Florence Carre
email: florence.carre@ineris.fr

Julien Caudeville

Roseline Bonnard

Valérie Bert

Pierre Boucard

Martine Ramel

Florence Carré

Soil contamination and human health : A major challenge for global soil security

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

Introduction

Soil security refers to the maintenance and improvement of the world's soil resources so that they can continue to face six major challenges which are contributions to: (1) provision of food and fiber, (2) energy security, (3) water security, (4) climate change abatement, (5) biodiversity protection, (6) ecosystem service delivery [START_REF] Koch | Soil Security: Solving the Global Soil Crisis[END_REF][START_REF] Koch | Global Soil Week: Put Soil Security on the Global Agenda[END_REF]. By being able to perform five functions, among them storing, filtering and transforming of nutrients, substances and water (CEC, 2006), soil largely contributes to the quality of air, food and water, which has a direct link to human health. This chapter aims to demonstrate that Human Health should be recognized as another major challenge of soil security. The focus is made on solid or liquid hazardous chemicals storage, filtration and transformation by soil, i.e. soil contamination. A state-of-the-art on worldwide soil contamination, the relations to human health and the emerging scientific and societal needs to identify and reduce soil contamination illustrate the demonstration.

Soil contamination worldwide 10.2.1 Main soil contaminants

Solid or liquid hazardous chemicals contaminants result mainly from industrial, agricultural land disposal, transport, urbanization, mining, irrigation and military processes [START_REF] Jones | The State of Soil in Europe: a Contribution of the JRC to the European Environmental Agency's Environment State Outlook report -2010[END_REF][START_REF] Panagos | Contaminated sites in Europe: Review of the current situation based on data collected through a European network[END_REF]. In Europe, the United States and Australia, the main contaminants which have been reviewed so far are for about 60% Heavy Metals and Total Petroleum Hydrocarbons [START_REF] Huber | Progress in the management of contaminated sites[END_REF][START_REF] Mulligan | Remediation technologies for metal contaminated soils and groundwater: an evaluation[END_REF]; State of the Environment Committee, 2011), then Polycyclic Aromatic Hydrocarbons (HAP), Benzene, Toluene, Ethylbenzene, and Xylene (BTEX), Chlorinated Hydrocarbons (CHC), cyanides and phenols [START_REF] Panagos | Contaminated sites in Europe: Review of the current situation based on data collected through a European network[END_REF]. These contaminants concern mainly sites operating under legislation which makes mandatory pollution monitoring and control, like the European Industrial Emission Directive 2010/75/EU1 .

Review of contaminated sites

Two kinds of contamination are usually distinguished [START_REF] Murphy | Chapter 5. Advanced tools for interpreting data[END_REF]):

• Local soil contamination occurs where intensive industrial activities, inadequate waste disposal, mining, military activities or accidents introduce excessive amounts of contaminants in soil;

• Diffuse soil contamination is the presence of a substance or agent in the soil as a result of human activity that caused it to be emitted from moving sources, from sources with a large area, or from many sources. Diffuse soil contamination occurs where emission, transformation and dilution of contamination in other media has occurred prior to their transfer to soil. Water and air actions can explain long-range transport of contaminants. As a result, the relationship between the contaminant source and the level and spatial extent of soil contamination is indistinct [START_REF] Jones | The State of Soil in Europe: a Contribution of the JRC to the European Environmental Agency's Environment State Outlook report -2010[END_REF][START_REF] Van-Camp | Report of the Technical Working Groups Established Under the Thematic Strategy for Soil Protection[END_REF]. This map presents the distribution of only one category of hazardous chemicals, over the 350,000 inventoried and regulated substances 2 . It shows that, where data are available, 80% of pesticides are over-used, leading to diffuse soil contamination. This is actually the case for North, Central and South America, Western Europe, Middle East, China and New Zealand. What about the developing countries where data are currently missing? An extrapolation of the available data based on categories of economies would certainly show that 70% of the globe is over-covered by pesticides. At this stage, more data on diffuse soil contamination are required at national level through systematic monitoring programs or food contamination controls.

As stated by [START_REF] Horta | Potential of integrated field spectroscopy and spatial analysis for enhanced assessment of soil contamination: A prospective review[END_REF], remediation rates on identified contaminated sites are quite modest:

• European countries have undergone, only 5% remediation [START_REF] Panagos | Contaminated sites in Europe: Review of the current situation based on data collected through a European network[END_REF] of the identified and potentially contaminated sites and the number of recorded polluted sites across whereas the number of recorded contaminated site Europe is expected to increase by 50% by 2025 (EEAa, 2015); • Australia proceeds to about 0.5% per annum of remediation (State of the Environment Committee, 2011) certainly about the same amount as the number of newly contaminated sites every year [START_REF] Horta | Potential of integrated field spectroscopy and spatial analysis for enhanced assessment of soil contamination: A prospective review[END_REF]. These small remediation numbers are explained by the high costs of remediation (see § 10.4.4) and lack of incentives for land valuation.

The next sections are describing the underlying processes of soil contaminants -human health relationships, the assessment procedure and some statistically-based cases.

Soil contamination and human health

The study of soils and human health is a complicated endeavor: traditional scientific approaches that isolate a single variable, such as a specific contaminant, and then investigate that variable are usually not effective, because many of the issues that affect human health involve complicated and synergistic relationships [START_REF] Brevik | The past, present, and future of soils and human health studies[END_REF]Brevik and Burgess, 2013).

General principles

Soil contaminants can be exposed to humans by:

-transport processes like leaching, infiltration, run-off, gas volatilization, dispersion, advection, diffusion, sorption/desorption due to close connections to soil with air, water and biota. -fate and transformation processes variable according to the types of contaminants: organic compounds can undergo hydrolysis, oxidation, biodegradation, sorption, while inorganic compounds undergo complexation, dissolution and /or changes in speciation [START_REF] Epaa | Fate and Transport, Risk Assessment Training and Experience, Exposure Assemment Course Series -EXA 404[END_REF].

These processes depend on several factors that explain the bioaccessibility of the soil contaminants:

-inorganic compounds depend on climate and soil conditions like pH, cation exchange capacity also function of type and content of clay and type and content of organic matter, redox potential, Iron/Manganese oxides, soil moisture content, soil micro-organisms; -Organic compounds depend mainly on their potential absorption in the food chain measured by their distribution coefficient (octanol/water), Henry constant, water solubility, half-life and bioconcentration factor [START_REF] Epaa | Fate and Transport, Risk Assessment Training and Experience, Exposure Assemment Course Series -EXA 404[END_REF]. A following section is dedicated specifically to persistent organic pollutants.

The routes of exposure to humans are inhalation of dust and vapor coming from soil contaminants, ingestion of contaminated soil particles (mainly for children) or contaminated food, and dermal absorption through the skin. Once the intake by inhalation, ingestion or dermal contact have been done, the soil contaminant is absorbed by the gastrointestinal and pulmonary systems or absorbed by the skin and enters the systemic circulation system, representing the uptake and the bioavailable fraction [START_REF] Murphy | Chapter 5. Advanced tools for interpreting data[END_REF][START_REF] Epab | General Concepts of Exposure, Risk Assessment Training and Experience, Exposure Assemment Course Series -EXA 404[END_REF][START_REF] Dudka | Permissible concentrations of arsenic and lead in soils based on risk assessment[END_REF][START_REF] Hawley | Assessment of health risk from exposure to contaminated soil[END_REF].

When it exists, a soil guideline value (SGV) is a figure for the concentration of a contaminant in the soil that sets off 'possible risk' alarm bells. It means that further investigation and/or risk management are needed. These SGVs are generally derived from estimates of toxicity from a certain human intake of the soil rather than actual human uptake of the contaminant (Science Communication Unit, 2013). It is elaborated according to soil type, soil usage and the population type who can ingest or inhale the soil contaminant.

Regarding a contaminant, human health risk assessment is generally not framed only to soil contamination, but it involves also the contribution of other exposure media. Indeed, the estimation of human health risk is the combination of the hazard and the exposure of the contaminants from multiple pathways and routes usually identified from a site conceptual model. The ingested or inhaled dose is compared to the reference toxicological value (RTV) varying according to the exposure route, age, sex, genetic and health of populations [START_REF] Ineris | Valeurs toxicologiques de référence et méthodes de construction pour les effets sensibilisants pour une exposition cutanée[END_REF][START_REF] Bonvallot | Valeurs toxicologiques de référence : méthodes d'élaboration[END_REF]. For a contaminant with threshold effects, a RTV means the dose or concentration below which the occurrence of an effect is not expected. For non-threshold effects, a TRV means the additional probability of occurrence of an effect to an exposure unit [START_REF] Ineris | Démarche intégrée pour l'évaluation de l'état des milieux et des risques sanitaires[END_REF].

Multimedia models (cf. example presented in Figure 10.2) which provide appropriate quantitative frameworks for evaluating the complex interactions between chemicals and the environment (Caudeville et al., 2012) can be used for assessing exposure. These models can be spatialized (Caudeville et al., 2012;[START_REF] Macleod | Betr North America: a regionally segmented multimedia contaminant fate model for North America[END_REF][START_REF] Feijtel | Development of geography-referenced regional exposure assessment tool for European rivers-GREAT-ER[END_REF], or not [START_REF] Bonnard | Integration of the predictions of two models with dose measurements in a case study of children exposed to the emissions of a lead smelter[END_REF]. They can also be integrated with Physicologically-Based Pharmaco-Kinetics models for assessing the uptake impact of a contaminant directly on a target tissue at individual levels [START_REF] Maurau | Linking multimedia environmental and PBPK models to assess health risks of lead associated to drinking water -A case study. 21[END_REF]. The contribution of soil contaminants to the total exposure can be evaluated dividing the average inhalation or ingestion daily dose of soil contaminants by the total average daily dose of this contaminant (Caudeville et al., 2012).

When the risk is considered as unacceptable, remediation should be applied on the contaminated site in regards to its future usage.

Focus on persistent organic pollutants

Persistent organic pollutants (POPs) are extremely toxic substances for environment and human health at a world scale. They are persistent, bioaccumulative and toxic (PBT) chemicals and have long-range transport [START_REF] Weber | Dioxinand POP-contaminated sites-contemporary and future relevance and challenges Overview on background, aims and scope of the series[END_REF]. In people, reproductive, developmental, behavioral, neurologic, endocrine, and immunologic adverse health effects have been linked to POPs. People are mainly exposed to POPs through contaminated food ingestion coming from contaminated soil and water. In people and other mammals alike, POPs can be transferred through the placenta and breast milk to developing offspring. A number of populations are at particular risk of POPs exposure, including people whose diets include large amounts of fish, shellfish, or wild foods that are high in fat and locally obtained. In addition, sensitive populations, such as children, the elderly, and those with suppressed immune systems, are typically more susceptible to many kinds of pollutants, including POPs. Because POPs have been linked to reproductive impairments, men and women of child-bearing age may also be at risk [START_REF] Epa | Persistent Organic Pollutants: A Global Issue, A Global Response[END_REF].

Since 1995 the international community has been working on implementing the Stockholm Convention3 measures to eliminate or reduce the release of POPs into the environment. This Convention entered into force in May 2004. Initial action has been taken towards twelve POPs: Aldrin, Chlordane, DDT, Dieldrin, Endrin, Heptachlor, Hexachlorobenzene, Mirex, Toxaphene, PCBs, PCDDs and PCDFs. In 2009, extension has been done to 9 substances: Alpha Hexabromocyclododecane, Beta hexachlorocyclohexane, Chlordecone, Hexabromobiphenyl, Hexabromodiphenyl ether and heptabromodiphenyl ether (commercial octabromodiphenyl ether), Lindane, Pentachlorobenzene, Perfluorooctane sulfonic acid, its salts and perfluorooctane sulfonyl fluoride, Technical endosulfan and its related isomers, Tetrabromodiphenyl ether and pentabromodiphenyl ether (commercial pentabromodiphenyl ether). Endosulfan and Hexabromocyclododecane were added to the list in resp. 2011 and 2013. These 23 POPs are either pesticides, either industrial chemicals or by-products unintentionally produced during most forms of combustion. All of them can then be found in soils.

Emissions of these substances are regularly monitored in Europe, as shown in Figure 10.3 (source: EEAb, 2015). The vast majority of the 33 countries members of the European Environmental Agency have decreased their emissions due to the reduction of industrial, commercial and household uses. But as explained previously, these substances remain in undisturbed soils for long time-period and can be transferred to other locations once the soils are disturbed. Soil monitoring is then useful to complement the emission monitoring. In Europe, two attempts were done for soil mapping of POP. [START_REF] Villanneau | Which persistent organic pollutants can we map in soil using a large spacing systematic soil monitoring design? A case study in Northern France[END_REF] mapped some POPs in the North of France and demonstrated that it is possible to discriminate soils with POPs spatially correlated from others more randomly distributed perhaps due to redeposition phenomena. [START_REF] Ballabio | Highly spatially-and seasonallyresolved predictive contamination maps for persistent organic pollutants: Development and validation[END_REF] showed that PCB concentrations of Northern Italy, in mountainous areas, are highly correlated with soil temperature and organic carbon content, meaning that PCB concentrations follow weather seasonality.

Because POP measurements and analysis can be very expensive, mapping the soil POP burden can be facilitated through environmental bio-indicators such as lichens and mosses as indicator of air pollution [START_REF] Máguas | Guidelines for biomonitoring persistent organic pollutants (POPs), using lichens and aquatic mosses -A review[END_REF]. Research on soil POP pollution bio-indicator is now at the initial stage. The increase of knowledge on soil microbial activity with the development of new tools could certainly lead to better identify and assess soil POP bio-indicators.

Some potential and statistically-based cases of health effects of soil contamination 10.3.3.1 Potential health effects of soil contaminants

WHO listed some soil contaminants having potential effects of human health. This list has been completed by Brevik and Burgess (2013). It is presented below. Organic pesticides accumulate in the food chain.

Organic chemicals, including pesticides, have been linked to a wide range of health problems, but humans tend to be exposed to a cocktail of these chemicals at low levels. Conclusive proof of cause and effect in humans is challenging.

Main of the soil contaminants are indirectly ingested via the food chain.

Some statistically-based health effects of soil contaminants

• Death Triangle of soil dioxins and heavy metal pollution (Italy).

Hazardous-waste sites in the Campania region of Italy differ in that they are distributed over a wide densely populated area, with an estimated 1230 illegal dump sites in what has been referred to as "The Triangle of Death" [START_REF] Martuzzi | Cancer mortality and congenital anomalies in a region of Italy with intense environmental pressure due to waste[END_REF]. This is because, since the 1980s, hazardous-waste dumping has gone on largely uncontrolled. In addition to voluminous amounts of household waste, the region has also been plagued by widespread illegal dumping of toxic industrial chemicals and low-level radioactive wastes. The situation has been aggravated by the ongoing practice of burning rubbish, which in turn creates dioxins and other toxic compounds (PAH, heavy metals). De Felice et al. ( 2012) have demonstrated that the soil pollution in this region is significantly associated with effects on exposed population like higher oxidative stress, shorter telomere length and lower telomerase activity. These are known determinants of cell senescence and aging-related meiotic dysfunction in women, in peripheral blood mononuclear cells from healthy pregnant women, subjected to therapeutic abortion in the second trimester of pregnancy.

• Soil organochlorine chemicals around Besançon (France): [START_REF] Viel | Increased risk of non-Hodgkin lymphoma and serum organochlorine concentrations among neighbors of a municipal solid waste incinerator[END_REF] worked on a study area of three electoral wards (170,000 inhabitants), containing or surrounding the municipal solid waste incinerators (MSWI) of Besançon City (Eastern France). The MSWI of Besançon was put into service in 1971. Some legal guidelines for incinerator emissions have not been followed at this location. For example, in 1997, exhaust gases were not maintained at sufficient temperatures, allowing dioxins to be emitted. The first time that the dioxin concentration of an exhaust gas was ever measured (December 1997), it was found to be 16.3 ng WHO1998-toxic equivalency factor (TEQ)/m 3 , whereas the European guide value is 0.1 ng WHO1998-TEQ/m 3 . Once emitted the dioxins and its congeners (organochlorines), they are deposed in topsoil in very short-time where they accumulate. Exposure pathway of organochlorines is mainly through ingestion of contaminated food (above all animal lipids from meat, poultry and eggs, fish, shellfish, and dairy products like cheese and milk). Viel et al. worked on epidemiology around the site and collected serum samples from people having declared non-Hodgkin lymphoma and from people having not declared any pathologies. They found correlations between serum organochlorine concentrations and non-Hodgkin lymphoma.

• Links between Cd and Pb soil pollution with nephrotoxicity in Mbeubeuss (Senegal): [START_REF] Cabral | Effects of environmental cadmium and lead exposure on adults neighboring a discharge: Evidences of adverse health effects[END_REF] studied the links between the population located nearby the discharge of Mbeubeuss (30 km from Dakar City centre) where more than 395,000 tons per year of household solid waste have been received since 1970 with highly lead and Cadmium concentrated soils and nephrotoxicity. Blood and urine concentrations were measured for subjects living on control (less exposure to lead and cadmium) and exposed sites for more than 5 years. They found that exposed subjects exhibited significantly higher Cd and Pb levels in blood and urine than the controls. It has already been reported that one of the major mechanisms of the toxicity of both these metals was certainly driven by induction of oxidative stress conditions due to the overproduction of reactive oxygen species. As a result of this excessive production of reactive oxygen species in exposed subjects, a disturbance of the antioxidant defense system as well as an occurrence of lipid peroxidation were evidenced. Furthermore, changes in several sensitive and specific markers of nephrotoxicity clearly suggested the occurrence of early signs of impaired renal function for the discharge neighboring population. Regarding to these results, reactive oxygen species generation following low to moderate environmental exposure to Pb or Cd could be a possible mechanism of genotoxicity.

Regarding the contribution of soil contamination to population diseases, these case studies should be considered with caution since, as already explained previously, exposure and human health risk assessment are case by case approaches. In a widespread goal, more data on the contribution of other media, on the population, the time and duration of exposure (genetics, behavior,…) and on the presence of other kinds of contaminants (types and concentrations) would be needed (see the exposome concept developed in §12.4.3).

Future scientific and societal challenges related to studies on Soil -Human health relations

This section is based on the dimensions of soil security which has been described by [START_REF] Mcbratney | The dimensions of soil security[END_REF]. These dimensions are discussed in relation to the soil contamination topics.

Increasing the knowledge on soil condition

Soil condition is the current state of the soil, including modification by human activities [START_REF] Mcbratney | The dimensions of soil security[END_REF]. In our case, the focus is made on soil contaminants.

Emerging contaminants: the unknowns of soil condition

The NORMAN4 European network of reference laboratories, research centres and related organisations for monitoring of emerging environmental substances, is providing definitions of emerging substances and emerging pollutants from the monitoring point of view:

• "Emerging substances" can be defined as substances that have been detected in the environment, but which are currently not included in routine monitoring programmes at EU level and whose fate, behaviour and (eco)toxicological effects are not well understood.

• "Emerging pollutants" can be defined as pollutants that are currently not included in routine monitoring programmes at the European level and which may be candidates for future regulation, depending on research on their (eco)toxicity, potential health effects and public perception and on monitoring data regarding their occurrence in the various environmental compartments.

Sauvé and Desrosiers ( 2014) gave a broader definition of emerging contaminants preferably termed "contaminants of emerging concern (CEC)", defined as naturally occurring, manufactured or manmade chemicals or materials which have now been discovered or are suspected present in various environmental compartments and whose toxicity or persistence are likely to significantly alter the metabolism of a living being.

In April 2015, the NORMAN network identified a preliminary list of the 969 currently most frequently discussed emerging substances and pollutants [START_REF] Norman | The list of currently most frequently discussed emerging substances and emerging pollutants[END_REF] in aquatic systems. Due to subsurface water movements or anthropogenic activities like application of sewage sludge [START_REF] Ineris | Substances "émergentes" dans les boues et composts de boues de stations dépurations d'eaux usées collectives-caractérisation et évaluation des risques sanitaires[END_REF], not all but main of these identified substances and pollutants can be found in soils. Some emerging contaminants are Persistent Organic Pollutants (see §10.3.2), Pharmaceuticals and personal care products (PPCPs), i.e. any product used by individuals for personal health or cosmetic reasons or used by agribusiness to enhance growth or health of livestock, Endocrine-Disrupting Chemicals (EDCs), including synthetic estrogens and androgens, naturally occurring estrogens, and other chemicals that affect at low-dose hormonal functions in aquatic and terrestrial organisms.

The main challenges related to contaminants of emerging concern will be, in the coming years, to better understand their concentrations in the environment [through very robust detection and analytical methods] as well as their toxic effects on organisms. Better management of risks to human health and the environment [START_REF] Sauvé | A review of what is an emerging contaminant[END_REF] should be done by prioritizing contaminants to include to existing regulations (e.g. the European Water Framework Directive, REACH Directive, Ground Water Directive, Waste Directive) for usage and production restriction at domestic and industrial levels, based inter alia on (eco)toxicological criteria.

Development of new tools for a better assessment of soil condition

Soil monitoring of contaminants (including those of emerging concern) would be too expensive to be achieved systematically. In addition to the collection of legacy data on historical uses of sites, one of the solutions would be, to intensify the coupling between soil biomonitoring and 12 analytical tools and methods, where health effects are observed on soil fauna and flora. This can be done for instance with Effect Directed Analysis which aims to identify the compounds causing these effects after reducing sample complexity by combining biotests with fractionations [START_REF] Fetter | Effect-directed analysis for estrogenic compounds in a fluvial sediment sample using transgenic cyp19a1b-GFP zebrafish embryos[END_REF]. More generally, further (eco)toxicological research would be necessary to better assess human health risk particularly on chemical forms of contaminants and their toxicity related to environmental and biological conditions. Research devoted to a better understanding of the soil/water/air/flora nexus and the contaminants behavior under climate change conditions, of endocrine disruptors low-dose (eco)toxicological effects and of soil contaminants mixture (eco)toxicological effects would be very useful in the future.

Once a site is considered as contaminated, it is necessary to provide enough accurate data to minimize lack of statistical representativeness and increase the spatial quantification. The time spent for evaluating the presence and extent of contamination can be reduced by an adequate sampling plan [START_REF] Malherbe | Designing a contaminated soil sampling strategy for human health risk assessment[END_REF]) which can at the same time, reduce the project costs [START_REF] Horta | Potential of integrated field spectroscopy and spatial analysis for enhanced assessment of soil contamination: A prospective review[END_REF]. Proximal sensing that is all methods that sense the soil from outside [START_REF] Mcbratney | Defining proximal soil sensing[END_REF][START_REF] Viscarra Rossel | Proximal soil sensing: an effective approach for soil measurements in space and time[END_REF] can help in supporting the identification and characterization of contaminated site particularly with conjoint use of Vis-NIR and Portable X-ray fluorescence proximal sensors and laboratory analysis [START_REF] Horta | Potential of integrated field spectroscopy and spatial analysis for enhanced assessment of soil contamination: A prospective review[END_REF]. Extending innovation on these proximal sensors would be then of great interest for characterizing soil contamination.

Development of new remediation techniques for improving the soil condition

Remediation is considered as the management of the contaminant at a site so as to prevent, minimize or mitigate damage to human health, property or the environment. Two distinct classes of soil remediation can be defined: (a) in situ, (b) ex-situ (with on-site and off-site interventions). In-situ remediation -meaning that no excavation of the contaminated soil occurs -is often preferred because it is generally less expensive. However, it generally takes a longer time to effect treatment to the desired limits and there is less certainty about the uniformity of treatment because of the inherent variability in soil and aquifer characteristics and difficulty in monitoring progress. On the other hand, excavating a contaminated area (ex-situ approach) and treating the material on the same site (ex-situ, on-site) or transporting it to a remote site for cleaning (ex-situ, off-site) can often be more complicated and expensive. Nevertheless, ex-situ off-site remediation has the added bonus of taking the bulk of contaminants away before they can spread further. It also allows homogenization of the contaminated soil before treatment and ensures monitoring so that soils are cleaned to the desired limits within a relatively short time [suitable with transaction time of attractive land as high value commercial and residential lands] [START_REF] Lodolo | EUGRIS: Portal for soil and water management in Europe. Further description:-Remediation options overview[END_REF]. Ex-situ remediation with soil excavation and disposal to landfill "dig and dump" currently represents one third of the remediation technologies in Europe [START_REF] Panagos | Contaminated sites in Europe: Review of the current situation based on data collected through a European network[END_REF]. However, since space is needed for ex-situ remediation and particularly for disposal to landfill, it enhances soil grabbing which is not compatible with the UNCCD "zero-net land degradation" Sustainable Development Goal for Rio + 205 . More in situ remediation should then be expected in the future. The related techniques are:

13

-Thermal processes which use heat to increase the volatility, to burn, decompose, destroy or melt the contaminants. Cleaning soil with thermal methods may take only a few months or several years. The time it takes depends on type and amounts of chemicals present, size and depth of the polluted area, type of soil and conditions present; -Physico-chemical treatments which use the physical and/or chemical and/or electrical properties of the contaminants or of the contaminated medium to destroy (i.e., chemically convert), separate, or contain the contamination. The technologies are also sensitive to certain soil parameters which influence the contaminant availability and extractability such as the presence of clay or humic materials, pH, soil moisture; -Biological treatment which is a process whereby soil contaminants are transformed or degraded into innocuous substances such as carbon dioxide, water, fatty acids and biomass, through the action of microbial metabolism. Biological processes are typically implemented at low cost. Contaminants can be destroyed and often little to no residual treatment is required. However, the process requires more time and it is difficult, in general, to determine whether contaminants have been completely destroyed.

Additionally, microbes may often be sensitive to toxins or highly concentrated contaminants in the soil [START_REF] Lodolo | EUGRIS: Portal for soil and water management in Europe. Further description:-Remediation options overview[END_REF].

Biological treatments and more specifically the Gentle Remediation Options (GRO), which include in situ contaminant stabilization ("inaction") and plant-based remediation (or phytoremediation), allow for enhancing ecosystem services by contributing to the restoration of soil functions. A lot of efforts have been done for the last ten years to increase the efficiency of Trace Element remediation by testing different soil management practices, different crops under different soil conditions [START_REF] Kidd | Agronomic Practices for Improving Gentle Remediation of Trace Element-Contaminated Soils[END_REF]. Further research and development are needed for remediating other kinds of contaminants and for increasing the knowledge on bioaugmentation techniques in order to improve the efficiency of these positive environmental balance technologies.

Regarding broad aspects of soil remediation, it is important to evaluate the effects of exhaustive remediation alternatives on soil functions when assessing the overall sustainability of decision options. To this aim, a generic approach conceptualizing linkages between soil functions, soil ecosystem services and the environmental, social and economic sustainability domains has been proposed by [START_REF] Rosén | SCORE: A novelmulti-criteria decision analysis approach to assessing the sustainability of contaminated land remediation[END_REF] through the development of the SCORE tool based on multicriteria decision analysis. This tool integrates also a quantification of the uncertainties and their impact on decision-making. This approach is revolutionizing the remediation approaches by combining experts and stakeholders' judgments and preferences -which deals with the integration of the connectivity dimension (cf §12.4.3)-and by integrating sustainable land management concepts -which deals with the integration of soil condition and capability dimensions-in the current risk-based approaches.

Increasing the connectivity and the codification related to soil contamination

Connectivity is the social connection of soil managers, custodians, and users of soil products and services to the soil and to each other whereas codification relates to policy frameworks, it is the identification of policies that degrade soil security and those that secure soil [START_REF] Mcbratney | The dimensions of soil security[END_REF]. These two dimensions are discussed together in this section because awareness raising of the broad society allows for enhancing best practices that can sometimes lead to either new policies either new standards, labels or voluntary certificates. Since connectivity is considered here as the driver of codification, this section is dedicated to connectivity.

As already emphasized by [START_REF] Bouma | Reaching out from the soil-box in pursuit of soil security[END_REF], one of the success keys for securing soil is the involvement of the society [and all concerned stakeholders] in the preparatory and implementation phases of a soil management project. The concerned stakeholders are those involved in field scale and regional scale spatial planning. The potential actors are policy / decision makers, private and/or public funders and citizens who live in the area and the surrounding area concerned by the project. The identification of the societal needs at the initial stages of the project, facilitated by knowledge brokers, increases the acceptability of the project and its sustainability. During the implementation phase, the societal involvement allows also for a better understanding of technical bottlenecks that could lead to deviations of the project target. Such trans-disciplinary research project eases the integration of research outcomes in decision making and policies.

Another success key raised by [START_REF] Bouma | Reaching out from the soil-box in pursuit of soil security[END_REF] is the development of inter and trans-disciplinary programs dealing with food, water, climate, biodiversity and energy problems. Health is also an important topic to target for which, as demonstrated previously, soil has a central place.

Monitoring soil, water, fauna/flora and human health through common programs would lead to a better understanding of the critical zone and would participate to the increase of knowledge on the exposome concept. The exposome is the measure of all the exposures of an individual in a lifetime and how those exposures relate to health6 . On a long-term, this knowledge will lead to a better prevention of pollution and a better land management through policies, standards or individual and societal voluntary basis actions.

Increasing the knowledge on soil capital

The dimension of soil capital is underpinned by the notion that by placing a monetary value on an asset enables a society to value or secure the asset and make meaningful comparisons of soil with different capabilities and conditions [START_REF] Koch | Soil Security: Solving the Global Soil Crisis[END_REF].

Evaluating the cost of soil contamination at global level allows for emphasizing the importance of protecting soil against contamination. The cost can be evaluated according to four components as described in Gorläch et al. ( 2004):

-The on-site or private cost (PC) of damage which is for instance the costs of the reclamation of the site within redevelopment project performed by private investor. It is also the cost of impact monitoring; -The on-site private cost of mitigation and repair measures (MC) which is the cost of e.g. demolition of contaminated buildings, soil decontamination and treatment, acquisition of contaminated land and refitting of forests; -The off-site (social) cost (SC) which is the cost of human and environmental impacts (e.g. cost of disease, loss of agricultural income, decrease of housing prices) -The non-user cost (DC) which is the cost of loss of non-use value for citizens. This cost varies according to the type of contaminant, the spatial extent of the pollution and its intensity, the natural characteristics of the contaminated site, the socio-economic characteristics of the surrounding area and the tolerable risk levels depending on the regulation of each country. Based on literature review of [START_REF] Horta | Potential of integrated field spectroscopy and spatial analysis for enhanced assessment of soil contamination: A prospective review[END_REF] which estimate the total number of locally contaminated sites to about 10 and 20 Millions, and evaluation of costs made by Gorläch et al. (2004) and [START_REF] Panagos | Contaminated sites in Europe: Review of the current situation based on data collected through a European network[END_REF] which provided data representative of the European continent (so easily upscalable to other continents) rough estimations can be made of the total cost of soil contamination (Table 10.3). [START_REF] Görlach | Assessing the Economic Impacts of Soil Degradation[END_REF] This table provides an estimation of the global cost of local contamination that is between 166 billion € (185 billion US $)/ yr and 1.4 trillion € (1.11 trillion US $)/ yr (between 0.25 and 1.89% of global GDP). This upper boundary represents 10% of the maximum cost of climate change estimated by [START_REF] Stern | Summary of Conclusions[END_REF] which is about 20% of the global GDP. This wide range cost estimation emphasizes the fact that many environmental and social drivers influence the total costs. Rough estimates of the cost are then associated with many uncertainties that would decrease when assessing the cost at field or regional scales. These high number estimates, which show that soil contamination is a highly relevant economic issue, are based only on local contamination data, not on diffuse contamination. Furthermore, in a context of bringing value to contaminated sites, these numbers should be analyzed in regards to the economic valuation of ecosystem services enhanced by soil restoration. Such evaluation could enhance a dynamic and smart green businesses related to the remediation market.

Conclusions

This chapter aimed to demonstrate that Human Health should be considered as another major challenge of global soil security by emphasizing the fact that:

(a) Soil contamination is a worldwide issue. Estimations can be done based on local contamination but the extent and content of diffuse contamination is largely unknown. (b) Although soil is able to store, filter and reduce contamination, it can also transform and make accessible soil contaminants and their metabolites, contributing then to human health impacts. This has been illustrated by several examples.

The future scientific and societal challenges related to Soil-Human Health studies and soil security dimensions are:

(a) For the condition and capability dimensions: more focus on emerging contaminants, more fast analytical tools and remediation techniques dealing with sustainable land management; (b) For the connectivity and codification: more transdisciplinary approaches, multi-actors involvement and multi-disciplinary Environment-Health monitoring programs; (c) For the capital dimension: better assessment of contamination costs but also economic value of remediation options.

  Panagos et al. (2013) estimated contaminated sites and potentially contaminated to be around 0.005 sites per capita for the European Union and a population of 1 billion. Based on these figures, Horta et al. (2015) estimated emerging economies to have 0.0025 contaminated sites and potentially contaminated per capita, their population being 2 billion, developing economies to have 0.001 contaminated sites and potentially contaminated per capita, their population being 4 billion. At global level, the estimates of contaminated sites and potentially contaminated are then between 10 million and 20 million sites (including uncertainties). These figures, representing big numbers, concern mainly local contamination. Estimation of diffuse soil pollution could be done for instance by integrating available global monitoring data on hazardous chemicals, e.g the quantity of pesticides per ha of arable land for the period 2005-2009 (FAO, 2013) represented in Figure 10.1.

Figure 10 . 1 -

 101 Figure 10.1 -Map of pesticides per ha of arable land (kg/ha-period 2005-2009) -Source: FAO (2013)

Figure 10

 10 Figure 10.2-Block diagram of the transfer and exposure pathways taken into account in the PLAINE GIS-multimedia platform (source: Caudeville et al., 2012).

Figure 10

 10 Figure 10.3-Emission trends of POPs from 1990 to 2011 (EEAb, 2015) -HCB -hexachlorobenzene, HCH -hexachlorocyclohexane, PCBs -polychlorinated biphenyls; dioxins & furans; and PAHspolyaromatic hydrocarbons.

Table 10

 10

	Chemical of concern,	Toxic to humans how?	Health effects
	Sources/uses
	Cadmium	Cadmium in soil or water	Liver and kidney damage, low
	Zinc smelting, mine	used for irrigation can lead	bone density.
	tailings, burning coal or	to accumulation in plants	These symptoms are known as
	garbage containing	that enter the human food	itai-itai disease. First identified
	cadmium, rechargeable	chain. Cadmium may also	when cadmium from mining in
	batteries (nickel-	accumulate in animals at	the Toyoma Prefecture of Japan
	cadmium batteries	levels that do not affect the	led to high levels of cadmium in
	account for over four-	animal's health, but can	rice, which accumulated in local
	fifths of cadmium	affect humans consuming	people. Diets poor in iron and
	consumption), pigments,	animal products.	zinc vastly increase the negative
	TVs, solar cells, steel,		health effects of cadmium.
	phosphate fertiliser,		Carcinogenic (by inhalation).
	metal plating, water
	pipes, sewage sludge.
	Dioxin	Human exposure to dioxin	Dioxins are highly toxic and can
	Including Polychlorinated	and dioxin-like substances	cause reproductive and
	dibenzodioxins (PCDD)	occurs mainly through	developmental problems, damage
	and Polychlorinated	consumption of	the immune system, interfere
	dibenzofurans (PCDF).	contaminated food. More	with hormones and also cause
	Waste incineration,	than 90% of human	cancer.
	reprocessing metal	exposure is through food,
	industry, paper and pulp	mainly meat and dairy
	industry, contaminated	products, fish and shellfish.
	herbicides (a major
	source). Stored PCB-
	based industrial waste
	oils (often with large
	amounts of PCDFs).
	Lead	Leaded fuel and mining	• Neurological damage
	Batteries, solder,	activities are common causes	• Lowers IQ and attention
	ammunition, pigments,	for elevated lead levels in	• Hand-eye co-ordination
	paint, ceramic glaze, hair colour, fishing equipment, leaded gasoline (vehicle exhausts), mining, plumbing, coal burning,	topsoil.	impaired • Encephalopathy • Bone deterioration • Hypertension • Kidney disease
	water pipes
	Mercury	Main exposure route for the	• Central nervous system (CNS)
	Electrical switches,	population at large is via	and gastric system damage
	fluorescent light bulbs,	eating contaminated seafood.	• Affects brain development,
	lamps, batteries,	For children is direct	resulting in a lower IQ
	thermometers, dental	ingestion of soil.	• Affects co-ordination, eyesight
	fillings, mining

.2-WHO chemicals of major public health concern directly in relation to soils and human health impacts. Sources: Science Communication Unit (2013), Brevik & Burgess (2013), US Agency for Toxic Substances & Disease Registry (website): www.atsdr.cdc.gov

Table 10 .3 -Estimation of the total cost of soil contamination based on data representative of the European continent (Panagos et al., 2013; Görlach et al., 2004) and rules of three.

 10

	Number of			Cost (in M€ / yr)
	sites (total
	estimation
	in bold)
		PC	MC	SC	DC	Total cost	Study	extent
		(%total	(%total	(%total	(%tota	(PC+MC+SC	(authorship)
		cost)	cost)	cost)	l cost)	+DC)
	1.5 M	192	6,658	17,126	965	24,941	European extent -
		(0.7)	(26.7)	(68.7)	(3.9)		intermediate
							costs estimated
	10 -20 M					166,273 -332,546	from case (Görlach et al., different studies
							2004)
	342,000	171	6,500	16,725	949	24,345	European extent-
	10 -20M					711,842 -1,423,684	Management Cost has been estimated based
							on	survey
							(Panagos et al.,
							2013) and other
							types of costs
							have	been
							estimated based
							on the %total cost
							of

http://ec.europa.eu/environment/industry/stationary/ied/legislation.htm

www.cas.org

http://www.pops.int/documents/convtext/convtext_en.pdf

http://www.norman-network.net/?q=node/19

http://www.unccd.int/Lists/SiteDocumentLibrary/Rio+20/UNCCD_PolicyBrief_ZeroNetLandDegradation .pdf

http://www.cdc.gov/niosh/topics/exposome/


Fazia Fouchal

Frédéric Lebon

Amna Rekik

Isabelle Titeux

Fouchal Fazia

Gemh

On the modeling of brick-mortar interface

Introduction

Traditionally, for thousand of years, masonry techniques were commonly used for the building of homes, monuments, walls, and retaining walls. Masonry is one of the oldest construction materials. Since masonry is a composite structure, however, failure of these structures will depend on the properties of the materials (mortar, bricks, etc.), as well as on the characteristics of the bonding between the various components. Two main methods of modeling masonry structures have been developed in the literature. The first method involves macroscopic models and homogenization techniques: the wall is assumed to be a single structural element characterized by a non-linear response when it is exposed to external forces. The second method has been developed for predicting the evolution of cracks and damage at the interface brick-mortar or brick-brick. This chapter deals with two families for the modeling of brick-mortar interface. The first part of this chapter deals with the experimental characterization of the materials (bricks and mortar) and the brick-mortar interface. Hereafter, we describe experimental studies on the shear behavior of masonry on the local scale, in the case of two different assemblies composed of two and three full/hollow bricks, with or without confinement. Two other structures are presented: a small wall made by seven bricks and the classical problem of a small wall under diagonal compression. The second part of this chapter deals with a phenomenological model of interface. The mechanical modeling approach (and in particular the RCCM [START_REF] Raous | A consistent model coupling adhesion, friction and unilateral contact[END_REF] adhesive model adopted) is first presented. The model is based on the concept of adhesion variable due to Frémond [START_REF] Frémond | Adhérence des solides[END_REF]. A variation equation of this variable is introduced and the coefficients are identified experimentally. The numerical procedure used is then described. Lastly, some numerical examples are given and compared with the experimental data. The third part presents a multi-scale model of interface. The method is based on homogenization theories and asymptotic analysis. In the present work, we assume the existence of a third material: the brick-mortar interface, which is considered as a mixture of brick and mortar with a crack density. To obtain the effective properties of the damaged intermediate material, three aim steps are performed. First, we calculate the exact effective properties of the crack-free material using homogenization techniques for laminate composites, and thus define a first homogeneous equivalent medium. In the second step, we assign a crack density to the material. To model the macroscopic behavior of the cracked material, we use the Kachanov model [START_REF] Kachanov | Effective elastic properties of cracked solids: Critical review of some basic concepts[END_REF] and then define a new homogeneous equivalent medium. Finally, in order to be sandwiched between the brick and mortar, this material is given a small thickness, and its mechanical behavior is derived using asymptotic techniques to shift from the micro to the macro level. A variation law of the crack length is introduced. The numerical procedure used is then described. Lastly, some numerical examples are given and compared with the experimental data.

Experimental Study of The Masonry

Introduction

The first part of this paper is dedicated to the experimental study of the mechanical behavior of the masonry. The experimental studies were performed on the materials and masonry specimens (single, couplet, triplet, wall) composed of full and hollow bricks in order to identify the mechanical behavior of the bricks, mortar and bricks /mortar joint, in particular under shear tests with and without confinement pressure.

Characterization of Materials

Mortar

The mortar used in this study is a ready-to-use mortar from "Weber and Boutrin" based on sand and cement (ciment is Portland type 52.5). The maximum size of the sand grains is 5 mm. The mortar characteristics are given in Table 1.

The standard tests following the EN 196-1 norm [START_REF]Norme Européenne , Norme Franc ¸aise, Méthodes d'essais des ciments -Partie 1: détermination des résistances mécaniques[END_REF] were performed to determine the traction and compression strength [START_REF] Fouchal | Contribution à la modélisation numérique des interfaces dans les structures mac ¸onnées[END_REF].

The results concerning the flexion and compression limits are summarized in Table 2. The flexion strength is around 4, 26M P a and the compression strength is around 23M P a [START_REF] Fouchal | Contribution à la modélisation numérique des interfaces dans les structures mac ¸onnées[END_REF]. The elastic modulus given in [START_REF] Gabor | Contribution à la caractérisation et à la modélisation des mac ¸onnerie non renforcées et renforcées par matériaux composites[END_REF] is equal to (4000M P a).

Bricks

Full and hollow cooked earth bricks were used for the mechanical tests. The dimensions of each brick are 210 mm (length), 100 mm (width), 50 mm (height). Hollow Bricks are composed with ten holes ( 25 × 25 mm 2 in size) arranged in two rows. A compressive standard tests using NF EN 772-1 norm [START_REF]Norme Européenne, Norme Franc ¸aise, Méthodes d'essai des éléments de mac ¸onnerie -Partie 1: détermination de la résistance à la compression[END_REF] were carried out on a series of three units full/hollow bricks in order to identify the compressive strength, elastic modulus and Poisson coefficient of the masonry units. Bricks are equipped with strain gauges glued in transverse and longitudinal directions (unidirectional compression test) and an extensometric sensor.

Compressive load was applied on the upper face of the brick up to failure in two steps: the load was gradually increased as shown in Table 3; half-way to maximum pressure within 1 min. The elastic modulus is determined from the strain-stress curve at 30 % of the ultimate load. Three tests are carried out on each kind of brick [START_REF] Fouchal | Contribution à la modélisation numérique des interfaces dans les structures mac ¸onnées[END_REF]. The curve giving the longitudinal deformation with respect to the normal stress and transversal deformation with respect to the normal stress are shown in Figures 1 and2.

The quantitative data obtained on these mechanical parameters are summarized in Tables 4 and 5.

The experimental results obtained were similar to the mean value recorded by two gauges. The dispersion of the results was very small. In order to determine the influence of the unit volume, two kinds of prism have been tested. The first kind is composed of two bricks, the second one is composed of three bricks (Figure 3). For each kind of unit volume, full or hollow bricks have been used. Mortar joint thickness used for the samples is equal to 10 mm. The aim of this experimental study is to determine the shear behavior and the rupture modes at the interface brick/mortar. Prisms were prepared following the standard NF EN 1052-3 norm [START_REF]Norme Européenne, Norme Franc ¸aise, Méthodes d'essai de la mac ¸onnerie -Partie 3: détermination de la résistance initiale au cisaillement[END_REF]. The samples were subjected to a monotonously increasing load until damage occurred [START_REF] Fouchal | Contribution to the modeling of interfaces in masonry construction[END_REF].

Relative displacement between the loading brick and the unloading brick is measured by extensometric LVDT captors. Test machine and captors are connected with a PC in order to record data during the test notably the longitudinal strain and the applied load data.

Curves giving the shear stress with respect to the relative displacement were plotted that will determine the shear behavior law. The results are presented and commented in the following paragraphs.

-0,0005 0 0,0005 0,001 0,0015 0,002 0,0025

Longitudinal strain

Normal stress (MPa) sensor gauge 1 gauge 2 mean Figure 5 shows the different failure modes obtained under shear test for the full brick prisms.

Hollow Bricks

Figure 6 represents the recorded displacements with respect to the shear load τ = F A where F is the imposed load on the upper face of the prism and A is the shear surface (A = hight × length = 210 × 100 mm 2 ).

Figure 7 shows the different failure modes obtained under shear test for the Hollow brick prisms.

Discussions

The experimental studies of different masonry samples presented have shown a nonlinear behavior on the local scale. We have observed a rigid elastic behavior to the rupture. The behavior of the specimen in full bricks is fragile in contrast to the response of the specimen in hollow bricks which is characterized by a softening behavior followed by the sliding movement between the adjacent bricks. The obtained results on hollow bricks samples have shown a wide dispersion. This is due essentially to the nonuniform distribution of the mortars spikes and local defects of the components of bricks masonry. We have noted that the couplet and the triplet samples made by a hollow bricks possess the same behavior. Consequently, the choices of basic cell have no influence on local scale. The rupture modes analysis confirms heterogeneity of masonry structures. This study allows us to identify phenomena that govern the rupture of the masonry at a local scale and to characterize the mechanical properties and the behavior law to take into account in finite elements computations [START_REF] Fouchal | Contribution à la modélisation numérique des interfaces dans les structures mac ¸onnées[END_REF] presented in the next section of this chapter.

Mechanical Behavior of Small Masonry Structures Under Shear Loading With Confinement

Small masonry structures subjected to both shear load and lateral confinement were study in [START_REF] Gabor | Analysis and modeling of the in-plane shear behavior of hollow brick masonry panels[END_REF]. In this section, we will focus on mechanical tests data obtained in [START_REF] Gabor | Contribution à la caractérisation et à la modélisation des mac ¸onnerie non renforcées et renforcées par matériaux composites[END_REF][START_REF] Gabor | Analysis and modeling of the in-plane shear behavior of hollow brick masonry panels[END_REF]. For this case, the dimensions of hollow ceramic bricks used are (210 × 100 × 50mm 3 ), composed of ten holes. The holes sizes are 25 × 25 mm 2 arranged in two rows. Mean value of compression strength and elastic modulus obtained by the standard compressive test on ten hollow bricks are 13, 7M P a and 5820M P a, respectively. Mortar used in this study is a ready-to-use mortar from "Lafarge-LANKO151" based on sand and cement (ciment is Portland type 52.5). The maximum size of the sand grains is 5 mm. The mortar characteristics are given in Table 1. Figure 8 presents the samples that were used for the mechanical tests performed according to RILEM recommendations [START_REF]LUMB5-Short -term shear test for interface between the masonry unit and mortar or moisture -Insulating interlayer[END_REF]. Eighteen prisms were tested under loads confinement with various values between 0M P a and 1.6M P a. The mechanical behavior of prisms showed in Figure 9 is characterized by a very rigid behavior for elastic domain, with little displacement (order of microns). The softening behavior is observed after the maximum stress followed by sliding movement between adjacent bricks. The confinement stress led to softening behavior in the masonry, when the confinement stress σ = 0M P a the failure appears immediately. Identical tests give the same curves but with dispersion on the value of shear stress limit. This difference can be explained by the presence of spikes in the brick holes. Figure 10 show than spicks in the holes prevents brutal failure of a shearing prism and conditioned the shear stress limit. Analysis of the interface brick-mortar damage can identify two phenomena which are responsible for the prisms failure.

• spicks shearing

• rupture of the inner walls of the brick

The stress confinement σ has no significant influence on the evolution of limit shear stresses. The experimental data of these tests identifies three main values: 1.63M P a, 1.85M P a and 2.2M P a, respectively, as the lower, middle, and maximal value.

Mechanical Behavior of Small Wall in Diagonal Compression

Now we present the mechanical results of the compression diagonal test obtained on the small wall masonry performed by Gabor [3]. This test can produce a stress and strain state where shear and compression are predominant. It is also possible to reproduce the failure by traction diagonal. Such loads are similar to loading developed in masonry construction subjected to earthquake. Figure 11 shows the experimental device used for this study. Test is monotonous with controlled loading. Wall dimensions are 870 × 840 × 100mm 3 ; it is made with the same materials presented in prevoius paragraphs as recommended by RILEM [START_REF]LUMB6-Diagonal tensile strength tests of small wall specimens[END_REF]. Walls were tested after 28 days after manufacture. Mortar joint thickness is 10mm. Three walls were created in this work.

To obtain a good load level during a test and produce a global stress -strains state on masonry in the aim to produce a failure on the wall diagonal corners have been set by a metal shoe filled with concrete. Two different values for metal shoe length were considered in mechanical test. The first is equal to L/10 the second one is equal to L/6. The first wall was tested with the first value in the second and third walls were tested with the second value.

State strain was measured by the compression (resp. tense) diagonal shortening (resp. elongation). Extensometric LVDT captors were fixed on the twice diagonal directions in order to measure the displacement between two points in the same diagonal.

Curves load-strain Figures 12 obtained experimentally can evaluate global response of masonry wall.

In the first test with L/10, a failure was produced by the sliding and crushing of the joints in support zone. The maximum load is equal to 160kN and failure is located on the three rows. In this case, the embedding conditions of corners wall " metal shoe length " cannot distribute the load in wall satisfactorily. In order to avoid these failure modes, the boundary conditions were changed to a new length support equal to L/10 was considered for next tests. In this case, failure was observed on central zone wall following the diagonals. Cracks were crossing both bricks and mortar joint, see Figure [START_REF] Moreau | On unilateral constraints, friction and plasticity[END_REF].

Elastic linear behavior was observed in analysis of the curves r 1 and r 2 (Figure 12). The first wall is characterized by an elastic post level which appears at 90% of the limit load that predicts a degradation of mechanical properties. Maximal load for the first wall is equal to 215, 3kN and 251, 8kN , for the second. Strains and loading measured are summarized in Table 6. Results shows a gap of 17% between maximal load obtained on the last two walls tested. This difference can be explained by the internal structure wall. The strength is governed essentially by the brick-mortar interfaces. That is confirmed by the experimental study presented in the first section of this work. In this section, we are interested in the mechanical behavior of the interfaces for masonry modeling structures when using the materials and interfaces characteristics that were determined experimentally in the previous section [START_REF] Fouchal | Contribution to the modeling of interfaces in masonry construction[END_REF][START_REF] Fouchal | Contribution à la modélisation numérique des interfaces dans les structures mac ¸onnées[END_REF]. First, RCCM model [START_REF] Raous | A consistent model coupling adhesion, friction and unilateral contact[END_REF][START_REF] Monerie | A model coupling adhesion to friction for the intercation between a crack and a fiber/matrix interface[END_REF] that is based on the adhesion intensity is presented. Second, this model was adopted to describe the interfaces between mortar and full or hollow bricks in particular; in this case, triplet assemblies subjected to shear loading. The mechanical behavior predicted by this model is compared with the previously obtained in the experimental data.

Presentation of RCCM Model

RCCM adhesion model was adopted to model the mortar/brick interfaces [START_REF] Raous | A consistent model coupling adhesion, friction and unilateral contact[END_REF][START_REF] Monerie | A model coupling adhesion to friction for the intercation between a crack and a fiber/matrix interface[END_REF]. This model combines the unilateral contact conditions (non-penetration between the mortar and the brick) with friction and adhesion between two deformable solids. The local constitutive equations required for this model are deduced from thermodynamic considerations and based on a material surface hypothesis for the contact zone. The basic idea underlying this model is to introduce a new state variable describing the contact state. This adhesion intensity variable, denoted β, was initially introduced by [START_REF] Frémond | Adhérence des solides[END_REF]. This variable gives the relative proportion of the active links between two bodies in contact. This variable is chosen as:

• β = 1,
total adhesion

• 0 < β < 1, partial adhesion • β = 0, no adhesion
We are working in the framework of the contact between two deformable solids. The contact could be defined by a punctual correspondence between two surfaces in contact Γ 1 c and Γ 2 c of the domains Ω 1 and Ω 2 of R d (d = 2, 3), respectively. At initial time t = t 0 , we assume that Γ c = Γ 1 c = Γ 2 c . The relative displacement between two points located on the two surfaces in contact is denoted by [u] with [u] = u 1 -u 2 . Let R be the density of the contact forces. We take n 1 and n 2 to denote the external unit normal vectors to the boundaries of the two domains. The decomposition into normal and tangential parts is written:

[u] = [u N ]n 1 + [u T ] with [u N ] = [u].n 1 (1) R = R N n 1 + R T with R N = R.n 1 (2)
The state variables for the thermodynamical description of this model are:

• Strain tensor e = (e ij ) • Displacement jump [u]
• Intensity of adhesion β b is taken to denote the adhesion viscosity coefficient, w to denote the Dupré energy, µ to denote the friction coefficient and C N (resp. C T ) to denote the initial normal (resp. tangential) stiffness of the interface. In what follows, ḟ denotes the rate of the function f . The constitutive equations of the interface are given by the following equations, as based on state laws and complementarity laws:

Unilateral Contact With Adhesion R N -C N [u N ]β 2 ≥ 0; [u N ] ≥ 0; (R N -C N [u N ]β 2 )[u N ] = 0 (3)
Friction With Adhesion

||R T -C T [u T ]β 2 || ≤ µ|R N -C N [u N ]β 2 | ||R T -C T [u T ]β 2 || < µ|R N -C N [u N ]β 2 | ⇒ [ uT ] = 0 ||R T -C T [u T ]β 2 || = µ|R N -C N [u N ]β 2 | ⇒ ∃λ ≥ 0, [ uT ] = λ(R T -C T [u T ]β 2 ) (4)
Evolution of The Intensity of Adhesion

b β = -(w -(C N [u T ] 2 + C T |[u T ]| 2 )β) -if β ∈ [0, 1[ b β ≥ -(w -(C N [u T ] 2 + C T |[u T ]| 2 )β) -if β = 1 (5)
Note that if there is no adhesion (β = 0), this model involves the classical Signorini-Coulomb problem.

A graphic interpretation of the tangential part of this RCCM model given in figure 14 shows the changes with time in the tangential forces depending on the tangential displacement jump. The changes in β lead to irreversible effects. If β decreases, the adhesive forces will decrease and eventually disappear. In the case of pure traction ([u N ] > 0), the adhesion resistance (R N = C N [u N ]β 2 ) is activated (elasticity without damage). β decreases when the displacement becomes sufficiently large for the elastic energy to become larger than the adhesion limit w.

Implementation of RCCM Model

The numerical problem was solved using the open computer code LMGC90 (http://www.lmgc.univ-montp2.fr/ dubois/LMGC90/). This code is a numerical platform dedicated to the modeling and simulation of dynamic multibody problems. Problems were approached in the general framework of dynamics. Discretized equations of the problem P are written as: M q = F (q, q) + P (t) + r, + interface conditions + initial conditions and boundary conditions [START_REF]Norme Européenne, Norme Franc ¸aise, Méthodes d'essai des éléments de mac ¸onnerie -Partie 1: détermination de la résistance à la compression[END_REF] with q is a parametrization of the system (degrees of freedom), M is the mass matrix, F (q, q)+P (t) are the internal and external loading vectors, r is the vector of contact forces. Problems were usually approached using θ-methods and the Non-Smooth Contact Dynamics (NSCD) method [START_REF] Moreau | On unilateral constraints, friction and plasticity[END_REF][START_REF] Moreau | Unilateral contact and dry friction in finite freedom dynamics[END_REF][START_REF] Jean | Frictional contact in rigid or deformable bodies: Numerical simulation of geomaterials[END_REF]. Due to the contact conditions, a fairly small time-step is chosen and the problem is condensed in the local frame associated with the contact nodes. The local problem is solved using a non-linear Gauss-Seidel method.

The interface is governed by the RCCM law as presented earlier in this chapter. Contact between bodies is defined by contact nodes. Contact nodes are located between two nodes in the mesh of an element in contact at distances of 0.2 and 0.8, respectively, along each segment in contact (figure 15). In this procedure, the bodies (bricks and mortar) are modeled using Q4 quadrangular finite elements. The numerical tests are performed with a constant time step equal to ∆t = 0.5 * 10 -3 s. The computations require 2000 increments in order to reach values resembling the experimental data, and θ (in the time integration method) is fixed and taken to be equal to 0.55.

Numerical Results: Mechanical Behavior of Small Masonry Structures Under Shear Loading

In this section, numerical simulations carried out using LMGC90 are presented. In particular, this study deals with various structures (triplets and couplets consisting of full or hollow bricks) previously studied [START_REF] Fouchal | Contribution to the modeling of interfaces in masonry construction[END_REF][START_REF] Fouchal | Contribution à la modélisation numérique des interfaces dans les structures mac ¸onnées[END_REF] and presented in the first section. It is attempted to model the same conditions as those pertaining in the experimental tests, in terms of the geometries, mechanical characteristics, boundary conditions, and loading conditions. The problems are treated under quasi-static conditions, adopting the plane strain hypothesis. For the sake of simplicity, the parameters used for the computations are: µ = 0.2, b ≈ 0, w = 0.9 J/mm 2 . Coefficients C N and C T , the normal and tangential stiffness of the interface, will be determined in the following sections. These parameters will be obtained by comparing the experimental and numerical data.

The mechanical characteristics of the materials are as follows Table 7:

Full Brick Triplets

In [START_REF] Fouchal | Contribution to the modeling of interfaces in masonry construction[END_REF], we noted the occurrence of two kinds of fracture processes:

1. The fracture occurs along the interface (tests N1 and N4)

2. The fracture begins along the interface and propagates into the mortar (tests N2 and N3).

Fracture along the interface The experimental data used here was published in [START_REF] Fouchal | Contribution to the modeling of interfaces in masonry construction[END_REF]. The mesh consists of 130 Q4 finite elements. For the sake of symmetry, only the half-structure is considered. The loading on the upper part ranges from 0 to 53 kN . The first step here consists in determining the stiffness values of the interface, C N and C T . Various results are presented in figure 16 on pairs of C N and C T . The global behavior can be seen to depend strongly on C N and C T . The rigidity of the assembly depends mainly on the interface stiffness. Since the problem is highly nonlinear, even small perturbations in the stiffness coefficients can greatly affect the numerical responses.

The results shown in figure 17 were obtained in tests numbers 1 and 4, and are most encouraging, since the general shape of the curves is similar to that of the experimental ones. This confirms that the model accounts accurately for the mechanical behavior of the interface. This is also confirmed by the rupture modes obtained numerically (see figure 18). The variations in the shear stresses σ xy show that the stress concentration develops in the regions containing the discontinuities, or more specifically, at the level of the interface.

Cracks developing into the mortar We now take the case where the interface and the mortar are fractured together. The results of the tests performed in this case are not as satisfactory as the previous ones. In this experimental part of this study, we note that the cracks started to develop at the brick-mortar interfaces but continued into the mortar itself It is therefore proposed to introduce the damage to the mortar, using a cohesive zone model. The mortar is split into sub-bodies. Each sub-body is meshed using a quadrangular mesh with Q4 finite elements (figure 19). The contact between sub-bodies is governed by the RCCM model. We take adh1 and adh2 to denote the law of adherence at the mortar/mortar and the brick/mortar interface, respectively (figure 19).

It can be seen from figure 20 that the behavior of the structure is sensitive to changes in the stiffness coefficients.

The numerical results are in good agreement with the experimental data from the qualitative point of view. They show the degradation of the rigidity induced by the propagation of the crack into the mortar in the two experimental tests 2 and 3 (figure 21). The model predicted the similar occurrence of cracks in the mortar joint to those observed in practice (figure 22).

Hollow Brick structures

In the case of hollow brick structures, the experimental data show that the behavior of the material at the interface is quite different between the hollow parts of the brick and the full parts. At the level of the hollow parts, spikes of mortar penetrate into the voids of the brick. It is therefore necessary to distinguish between two zones: the zone (adh1) corresponding to the mortar/brick interface as in the case of full brick structures; and the second zone (adh2) corresponding to the spikes. Figure 23 shows these two zones.

By suitably choosing the stiffness coefficients, this strategy makes it possible to ap- proach the experimental results, as can be seen from figure 24. However, it is necessary to find several coefficients, which reduces the efficiency of the method. This situation could possibly be improved by averaging the two zones, but this approach has not yet been attempted. The changes with time in the shear stress and in the deformed structure are shown in figure 25.

Partial Conclusion

The adhesion model presented here was successfully used to simulate the experimental tests described in [START_REF] Fouchal | Contribution à la modélisation numérique des interfaces dans les structures mac ¸onnées[END_REF][START_REF] Fouchal | Contribution to the modeling of interfaces in masonry construction[END_REF], which provided the coefficients required to model the interface: stiffness parameters, viscosity coefficient, Dupré's energy and friction coefficient. The model is sensitive to these characteristics but the results obtained are in line with the experimental data.

The two kinds of rupture modes observed experimentally were described using two different adhesive characteristics. It was thus possible to model the fracture process that occur along the interface as well as where it involves mortar.

Structures composed of hollow bricks can also be modeled in this way using two adhesive characteristics. In particular, the model was used here to study the fracture process when it occurs along the interface of a small structure that consists of three hollow bricks. Further studies are now required on the fracture processes crossing the mortar in structures of this kind. In this part of the paper, one presents a multi-scale model of interface [START_REF] Rekik | Identification of the representative crack length evolution in a multi-level interface model for quasi-brittle masonry[END_REF][START_REF] Rekik | Homogenization methods for interface modeling in damaged masonry[END_REF]. The method is based on homogenization theories and asymptotic analysis. In this context, we assume the existence of a third material: the brick/mortar interface, which is considered as a mixture of brick and mortar with a crack density. To obtain the effective properties of the damaged intermediate material, three steps are performed. First, we calculate the exact effective properties of the crack-free material using homogenization techniques for laminate composites, and thus define a first homogeneous equivalent medium. In the second step, we assign a crack density to the material. To model the macroscopic behavior of the cracked material, we use the Kachanov [START_REF] Kachanov | Effective elastic properties of cracked solids: Critical review of some basic concepts[END_REF] model and then define a new homogeneous equivalent medium. Finally, in order to be sandwiched between the brick and mortar, this material is given a small thickness, and its mechanical behavior is derived using asymptotic techniques to shift from the micro to the macro level. A variation law of the crack length is introduced. The numerical procedure used is then described. Lastly, some numerical examples are given and compared with the experimental data.

Principle of the Model

The procedure used in this paper is summarized in figures 26 and 27.

1. In the first step, we consider the masonry made by bricks and mortar at a local level 2. At its local level, an inter-phase is considered a mixture of brick and mortar (Z+2).

In order to simplify, we consider the composite inter-phase as stratified.

3. The stratified is homogenized using classical theory of homogenization (H1). A new material is obtained which is transversely isotropic [START_REF] Kachanov | Effective elastic properties of cracked solids: Critical review of some basic concepts[END_REF]. The new material characteristics are obtained directly from the materials characteristics of brick and mortar.

The constitutive equation for each material is given by:

ε c ij = S c ijkl σ c lk = 1 + ν c E c σ c ij - ν c E c σ c kk δ ij (7)
where S c , E c , and ν c are respectively the compliance tensor, the Young's modulus and the Poisson ratio of phase c (c = b for the brick, c = m for the mortar). ε c and σ c are the strain and the stress tensor, respectively.

The macroscopic behavior law of the laminate brick/mortar reads: where ε = c=b, m f c ε c = c=b, m f c S c : σ c , f c denotes the volume fractions of phase c, and S 0 is the effective fourth-order compliance tensor of the transversely isotropic stratified. According to the modified Voigt notations, the macroscopic law reads:

ε = S 0 : σ (8)
         ε 11 ε 22 ε 33 √ 2ε 23 √ 2ε 13 √ 2ε 12          =          S 0 1111 S 0 1122 S 0 1133 0 0 0 S 0 1122 S 0 1111 S 0 1133 0 0 0 S 0 1133 S 0 1133 S 0 3333 0 0 0 0 0 0 2S 0 1313 0 0 0 0 0 0 2S 0 1313 0 0 0 0 0 0 S 0 1111 -S 0 1122                   σ 11 σ 22 σ 33 √ 2σ 23 √ 2σ 13 √ 2σ 12          (9)
4. We introduce a crack which is representative of the cracks included in the new material (F1). The crack is represented by its average (half-)length l and its average direction φ.

5. The cracked material is homogenized using the Kachanov theory [START_REF] Kachanov | Effective elastic properties of cracked solids: Critical review of some basic concepts[END_REF] (H2). In this theory, the crack is approximated by an elliptic crack. Approximated material characteristics are obtained depending on the length and direction of the crack, and the mechanical characteristics of the brick and mortar. The average strain ε in a solid with one crack can be written in the form:

ε = S : σ = S 0 : σ + l A (n⊗ < b > + < b > ⊗n) = (S 0 + ∆S) : σ ( 10
)
where S is the effective compliance tensor of the cracked material, < b >= n.σ.B is the average displacement discontinuity (COD) vector of the crack, B is the COD tensor of the crack, n is the normal to the crack and A is the area of the representative 2D-domain.

In the plane (e 1 , e 3 ) of the elementary volume, the tensor B is given by:

B = (C(1 -D)e 1 ⊗ e 1 + C(1 + D)e 3 ⊗ e 3 )l (11)
where

                 C = π 4 E 0 1 + E 0 3 E 0 1 E 0 3   1 G 0 13 -2 ν 0 13 E 0 1 + 2 E 0 1 E 0 3   1 2 D = E 0 1 -E 0 3 E 0 1 + E 0 3 ( 12
)
and E 0 1 , E 0 3 , ν 0 13 and G 0 13 are given by:

                         E 0 1 = 1 S 0 1111 E 0 3 = 1 S 0 3333 ν 0 13 = - S 0 1133 S 0 1111 G 0 13 = 1 S 0 1313 (13)
The tensor ∆S is given by:

∆S = 2l A e 3 ⊗ B ⊗ e 3 = 2l 2 A (e 3 ⊗ (C(1 -D)e 1 ⊗ e 1 + C(1 + D)e 3 ⊗ e 3 ) ⊗ e 3 ( 14
)
The compliance of the cracked material is thus given by:

S 1111 = S 0 1111 S 3333 = S 0 3333 + 2ρC(1 + D) S 1133 = S 0 1133 S 1313 = S 0 1313 + 2ρC(1 -D) (15)
where ρ = l 2 /A is the crack density parameter. The elastic constants are given by: [START_REF] Rekik | Identification of the representative crack length evolution in a multi-level interface model for quasi-brittle masonry[END_REF] where

E 1 = E 0 1 E 3 = E 0 3 /(1 + 2ρB nn E 0 3 ) G 13 = G 0 13 /(1 + ρB tt G 0 13 ) ν 13 = ν 0 13
B tt = C(1 -Dcos(2φ))l B nn = C(1 + Dcos(2φ))l B tn = CDsin(2φ)l (17)
6. The cracked material obtained is considered as the inter-phase material (Z-1).

7. The interface law is obtained, considering that the inter-phase is thin (H3). Using asymptotic theory (the thickness of the thin inter-phase η is a small parameter), we obtain an interface law which links the stress vector to the jump of displacement along the interface toward which geometrically inter-phase tends [START_REF] Lebon | Asymptotic analysis of a thin interface: The case involving similar rigidity[END_REF]. The stiffness of the interface depends on the material characteristics of the brick and mortar, and on the length and the direction of the crack.

We take [u ] to denote the jump along the interface. If the interface is normal to the third direction, we obtain

σ i3 = A i3 [u i ]
The stress vector σ .3 is linearly linked to the jump of displacement [u]. The second order matrix A .. is diagonal. The terms C N and C T in this matrix, corresponding to the normal and tangential stiffnesses of the interface are given by:

       C N = C3333 (η → 0) where C3333 = C 3333 η C T = C1313 (η → 0) where C1313 = C 1313 η (18)
where the fourth-order stiffness tensor C is the inverse of the compliance tensor S.

In our case ρ = l 2 /η L 0 , where L 0 denotes the joint length, it can be established that the normal and tangential joint stiffnesses read:

C N = L 0 2C(1 + D) l 3 C T = L 0 4C(1 -D) l 3 (19)
We obtain an explicit relation between the stiffness coefficients and the crack length l. [START_REF] Lebon | Contact problems with friction: Models and simulations[END_REF] are introduced (UC). These conditions prevent the penetration between the two adherents (brick and mortar, in our case). In a first approach friction conditions are neglected.

Unilateral conditions

Let F be the density of the contact forces. We take n b to denote the external unit normal vector to the boundary of the brick. The displacement and the contact force are decomposed into normal and tangential parts:

[u] = u N n b + u T with u N = [u].n b . F = F N n b + F T with F N = F.n b .
The unilateral contact is given by the following relations

u N ≥ 0, F N -C N u N ≥ 0, u N (F N -C N u N ) = 0. (20)
9. An evolution law for the crack length is introduced (F2). In the first step a very simple law is chosen (identified experimentally in practice).

We take τ to denote the shear stress along the interface.

.3 if τ ≤ τ c then l = l c if τ c ≤ τ ≤ τ u then l = aτ + b (21) a = l u -l c τ u -τ c b = l u -aτ u (22)
where τ u , τ c , l c and l u are four given values (In practice, l c and l u are identified).

10. The interface law can be used for a structural analysis by finite element (Z-2). In this case, the masonry is made by bricks, mortar, and interface.

A Numerical Example

We consider two-dimensional masonry structures subjected to shear loading. The obtained numerical results are then compared with experimental data [START_REF] Fouchal | Contribution to the modeling of interfaces in masonry construction[END_REF]. Two cases are considered: a triplet of full bricks and a triplet of hollow bricks, both subjected to the same nominal loading (with no lateral confinement). Table [START_REF]LUMB5-Short -term shear test for interface between the masonry unit and mortar or moisture -Insulating interlayer[END_REF] lists the material properties of the mortar and full bricks used to simulate a triplet of full bricks under the shear loading conditions described (see Fig. 28). For full bricks, the compliance tensor S 0 therefore reads:

         (23)
The normal and tangential stiffnesses (N/mm 2 ) of the interface are given by the following expressions:

C N = 242365/l 3 C T = 127600/l 3 (24)
where the direction φ is assumed to be equal a zero. The normal and tangential stiffnesses of the interface sandwiched between mortar and hollow brick are given by the following expressions:

C N = 200396/l 3 C T = 100490/l 3 (26)
The first step in order to compare experimental data and numerical results is to identify the parameters of the model, in particular the crack length and its evolution [START_REF] Rekik | Identification of the representative crack length evolution in a multi-level interface model for quasi-brittle masonry[END_REF]. For the fulls bricks, a comparison between experimental data and numerical results is given in figure 29. For the hollow bricks, a comparison is given in figure 30.

Partial conclusion

The numerical results obtained with the present model match the experimental data and are in good agreement particularly with the test data obtained in previous sections. Thus, the present model, with a simple crack evolution law, seems a good way to provide estimations for the stiffness of masonry interfaces.

Conclusion

In this chapter, we have presented some experimental data issued from the literature, with a particular focus on small structures and the local behavior of brick-mortar interfaces. We have shown that three aim modes appear in the stress-strain relationship. In the first part, there is a linear (elastic) relationship between the stress and the displacement. After a maximum, in a second step, the stress decreases, due to local damage, to a (quasi) constant value (third part) corresponding to friction. We have presented two families of models able to predict the behavior of the interface. The first one, phenomenological, is based on the notion of the evolution of the adhesion variable. The second one is based on micromechanics analysis and crack evolution. For these two models, some numerical results are presented and compared with experimental data. The results show the efficiency of these two models. In the future, various paths are possible. The first one concerns the dynamical aspects that is necessary to take into account, in order to approach earthquakes which generate severe in-plane and out-of-plane forces. It is therefore necessary to generalize our methodology to three-dimensionnal problems. A second possible way concerns the development of efficient numerical schema which is necessary to approach large structures such as monuments. The last line of research could involve the improvement of the models presented in this work to introduce new physical considerations as plasticity, damage evolution, etc.

Figure 1 .

 1 Figure 1. Compression test on full bricks: Elastic modulus and Poisson's coefficient

Figure 2 .Figure 3 .Figure 4

 234 Figure 2. Compression test on hollow bricks: Elastic modulus and Poisson's coefficient

Figure 4 .Figure 5 .Figure 6 .

 456 Figure 4. Shear test for full brick prisms

Figure 7 .

 7 Figure 7. Failure modes -Hollow brick prisms

Figure 8 .

 8 Figure 8. Experimental shear test: Hollow bricks [3]

Figure 9 .

 9 Figure 9. Measured Shear-displacement diagram for test σ = 0, 6M P a confinement stress

Figure 11 .

 11 Figure 11. Experimental device for compression diagonal test

Figure 12 .Figure 13 .

 1213 Figure 12. Compression diagonal test -Strain of compressive diagonal

  adhesion

Figure 14 .

 14 Figure 14. Normalized tangential forces against normalized tangential jump of displacement

Figure 15 .

 15 Figure 15. Position of contact nodes between two bodies

Figure 16 .

 16 Figure 16. Influence of parameters CN and CT on the behavior of full brick triplets

Figure 17 .

 17 Figure 17. Shear tests: tests N1 (CN = CT = 4 10 6 N/mm 3 ) and N4 (CN = CT = 10 6 N/mm 3 )

Figure 18 .

 18 Figure 18. Shear stress in full brick triplets at steps 0, 100, 207 and 208

Figure 19 .Figure 20 .

 1920 Figure 19. Full brick triplets: a) Mesh with cohesive mortar b) Mortar/mortar and mortar/brick adhesion

Figure 21 .

 21 Figure 21. Results of numerical shear tests: tests N2 (adh1: CN = CT = 10 7 N/mm 3 , adh2: CN = CT = 10 8 N/mm 3 ) and N3 (adh1: CN = CT = 10 9 N/mm 3 , adh2: CN = CT = 10 8 N/mm 3 )

Figure 22 .

 22 Figure 22. Shear stress in full brick triplets at steps 1, 350, 360 and 371 (cohesive zone)

Figure 23 .

 23 Figure 23. Mortar spike modeling

Figure 25 .

 25 Figure 25. Shear stress in hollow brick triplets atsteps 1, 53, 191, and 196

Figure 26 .Figure 27 .

 2627 Figure 26. Description of the process 1

Figure 28 .

 28 Figure 28. Initial geometrical configuration and loading conditions imposed on the triplet of full bricks (a), deformation of the triplet of full bricks in a shear test (b)

Figure 29 .

 29 Figure 29. Stress-displacement diagrams of the triplet of full bricks under shear, numerical, and experimental results [16, 17].

Figure 30 .

 30 Figure 30. Stress-displacement diagrams of the triplet of full bricks under shear, numerical and experimental results [16, 17].

Table 1 .

 1 Characteristics of the mortar

	Granulometry	0 -5 mm
	Dosing of bond / m 3 dry sand	350 kg
	Water for mixing	12.5%
		• 5 L/ sack of 40 kg
	or:
		• 3 L/ sack of 25 kg
	Density after 28 days	2.25
	Contraction after 28 days	0.65

Table 2 .

 2 Mechanical characteristics of the mortar

	Nb.	Flexural test		Compression test
		Traction	Flexion	Compression	Compression
		loading (kN ) strength (M P a)	loading (kN )	strength (M P a)
				1 st half 2 nd half	1 st half	2 nd half
				prism	prism	prism	prism
	1	1.95	4.56	39.5	36.9	24.7	23.1
	2	1.87	4.39	39.2	34.4	24.5	21.5
	3	1.69	3.95	33.6	30.7	21.0	19.1
	4	1.91	4.47	37.7	44.7	23.5	27.9
	5	1.65	3.86	37.3	35.8	23.3	22.4
	6	1.85	4.33	31.8	39.5	19.8	24.7
	Mean value	1.82	4.26	36.5	37.0	22.8	23.1

Table 3 .

 3 Loading rate

	Expected Strength	Loading rate
	(N/mm 2 )	(N/mm 2 )/s
	< 10	0.05
	from 11 to 20	0.15
	from 21 to 40	0.3
	from 41 to 80	0.6
	> 80	1.0

Table 4 .

 4 Mechanical properties for full bricks

	Nb	compression strength	Elastic Modulus	Poisson
		(M P a)	(M P a)	Coefficient
	1	11.7	9 439	0.13
	2	10.2	10 447	0.14
	3	13.3	8 429	0.13
	Mean value	11.7	9 438	0.13

Table 5 .

 5 Mechanical properties for hollow bricks

	Nb	Compression strength	Elastic modulus	Poisson
		(M P a)	(M P a)	coefficient
	1	4.4	5 934	0.14
	2	4.4	6 737	0.14
	3	4.6	5 505	0.12
	Mean value	4.46	6 059	0.13
	2.3. Mechanical Behavior of Small Masonry Structures Under Shear Load-
	ing Without Confinement
	2.3.1. Experimental Procedure

Table 6 .

 6 Compression diagonal test data L/6

	Wall and diagonal	Load (kN )	Strains (mm/mm)
	Test	Diagonal Elastic Maximal Elastic Maximal
	r1	Compressive	188,3	215,3	415	520
		tense			98	190
	r2	Compressive	251,8	215,8	670	700
		tense			170	220

Table 7 .

 7 Characteristics of Mortar and Bricks

	Materials	Young's modulus M P a	Poisson's ratio
	Mortar	4 000	0.3
	Full bricks	9 439	0.13
	Hollow bricks	6 058	0.13

Table 8 .

 8 Mechanical properties of the three-fold masonry constituents

	Young's moduli (MPa) of full brick	9438
	Poisson ratio of full brick	0.13
	Young's moduli (MPa) of hollow brick	6059
	Poisson ratio of hollow brick	0.13
	Young's moduli (MPa) of mortar	4000
	Poisson ratio of mortar	0

Fazia Fouchal,Frédéric Lebon,Amna Rekik et al.