Lanciano Emilie
email: emilie.lanciano@univ-lyon2.fr

Lapoutte Alexandrine
email: alexandrine.lapoutte@univ-lyon2.fr

Saleilles Séverine
email: severine.saleilles@univ-lyon1.fr

What business models for the food justice? 1

Keywords: food justice, business models, hybrid organization, social enterprise Résumé alimentaire, modèles d'affaires, organisation hybride, entreprise sociale

The Food Justice Movement is a grassroots initiative now reaching public, political and academic spheres. Our purpose in this article is to explore how do these organizations manage to solve the coexistence of food justice imperatives and economical ones in their business models. Thanks to a qualitative study, we propose a framework to understand the diversity of business models that take in charge the food justice issue, and a typology of business model for food justice.

What business models for the food justice? Introduction

Food constitutes the source of multiple problems in public health. The links between economic disparities, agro-industry food and health problems (obesity, food-related pathologies) are more and more obvious. Figures are alarming. In France, we consider that individuals experiencing food insecurity represent 12,2 % of the population2 . Far from being a right for all, the access to a good, quality and healthy food stays a privilege for those who have enough economic or cognitive resources (Chiffoleau and Paturel, 2016).

The Alternative Food Systems -AFS later -that emerged from the late 2000s to propose an alternative to the agro-industry and reconnect producers and consumers (Le [START_REF] Velly | Sociologie des systèmes alimentaires alternatifs: une promesse de différence[END_REF] are today confined in a niche. The diverse new markets of AFS helped to introduce the idea of a transformation of agriculture and food toward an alternative [START_REF] Kirwan | Alternative Strategies in the UK Agro-Food System: Interrogating the Alterity of Farmers' Markets[END_REF]. AFSs may have impacts on the wider food system by ''sending a signal to other actors within the food system that may in turn influence their actions'' (Kirwan 2004, p. 412). However, it concerns a certain part of the population. Rural and/or perirurban populations and more generally poor populations do not yet have access to these innovative and alternative food systems.

The notion of food justice emerges in this context to embody both social justice dimension and food sector transformations [START_REF] Hochedez | Food Justice and Agriculture[END_REF]. Seen as an imperative for public action, the notion of food justice has an ambiguous status, between activist and academic spheres. Generally embedded in the solidarity economy, more and more experimental initiatives intend to fight against the forms of exclusion inside the alternative food systems. Solidarity food boxes, community gardens, buying groups of sustainable food, local supply of food aid, social groceries are some example of such initiatives (Darrot and Noël, 2018).

While the criticism of the food aid system and the food justice movement is already embodied by literature, the modus operandi of organization acting for food justice is however still confusing and fragile. The question about the nature of the business models that allows and stabilize the food justice project is crucial.

This article aims to explore how these initiatives manage to answer the food justice issues, focusing specifically on their business models, and how these firms address the hybrid nature of their activities. These initiatives constitute hybrid organizations as they intend to solve a social problem by relying on hybrid, public, commercial and social resources and modes of operation [START_REF] Santos | Making Hybrids Work: Aligning Business Models and Organizational Design for Social Enterprises[END_REF]. It involves mobilizing business models that combine economic value creation and social value creation. The balance is delicate to find since an imbalance poses a risk either on the raison d'être or on the economic viability of the organization. We explore how they solve the contradictions of the economic and social logics, which they have to face, and how the concept of food justice is embodied in the practices of these organizations.

The first part introduces the concept of food justice and considers the ways in which it can be embodied in the business models of organizations. We propose to mobilise the typology of Social Business hybrids developed by [START_REF] Santos | Making Hybrids Work: Aligning Business Models and Organizational Design for Social Enterprises[END_REF]. The second part presents the methodology, the area of analysis explored. The last part gives our results and their discussion.

Articulate business models and food justice missions

In this section, we present the concepts of food justice and Business Model hybrids that will form the framework of our empirical analysis.

Food Justice as a Mission: Organizational Issues

Even if they are concerned with food access inequalities, the AFS have difficulties to serve the poorest or the most vulnerable people (Darrot and Noël, 2018). In reality, AFS's consumers are mainly from the middle class with a strong cultural capital (Dubuisson-Quellier, 2013). Therefore, areas which the AFS pretends to create or recreate regarding the dominant food system, also become excluding areas and create new inequalities [START_REF] Hochedez | Food Justice and Agriculture[END_REF]. A food justice movement was recently developed to alert on this risk of two-tier system (AFS and quality food for the rich people, conventional system and junk-food for the poor people) and to propose solutions. It seeks to ensure that the benefits and risks of where, what and how food is grown and produced, transported and distributed, and accessed and eaten are shared fairly [START_REF] Gottlieb | Food Justice[END_REF]. The academic literature seized this concept of food justice to define outlines, in particular towards the concepts of food accessibility and food security. [START_REF] Hochedez | Food Justice and Agriculture[END_REF] consider that a just food system has to act at three levels: to address the food accessibility issue; to ensure food security and to act on the roots of inequalities. According to Cadieux and Slocum (2015), we need to be more clear on what it means to do food justice. In this objective, we review the literature in order to identify what an organization can do to address the three issues of a food justice mission.

To address the food accessibility issue

The food accessibility is the object of diverse works, in particular around the notion of "food desert" (Guy and David, 2004) where people lack access to foods that meet their nutritional needs (VerPloeg et al.,2009). As people tend to make food choices based on the food outlets that are available in their immediate neighbourhood, these works underline the problems of physical accessibility on a healthy and culturally-appropriate food. The food stores can be geographically far (in terms of access time in public transportation in particular), but moreover when food stores exist nearby, they propose a choice of less wide products.

Accessibility is also envisaged from an economic point of view. The lack of financial resources presents a barrier to healthy eating and the price is an often-advanced obstacle to make a commitment towards food of quality 3 . However, if the price sensibility is strong for low-income population, their flexibility in the substitutions between products remains weak, which is quite paradoxical. For example, in spite of competitive prices compared with markets and supermarkets, Community Supported Agriculture (CSA) have difficulty in opening socially, including when they opt for a price reduction strategy for low-income populations [START_REF] Mundler | Le prix des paniers est-il un frein à l'ouverture sociale des AMAP ? Une analyse des prix dans sept AMAP de la Région Rhône-Alpes[END_REF].

Indeed, the accessibility issue is not a question of commercial equipment or price reduction. In the case of Toronto, [START_REF] Loopstra | Perspectives on Community Gardens, Community Kitchens and the Good Food Box Program in a Community-based Sample of Low-income Families[END_REF] study, there was a very low participation of households of poor areas on programs such as community gardens, community kitchens and food box programs. They showed it is more understandable by a lack of accessibility (geographical but also lacked knowledge about/of programs) and of practicality (programs did not fit with the needs, interests and lives of study participants) than for financial reasons. To attract new consumers in alternative food networks, some studies recommend developing shopping forms with least efforts possible for the consumer4 . The food practices are strongly inherited from the parents and from the social background. The exposure with new standards is not enough; the individuals have to be inclined to modify the pre-existent standards. It depends on the legitimacy that the individuals agree in the FAO choice of their own practices and the legitimacy that they grant to the influencers (Dubuisson-Quellier, 2016). From then on, we can translate the food accessibility mission in organizational issues as to implement healthy food stores in the popular districts, price reduction strategies but also awareness activities and adaptation to consumers more taken away socially from sustainable food practices.

To address the food insecurity issue

Food security is the object of a consensual definition since the World Food Summit of 1996. It exists "when all people, at all times, have physical and economic access to sufficient, safe and nutritious food that meets their dietary needs and food preferences for an active and healthy life."5 However, in a food justice perspective, food security needs to evolve from a matter of logistic and world production to a food associated with the "health" of the people, the planet and the economy (Alkon, 2012, quoted by [START_REF] Hochedez | Food Justice and Agriculture[END_REF]. Beyond a better availability of food, it is well the asymmetries of power in food systems that it is necessary to question. Thus, AFS have been particularly seen as sustainable and social innovations: in deed, they appears as able to create new practices, that go against essential aspects of the dominant food system as the exchanges at long distance, the homogenization of products or their detachment of places and conditions of production [START_REF] Velly | Sociologie des systèmes alimentaires alternatifs: une promesse de différence[END_REF]. We need to consider the nature of the foods that are circulating in the networks and their production processes, the networks used to arrange the supply of food, and the mechanisms of coordination. The table 1 describes the main features of AFS that could contribute to sustainable and social innovation.

Table 1. Main features of AFS as a sustainable and social innovation

Source: authors from [START_REF] Forssell | The sustainability promise of alternative food networks: an examination through ''alternative'' characteristics[END_REF] AFSs can bring potential food security through this criterion and particularly thanks to the inclusiveness of coordination rules. All AFSs do not tackle all these dimensions. Consequently, other approaches adopt a more nuanced method, describing AFS as a mosaic-: from WEAK experiences, enacting partial change, to STRONG experiences, committed to radical change practices (Watts et al., 2005). "Strong AFSs" seem better suited to create social and political change because they challenge the foundations of the conventional food system (Follett, 2009). Increasingly, they represent spaces where producers and consumers go beyond the practices and relationships related to food provisioning and become engaged together in new, more significant forms of food citizenship (Renting et al., 2012). Strong AFS (SAFS) prioritize social usefulness, democratic governance, fair trade and support of peasant and organic agriculture of economic projects.

To act on the roots of inequalities

Accessibility and food security are not enough in defining food justice. Social justice appears to be a prerequisite. The social justice dimension of a food justice mission is not obviously well-to-do to achieve so much it is difficult to fight against structural inequalities (economic, sociocultural, demographic, geographical, etc.) and to overtake the presupposition that local food systems are necessarily socially just.

In the literature, we identify diverse types of possible organizational practices to act on the causes of the food inequalities. It imply a commitment dedicated to the social justice (a prioritization of this objective), a creativity in the ways to incorporate vulnerable people into a deliberative democratic process and a fight against opposite ideologies in this justice (Allen, 2010).

First, social inclusion and creation of social links appear to be an impact of social justice initiatives. Studying a buying group in a Montreal suburb, [START_REF] Enriquez | L'insécurité alimentaire et la réponse locale. Un cas d'initiative innovatrice dans un quartier précaire à Montréal[END_REF] show, for example, that this one allows to obtain quality food at a good price but at the same time to break the isolation of people affected by diverse forms of exclusion and to favour mutual aid, empowerment and skills development.

For Cadieux and Slocum (2015), food justice implies to acknowledge and confront trauma and persistent race, gender, and class inequalities and to design exchange mechanisms that build communal reliance and control. Moreover, successful food justice

Perspectives

Core characteristics Exeamples

The nature of the foods and their production processes Products as ''natural'' (unprocessed and/or without additives) Environmentally benign (using artisanal or traditional production methods)

Organic food label Ecological production

The networks used to arrange the supply of food Reduced distance between producers and consumers, which relates to the network and distribution arrangements notions of localness,small size of networks, transparency, information, and ''shortening'' the supply chain.

The participants and the mechanisms of coordination

New forms of market governance, or new ways to coordinate production, purchasing and commercialization Community Supported Agriculture, consumer or producer cooperatives, Fair initiatives involve systemic change around inequalities based on race, gender, and class as well as promotion of economic exchange and labor systems that foster empowerment and autonomy among historically marginalized groups (Allen, 2010, Gottlieb and[START_REF] Gottlieb | Food Justice[END_REF].

Second, empowerment of poor people is a great concern of the food justice movement, which concerns also the capacity to make one's voice heard so as to have access to food and resources. For example, food aid is well criticized because it depends on non-sustainable products and it does not empower the beneficiaries, sometimes going as far as depriving them of the choice of their food (Darrot and Noël, 2018). Chiffoleau and Paturel (2016) seek to understand how to overtake a charitable approach (which does not finally touch the causes of the inequalities) and to favour the participation of precarious people. They study two cases and show that the status of the beneficiaries evolves. These social innovations transform the "poor man" into a competent citizen, conscious of consequences of cheap food for the farmers and the environment. Education and (cooking, gardening, sourcing, etc.) skills development appears to be key tools.

Finally, to address the root causes of food inequalities, it appears necessary to move beyond a discourse of individual choice and to link with other social movements (Allen, 2010). For example, [START_REF] Myers | Bridging good food and good jobs: From secession to confrontation within alternative food movement politics[END_REF] study new forms of alliances between alternative food activists and labor activists, which fight in a common way to require a bigger economic justice in the conventional food system.

Diversity of social hybrid business models

If organizations implement practices of food justice, these practices have to be coherent with their model of value creation. So, the Business Model (BM) is a relevant prism to study the functioning of organizations. It demonstrates the feasibility of a project and reports choices which the company makes "to generate income, …, choice which concern at the same time the resources and the skills to be valued or to be developed, on the offer or on the offers developed from the valuation of these resources and skills, and finally, on the implemented organization" (Demil and Lecocq, 2008, p. 115). In a shared meaning, [START_REF] Osterwalder | Business Model -Nouvelle génération : Un guide pour visionnaires, révolutionnaires et challengers[END_REF] draw a BM as the principles according to which an organization creates delivers and captures value. Therefore, the BM allows us to understand the activity of an organization through the description of its valuable offer, its target and the type of customer relationship, its cost structure and resources, his main partners, its distribution channels. Created value, although generally economic, may also be social. Specific frameworks picture this coexistence of social and economic value, by taking into account social impacts on beneficiaries.

In addition, social organizations allowing access of the precarious populations to a quality food can be compared to social business hybrid enterprises defined by Santos and al. (2015, p. 38): "social business hybrids primarily use commercial means to achieve a social or environmental mission and adopt different legal forms depending on their regulatory context (e.g., associations, cooperatives, [...])". Thus, practices and objectives of food justice join the globally social logic; it is then a question of understanding how these organizations articulate their practices of food justice with a more traditional logical, generating economic value. [START_REF] Santos | Making Hybrids Work: Aligning Business Models and Organizational Design for Social Enterprises[END_REF] propose a typology of social business hybrids. This typology is built on two dimensions. The first one concerns the modalities of generation of the social value. The commercial relation can directly generate it («automatic value spillovers»). On the contrary, social values can be produced in an indirect way in the commercial relationship, through associated services ("contingent value spillovers").

The second axis deals with ways of capturing economic value. Thus, the activity may be funded, first directly by the costumers that receive the benefits of the action. Second, the funder may be another actor that does not get any direct benefits from the social action. It results in four types of models, which are associated with organizational design principles in terms of structure, governance, human resources and performance as shown in table 2 below.

Table 2. Typology of Social Business Hybrids (Santos et al., 2015, p. 45)

The first hybrid model is qualified as "Market Hybrids"; it consists of commercial and trade mechanisms for the public with low consumption capacity. The model corresponds to the BOP model [START_REF] Prahalad | Fortune at the bottom of the pyramid: Eradicating poverty through profits[END_REF] which, thanks to organizational and technological innovations, allows opening new spaces of market with low prices to categories that were until then excluded from it. In this model, customers are thus the direct beneficiaries and no additional support is required to allow an improvement of the living environment (direct social impact).

The second model is qualified as "Blending Hybrids", because it does not associate the commercial and social dimensions directly. As in the purely market model, customers are the beneficiaries, but additional interventions are necessary to allow a real social impact (indirect thus). An example is an organization working in microfinance, education, which organize trainings to increase the proper use of the supplied good or service. In this case, beneficiaries are associated with the governance of the organization.

The third model is "Bridging Hybrids". It postpones the first ones because the beneficiaries of the activity do not participate mainly in financing the activity. The organization has to build from then a bridge between the group of the beneficiaries and that of the paying customers. On the other hand, as in the market model, the object of the commercial relation is enough to reach the social goal and no intervention is required. The authors take the example of a private hospital, which proposes cataract operations to middle or upperclass customers to create a financial margin and charge the same operations at reasonable prices for people in trouble. Here, the risk of mission drift and competition between the various activities is relatively strong; also, the way of structuring the organization in an integrated or segmented way is crucial. For that purpose, beneficiaries can be integrated into the governance of the organization.

Finally, the last model is the most difficult to organize and to perpetuate. Qualified as "Coupling Hybrid", it associates paying customers and beneficiaries who are supported by specific actions. It corresponds to the model of Work Integration Social Enterprises (WISEs) in France, which offers at the same time a job to long-term unemployed people, and a social support with trainings etc. So, the organization has to take into account two types of stakeholders, but it offers different activities which can enter in competition and threaten the sustainability of the company. As in "bridging hybrids", the inclusion of the beneficiaries already constitutes an accompaniment of the commercial relation.

Our goal is, therefore, to test the concept of food justice to characterize the diversity of practices of organizations that intend to take charge, even modestly, of what they identify as a social problem. For this reason, the typology of hybrid models provides a fruitful framework for analysis.

Methodology and presentation of the cases

2.1.An exploratory study

In this exploratory study, we adopted an interpretative epistemological posture. It is a matter of understanding the intentions of the actors. The paper is therefore based on a qualitative methodology using three techniques (semi structured interviews, observations and documentations) triangulated to each other in order to consolidate the richness of information and gain additional perspectives on key issues. The data collection took place as part of a research program between March and November 2016.

We conducted semi-directive interviews with the founder of each studied organizations, as well as with three representatives of professional networks in which the studied organisations are embedded. These nine interviews (see Table 3), which lasted between one to two hours are the core of our material. The interview guide tries not to explicitly refer to notions of food justice and business models. All interviews were audiorecorded.

Table 3. The semi-directive interviews

In addition, we triangulate the data by participating observation of several meetings where the interviewees intervened: six meetings of the local group of Urbact programme "sustainable food", two meetings of the Local Sustainable Food Council of the city of Lyon, five meetings of the Bol, an alternative food cluster.

The analysis of the data is interpretative and abductive. First, we described, for each case, the beneficiaries (people identified in a precarious situation with difficulty to access to healthy food), the sources of revenue (for each "clients", we identify the value proposition) and the value creation process. Then, we positioned the cases on the two axis of the typology of [START_REF] Santos | Making Hybrids Work: Aligning Business Models and Organizational Design for Social Enterprises[END_REF] and associated each case with a Business Model of the latter (see Table 4). Second, the open coding began with the identification of food justice practices in the data and grouping them into first order categories. From this base, we pursued the analysis to search for relationships between and among first-order categories in order to assemble them into higher-order themes. Those emerging themes were discussed in the light of the literature to achieve aggregate dimensions (See Table 5). Third, we identify how each case considers food justice in its organizational mission.

2.2.The studied organizations

The analysis concerns in a specific way six organizations anchored on the territory of the metropolis of Lyon. The metropolis of Lyon constitutes a dynamic territory with an average standard of living compared with the national average. It is indeed lined with rural or semi-urban territories with an important farming specialization. For several years, the territory is marked by the development of the food short supply chains. It also joins in a tradition of open markets and more recent initiatives as farmer-markets and farmershops, which are particularly well developed in the region of Rhône-Alpes.

However, the territory is also characterized by strong socio-territorial disparities with difficulties of access to sustainable food. The organizations which we consider join the context of the development of alternative food networks but they have for objective to solve the problem of sustainable food access for precarious people. So, most of them were created at the end of 2000s, in the phase of growth of the alternative food networks on the and it constitutes in this respect a certain reference for other organizations. The six organizations that were studied emerge from the same diagnosis: the problem of inequality in access to a quality diet, but they each respond to it differently. These six organizations have quite the associative status and develop an autonomous economic activity. Arbralégumes and A 2 prés de chez vous (A2PC) deliver local fruits and vegetable boxes and organize events of raising awareness. Passerelle d'Eau de Robec is a part of the social groceries network GESRA (Interview 7). It is a shop for low-income people who are supported during six months by social workers to develop a personal project (beneficiaries), but also for classic consumers (solidarity customer). It offers animations of awareness to the peasant farming and the sustainable food. VRAC is a buying group of organic products (dry products and cleaning products) in some popular districts of Lyon. It is partially funded by public housing offices. Marmitte Urbaine develops catering for enterprises and leads, in parallel, awareness-raising activities though gardening in popular districts. Finally, Légumerie organizes cookingworkshops to promote sustainable food.

The majority of these organizations deploy their activities in target areas of the city's policy and benefit from grants or local public support. Some of them are supported by a social incubator. They employ one to three employees and they regularly host "services civiques"6 and volunteers.

Towards a typology of business models for food justice

Our cases differ first in the choice of their targets and resources (3.1) and then in the choice of food justice logics (3.2). We finally propose a new typology of business models for food justice (3.3).

Business models combining differently clients and beneficiaries

An important dimension to differentiate the business models of these organizations concerns the nature of the target and exact correspondence between the customer who finances activity and the beneficiary. This question, tested in the first axis of the typology of [START_REF] Santos | Making Hybrids Work: Aligning Business Models and Organizational Design for Social Enterprises[END_REF] introduces different modalities of financing and income generation. Table 4 describes the organizations thought their business models, and precisely how and by what kind of actors the economic value is generated. In three organizations (A2PC, Arbralégumes and Passerelle d'Eau de Robec), beneficiaries are considered as customers. It means that there are no peculiar efforts to individuate beneficiaries; the inclusive scope of the organization appears in the general mission and activities of the organization. The economic model rests then on a principle of solidarity between customers. For example, A2PC and Arbralégumes offer boxes of local and organic fruits and vegetables to nonspecific clients. The price lists of boxes are spread out according to income (students, basic welfare benefits). The Passerelle d'Eau de Robec is a social grocery. The public consists of customers with different profiles: classic customers-members who have access to the goods at market prices, or beneficiary customers-members having a rest to live to feed of 2,80 € a day per capita. In these cases, prices of the sold goods are adapted to the situation of the beneficiaries, but commercial relation remains. Financial resources are crossed but still mainly marked based.

Other organizations distinguish the client and the beneficiary. In this case, social activities are financed by philanthropic organizations (VRAC), public actors in the form of a delegation of public service (Légumerie) or grants (VRAC), or by private commercial activities of the organisation (Marmite Urbaine). The economic model of Marmite Urbaine is built on the creation of a margin by selling meal trays in Business to Business, in order to finance awareness-raising activities and festive meals to people in precarious situations. "We have the luxury of economic activity that can ensure our sustainability…. And so this commercial activity, it finances the associative side, it funds associative life, and awareness and all that. (…) » (Marmite Urbaine). Social activities and funding activities are consequently distinct, and not completely interactive. In these three cases, the spatial dimension is crucial to achieve to identify and include the beneficiaries: they are precisely located in popular and suburbs district.

Food accessibility, food security and social justice: different logics combined

The typology of [START_REF] Santos | Making Hybrids Work: Aligning Business Models and Organizational Design for Social Enterprises[END_REF] retains as the second axis the direct or indirect nature of the commercial transaction effect. We adapt this axis by retaining as criterion the way the three logics inherent to the food justice mission are prioritized. Indeed, the social impact looked for by every structure is different. Some organizations primarily look for the improvement of their impact in terms of food security, the accessibility is then essentially envisaged in its financial dimension, and to a lesser extent spatial. It would correspond to the Automatic Value Spillovers of the typology of [START_REF] Santos | Making Hybrids Work: Aligning Business Models and Organizational Design for Social Enterprises[END_REF].

Table 5 shows the different practices of food justice according to the three dimensions we identify in the literature. It appears firstly that the six organizations we consider are not taken in charge of all these dimensions; we observe rather a specialization on certain issues of the food justice.

The fruit and vegetables boxes A2PC and Arbralégumes clearly announce to prioritize the support for the small farmers. These structures address firstly activist customers. "We have a public who is rather young and already enough committed. I think that there is already a reflection just a little on all which is alternative also at the level of the food." (Interview, Arbralégumes). The offer they develop for low-income people (based on financial accessibility) meets however a reserved success and especially does not succeed to touch less activist customers. It is without a doubt understandable by the fact that the other dimensions of the accessibility (spatial and practical) are not implemented. For example, A2PC explains this mixed result, in spite of the attractive price "For certain populations it is impossible not to be able to choose the vegetables» (interview, A2PC).

In this category, we also find organizations whose main mission is raising awareness (by cooking/gardening workshop): Légumerie and La Marmitte Urbaine. It is a question of "handing urban people to the contact of their nourishing earths, to tempt them to cultivate oneself, to cook with vegetables" (Interview, Légumerie). The food security always constitutes the main mission but the objective is more to transform the practices of consumption towards quality and to reconnect with farming than to directly support small farmers. It is a question of "proposing to people a better food and while proposing a social support" (Interview, Légumerie) and to break the isolation of the people in precarious situations. Besides the financial accessibility, these structures also work the spatial and practical dimension of the accessibility. They organize workshops as closely as possible to the targeted inhabitants Other organizations favour the social justice as impact of their structure and handle food as a tool to try to act on the roots of economic and social inequalities. They work on all dimensions of accessibility: financial of course, but also spatial, and practical. The food security becomes then a secondary logic, envisaged essentially in its dimension "healthy food for people". It corresponds then to the Contingent Value Spillovers of the typology of [START_REF] Santos | Making Hybrids Work: Aligning Business Models and Organizational Design for Social Enterprises[END_REF]. We find in this category VRAC and the social grocery Passerelle d'Eau de Robec. These two organizations build themselves from a criticism of the dualistic system: criticism of food aid system and its purely quantitative treatment of the food inequalities for Passerelle d'Eau de Robec, criticism of the social segmentation of the alternative food networks for VRAC. They wish "to fight against the inequalities regarding consumption" (Interview, VRAC). "We wanted to make quality food accessible for all. And the word quality, it returned to us in teeth to a full speed" (Interview, Passerelle d'Eau de Robec). They worked the food accessibility in all its dimensions: financial of course but also spatial and practical.

The fit with the needs of the target is a constant concern. "We make many analysis of the target. Because it is the only way to not disconnect from needs, to not disconnect from problems " (Interview, Passerelle d'Eau de Robec). Here food appears at the same time as an objective and as a pretext to support the beneficiary in his social and economic reintegration and develop actions affecting the causes of the inequalities. The beneficiaries participate in the creation of the offer (of products, animations, etc.) and are included in the governance of the structure. "We are going to put them in the governance. They are going to manage the grocery, to make the decisions; we are going to be proactive to support them. At the same time as a result, we are going to train them on things, that can be good for some who want to get involved,that can help them to show their know-how." (Interview, Passerelle d'Eau de Robec). At VRAC, these activities of valuation of the skills of the inhabitants took the shape at first of a cooking competition and recently of the publishing of a cookbook, which generate income.

Discussion: Diversity and risks of business models for food justice

Our contribution and results are currently exploratory, and should be extended to other contexts and organizations for validation. Nevertheless, our first theoretical contribution is a better characterization of what it means to do food justice (Cadieux and Slocum, 2015) at the organizational level. We identify diverse practices, which can be implemented to act on the three gradients of food justice [START_REF] Hochedez | Food Justice and Agriculture[END_REF]. It provides a reflexive framework for organizations already engaged for food justice in order to evaluate their practices. Some organizations focus more on the food security, the sustainable development and the solidarity with farmers. Others favour education and empowerment of disadvantaged consumers, even if it means relegating in the background the solidarity with farmers. We highlighted a certain specialization of organizations. The mission of food justice is with difficulty reachable by an isolated organization. The panel of food justice practices constitute a source of inspiration but not a to-do-list applicable to all. The question of complementarities between organizations on the raises itself from then on. The second theoretical contribution is the proposition of a typology of Business Models for food justice. We mobilized an existing typology to characterize the diversity of organizations leading a mission of food justice, according to their sources of revenues and the nature of the problem addressed primarily. This plurality of the social missions in itself allows us to enrich the typology of [START_REF] Santos | Making Hybrids Work: Aligning Business Models and Organizational Design for Social Enterprises[END_REF], based on the direct/indirect social impact of the commercial activity.

We discuss the managerial implication of our research, by identifying, for each Business Models for food justice, risks and levers for reducing them. Indeed, the analysis carried out makes it possible to highlight the risks of institutional tensions that hybrids encounter. When the economic mission takes precedence over the social mission, we speak of mission drift [START_REF] Ebrahim | The governance of social enterprises: Mission drift and accountability challenges in hybrid organizations[END_REF]. If the company neglects the economic imperatives and the financial needs, it risks disappearing for lack of means. In a paradoxical way, the studied organizations are in a growing market: the sustainable food indeed constitutes a niche particularly appreciated by consumers. Consequently, they are exposed at the risk of seeing the economic imperatives overriding the social mission of food justice. Our results allow identifying in a finer way specific mission drift risks.

In the case of "Market Hybrids" (A2PC or Arbralegumes), the risk consists in not succeeding in realizing the mission in terms of accessibility. Their offer is completely coherent with moderate/high-income consumers, but less with low-income consumers who adopt less naturally this type of consumption. A price reduction strategy can not be enough to attract low-income consumers. To better reach this audience, "Market Hybrids" should be inspired by the practices of "Coupling/Blending Hybrids" in order to reinforce spatial and practical dimensions of accessibility. For example, they need to accept that some characteristics of their offer (localization, no choice) can constitute a barrier for the targeted people and that it is necessary to include them more in the definition of the offer.

The risk is rather close in the case of "Bridging Hybrid" (Marmitte Urbaine or Legumerie). Indeed, the frank segmentation between the economic and social missions can bring to the fast development of the branch dedicated to the economic logic to the detriment of that dedicated to the food accessibility. On this point, the hybridization of financial resources can be a railing; public authorities but also sponsors and customers scrutinizing the results in terms of social impact of the structure. To reinforce their social impact, "Bridging Hybrids" could be inspired by "Coupling Hybrids" that are able to propose to the beneficiaries a support (education / skills valorisation), not directly connected to the paid service.

The model of "Coupling Hybrid" (VRAC) can be threatened by the dependence on funders, what requires besides an important work of fundraising, reporting and staying in coherence with their expectative. The sustainability imply a professionalization of the administrators. They need to develop a capacity to cross resources and to evaluate social impact. "Coupling Hybrids" could be inspired by "Market/Blending Hybrid" that are able to derive the majority of their income from their beneficiaries. But it also implies to recognize the hybridization of resources as a permanent and not a temporary model before a complete financial autonomy.

Finally, the "Blending Hybrids" (Passerelle d'Eau de Robec) model is built on a coherence of its food justice mission and economic model. Indeed, the integration on the beneficiaries into the governance of the organization is a "Blending Hybrids" practice, that can inspire others models. Moreover, the relative low dependence on external funds and the development of many peripheral actions testify to the soundness of the model. Built essentially as a counter model for food aid, the risk may be an excessive focus on the poorest and more activist populations. As farmer support is not a priority, "Blending Hybrids" could activate synergies with "Market Hybrids" in order to reinforce their social impact.

Conclusion

The general purpose of the paper deals with the capacity of AFS to address food justice issues. We propose a first typology of four Business Models for food justice and discuss the risks and lever of improvement of each models. Finally, our research suggest the value of a system approach to create synergies between models in order to transform the system towards food justice. The question of the food justice concerns the economic sphere (from production to consumption) of course but also education, health, urban planning, etc. Food justice constitutes an opportunity of important research to extend and enrich the works on the alternative/local food systems (Le Velly, 2017).

Références

  The case of Passerelle d'Eau de Robec is older because it is dated 2002

	territory of Lyon.
	Interview	Organizations	Activity	Date of creation
	1	Légumerie	Awareness of sustainable food through cooking workshops	2009
	2	Passerelle d'Eau de Robec	2 social groceries	2002
	3	A deux prés de chez vous	Fruit and vegetables boxes (with price reduction for low-income people)	2012
	4	Arbralégumes	Fruit and vegetables boxes (with price reduction for low-income people)	2008
	5	VRAC	Buying group of organic products in popular districts	2014
	6	Marmite Urbaine	Catering (BtoB) + urban agriculture in a popular distric	2012
	7	GESRA	Rhône-Alpes social groceries network	2004
	8	Le Passe Jardin	Urban collective gardens network	1998
	9	Le Bol	Alternative food cluster of Lyon	2015

Table 4 . Business model of studied organizations A 2 prés de chez vous Arbralégumes Passerelle d'Eau de Robec

 4

	Marmite urbaine	VRAC	Légumerie

  Allen P., 2010, « Realizing justice in local food systems », Cambridge Journal ofRegions, Economy and Society vol. 3, Cadieux KV., Slocum R., 2015, «What does it mean to do food justice? », Journal of Political Ecology, vol. 22, p. 1-26. Chiffoleau Y., Paturel D., 2016, « Les circuits courts alimentaires « pour tous », outils d'analyse de l'innovation sociale », Innovations, vol. 2 n° 50, p. 191-210. Darrot C., Noël J., 2018, « Vers des solidarités alimentaires territorialisées... Retour sur la recherche-action SOLALTER menée en Bretagne », Anthropology of Food, Online since 27 February 2018 Demil B., Lecocq X., 2008, « (Re)penser le développement des organisations. Les apports du modèle économique », Revue française de gestion, vol. 1, n° 181, p. 113-122. Dubuisson-Quellier S, 2016, Gouverner les conduites, Presses de Sciences Po, Paris Dubuisson-Quellier S., 2013, « A Market Mediation Strategy: How Social Movements Seek to Change Firms' Practices by Promoting New Principles of Product Valuation », Organization Studies, vol. 34 n° 5-6, p. 683-703.

Bocquier A, Vieux F, Lioret S., Dubuisson C., Caillavet F., Darmon N. (2015) « Socioeconomic characteristics, living conditions and diet quality associated with food insecurity inFrance », Public Health Nutrition, vol. 8, n°16, p. 2952-2961

Lionel J, François M., Chiffoleau Y., Hérault-Fournier C., Sirieix L., Costa S. (2015), La consommation alimentaire en circuits courts : enquête nationale, rapport programme Programme CODIA : Circuits courts en Europe : opportunités commerciales et dialogue avec la société.

Ibid.

FAO,1996, Sécurité alimentaire, notes d'orientation n°2

"Service Civique" is a voluntary commitment whose duration can be from six to twelve months, with a state provided allowance, open to people aged between 16 and 25, where the community work assignments are recognized as a national priority.

To implement healthy food (shop, workshop, urban agriculture) in the popular districts X X X X

To make the healthy food offer known from targeted people (ex: social workers as prescribers) X X

Pratical access

To create a fit with the needs, interests and lives of the target (ex: studies on targeted people, culturally-adequate products)

Price negociation with some wholesalers (no farmers) X X

Search for quality products at the lowest possible price: farmers donations, partnership with organic shops, etc. X

To address the food insecurity issue

Healthy food for people

To aware inhabitants about sustainable food (gardening, cooking of raw products, etc.) X X X X

To influence purchases towards nutritionally good products (labeling system) X

Healthy food for the planet

To support peasant agriculture: payment in advance, solidarity in case of bad harvests, commitment contract X

To choose organic products, to limit travel, to reduce waste X X X X X

Healthy food for the economy

To do fair trade with wholesalers X X X X

To adopt a democratic governance X X X X X

To act on the roots of inequalities

Social and economic inclusion

To mix classic and low-income consumers X X X X Creation of activities in popular district and willingness to hire X X X

To support a personal project with social workers X

Empowerment

To valorize inhabitants skills (cooking context, cookbook) X

To develop gardening/cooking skills of targeted people X X X

To develop links between farmers and targeted people (farm visits) X Inclusion of beneficiaries in the governance X

Food justice business models : a typology

Our analysis allows us to draw an exploratory typology of organizations associating for each business model, some dimensions of food justice (Table 6). As we saw previously, the innovative practices of food justice, described in Table 5, are not quite applied in all organizations, nor even in an unambiguous way. We observe that all the organizations develop actions to facilitate food accessibility through different modalities: price policy targeted at particular populations (direct spillovers) or measures of support (indirect spillovers), be the customers the beneficiaries or not.

On the other hand, the dimensions concerning food security and concerning social justice do not appear in all the organizations. The problem of food security (that we translated in efforts on the quality of products and construction of links with local farmers), is really taking care of direct spillovers, organizations which reach the social objective by direct effects (market and bridging hybrids). Indirect spillovers, organizations producing social value with also measures of support (VRAC, Passerelle d'Eau de Robec), act more on the roots of the inequalities. Actually, they increase food justice by measures ensuring empowerment of people introduced during the commercial transaction.

Table 6. Business Models for food justice While all these organizations are developing food justice practices, the level of integration of these practices into business models is different. It can thus be said that, in a gradual manner, the integration is more extensive in the "blending hybrids" and "coupling hybrids" models and less in the more marketable "market hybrid" model. Our contribution thus makes it possible to bring two elements: that is the difficulty for organizations to integrate the diversity of food justice practices in their hybrid economic models and therefore the need to consider in a complementary way all of these practices, especially at the level of AFSs.


Santanu Bose
email: bose.santanu@gmail.com

Puspendu Saha

James J Mori

Christie Rowe

Kohtaro Ujiie

Frederick M Chester

Marianne Conin

Christine Regalla

Jun Kameda

Virginia Toy

James Kirkpatrick

Francesca Remitti

J Casey Moore

Monica Wolfson- Schwehr

Yasuyuki Nakamura

Anchit Gupta

Deformation structures in the frontal prism near the Japan Trench: insight from Sandbox Models

Keywords: sandbox experiments, inner and outer wedge, slope-break, horst-andgraben structure, fault friction

We have used sandbox experiments to explore the mechanics of the frontal prism structures documented by new borehole and seismic reflection data from IODP Expedition 343 (JFAST). This study investigated the effects of down-dip (across 2 trench axis) variations in frictional resistance along a decollement on the structural development of frontal wedges near subduction zones. To clarify our understanding on the wedge growth over horst-and-graben structures in the subducting plate near the Japan Trench, we performed sandbox experiments with alternate zone of relatively high and low friction on the basal decollement. Our experiments verify that high frictional resistance on the basal fault is needed to produce the observed internal deformation and fault-and-fold structures in the core samples collected during JFAST.

Varying down-dip frictional resistance along the decollement causes a temporal change in the style of internal deformation within the wedge and often gives rise to two distinctive structural domains, separated by a break in the surface slope of the wedge: (i) complexly deformed inner wedge with steep surface slope and (ii) shallow taper outer wedge, characterized by a sequence of imbricate thrusts. Our experiments further demonstrate that the topographic slope-break in the wedge develops when the hinterland part of the wedge essentially stops deforming internally, leading to insequence thrusting with the formation of outer wedge with low taper angle. For a series of alternate high and low frictional conditions on the basal fault the slope of the wedge varies temporally between topographic slope-break and uniformly sloping wedge.

Introduction

It is now well known that the subduction of bathymetric features in the oceanic plate, e.g., seamounts, aseismic ridges, volcanic plateaus has a strong influence on the development of diverse morphological features and deformation structures in the overriding plate (Domingues et al., 2000;[START_REF] Malavieille | Modelisation experimentale des chevauchements imbriques; application aux chaines de montagnes[END_REF][START_REF] Von Huene | Tectonic erosion at the front of the Japan Trench convergent margin[END_REF][START_REF] Von Huene | Tectonic erosion along the Japan and Peru convergent margins[END_REF][START_REF] Lallemand | Effects of oceanic ridge subduction on accretionary wedges: experimental modeling and marine observations[END_REF][START_REF] Lallemand | Coulomb theory applied to accretionary and nonaccretionary wedges: Possible causes for tectonic erosion and/or frontal accretion[END_REF][START_REF] Von Huene | Generic model of subduction erosion[END_REF][START_REF] Park | A subducting seamount beneath the Nankai accretionary prism off Shikoku, southwestern Japan[END_REF][START_REF] Wang | Accretionary prisms in subduction earthquake cycles: The theory of dynamic Coulomb wedge[END_REF]. However, their studies indicate that the styles of deformation in the overriding plate vary with the geometry of bathymetric features in the subducting plate. For example, the subduction of seamounts develops steeper surface slope in the inner wedge than that in the outer wedge [START_REF] Park | A subducting seamount beneath the Nankai accretionary prism off Shikoku, southwestern Japan[END_REF]Domingues et al., 2000). On the contrary, the subduction of aseismic ridges develops steep outer wedge slope associated with almost flat inner wedge [START_REF] Lallemand | Effects of oceanic ridge subduction on accretionary wedges: experimental modeling and marine observations[END_REF]. Despite dominance of horst-and-graben structure at most trenches, its influence on frontal wedge growth has still remained relatively unexplored. We therefore focus the present work to analyze the impacts of subducted horst-and-graben structures on the evolution of frontal wedge near the Japan Trench.

Geophysical investigations along several sections across the Japan Trench (Fig. 1b andc) recorded a series of horst-and-graben structures on the subducting plate beneath the frontal wedge [START_REF] Tsuru | Along -arc structural variation of the plate boundary at the Japan Trench margin: Implication of interplate coupling[END_REF][START_REF] Kodaira | Coseismic fault rupture at the trench axis during the 2011 Tohoku-oki earthquake[END_REF][START_REF] Nakamura | High resolution seismic imaging in the Japan Trench axis area of Miyagi, Northeastern Japan[END_REF]. Moreover, earlier studies have shown that the sediment thickness in the incoming Pacific plate near the Japan Trench is thin and the thinning of sediment cover mostly occurs above the horst block [START_REF] Groshong | 3-D Structural geology: a practical guide to quantitative surface and surface map interpretation[END_REF]. The combination of the effects of the differences in sediment thickness and surface roughness over horst-andgraben structure in the subducting plate cause varying degrees of coupling at the plate interface, creating varying frictional properties on the decollement [START_REF] Pacheco | Nature of seismic coupling along simple plateboundaries of the subduction type[END_REF][START_REF] Tanioka | What controls the lateral variation of large earthquake occurrence along the Japan Trench? IslandArc[END_REF]von Huene et al., 1999;[START_REF] Bilek | Influence of Subducting Topography on Earthquake Rupture[END_REF][START_REF] Das | Effects of subducting seafloor topography on the rupture characteristics of great subduction zone earthquakes[END_REF]. In the present study we have used sandbox experiments to simulate the effects of down-dip variations in the frictional strength on the basal decollement to investigate the structural development of frontal wedge and finally, provide a mechanical model for explaining the structural evolution of frontal wedge over horst and graben structure near the Japan Trench.

Integrated Ocean Drilling Program (IODP) Expedition 343 (JFAST) drilled to a depth of 836 meters below seafloor (mbsf) near the Japan Trench at site C0019 through the plate boundary fault zone over the horst block, located about ~ 6 km westward from the trench axis (Fig. 1a). Core samples collected during the expedition have provided a great opportunity to compare our experimental results with the observed deformation structures within the frontal wedge (Chester et al., 2013[START_REF] Kirkpatrick | Structure and lithology of the Japan Trench subduction plate boundary fault[END_REF]. Borehole data and associated seismic images provide new structural information that has been modeled in this study to show the effects of friction on the megathrust near the Japan Trench.

.

Experimental methods and materials

Sandbox experiments have proved to be useful in understanding the mechanics of thin-skinned accretionary wedges using the concept of critical taper theory [START_REF] Chapple | Mechanics of thin-skinned fold-and-thrust belts[END_REF][START_REF] Boyer | Thrustsystems[END_REF][START_REF] Davis | Mechanics of fold-and-thrust belts and accretionary wedges[END_REF][START_REF] Dahlen | Critical Taper Model of Fold-and-Thrust Belts and Accretionary Wedges[END_REF]. The angle of critical taper is defined by the summation of basal inclination (β) and surface slope (α). According to critical taper model, a wedge deforms internally and thereby, increases its taper and at a critically tapered angle the wedge develops internal stresses, leading the wedge on the verge of failure. At this stage, shear stress at the base reaches a value that assists frictional sliding at the decollement [START_REF] Davis | Mechanics of fold-and-thrust belts and accretionary wedges[END_REF][START_REF] Boyer | Thrustsystems[END_REF]. Theoretically and experimentally it has been shown that the angle of critical taper is proportional to the frictional condition on the basal decollement according to the following equation [START_REF] Dahlen | Critical Taper Model of Fold-and-Thrust Belts and Accretionary Wedges[END_REF]:

α + β = β + µ b ( ) 1 -sinφ c 1+ sinφ c       (1)
where, µb is the coefficient of static friction on the decollement and φc is the angle of internal friction of the frontal prism material.

In the present study, we have prepared our experimental models over varying down-dip frictional conditions on the decollement to simulate the effect of horst-andgraben structure along the basal decollement (Fig. 2). We have considered relatively higher frictional coefficient on the decollement above the horst block because of its enhanced surface irregularities due to little or no sediment cover, leading to a strong coupling with the overriding plate than that over the graben sediments. Thus the horst and graben structure gives rise to alternate zones of relatively strong and a weak contact respectively with the overriding plate on the decollement. In the laboratory scaled experiments the higher basal friction (µb= 0.46), simulating the decollement immediately above the horst block, was achieved by pasting commercial sand paper (P30, average grit size 622.0 microns) on a glass plate and a relatively lower basal friction (µb = 0.36) was obtained by sieving a veneer of boric acid powder (0.001mm beads) over the glass plate in order to model the frictional strength above the graben sediments. However, in some experiments we pasted rigid block of 5mm thick acrylic sheet over the basal glass plate to model the horst block. However, in the second set of experiments, we had to stop the experiment once the buttress reached the edge of the acrylic block. Experimental results from these two different sets of experiments, however, show that frontal wedge propagation ceases once the decollement propagation reaches the high frictional patch / edge of the rigid acrylic sheet (see electronic supplementary Fig. S1). This finding suggests that the use of high frictional patch on the basal glass plate is a suitable analog for simulating natural horst-block.

The advantage of using sandpaper over rigid block is that the hinterland buttress can override the high frictional patch without limiting the amount of shortening during the experimental run.

In the model setup, Zone I represents a graben in the seismogenic plate interface and Zone II corresponds to a horst block in the subducting plate (Fig. 2). Although a majority of our experiments were carried out with one high frictional patch between zones of relatively lower friction on the basal fault, a few experiments were carried out with two zones of high frictional patches to understand the effects of a series of horst-and-graben structures. Experimental models were prepared by sieving sand layers from a constant height of 20 cm in a rectangular glass-walled sandbox apparatus over a rigid base of varying basal friction (µb) (Fig. 2). The length and width of the apparatus are 110 cm and 35 cm respectively. The model width was more than fifteen times its thickness to avoid the effects of friction at the interface of sand layers and the glass sidewalls [START_REF] Souloumiac | Bias due to side wall friction in sand box experiments[END_REF]. The coefficients of basal friction (µb) were calculated separately from sliding experiments using dry noncohesive sand. Note that the values of µb used in our experiments are merely imposed qualitatively for simulating natural situation that do not claim the exact values for natural analogue. The glass walls of the sandbox were cleaned and dried carefully to remove surface moisture. This process is important in order to prevent sticking of sand to the glass walls. Experiments were carried out in controlled laboratory conditions to avoid the influence of atmospheric moisture contents.

We used dry, non-cohesive natural quartz-rich (>90%) sand, texturally matured with well rounded grains (average sphericity of 0.8), as analogue material for scaled model experiments simulating crustal scale brittle deformation [START_REF] Davis | Mechanics of fold-and-thrust belts and accretionary wedges[END_REF][START_REF] Mulugeta | Modeling the geometry of Coulomb thrust wedges[END_REF][START_REF] Koyi | Mode of internal deformation of sand wedges[END_REF][START_REF] Mandal | Imbricate thrust spacing: experimental and theoretical analyses[END_REF][START_REF] Schellart | Shear test results for cohesion and friction coefficients for different granular materials: scaling implications for their usage in analogue modelling[END_REF]. The sand material had a bulk density of 1600 kg/m 3 , and a coefficient of internal friction close to 0.57.

Our model scales to nature with a ratio of 2.7x10 -5 , where 1 cm in the model is equivalent to 360 m in nature (Table 1). The cohesion of model material (dry quartz sand) in our experiment is around 20 Pa, which scales to 2 MPa [START_REF] Gutscher | Material transfer in accretionary wedges from analysis of a systematic series of analog experiments[END_REF] for unconsolidated marine sediments [START_REF] Hoshino | Mechanical properties of Japanese teritary sedimentary rocks under high confining pressures[END_REF]. The models were deformed in a pure shear box at a uniform velocity of 5 mm / minute using a computer controlled step-up motor by setting a backstop at the rear of the sand layers.

Previous studies revealed that buttress geometry is important in the development of wedge geometry in sand layers (Byrne et al., 1988;[START_REF] Persson | Analogue models of orogenic wedges controlled byerosion[END_REF].

However, we used planar vertical buttress in our experimental setup in order to model a mono-vergent accretionary wedge observed in the Japan Trench [START_REF] Mulugeta | Modeling the geometry of Coulomb thrust wedges[END_REF][START_REF] Storti | Influence of syntectonic sedimentation thrust wedges in analogue models[END_REF][START_REF] Gutscher | Material transfer in accretionary wedges from analysis of a systematic series of analog experiments[END_REF][START_REF] Bose | An unstable kinematic state of theHimalayan tectonic wedge: Evidence from experimental thrust-spacing patterns[END_REF].

Experimental Results

Our experiments suggest that the frontal wedge near the Japan Trench has evolved over varying down-dip frictional condition on the decollement during subduction of horst-and-graben. In our experiments, the wedge started to grow above Zone I by in-sequence thrusting at the initial stage and developed a gentle surface slope (α) at uniform shortening rate 4a). The vertical growth of the wedge at the backstop attained an almost stationary value when the model was shortened by 5 cm in all experiments (Fig. 4b). At this stage, the frontal propagation of the wedge dominated over the vertical growth through sequential thrusting until the deformation front reached Zone II. During this stage the wedge developed a critical taper, α equals 7.5° (Figs. 3d, 4a), which is closer to the theoretical value of surface slope (α) of 6° obtained from "equation 1" for β = 0, µb = 0.36 and φc = 0.57.

However, the overestimation of α in the experimental result is self-consistent.

The mode of internal deformation and its geometry changed completely when the decollement propagation reached the edge of high frictional patch (Zone II, µb= 0.42), simulating a horst (Fig. 3e, see electronic supplementary Figs. S1 A [d] andB [d]). At this stage, decollement propagation ceased and the wedge formed over Zone I started deforming internally by increasing the wedge height consistently, developing a steep topographic slope (Fig. 4). This stage of wedge growth has been defined as intermediate stage . The topographic slope of the wedge at this stage became much higher than the predicted value from "equation 1", leading the wedge to grow to a super critical state. It is likely that the cessation of decollement propagation promotes the development of supercritical wedge in order to accommodate the amount of horizontal shortening, and eventually facilitates slope failure (Fig. 3f).

During this stage experimental models demonstrated mechanical rotation and reorientation of already deformed sand layers in the hanging wall, giving rise to a complex deformation structures within the deforming wedge. and4, see electronic supplementary Fig. S3).

The development of slope-break in the wedge geometry thus can be treated as a potential indicator for interpreting long term frictional condition on the decollement.

Experiments with more than one high frictional patch (Zone II) on the basal fault showed that the surface slope of outer wedge (e.g., the wedge over low µb) was increasing progressively with ongoing shortening once the decollement propagation was again resisted by another high frictional patch in the front. As a consequence, the wedge geometry was completely modified along with the destruction of topographic slope-break (Fig. 6h). With further shortening the outer wedge progressively merged with the inner wedge, giving rise to a single wedge with steep uniform surface slope (Fig. 6i). During this process of wedge modification, the inactive inner wedge again resumed to deform by mechanically rotating all preexisting structures and thereby, show that the growth of the inner wedge begins by in-sequence thrusting over low frictional base following the model of critical angle of taper [START_REF] Davis | Mechanics of fold-and-thrust belts and accretionary wedges[END_REF][START_REF] Mulugeta | Modeling the geometry of Coulomb thrust wedges[END_REF][START_REF] Koyi | Mode of internal deformation of sand wedges[END_REF][START_REF] Gutscher | Material transfer in accretionary wedges from analysis of a systematic series of analog experiments[END_REF][START_REF] Yamada | Analogue and numerical modeling of accretionary prisms with a decollement in sediments[END_REF][START_REF] Bose | An unstable kinematic state of theHimalayan tectonic wedge: Evidence from experimental thrust-spacing patterns[END_REF]. However, with ongoing shortening the taper angle of the wedge progressively

Interpretation of wedge development near the Japan Trench

The present study has an important implication in understanding the development of frontal wedge near the Japan Trench. Seismic sections across the Japan Trench show that the slope of the frontal prism over horst-and-graben structure changes from 10° in the landward part to 4° towards the trench (Fig. 1b). Comparing our experimental results with seismic data from frontal wedge near the Japan Trench suggest that the varying down-dip frictional strength along the basal decollement caused the present geometry of the wedge and deformation structures within it near the Japan Trench (Fig. 1b and1c). Our experimental results suggest that the subduction of horst-and-graben structure near the Japan Trench are potential factors for creating varying degree of coupling with the overriding plate that eventually developed the characteristic topographic slope-break. It further reveals that the inner wedge with steep slope over the horst block must have formed prior to the propagation of deformation front over the graben sediments. Our experimental study

shows that initiation of growth of the outer wedge over low basal friction deactivates the internal deformation of the inner wedge. This has led to infer that the present day plate convergence near the Japan Trench is accommodating entirely by in-sequence thrusting over the low friction graben sediments. Previous experimental findings [START_REF] Huiqi | Physical models of thrust wedges[END_REF][START_REF] Bose | An unstable kinematic state of theHimalayan tectonic wedge: Evidence from experimental thrust-spacing patterns[END_REF] along with the present study indicate that the occurence of a series of imbricate thrusts over graben sediments, preserved in the outer wedge of the Japan Trench [START_REF] Kodaira | Coseismic fault rupture at the trench axis during the 2011 Tohoku-oki earthquake[END_REF][START_REF] Nakamura | High resolution seismic imaging in the Japan Trench axis area of Miyagi, Northeastern Japan[END_REF], have formed over relatively weak decollement (Figs. 7c).

The structural interpretations from the drill core samples collected during JFAST and seismic data reveal that the frontal prism lying over the subducted horst block (~ high frictional patch) is structurally chaotic, which is also consistent with the observed deformation structures in our experimental models. The dip of beds measured in the core samples varies from 20° to 80° and they are also traversed by numerous closely spaced core scale faults (Chester et al., 2013;[START_REF] Nakamura | High resolution seismic imaging in the Japan Trench axis area of Miyagi, Northeastern Japan[END_REF][START_REF] Kirkpatrick | Structure and lithology of the Japan Trench subduction plate boundary fault[END_REF] (Fig. 7). Our experimental results show that the complexity in the internal deformation within the inner wedge increases with the onset of steepening of inner wedge slope when the frontal propagation of the decollement is resisted by the high frictional patch during ongoing shortening (Figs. 3 and4). This has led to infer that the variably steeply dipping beds in the core samples might have evolved through the process of mechanical rotation of earlier structures within the hanging wall when the decollement propagation was either temporarily stopped or was very slow due to high-frictional resistance along the horst block. Based on above discussions, it appears that subduction of horst-and-graben structure played a crucial role in increasing the complexity of deformation structures observed at the drill site near the Japan Trench. With continued plate convergence over time the deformation front eventually crossed the high frictional patch resulting the break in the surface slope observed between the inner and outer wedges in the frontal prism. In the laboratory experiments, the break in the surface slope of the wedge becomes prominent once the backstop overrides the high frictional patch and consequently, develops outer wedge by in-sequence thrusting (Figs. 3g,6f and 6j). Comparing our experimental results with seismic images reveal that the buttress (~ backstop in the experimental setup) in the natural situation near the Japan Trench currently lies on the west of the JFAST drilling site towards landward part of the wedge, as also predicted by earlier workers [START_REF] Tsuru | Along -arc structural variation of the plate boundary at the Japan Trench margin: Implication of interplate coupling[END_REF] (Fig. 7b and7c). Our experimental results further reveal that the observed slope sediments between the inner and outer wedge in the Japan Trench might have accumulated during the growth of supercritical wedge as identified in the intermediate stage in experiments and the sediment accumulation continued until the deformation front crossed the horst block (Fig. 3f). This, however, does not rule out the possibility of rotational slumping of the slope sediments at the frontal wedge by later reactivation during the 2011 megaearthquake event [START_REF] Strasser | A slump in the trench: Tracking the impact of the2011Tohoku-Okiearthquake[END_REF].

The present experimental study has also predicted why there is lack of natural examples of the occurrence of multiple slope-breaks in accretionary prisms.

Experiments with two high frictional patches show that the cessation of the propagation of outer wedge by another zone of high frictional patch in the front modifies the wedge geometry thoroughly by mechanical rotation of all pre-existing deformation structures including the zone of topographic slope-break, forming a wedge with a uniformly steep surface slope (Fig. 6). These observations have led to infer that the subduction of the horst block in the Pacific plate lying currently on the east of the Japan Trench will eventually modify the present wedge geometry having a topographic slope -break to a uniformly steep slope.

Conclusion:

Our main conclusions are as follows: 1) Down-dip frictional variations on the decollement cause temporal and spatial variations in the geometry of the frontal wedge.

2) Surface slope-break develops when the deformation front crosses from high to low basal friction. The break in the surface slope separates the entire wedge into two distinct structural domains: inner and outer wedges.

3) The inner wedge is characterized by steep wedge slope and complex internal structures, whereas the outer wedge is deformed by in-sequence thrusting, leading to shallow taper angle.

4) The experimental models thoroughly explain the structural evolution of the frontal wedge near the Japan Trench observed in seismic images and borehole data. Note that the deformation propagation towards front stopped after shortening of 14. 40 cm, but hinterland elevation continued to increase (e). 18.10 cm shortening was accommodated within the wedge, reorienting earlier structures during intermediate stage (f). Further shortening moves the deformation front above the lower frictional base developing distinct slope-break (g-h). [START_REF] Kodaira | Coseismic fault rupture at the trench axis during the 2011 Tohoku-oki earthquake[END_REF]. Note that experimental model closely reproduces geometrical and structural features observed in seismic image. Both experimental and seismic section show that surface slope of the inner wedge is steeper than that of the outer wedge. Imbricate thrusts are prominent within the outer wedge. The blue arrow marks the zone of topographic slope-break between inner and outer wedges in Figs. 7b and7c.

  Although sand layer of 1cm thickness should have been used in our experiments according to the scaling law, we have exaggerated the thickness of sand layers to 2 cm in all experiments for obtaining better resolution of deformation structures as well as to understand the deformation mechanism clearly during the experimental run. However, we ran experiments with sand layers of 1 cm thickness to verify the influence of model thickness in experimental results. These experiments show broad resemblance in the first order geometry of the wedge (see electronic supplementary Fig. S2) and therefore validates the use of 2 cm thick sandlayers in the model experiments. During the experimental run, we photographed through the lateral glass wall continuously after an interval of 5 seconds, keeping the camera at a fixed distance from the model. Model deformations were analyzed from successive photographs taken during the experimental run.

  With further horizontal shortening, the deformation front crossed the Zone II and propagated onto the region above zone I over low µb, simulating another graben, by the process of in-sequence thrusting and eventually, developed a separate wedge with a low angle of taper as expected to occur over low basal friction. Such spatial and temporal variations in the style and intensity of deformation across the wedge finally gave rise to distinct topographic slope-break in the wedge geometry separating the steep inner wedge from the low tapered outer wedge (Figs.3g-3h and 4a). During the growth of outer wedge, the internal deformation in the inner wedge completely stopped (Fig.4b) and the horizontal shortening was entirely accommodated by insequence thrusting over weak fictional base. For simplicity in description, we describe this stage of wedge growth as final stage, which characterizes the development of topographic slope-break with the cessation of internal deformation within the inner wedge. Experiments with varying width of Zone II showed that increasing the width of the Zone II (e.g. 30 cm) required large amount of shortening for the development of the topographic slope-break(Figs. 5

  increasing the complexity of deformation structures towards the hinterland part of the wedge (Fig. 6i, 6k). With continuous shortening, the deformation within this steep wedge completely stopped once the deformation front propagated over another low frictional base in the front with the onset of the development of new outer wedge by in-sequence thrusting (Figs. 6j, 6k). Based on above results, it is evident that the geometry of the frontal wedge is essentially transient with varying down-dip frictional strength on the decollement in tectonically active convergent belts over long time scale. Implication of varying down-dip basal friction On the basis of the above observations and interpretations on the experimental results we discuss below the role of basal friction in the structural development of frontal wedge near the Japan Trench. Our study reveals that varying down-dip frictional strength on the decollement causes a drastic change in the wedge taper, giving rise to a steep inner wedge and gentle outer wedge. This lateral change in the surface slope across the wedge separates the entire wedge into two distinctive structural domains: (i) complex internal deformation within the inner wedge and (ii) the outer wedge is deformed mostly by sequential thrusting. Experimental results

  steepens with the termination of decollement propagation by the increased frictional resistance along the decollement. The steepening of the wedge slope couple with intense internal deformation within it continues until the deformation front crosses from the zone of high to low friction on the basal decollement. The progress of the deformation front over the lower frictional base immediately stops internal deformation within the deformed wedge (Figs.3g-3h) and thereby, initiates a renewed phase of in-sequence thrusting in response to continuing horizontal shortening, leading to the development of shallow taper outer wedge. This process of wedge propagation over varying basal friction gives rise to the development of topographic slope-break between the inner and the outer wedges. The characteristic geometry of the slope-break in the tectonic wedge becomes prominent when the wedge front continues to deform over a uniform low frictional base for large horizontal shortening (Fig.5a-g).

5)

  Figure Captions: Figure 1: (a) Location map, showing the eastern coastline of Honshu, bathymetry

Figure 2 :

 2 Figure 2: A sketch of the experimental setup showing 3D view of the model setup.

Figure 3 :

 3 Figure 3: Progressive development of frontal wedge in sand models with 10 cm

Figure 4 :

 4 Figure 4: Plots show different stages of wedge growth for varying width of zone II

Figure 5 :

 5 Figure 5: Final stage of wedge development for varying widths of high frictional

Figure 6 :

 6 Figure 6: Progressive development of frontal wedge growth over multiple high

Figure 7 :

 7 Figure 7: Compilation of core data with depth at IODP sites C0019 and comparison

Table 1

 1 Modeling Parameters and material properties

	Parameter and model	Sand	Natural	Ratio:
	properties	(analogue	ptototypes	model/nature
		model)
	Length, L (m)	0.01	360	λ = 2.7x10 -5
	Density (kg m -3 )	1600	2700	δ =0.59
	Internal friction angle, φ

Acknowledgement: We thank scientific and drilling staff on Drilling Vessel Chikyu for their constant assistance during the IODP expedition 343. We thank Ylona van Dinther and Marc-Andre Gutscher for their insightful reviews and constructive suggestions for improvement of this work. We also thank W.P. Schellart for his guideline to revise the manuscript. The work is supported by MOES, Govt. of India and DST, Govt. of India grants to SB and PS acknowledge CSIR, India for financial support.