measures compound with the myriad preexisting norms and security measures, including: anti-terrorist measures for all airports (magnetic gates, detection of explosive materials, video surveillance, etc.); seismic risk measures for certain airports (evacuation zones at Istanbul airport); and, increasingly, marine flooding risk measures due to the rise in sea levels in coastal areas [START_REF] Yesudian | Global analysis of sea level rise risk to airports[END_REF]. The consequences of this superposition of measures merits further investigation.

II Crisis and uncertainty (Beraud, Durand) Although each disaster is unique and varies in form and scale, the dynamics that burden networks and exacerbate these situations are little documented.

As such, it is critical to develop approaches that connect urban networks and combined approaches to risks, that we call "multi-risk" approaches. This article documents the interrelationships between risk dynamics and urban network dynamics. We hypothesize that, by highlighting these interrelationships, we can better understand crisis and disaster situations. Revealing the many ways multi-risk situations and networks can overlap and become entangled is heuristically important for the risk and crisis field.

To this end, we will explore the interrelationships between risks and networks from three angles. The first is that of the moment of the crisis itself. As stated earlier, crises are often revelatory hitherto underdetected dynamics. In consequence, it is critical to observe how actors handle combined dynamics with regard to risks and networks. The second angle is multirisk perspective. Exploring networks through such approaches sheds light on potentially atypical relationships between local actors. The third angle involves including the multi-scalarity of networks and risks to better highlight the rapprochement (or sticking points) between different scales to better appreciate their interactions.

Empirically speaking, we used a multi-site approach commonly employed in the social sciences [START_REF] Bocquet | Les études multi-situées : entre pragmatisme et construction scientifique d'une posture[END_REF]. We analyzed three urban systems in which multi-risk practices and questions emerged: the French agglomerations of Nantes and Le Havre, and the city of Istanbul in Turkey (1). Though the investigations did not focus specifically on the interactions between networks and risks, several convergent examples emerged when we reinterpreted them in light of networks. As the multi-site approach did not call for strict comparison, we have provided an overview of the three case studies to explore multi-risk interactions on a generic object: networks. This allowed us to observe how these "network" objects impact multi-risk analyses and vice versa, by shifting our analytical focus from the institutional/political context to urban systems in dense agglomerations and negotiations between the actors, namely the national government and local actors.

After a short review of the literature on the conceptual diversity of multi-risk approaches and networks as a sociotechnical apparatus, we will look at the multi-risk concept as an operational practice used by urban actors in our three case studies. The third section explores a specific example in each of the three cities to highlight different ways multi-risk reflections can be incorporated into the design and operation of structuring networks and the flows generated by them. The final discussion underscores the added value of analyzing urban networks in a multi-risk perspective with regard to crises, multi-actor relationships and multi-scalarity.

MultI-rIsk approaches, networks and terrItorIes

Multi-risk approaches are relatively recent in literature on risks and disasters, but have become increasingly essential in the field. After exploring multi-risk approaches and proposing a generic definition of networks, we tested these concepts in the three territories and thus revealed the first dynamics and interrelationships.

Multi-risk approaches are in line with disaster and crisis management analyses, and encompass a wide variety of risks, not only "natural" ones. The Sendai Framework for Disaster Risk Reduction (2015Reduction ( -2030) ) suggests the need to consider different types of risks jointly, but does not specifically discuss their interactions (Gill, Malamud 2016). Such approaches are in line with "all-hazard" approaches, which propose generic responses in anticipation of unforeseen events during crises rather than hazard-specific scenarios [START_REF] Perry | Preparedness for emergency response: guidelines for the emergency planning process[END_REF][START_REF] Wise | Organizing for homeland security after Katrina: Is adaptive management what's missing?[END_REF][START_REF] Lakoff | Preparing for the next emergency[END_REF]. In this respect, it is more accurate to use the term "multicrisis" approaches than "multi-risk."

These approaches are akin to operational analysis methods for evaluating risks and their territorial relationships in greater depth with tools that allow for harmonized approaches. The result is a comparison or prioritizing of risks (Komendantova et alii. 2016). Gill and[START_REF] Galland | Hazard interactions and interaction networks (cascades) within multi-hazard methodologies[END_REF] suggest going beyond "multi-layer, single hazard" approaches to truly grasp the interactions between different hazards and territories. They lay out three types of relationships: triggering, increased probability and catalysis/impedance. The case of Fukushima is often cited as an almost "ideal type" disaster with cascading effects: an earthquake causes a deadly tsunami that sparks a nuclear disaster. The erraticism and indeterminacy of such disasters that transcend time and space require more horizontal and inclusive crisis management tools.

Secondly, multi-risk approaches also employ the notion of "systemic risks." This refers to emerging phenomena that broadly threaten fundamental societal systems (OECD, 2003). Poised between the analysis of complex systems and risks, the concept refers to the existence of risks that cannot be remediated using classical methods for calculating probability and of collective insurance [START_REF] Renn | Systemic risks: a new challenge for risk management: As risk analysis and risk management get increasingly caught up in political debates, a new way of looking at and defining the risks of modern technologies becomes necessary[END_REF]. The characteristics used to them are based on two key features: complexity and uncertainty. Risks are complex because reconstructing, modeling or understanding causal chains when multiple, undetermined factors are involved proves challenging [START_REF] Renn | The Systemic Risk Perspective: Social Perception of Uncertainty and Tipping Points[END_REF]. Consequently, deterministic approaches such as probability distribution are ineffectual when it comes to anticipating them (Van Asselt, Renn 2011). Like "multi-layer" analyses, systemic analyses highlight the "transboundary" nature of risks. This refers to the blurring of conventional limits and borders (sectoral and territorial) and the ability of risks to cut across distinct areas of society [START_REF] Schweizer | Systemic risks -concepts and challenges for risk governance[END_REF]. Systemic risks are characterized by their non-linear development, threshold effects and tipping points [START_REF] Renn | The Systemic Risk Perspective: Social Perception of Uncertainty and Tipping Points[END_REF]. Their unpredictability and irreversible consequences render their management complex. The specificity of systemic risks ("climate change" being a common example) has led some researchers to emphasize the need for "inclusive" approaches [START_REF] Schweizer | Systemic risks -concepts and challenges for risk governance[END_REF], particularly as regards decision-making processes.

A third, more recent approach is that of "compound," or combined, risks, which refers to the simultaneous existence of several distinct risks in a single area. This approach aims to show that seemingly unrelated crises can nevertheless strongly interact, often compounding and reinforcing like vulnerabilities. In such cases, the response to these risks must be all the more inclusive and flexible. While the Fukushima accident may seem emblematic of "multi-risk" situation and climate change emblematic of "systemic risks," it is the Covid-19 pandemic that truly has fueled the development of the "compound risks" concept, especially in thinking about relationships based on the consequences climate change [START_REF] Phillips | Compound climate risks in the COVID-19 pandemic[END_REF][START_REF] Kruczkiewicz | Compound risks and complex emergencies require new approaches to preparedness[END_REF].

This abundant semantic and conceptual offering shows the importance of a framework for understanding how risks interact when analyzed in combination. To respond to this issue, we used socio-technical approaches to better comprehend the way in which the definition of risks is built in close connection with their management options.

With regard to urban networks, the socio-technical approach considers how networks materialize in the urban space and contribute to forging the social, institutional and organizational structures present in them. Using this approach, we can also consider the material, organizational and symbolic conditions of these networks in the urban space. Numerous studies have shown that network dynamics occasion novel reconfigurations of the actors who rely on them, resulting in the rearranging of these urban systems. Notably, we wish to cite a special issue of the Flux magazine (guest edited by Sylvy Jaglin and Benjamin Steck (2008)) that explores how flowswhich result from interdependencies between components of the global system -require territorial and societal readjustment. The concept of infrastructure therefore offers an interesting critical approach for questioning their networking and societal functioning [START_REF] Vertesi | Seamful spaces: Heterogeneous infrastructures in interaction[END_REF][START_REF] Coutard | Au-delà de la ville des réseaux[END_REF]Chatzis et alii. 2017;[START_REF] Furlong | Small technologies, big change: Rethinking infrastructure through STS and geography[END_REF][START_REF] Furlong | Geographies of infrastructure II: Concrete, cloud and layered (in)visibilities[END_REF]. This approach emphasizes the importance of actors and their interdependencies, as well as the underlying issues present. Several researchers have shown that certain features of networks only come to light in the event of a problem (Graham, 2010; November, Gueben-Venière 2017). The concept of critical infrastructure also underscores large-scale failures with a high level of interconnectivity between the actors [START_REF]L'empreinte des risques : éléments de compréhension de la spatialité des risques[END_REF].

In cities, networks have become denser and increasingly interconnected, to the extent that in the event of a failure, they can paralyze an entire urban system [START_REF] Reghezza-Zitt | Territorialiser ou ne pas territorialiser le risque et l'incertitude. La gestion territorialisée à l'épreuve du risque d'inondation en Île-de-France[END_REF][START_REF] Reghezza-Zitt | Gestion de crise et incertitude(s) ou comment planifier le hors-cadre et l'inimaginable. Application aux crises résultant de crues majeures en Île-de-France[END_REF][START_REF] Little | Controlling Cascading Failure: Understanding the Vulnerabilities of Interconnected Infrastructures[END_REF][START_REF] Little | Managing the risk of cascading failure in complex urban infrastructures[END_REF] and propagate risks due to the strong actor interdependency [START_REF] Lhomme | Analyse spatiale de la structure des réseaux techniques dans un contexte de risques[END_REF]. Interdependencies and dysfunctions linked to networks have led researchers to use the term "network risk" [START_REF] Blancher | Risque et densité[END_REF][START_REF] Galland | Calculer, gérer, réduire les risques : des actions disjointes[END_REF] to describe disaster situations generated by hazards triggered by networks themselves.

We will not linger on the notion of network in this article. Rather, we simply wish to reiterate that the notion of urban networks is useful for shedding light on relationships of connectivity between risks and individuals, organizations and territories.

Let us now explore how multi-risk approaches, which are included in territorial risk analyses, have diversified since the late 1990s. These approaches first consider the spatiality of risks (diffuse, network, localized-territorialised) [START_REF] Galland | Hazard interactions and interaction networks (cascades) within multi-hazard methodologies[END_REF] and go on to highlight the multifaceted relationships between risks and territories. This facilitates an understanding of accumulation, transfer and diffusion phenomena between risks [START_REF]L'empreinte des risques : éléments de compréhension de la spatialité des risques[END_REF]. Thus, it is less a question of acquiring IV Crisis and uncertainty (Beraud, Durand) multi-risk operational analysis tools than of using multi-risk approaches to interpret the relationship dynamics between territory and risks. Finally, our goal is to better understand how the multi-risk question emerges locally.

the dIversIty of MultI-rIsk practIces In urban areas

Many studies have shown that, because of their density, the risk potential in urban areas is higher than elsewhere [START_REF]Risques naturels et croissance urbaine : réflexion théorique sur la nature et le rôle du risque dans l'espace urbain[END_REF][START_REF] Blancher | Risque et densité[END_REF][START_REF] Chaline | La ville et ses dangers : prévention et gestion des risques naturels, sociaux et technologiques[END_REF][START_REF] Maury | Les risques urbains[END_REF]. In urban spaces, certain risks transcend their category type. For this reason, some researchers speak of "hybrid" risks [START_REF] Reghezza-Zitt | Géographes et gestionnaires face à la vulnérabilité métropolitaine. Quelques réflexions autour du cas francilien[END_REF]. Taking only the Ministry of the Environment's legal definition of "major risks," the Le Havre conurbation, for instance, has three risk prevention plans (PPR): flooding, technological and coastal. However, certain local authorities took on new responsibilities and risk categories above and beyond the regulatory obligations in force starting in the 1990s [START_REF] Gralepois | Face aux risques d'inondation : entre prévention et négociation[END_REF]. The greater metropolitan areas (2) of both Nantes and Le Havre created new services to explore risks, building knowledge and developing specific tools such as population alert systems, internal emergency coordination platforms, etc. Contrary to the national government's environmental services, whose definition of regulatory risks is category based (major risks are essentially based on criteria of probabilities), local governments offer an endo-urban, or integrated, definition of risks [START_REF] Boin | Organising for future crises: the case of integrated risk management in French cities[END_REF], following Mathilde Gralepois' concept. In other words, the definition of risks is contingent on urban systems as functional, "just in time" spaces [START_REF] Gralepois | L'agglomération à flux tendus. La politique de sécurité civile française au secours des pannes urbaines[END_REF]. This definition combines the concept of risk with the "crisis"/civil safety approach applied by the Ministry of the Interior, which is responsible for relief organization and planning. The risks borne are therefore broad, and include both "major risks" co-determined with the national government as well as fires, major road accidents, storms, urban runoff, epidemics, etc.

In Turkey, the term "risk" (risk) has its origins in the Arabic term "razk," which refers to a blessing. However, this term is rarely used in Turkish planning or in risk management tools. Instead, the term for disaster (afet) or danger (tehlike) is preferred, showing that "risk management" refers directly to the event itself. The idea of risk as a potentiality or that a situation need not become a disaster is relatively recent. The notion of risk has only come into use in the past decade, following the implementation of the Sendaï framework for Disaster Risk Reduction in 2015, when AFAD (Afet ve Acil Durum Yönetimi Başkanlığı, Disasters and Emergency Management Presidency) shifted from "crisis management" (kriz yönetimi) to "risk management" or "reduction" (risk yönetimi or azaltma) (3). This explains why the institutions that manage risk and crisis are named according to the disaster. In the Turkish context, one effectively speaks of "disaster risk" (afet riski), and not simply "risk." As risk studies in Turkey think in silos, risk and crisis management institutions nonetheless must manage several categories of risk at the same time. At the government level, one of AFAD's jobs is producing risk maps (tehlike haritası) on specific hazards (earthquakes, floods, and tsunamis), which increase the data from various scientific expertise studies. In Istanbul, the Central Disaster Coordination Directorate (Afet Koordinasyon Merkezi Müdürlüğü) is linked to the Istanbul Metropolitan Municipality (Istanbul Büyükşehir Belediyesi) and is charged with attenuating threats through risk prevention and planning. This directorate is required to cooperate with the Istanbul Transport Directorate (IETT, İstanbul Elektrik Tramvay ve Tünel İşletmeleri) and the office of water management and pipes (ISKI, İstanbul Su ve Kanalizasyon İdaresi).

Despite differences in size and radically different local contexts, the advantage of comparing the cases of Le Havre and Nantes with that of Istanbul is the possibility of illustrating the issue of networks based on two conceptions of the multi-risk approach. Three key practices were identified in these urban spaces: 1) a flexible definition of risks, 2) the sharing of management tools, and 3) reflections on the interactions between risks.

In the three urban areas studied, risk actors were found to have a flexible definition of risks. In Nantes and Le Havre, local governments intervene in a variety of "disturbances" in urban operations (collapses of underground cavities, pollution, heat waves, the flu, etc.). In particular, officials in Nantes are summoned for so-called "public safety" missions, for which their emergency and crisis response systems are reused: emergency shelters, local feedback, mobilization and coordination of volunteers, etc. While reluctant to fully embrace a decompartmentalized approach (which includes terrorist risks and attacks), they were widely mobilized to help manage the "Covid crisis." In Istanbul, defining public policies based on potential disasters (afet) also elicits a flexible definition of risks. This definition covers broad range of notions and can be subject to interpretation in the framework of planning or crisis management systems. Some actors take advantage of the intricate nature of the term "risk" to justify their decisions.

Furthermore, these local actors are adopting management practices that aim to transcend segmented regulations and create greater coherence in public action as regards risks. In France, this means similar tools used for different types of risks. This was the case for the concept of "major risks," and led to the creation of systems based on a similar prevention (Prevention Plans -PPR) and crisis management planning (ORSEC), which offers a common response system for all types of events. Local actors are deepening this logic by comparing these systems and creating measures that are transferrable to several types of risks (global risk mapping, multi-risk alert systems, etc.). The multirisk approach therefore considers and acts on the "generic" characteristics of risk situations. The principle was similar in Turkey. In urban planning, tools utilize the notion of "disaster reduction" (afet azaltması) or "disaster management" (afet yönetimi), in which risks are amalgamated, though they are studied separately and more or less in depth depending on the location. Thus, Law No. 6306 of 2012 on the transformation of disaster risk areas and micro-zoning for urban transformation (2018) applies the concept of disaster generically to situations that can be potentially disastrous.

Multi-risk approaches attempt to go beyond mere superposition when different regulations by risk type apply (for example, when different PPRs are implemented in Le Havre). Local actors are particularly attentive to the cohabitation of different regulations and to the conjunction of two or more risks. They are especially interested in "NaTech" risks and the potential impact of flooding on local industries, as well as critical crisis management infrastructure. For Istanbul, the blanket term "disaster" culminates in a uniform response to risk identification in urban areas in the form of urban transformation (kentsel dönüşüm).

The multi-risk approach, however, is a way of challenging the implementation of certain projects. Recent publications by scientists, civil society and even the Istanbul Metropolitan Municipality cross-compare risks in order to highlight the incompatibility of certain urban projects (the new Istanbul canal project, for instance) or public policies (urban transformation) with preexisting environmental, social and/or economic issues (Kuzucu et alii. 2021;Görür et alii. 2020).

Implementing these multi-risk approaches nevertheless gives rise to obstacles: while many systems focus on a single risk, the timing of different procedures may not be compatible. More importantly, the recommendations and operating principles emitted by different services can prove contradictory. In France, connecting various risk and crisis management procedures is not an easy task (Rey-Thibault, 2021). Moreover, risk spatialization systems do not aptly reflect the complexity of risks and their spatial interconnections [START_REF]What does 'mapping risks 'mean in a risk society?[END_REF]. Similar observations have been made with regard to crisis management. Servane Gueben Venière shows the usefulness of certain cartographic projection tools for linking heterogeneous objects in the space and time of the crisis. This has helped highlight the domino effects of certain dysfunctions (Gueben Venière, 2019). Finally, a point was raised through the prism of the sociology of science [START_REF] Akrich | La construction d'un système socio-technique[END_REF] regarding the importance of investigating how actors translate crisis management from disparate experiences and cultures into a common language. With inherent processes and tools that unify actors from different fields (scientists, planners, builders, real estate companies), urban planning and development faces challenges when it comes to designing cities. Nevertheless, managing risks, observing how they unfold and understanding their interrelationships in the urban space can generate controversy due to the potentially divergent interests of the actors involved and their means of action. In Turkey, an examination of seismic risk reduction policies for buildings reveals adjustments within the framework of decision-making aid mapping systems. These adjustments have generated unforeseen risks during the transformation of certain neighborhoods [START_REF] Gourain | Cartographier le risque et produire la ville : le cas du microzonage sismique à Istanbul, Cartes & géomatique[END_REF].

Multi-risk approaches applied in urban areas confirm that urban actors have the capacity to conceptualize and plan for unforeseen interactions between multiple risks. How does the management of material networks resonate with networks of actors and risks? case studIes: three urban networks favorable to MultI-rIsk approaches

Le Havre: the vulnerability of electrical networks in an industrial port city

In France, there is no formal framework for addressing the issue of vulnerability of networks and infrastructures (transportation, energy, water, sanitation, etc.) at the infra-urban scale. Most regulations regarding electricity concern transportation VI Crisis and uncertainty (Beraud, Durand) infrastructure, and not low-voltage distribution. At the national level, Enedis, the French electricity distribution grid operator, revisited its operational crisis management capacities through the development of a specific service, Rapid Electricity Intervention Force (FIRE (4)). However, network security is a recent endeavor [START_REF] Derdevet | La résilience des réseaux d'électricité face aux aléas climatiques et aux nouveaux paradigmes[END_REF]. Thus, use of the "risk" concept, as well as risk-based methods and approaches in these urban networks is based on local initiatives.

In Le Havre, the issue of network vulnerability surfaces sporadically through the aggregation of initiatives in collaboration with the inter-municipal risk service, the Major Risks Information Department (DIRM) and Enedis local representatives. Early collaboration between the risk department and Enedis dates back to 2015, when a local power outage resulted in a potentially dangerous industrial incident. The incident involved a company in the industrial port area that lost control of its production processes and risked emitting ammonia fumes. The director of the DIRM was nearly obliged to sound warning sirens to alert the population. As part of the feedback organized by the prefecture's crisis center, he contacted Enedis' local representative to propose collaboration. They began by sharing their respective crisis plan models and suggesting means to improve them. The scope of the risk situations discussed was broad, and included storm risks, which potentially could bring down electrical network infrastructures. The FIRE relies on local relays for more effective intervention. The DIRM tried to sensitize and mobilize the municipalities -especially peri-urban ones -to ensure their role as intermediaries. The collaboration also focused on the domino effects on urban infrastructure (sewage and water networks, in particular), to improve temporary energy self-sufficiency capacity in the event of a power outage. Most notable, however, was another major and rapidly emerging local risk -that of marine flooding. As part of a Coastal Risk Prevention Plan (PPRL) prescribed in 2015 for the Le Havre conurbation, the modeling of hundred-year floods was the occasion to consider the vulnerability of certain urban and port infrastructures. After an initial experimental study to assess the susceptibility of a strategic lock in the Grand Port, the local authority began negotiating a work program with Enedis to improve the resilience of existing electrical substations.

In this case, the metropolitan risk service, the DIRM and the local representative of Enedis opted for a relatively generic definition of risks, allowing them to alternate between a "multilayer" and a systemic approach to risks. From this flexible definition, local actors are envisaging multiple entry points between the territory and urban electrical networks at different scales (figure 1). Such collaboration has led to greater awareness of the symbiotic relationship between different "disasters" and the multifaceted relationships between risk and urban networks. In Istanbul, we observed a very different dynamic of the multi-risk problematization.

Istanbul: When managing citizen evacuation raises issues during a pandemic

In early 2019, the metropolitan municipality launched the "earthquake parks" (deprem parkı) project. This projected was created to designate specific parks as civilian evacuation areas in the event of an earthquake in the framework of the local town plan. These parks were also meant to accommodate infrastructure for managing and regulating seismic events (tents for civilians, logistics buildings, drinking water and electricity supply, and a temporary canteen). Topkapı Park on the Golden Horn near the historic center was the first such earthquake park. Deniz Gezmiş Park, which takes its name from an emblematic, far-left Turkish activist, was the second. While these parks have seen certain fixings and fittings (notably in the form of signage), the strategy for their legal conversion is mainly political and rooted in conflicts of interest and use between Recep Tayyip Erdoğan's central government and opposition mayor Ekrem Imamoğlu, who heads Istanbul's Metropolitan Municipality. The government's right to transform the urban space without coordination with the Metropolitan Municipality has pushed the latter to stake a claim to protect its spaces. Public spaces in Turkey, and Istanbul in particular, are often fodder for conflicts of interest between actors due to significant land speculation. In the past, this has led to controversies that were then spearheaded by "spatial justice" associations (mekânda adalet). It has also given rise to protest movements. The Taksim Square protests (2011) against the building of a shopping center and the densification of the emblematic square in Istanbul were illustrative in this sense. Since the earthquakes in the Marmara region in 1999, several risk management institutions (AFAD and AKOM) have pleaded for the opening of public spaces as evacuation zones. Yet, the measures implemented by the municipalities in favor of such areas have often failed. Thus, the objectives of opening the Zeytinburnu pilot zone (figure 2) in a neighborhood close to the Golden Horn did not have the expected results due to intense real estate pressure.

Figure 1: Multi-risk approaches to urban networks in the Havre urban conurbation

Topkapı Park is coveted by developers due to its proximity to the historic and touristic center and to the Zeytinburnu district. The same is true for Deniz Gezmiş Park in the Ataşehir district, the home of Istanbul's future financial center in the Asian portion of the city. This second park is unique in that it is located near a dammed watercourse, which poses soil liquefaction issues. As they are close to the fault line, these areas will likely be affected by a strong earthquake in the coming years. These earthquake parks are geared to the highly specific management of seismic risks. Effectively, the aforementioned facilities, toponyms and communication the municipality has implemented concerning these parks attest to this. Moreover, the civilian evacuation plan was developed conjointly by AKOM, the Istanbul disaster coordination agency, and civil and transport engineers to consider road obstructions linked notably to debris from buildings and potential water and electricity network malfunctions (Figure 2).

VIII Crisis and uncertainty (Beraud, Durand) However, the Covid-19 pandemic has brought awareness of new risks (namely health risks) and fostered greater vigilance as regards public spaces and communication channels, with compulsory gauges, social distancing and hygiene devices to limit disease transmission in a dense setting. The fear of a possible cluster during a pandemic thus combined with the pressure of evacuating individuals in the event of an earthquake. The January 2020 earthquake in Izmir demonstrated the incompatibility of managing two concomitant crises, according to reports by the Turkish Medical Association (TTB) who were present on the scene. "Measures such as physical distancing, masks and hygiene rules are disrupted in rescue areas and [during] the transport of injured persons," (DW, 02/11/2020). Emergency services were effectively forced to juggle between precautions to avoid virus transmission and expeditiously assisting earthquake victims. The example of earthquake parks in Istanbul helps emphasize the need to develop flexible urban systems to manage multiple crises through the prism of multi-risks, hitherto approached as "multi-layers."

Nantes: Urban networks in flood zones with other risks

As we saw in the case of Le Havre, Enedis has prioritized the integration of storm-related issues. The operator's first "climate hazard" plan was mainly designed to reduce the vulnerability of overhead power distribution systems during storms. Between 2006 and 2016, the company buried overhead networks, particularly in wooded rural areas. However, the strategy was called into question in light of multi-risk approaches and the issue of climate change [START_REF] Derdevet | La résilience des réseaux d'électricité face aux aléas climatiques et aux nouveaux paradigmes[END_REF].

At the national scale, the company is reflecting on the resilience of its network and has identified multiple vulnerabilities: in addition to overhead networks' susceptibility to storms and snowfall, it has also identified underground networks' vulnerability to high temperatures and transformer stations' vulnerability to flooding. The latter is being taken more seriously by the inter-municipal risk service for Greater Nantes, which has been concerned about the potential consequences of flooding on urban infrastructure since 2010. After several unsuccessful attempts with the electric company, the service finally obtained a statute for a vulnerability analysis for the PPRi for the Lower Loire. Hence, it was the State that obliged the company to analyze and communicate on its findings regarding vulnerability to flooding. This statute was the fruit of close negotiations with the company. Initially, the State and community services wanted to mandate unilaterally that all electrical substations be protected from flooding. Given the costs of such an operation, the company argued that exposure to water does not necessarily equate to vulnerability; rather, situations must be analyzed on a caseby-case basis. The metropolitan service did not intend to stop there. Once the vulnerability study was complete, it proposed that a working group comprised of all of the urban providers be formed to study the domino effects of their failures in the event of flooding. The true goal is planning operations to reduce the vulnerability of these networks.

Most importantly, the issue of maintaining networks is particularly relevant at a time when renewal projects in floodprone areas are taking shape in these agglomerations. Several neighborhoods vulnerable to 100-year or 1000-year floods have effectively been targeted for development projects to make them denser and create new urban centers through the construction of new residential neighborhoods (the Chantenay district, Nantes Island hospital center, and Pirmil-les-Isles district, for instance). The federal government only authorized the redevelopment of these neighborhoods on the condition that they function "in a way as to reduce vulnerability to flood risk in order to increase the territory's resilience to this risk" (regulation of the PPRi the Lower Loire). The operationalizing of this resilience notably occurs through the designing of networks that "remain operational during flood periods." The document even encourages the deployment of overhead networks. Network "resilience" therefore means different things to different actors. Enedis' strategy effectively consists in not protecting the low-voltage distribution network from flooding, but rather in equipping it with warning devices that cut off the network in the flooded area as a precautionary measure. On the other hand, key infrastructures can be waterproofed, thus limiting potential damage and ensuring their rapid reactivation once the flood risk has subsided. Again, the multi-risk approach is based principally on the superposition of different layers of hazard (multi-layer) whose possible interactions are well thought out. While overhead installation of distribution networks is possible in new built areas, the issue is becomes more complex in a context of urban redevelopment with preexisting networks.

Above all, the resilience of a neighborhood's electrical network presupposes the resilience of the entire urban electrical infrastructure, and the transportation network in particular. This is far from being the case, as the vulnerability study at the urban scale is not yet broken down into operations to reduce vulnerability. In this situation, Enedis can encourage measures geared towards the creation of electricity autonomy in the flood-prone neighborhood (as it already does for sensitive equipment such as industrial operators). This can be done using specific resources such as generators, or through decentralized productions such as photovoltaic panels, which can operate independently. The Nantes conurbation seemingly has not envisaged such a scenario. Adapting the electrical network for the event of potential flooding therefore is not simple and challenges the systematic burying of network distribution lines.

dIscussIon

How do multi-risk approaches change the analysis of the links between urban networks and disasters in these three cases? While crisis management underscores the need to consider multiple combinations between multi-layered, interrelated systemic risks, the inclusion of risks in networks allows for consideration of multi-risk thinking through the prism of the actors and over diverse time frames.

• Crisis can be key opportunities for highlighting the multirisk dimensions of networks. The challenge for actors is to include them in a long-term operational framework.

X Crisis and uncertainty (Beraud, Durand)

Whereas the pandemic brought out the multi-risk dimension of the network of parks in Istanbul, it was a potential ammonia leak that incited collaboration around the vulnerability of the networks in Le Havre. The initial power outage resulted from a voluntary interruption by Enedis resulting from high temperatures that disrupted the national grid. This led to a local crisis around the control of toxic industrial processes and, potentially, the immediate confinement of the population. From this first multi-risk experience (corresponding to a cascade diagram where vulnerability of the electrical network appears systemic), local actors conceptualized a multi-risk vision of the network by associating other dimensions (flooding, storms, etc.). In addition to simply identifying cascading effects, they also attempted to develop a more transversal understanding of risks.

Nevertheless, the example of Nantes shows that multi-risk issues can arise outside of specific scenarios that constitute "crises" for local actors. The choice between overhead and underground systems in flood zones emerges when the urban electricity network is challenged by divergent conceptualizations of risks.

A comparison of the case studies shows that, while multirisk dimensions exist in urban planning, their coexistence can be fraught with tension. At times, they are even obliged to compete within the framework of spatial planning, with the final project being comprise between them. The choice between overhead and underground electrical networks in Nantes could engender different forms of vulnerability depending on the phenomena or space, and results in different risk layouts. The same is true of earthquake parks in Istanbul, for which the urban planner from the urban transformation department of the Istanbul Metropolitan Municipality acknowledges not having counted on the risk of a pandemic. Effectively, the shelters turned out to be undersized with respect to social distancing (sosyal mesafe). Here, the underlying issue of creating an open public space guided the program and project design. It turns out that seismic risk prevention (deprem odaklı riski azltması) carried more weight than health risk when defending the project to the Turkish Ministry of Urban Planning and the Environment.

The inclusion of multi-risk management in operational systems runs up against several obstacles. In Istanbul, the conversion of the first two public spaces into earthquake parks (Deniz Gezmiş Park and Topkapı Park) went smoothly, with the installation of modular infrastructure for the evacuation of residents. Their design incorporated modulation and flexibility capacities to quickly accommodate for higher densities, manage relief and provide support for disaster victims for periods of several weeks. This spatial flexibility was scalable in terms of the flows of people and uses in the event of disruption. Yet, the Ministry of the Environment and Urban Planning regularly pushes back attempts to include earthquake parks in the local urban plan (imar planı) due to conflicts of interest and use around certain parcels because of speculation. Blockages also make these evacuation spaces vulnerable to urban transformation processes, as they are still public land reserves for the central government, which promotes their sale to developers. Similarly, Enedis dedicated its efforts almost exclusively to storm risks for some time: nowadays, it can more easily integrate other types of hazards into its operational crisis management systems (FIRE, local correspondents, etc.) than in the materiality of the network itself.

While crises can be ocpportunities for underlining the multi-risk scenarios in which networks are entangled, they rely on other mechanisms and dynamics to make them sustainable.

• Exploring the network from a multi-risk perspective reveals new networks of unexpected actors The inherent nature of networks' development allows for alliances with new actors with different practices. These practices add other risk dimensions to network design. Certain networks that were not designed using multi-risk logic can nonetheless generate alliances capable of highlighting new dimensions. The case of Le Havre is an obvious example of multiple actors being brought together through the electricity and multi-risk network association (elected officials, agents of small municipalities, network operator compagnies who are dependent on the electricity supply, ports, etc.). In the case of Istanbul, reflection on earthquake parks comes from working groups that unite various scientific actors (geophysical engineers, geomaticians, etc.), urban planning, and disaster management organizations (afet yönetimi), including AFAD at the national level and AKOM at the metropolitan level.

In Istanbul, three other levels of alliances were more original in the context of this project. To begin, earthquake parks were the initiative of Tayfun Kahraman, who recently headed the urban transformation directorate of the Istanbul Municipality under the new opposition party mayor, Ekrem Imamoğlu. They quickly showed their willingness to involve civil society in the designing of development and risk management systems. This was particularly the case for associations of first responders in the event of an earthquake. The second is an alliance with other private organizations mobilized to finance the establishment of earthquake parks selected by the municipality based on more "holistic" criteria. As such, the new mayor has supported the joint-stock company Istanbul Imar A.Ş, which conducts urban development projects, to follow indications of risk prevention and to serve the population. Requests for support from private companies is a way for the project initiators to legitimize the inclusion of parks in the local plan via infrastructures: "The inclusion [of parks] is not easy because the budget is almost finished. He [Tayfun Karaman] called upon our people in Turkey. [...]. We are trying to set up the shelter zones [...] and then we will write the rules. They won't be able to do anything anymore. We'll put up the flag: these are shelter areas, you can't touch them anymore," (interview with D., urban planner at the Urban Transformation Directorate of the Istanbul Metropolitan Municipality, 02/11/2020). Finally, the district municipalities (ilçe belediyesi) welcomed the foundation of these parks as a means of creating links between the inhabitants and disaster education associations, where other official spaces have been less successful.

The multi-risk approach allows for the involvement of more actors, which in turn makes possible the implementation of the partners' network to ensure the sustainability of their spatial inclusion in urban networks.

• The multi-scalarity of networks at the local level allows for the creation of operational links between risk and crisis, and between risk prevention and crisis management more generally.

"When small projects can become big without changing the nature of the project, we call that design feature "scalability," [...] "Scalable projects are those that can expand without changing." [START_REF] Tsing | On Nonscalability. The Living World Is Not Amenable to Precision-Nested Scales[END_REF]). Defined at multiple scales both locally and generically, urban networks seem eminently scalable. Blackouts and general power outages notably demonstrate scalar interconnections within the network.

However, exploring the multi-risk dimension of urban networks nuances this understanding. The creation of earthquake parks in Istanbul or the protection of sensitive electrical infrastructure (electrical substations, locks) against flooding in Le Havre and Nantes are local measures that sometimes are extended to the agglomeration at large. Seven earthquake parks have been created by the Istanbul municipality but have yet to be included in the local plan (as of May 2022). The protection of electrical infrastructure in Le Havre was forged around a few strategic sites (a lock and the town hall) but the measure is far from being widespread. Risks do not take the same form from one space to the next because of the many translations they undergo through actors' management of them [START_REF]Les territoires du risque : le risque comme objet de réflexion géographique[END_REF]. While the case studies essentially focused on the micro scale, shifting them into the macro scale raises the following question: can these measures and projects be considered as levers to facilitate crisis management at the scale of global agglomerations? The cases provide contrasting answers. Ultimately, it is by anticipating urban crises (earthquakes, major flooding, etc.) that urban networks transform their capacity to manage one or more risks simultaneously. In this sense, networks contribute to the "territorializing" of crisis management and can perpetuate this tendency over time, and thus aid in the shift from "crisis" to "risk."

However, it turns out that these ad-hoc facilities, even when seen through the multi-risk prism, cannot extend their reasoning to entire agglomerations. The earthquake parks of Istanbul cannot realistically shelter millions of inhabitants in the event of a strong earthquake. On the other hand, the myriad forms of action and risks undoubtedly require a multitude of scenarios that are sufficiently flexible to take into account the potential interactions between risks that are still largely unknown.

Finally, multi-risk analyses themselves can be enriched by introducing urban networks. While "multi-layer" and "systemic" approaches to risks -forms that we have identified in our case studies -view their interrelationships differently, both can benefit by adding a distinct perspective on networks. Whereas "multi-layer" approaches struggle to identify the interconnections between different risks in the same territory, networks offer an element of continuity and flow. Similarly, while systemic risks are difficult to grasp, using urban networks as a jumping off point allows us to explore the interactions and interconnections between several risks simultaneously (figure 3).

conclusIon

Exploring the relationships between risks in the context of urban networks shed light on several aspects of the dynamics between networks and disasters. To begin, we observed that risks seem to be more entangled than not. This entanglement reflects complex situations that are challenging for actors to manage, especially given that crisis management can contradict the means used to manage a simultaneous crisis in the same space.

XII Crisis and uncertainty (Beraud, Durand) Thus, risk management often seems to struggle to fit into socio-technical networks such as urban plans. Moreover, integrating multi-risk logic in the long term is difficult due to actors' recalcitrance, conflicts of interest, or even incompatibility between the measures taken to respond to risks. This entanglement is also multi-scalar given that certain crises, such as blackouts, are revelators of scalar interconnections. Within these interconnections, unexpected actors and unforeseen risks appear as they circulate through physical networks and in those generated by the assumption of risks. What plays out in these dynamics is an operational rapprochement between risk prevention and crisis management that is difficult to implement.

Our analysis has demonstrated the importance of context, actors and spaces in their ability and willingness to take into account multiple risks. The generic dimension of networks has allowed us to compare three radically different cases. However, their spatial dimensions reflect much more complex situations that require actors to adapt in the time and space context. In such cases, the density of networks can trigger a broader crisis, as the Covid-19 pandemic has taught us.

acknowledgeMents

We would like to thank the people we met and interviewed during the field surveys in Istanbul, Nantes and Le Havre. We also thank the reviewers of FLUX magazine for their comments and recommendations. (2) Because of the large high number of French communes, the latter are strongly encouraged to collaborate "intercommunally," which includes the corresponding larger urban areas.

Theses intercommunes constitute a specific type of local government that is independent and complementary to communes.

Cassandre Rey-Thibault, Youenn Gourain, Valérie November -Does a multi-risk approach help in understanding urban networks? Reflections on entangled dynamics based on two French cities and a Turkish metropolis

The Covid-19 global pandemic powerfully demonstrated the key role networks play during disasters, as both vectors for the propagation of outbreaks and as support for prevention measures. This article links urban networks with a combined approach to risks, which we will call multi-risk approaches.

In particular, it aims to examine the interrelations between risk dynamics and urban network dynamics based on three urban systems in which multi-hazard practices and issues emerge: the French cities of Nantes and Le Havre, and the Turkish metropolis of Istanbul. The exploratory analysis highlights three notable findings: firstly, that crisis episodes can be excellent revelators of the multi-risk dimensions of networks; for actors, the challenge is including them in a long-term operational framework. Secondly, the multi-risk perspective reveals new and often unexpected networks of actors. Thirdly, the multi-scalarity of networks at the local level will likely allow for the creation of operational links between risk and crisis, and between risk prevention and crisis management more generally. We therefore conclude that the hybridization of network dynamics with those of risks reveals the existence of "entangled" risks that merit further exploration.

Figure 2 :

 2 Figure 2: Deniz Gezmiş Park, Istanbul. Modularity before and during crisis management

Figure 3 :

 3 Figure 3: The role of networks in multi-risk analyses

notes ( 1 )

 1 These fields are explored in greater depth as part of two longitudinal thesis surveys through semi-structured interviews and observations with urban risk and crisis management actors. 80 interviews were conducted in Istanbul from August 2019 to August 2021; 27 interviews in Nantes from July 2018 to May 2020, and; 45 in Le Havre from July 2018 to May 2020.

  Research Professor at LATTS CNRS.She is specialized in urban, environnemental, and natural risks, and their relationship with territories. She is especially interested in the continuity between risks and crises, mainly in urban areas.valerie.november@enpc.fr

		Youenn Gourain is a PhD candidate at LATTS and
		an associate researcher at the French Istanbul of
		Anatolian Studie (IFEA). His works focus on the
		coevolution between risk and urban space,
		Turkey being his main fieldwork.
		youenn.gourain@enpc.fr
	Cassandre Rey-Thibault is a PhD candidate at LATTS, and a
	visiting fellow in the Program on Science, Technology and	Valérie November is a
	Society at the Harvard Kennedy School. She studies continuities
	and discontinuities between risk prevention, emergency
	management and disaster risk reduction policies, mainly on
	francophone countries.
	cassandre.rey-thibault@enpc.fr

Cassandre Rey-Thibault, Youenn Gourain, Valérie November -Une approche multirisque aide-telle à comprendre les réseaux urbains ? Réflexions sur des dynamiques enchevêtrées à partir de deux ag- glomérations françaises et une métropole turque

  Key words: Socio-technical approaches; local actors; crises; multi-risk practices; urban networks; entangled risks La pandémie mondiale de la Covid-19 a agi comme un puissant démonstrateur du rôle central des réseaux dans les catastrophes, à la fois comme vecteurs de diffusion de la crise, et comme supports de mesures de prévention. Cet article propose une réflexion qui articule réseaux urbains et approche combinée des risques (que l'on peut synthétiser par approches multirisques). Il vise en particulier à examiner les interrelations entre dynamiques de risques et dynamiques de réseaux urbains, en s'appuyant sur trois systèmes urbains, dans lesquels émergent des pratiques et des questionnements multirisques : les agglomérations françaises de Nantes et du Havre, et la métropole d'Istanbul, en Turquie. L'analyse exploratoire fait ressortir trois résultats : premièrement que les épisodes de crise peuvent constituer des moments privilégiés pour faire apparaître les dimensions multirisques des réseaux. L'enjeu pour les acteurs est alors de les inscrire dans un cadre opérationnel et sur le long terme. Deuxièmement, la perspective multirisque donne à voir de nouveaux réseaux d'acteurs insoupçonnés. Troisièmement, la multi-scalarité des réseaux à l'échelle locale est susceptible de créer des liens opérationnels entre risque et crise, entre prévention des risques et gestion de crise globalement. Nous concluons ainsi que le croisement des dynamiques des réseaux à celles des risques fait apparaître l'existence de risques « enchevêtrés », qui méritent d'être approfondis. Mots-clés : approches socio-techniques, acteurs locaux, crises, pratiques multirisques, réseaux urbains, risques enchevêtrés

© Université Paris-Est Marne la Vallée | Téléchargé le 24/11/2023 sur www.cairn.info (IP: 194.5.53.146) © Université Paris-Est Marne la Vallée | Téléchargé le 24/11/2023 sur www.cairn.info (IP: 194.5.53.146)

© Université Paris-Est Marne la Vallée | Téléchargé le 24/11/2023 sur www.cairn.info (IP: 194.5.53.146) © Université Paris-Est Marne la Vallée | Téléchargé le 24/11/2023 sur www.cairn.info (IP: 194.5.53.146) Crisis and uncertainty (Beraud, Durand) V

© Université Paris-Est Marne la Vallée | Téléchargé le 24/11/2023 sur www.cairn.info (IP: 194.5.53.146) © Université Paris-Est Marne la Vallée | Téléchargé le 24/11/2023 sur www.cairn.info (IP: 194.5.53.146) Crisis and uncertainty (Beraud, Durand) VII

© Université Paris-Est Marne la Vallée | Téléchargé le 24/11/2023 sur www.cairn.info (IP: 194.5.53.146) © Université Paris-Est Marne la Vallée | Téléchargé le 24/11/2023 sur www.cairn.info (IP: 194.5.53.146) Crisis and uncertainty (Beraud, Durand) IX

© Université Paris-Est Marne la Vallée | Téléchargé le 24/11/2023 sur www.cairn.info (IP: 194.5.53.146) © Université Paris-Est Marne la Vallée | Téléchargé le 24/11/2023 sur www.cairn.info (IP: 194.5.53.146) Crisis and uncertainty (Beraud, Durand) XI


Elodie Ehrmann

Feghali Sara

Marie Bernabeu

Yannick Tillier

Sara Feghali

Finite Element Modeling of The Masticatory System: Application To Bruxism

Introduction

Bruxism is responsible for temporo-mandibular joint (TMJ) disorders and tooth wear [1]. This work is part of a larger project that aims to better understand the biomechanical impact of such a parafunction on the TMJ and teeth, by comparing two finite element models (FEMs) of the masticatory system of a patient, before and after an oral rehabilitation. Retrieving the geometry of the different tissues from medical images is relatively common. The originality of this work is to propose to use an extraoral device (Modjaw® [2]) to record the kinematic data of a patient and apply them, as a loading condition, to the FEMs.

Materials and Methods

A FEM corresponding to the situation before oral rehabilitation of a 37-year-old male patient with mild bruxism was created. Geometric data were obtained after the alignment of multimodal medical images (CBCT, MRI, 3D scan acquisition of a dental arch plaster model). The bones, the soft tissues, and the teeth were modelled (segmented and meshed with Mimics (Materialize®), and transferred to the FE analysis software FORGE (Transvalor®). Mechanical properties were assigned to each anatomical structure (all of which are considered linear elastic materials). Particular attention was paid to the application, as a loading condition, of the real kinematics of the patient. For this purpose, he was asked to perform 3s grinding movements (a right and then left latero-deviation). The Modjaw® medical device was used to record, as a function of time, the coordinates of 3 points denoted I, RC and LC on Fig. 1 and corresponding respectively to the inferior incisal edge point, and 2 points away from the right and left condyles. Three rigid objects were then created in the FEM and assigned the same coordinate evolutions to set the mandible in motion.

Results

The von Mises stress distribution, given by the FEM, on the teeth and in both joints during a grinding cycle was analysed and compared to the experimental contact areas given by the Modjaw® device (Fig. 2).

Discussion and Conclusions

The similarities observed seem to confirm the accuracy of the chosen approach, although we can note a very high level of stress at the I-point used to move the mandible. It is interesting to note that tooth 44 at the neck of which a stress peak is observed numerically (red circles in Fig. 2) is slightly worn in the patient and that gingival recession was clinically observed on the facing tooth 14 (red arrow in Fig. 2).

Figure 1 :

 1 Figure 1: Application in Forge® of the boundary conditions recorded by Modjaw®

Figure 2 :

 2 Figure 2: Right lateral excursion. Comparison of von Mises stress distribution (FEM, right) vs dental contact areas (Modjaw®, left). Teeth 44/14 in red.


Arnaud Quérel

Denis Quélo

Yelva Roustan

Anne Mathieu

IMPLEMENTATION OF A NEW IN-CLOUD WET DEPOSITION SCHEME INTO THE LDX ATMOSPHERIC TRANSPORT MODELLING

Keywords: Atmospheric transport modelling, wet deposition, rain, cloud, Fukushima, Caesium-137

Wet deposition is a key element of the atmospheric transport and deposition modelling. Following the emission and the transport, it is the final process to obtain a map of deposit consecutive to an accidental release. The operational wet deposition schemes of the atmospheric transport modelling are currently rough because a greater accuracy is not required considering the uncertainties on the source term and the meteorological data. However, meteorological data are improving in term of resolution and quality. As a result of this improvement, it may become relevant to use a finer in-cloud wet deposition model, dealing explicitly with the vertical composition of the cloud and the precipitation. In this study, the impact of the integration of the vertical profile of cloud water content and precipitating water is examined on Cs-137 deposition of the Fukushima case. Results show an impact on the final deposit by using vertically resolved deposition schemes. However, these wet deposition schemes will require significant future improvements.

INTRODUCTION

Atmospheric transport models are elements of the nuclear crisis management. For example, IRSN has developed an operational model, LdX [START_REF] Groëll | Sensitivity analysis of the modelled deposition of 137Cs on the Japanese land following the Fukushima accident[END_REF]), which has served in particular to make recommendations during the Fukushima accident. LdX is based on the chemistry transport model Polair3D which is part of the Polyphemus platform [START_REF] Mallet | Technical Note: The air quality modeling system Polyphemus[END_REF][START_REF] Quélo | Validation of the Polyphemus platform on the ETEX, Chernobyl and Algeciras cases[END_REF]. This type of operational model is usually kept as simple as possible to provide a quick response to urgent management questions. To represent the atmospheric transport we are looking for robust and simple schemes to implement and, also, schemes whose complexity proves to be sufficient considering the uncertainties encountered in this type of situation: source term poorly known, particle size unknown, etc.

Modellers faced difficulties and took advantage of this case study to update wet deposition modelling. Improvements in water description included in meteorological fields allow now to use more complex parameterisations and one may wonder if this leads to significant changes in atmospheric transport models capabilities.

PARAMETRISATION OF THE WET DEPOSITON

Several reviews of the wet deposition schemes intended to the atmospheric transport modelling are available in the literature [START_REF] Sportisse | A review of parameterizations for modelling dry deposition and scavenging of radionuclides[END_REF][START_REF] Quérel | Hints to discriminate the choice of wet deposition models applied to an accidental radioactive release[END_REF]Quérel et al. , 2016;;[START_REF] Draxler | Third meeting of WMO task team on meteorological analyses for Fukushima-Daiichi nuclear power plant accident[END_REF]. From these reviews three common types of in-cloud scavenging schemes used in operational models are considered. The common feature between these schemes is to represent the scavenging with a coefficient (noted ߉, in s -1 ). The evolution of the air concentration (ܿ) due to the wet deposition is calculated as follow:

+ݐ(ܿ )ݐ݀ = )ݐ(ܿ × ݁ ି௸ௗ௧ (1)
The most common scavenging coefficient scheme uses only the rainfall intensity at the ground level as input data. The scheme is represented by the equation (2). ܽ and ܾ are coefficients, depending on the transport modelling . They may depend of the precipitation type (rain or snow). These coefficients are different for the in-cloud and the below-cloud scavenging (e.g., like in the NAME model [START_REF] Leadbetter | Sensitivity of the modelled deposition of Caesium-137 from the Fukushima Dai-ichi nuclear power plant to the wet deposition parameterisation in NAME[END_REF])) [START_REF] Hertel | Development and testing of a new variable scale air pollution model -ACDEP[END_REF] proposed a scheme dedicated to the in-cloud scavenging. The idea is to consider that a fraction (݂) of particles are included in cloud droplets (or crystals), this fraction is set as a constant which is equal to 0.9 in [START_REF] Hertel | Development and testing of a new variable scale air pollution model -ACDEP[END_REF]. The loss due to in-cloud scavenging is then related to the ratio between the precipitating water and the cloud water. The cloud water is given by the meteorological data. [START_REF] Hertel | Development and testing of a new variable scale air pollution model -ACDEP[END_REF] used a global cloud liquid water content for this purpose. Finally, the Hertel scheme is given by the equation ( 3) with ܹܮ ܥ the liquid water content of the air (kg.m -3 ) and ܪ the precipitating cloud thickness. The liquid water content is linked to the cloud water mixing ratio by the air density.

߉ = ܽ × ܫ (2)
߉ = ଷ ூ ௐ ×ு (3)
Another scheme dedicated to the in-cloud scavenging was proposed by [START_REF] Pudykiewicz | Simulation of the Chernobyl dispersion with a 3-D hemispheric tracer model[END_REF]. For this scheme, the scavenging coefficient is calculated with the relative humidity ܪܴ( , equation 4). The two parameters are the relative humidity threshold ܪܴ( ௧ ), fixed at 80% by Pudykiewicz and the maximum relative humidity ܪܴ( ெ ௫ , equal to 100%). The rainfall is not used in this scheme.

߉ = 3.0 × 10 ିହ ோுିோு ோு ಾ ೌೣ ିோு (4)

Benefits and limitations of the Hertel scheme

The Hertel scheme combines the advantages of the explicit use of water content and the considering of the cumulative rainfall. This approach is much more representative of the in-cloud physical processes than the only rainfall dependent scheme or the only relative humidity dependent scheme.

However, the Hertel scheme is impaired by some implicit hypothesis:  It supposes a homogeneous precipitation forming inside the cloud. Then its use with vertically resolved LWC (MRI 2015) leads the cloudiest fraction of the cloud to have the lowest scavenging coefficient  It ignores any evaporation of the precipitation. The precipitation at the ground level is then equal to the precipitation coming out of the cloud, which is not always true.  It supposes that the cloud water content and the precipitation time scales are consistent. The issue is that the cloud water is an instantaneous value while the precipitation is a cumulated value. The cumulated value may not be representative of the cloud water given at one instant.

POSSIBILITIES RESULTING FROM THE METEOROLOGICAL SIMULATIONS IMPROVEMENTS

Two expected improvements of the meteorological data output can enhance the wet deposition schemes of the operational atmospheric transport modelling: the refinement of the temporal resolution and of the quantity of data vertically resolved. These improvements may make the Hertel scheme more reliable.

Case study

The radionuclides atmospheric transport of the Fukushima accident has been actively studied since 2011 [START_REF] Mathieu | Fukushima Daiichi-derived radionuclides in the atmosphere, transport and deposition in Japan: a review[END_REF]. This accident has already been used to study the deposition processes [START_REF] Quérel | Hints to discriminate the choice of wet deposition models applied to an accidental radioactive release[END_REF](Quérel et al. , 2016;;[START_REF] Leadbetter | Sensitivity of the modelled deposition of Caesium-137 from the Fukushima Dai-ichi nuclear power plant to the wet deposition parameterisation in NAME[END_REF]. A meteorological simulation of [START_REF] Sekiyama | Horizontal Resolution Dependence of Atmospheric Simulations of the Fukushima Nuclear Accident Using 15-km, 3-km, and 500-m Grid Models[END_REF] is used to understand the potential changes implied by an improved meteorological data output. This meteorological simulation has a time resolution output of ten minutes and a horizontal resolution of 0.03°(~3 km). The original data have a vertical resolution of 40 layers. It is interpolated to 17 layers in our transport modelling to reduce the computation time without loss. The period covered is from the March 11 th to April 1 st 2011.

Temporal resolution

With a 3 km resolution, it is not always possible to follow a cloud evolution with an hourly resolution.

The Figure 1 shows strong differences which can occur between two cross-sections of clouds only separated by one hour. However, a temporal resolution of ten minutes allows a better tracking of the cloud evolution. It leads to a better consistency between the cumulated data (rainfall) and the instantaneous data (rainwater content) (Figure 2). For this case, the ten minutes data of rainwater mixing ratio and rainfall are correlated at 83%. The correlation decreases to 54% with the hourly data.

Data vertically resolved

Today, only the rainfall intensity, the relative humidity and the liquid water are commonly used for the wet scavenging. But, a larger quantity of vertically resolved water data can be available for operational purpose. For our case study, we have a complete vertical profile of the non-precipitating fields cloud water mixing ratio (Q C ) and ice water mixing ratio (Q i ). The graupel mixing ratio (Q G ), the snow mixing ratio (Q S ) and the rain mixing ratio (Q R ) are available as precipitating fields. An example of a vertical profile of each kind of water is presented on the Figure 3. The vertical cloud presence is identifiable thanks to the cloud water mixing ratio and the altitude where precipitating water are formed.

A fine description of the wet deposition seems then possible, taking into account at each level the different water forms and the ratio between the precipitating water and the cloud water. This information could lead to another expression of the Hertel scheme, without the hypothesis of a homogeneous repartition of the precipitating water. The in-cloud scavenging could be estimated with a scavenging coefficient defined as the ratio between the locally formed precipitating water and the non-precipitating water.

It is however not straightforward to split the precipitating water mixing ratio into locally formed and the contribution of the cloud layer above. This information is merged in the currently available meteological model output. Implementing a scheme that neglect this problem leads to unrealistic results. The potential use of these detailled fields needs to be further investigated.

Figure 1

 1 Figure 1. A cross-section of cloud water mixing ratio (Kg.Kg -1 ). The dotted line corresponds to the location of Fukushima-city. (a) corresponds to the West-East cross-section on March 15 th at 19 am UTC; (b) corresponds to the West-East cross-section on March 15 th at 20 am UTC.

Figure 2 .

 2 Figure 2. A cross-section of cloud water content at ten minutes interval between 19h10 and 19h50, the March 15 th . The dotted lines correspond to the location of Fukushima-city. The cyan lines correspond to the cloud water mixing ratio (Kg/Kg).

SCAVENGING COEFFICIENTS

Scavenging coefficient values obtained with the three corresponding schemes presented are compared. The scheme based on Hertel gives a scavenging coefficient more than ten times larger (6.2×10 -3 s -1 ) than the NAME scheme (3.36×10 -4 s -1 ). Finally, Pudykiewicz gives the smallest scavenging coefficient in mean (3.4×10 -5 s -1 ). An example of results is given by the Figure 3. It shows the relative strength of each scavenging coefficient scheme and the vertical variation obtains by using Hertel scheme. The differences between the schemes are dominated by the mean value, rather than the vertical dependencies.

CONCLUSION

Ten minutes time step of the meteorological output data and the access to additional vertical water content data offer new possibilities for the wet deposition modelling. To evaluate future deposition modelling developments, the Fukushima case has been chosen. Dealing with the input data, the ten minutes resolution allows a better tracking of the cloud and precipitation. Moreover, the instantaneous precipitating water at ground level has a better correlation with the cumulated precipitation data.

The vertical profile of cloud water and precipitating water allow the use of more physical deposition schemes for the in-cloud scavenging, prolonging the Hertel scheme concept. It is confirmed that the rainfall intensity is poorly representative of the mechanism occurring in the cloud. Besides, the scavenging schemes can have an important influence over the final deposition maps. The scheme using the vertical profile of water (MRI 2015) is the most scavenging.

A consistent in-cloud scavenging scheme has to distinguish, at least, the precipitating water coming from a higher altitude and the precipitating water formed by the cloud water conversion. Then, a more detailed in-cloud scavenging scheme is expected to used favorably the possibility provided by a ten minutes resolution of the meteorological data and by the use of a larger number of water content fields.


Tianqi Huang

Julie Alves

Romain Castellani

Yannick Tillier

Jean-Luc Bouvard

Rheological

Rheological and mechanical behaviour of polyethylene-based vitrimers

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.

Rheological and mechanical behaviour of polyethylene-based vitrimers

T. Huang1 , J. Alves 2 , R. Castellani 1 , Y. Tillier 1 , J.-L. Bouvard 1 1 Mines Paris, PSL University, Centre for material forming (CEMEF), UMR CNRS, 06904 Sophia Antipolis, France (tianqi.huang.mines@gmail.com) 2 Aliaxis Research & Technology, Omega Park, Building 7, 3 Bd Jean Moulin, 78990 Élancourt, France

The use-driven classification of polymers tends to separate them into two groups, thermoset and thermoplastic polymers, depending on their mechanical and rheological behaviour with temperature. The former usually show better mechanical performances while the latter present interesting reprocessing abilities thanks to the reversibility and thermal dependency of its flowing properties. Recently, an interesting kind of material has emerged, that presents both characteristics: vitrimers. They consist of polymer chains "crosslinked" using thermo-activated labile bonds, forming a dynamic network that allows relaxation and chain mobility at high enough temperatures. A characteristic temperature Tv (or "topology freezing transition temperature") can be associated with this process, above which the vitrimer will exhibit thermoplastic-like healing and shaping properties, and below which it will show interesting thermoset-like mechanical properties.

In this work, three different polyethylene-based materials are studied: (i) a common HDPE, (ii) a silane-crosslinked polyethylene (PEXb) and (iii) PE-vitrimers 1 . Mechanical and flow properties are compared, using rheology and DMA. Measurements highlight how the PEvitrimer falls between HDPE and PEXb at high temperatures; The variation in vitrimer bond density also refines the behavior from entangled polymer chains to a cross-linked network. Interestingly, the attempt to draw a master curve from the rheological data at different temperatures only works in certain frequency ranges, as highlighted in Figure 1. This seems to highlight different relaxation processes due to the characteristic times and activation energies of the PE-chains and vitrimer network bonds respectively.

Figure 1 :

 1 Figure 1: Master curves of G' and G'' for one of the studied PE vitrimers (PE-v-035), from 150°C to 200°C using shifts in a) high-frequency range or b) low-frequency range (blue squares).

M. Maaz, et al., Macromolecules. 54,

(2021).