Soizig Le Stradic
email: soizig.lestradic@gmail.com

Geraldo Wilson Fernandes

Elise Buisson

No recovery of campo rupestre grasslands after gravel extraction: implications for conservation and restoration

Keywords: tropical grassland restoration, quarrying, seed bank, regeneration, rupestrian grasslands, resilience

Introduction

Old-growth grasslands, including savannas and tropical grasslands, are species-rich ecosystems whose assembly develops over centuries [START_REF] Bond | Beyond the forest edge: ecology, diversity and conservation of the grassy biomes[END_REF][START_REF] Overbeck | Adaptive strategies in burned subtropical grassland in southern Brazil. Flora -Morphology, Distribution, Functional Ecology of Plants 202[END_REF]Veldman et al. 2015a). Old-growth grassland communities are resilient to the disturbances they have evolved with, such as fires or herbivory by native fauna (Veldman et al. 2015a).

Due to the lengthy duration of their assembly, these plant species rarely succeed at establishing from seed, and their ability to colonize is poor (Veldman et al. 2015a); they are therefore expected to have low resilience to strong and intrusive exogenous disturbances (sensu [START_REF] Mcintyre | A framework for conceptualizing human effects on landscapes and its relevance to management and research models[END_REF] and destruction, such as tilling (prior to cultivation), road construction, gravel extraction or mining.

Old-growth grasslands are often degraded or interspersed with recent anthropogenic grasslands. Nevertheless, they are usually neglected in global conservation and restoration programs [START_REF] Overbeck | Adaptive strategies in burned subtropical grassland in southern Brazil. Flora -Morphology, Distribution, Functional Ecology of Plants 202[END_REF][START_REF] Bond | Beyond the forest edge: ecology, diversity and conservation of the grassy biomes[END_REF][START_REF] Bond | Ancient grasslands at risk[END_REF]Veldman et al. 2015aVeldman et al. , 2015c)), despite their high biodiversity and numerous ecosystem services [START_REF] Overbeck | Adaptive strategies in burned subtropical grassland in southern Brazil. Flora -Morphology, Distribution, Functional Ecology of Plants 202[END_REF]Veldman et al. 2015b), which include a crucial role in water recharge [START_REF] Honda | Woody encroachment and its consequences on hydrological processes in the savannah[END_REF]Fernandes 2016). Because they are situated in regions currently affected by increasing anthropogenic activities, such as urbanization, mining operations, land use changes and afforestation [START_REF] Veldman | Tyranny of trees in grassy biomes[END_REF](Veldman et al. , 2015c;;Fernandes et al. 2016), initiatives to conserve and to restore oldgrowth grasslands are urgently needed. However, the dearth of knowledge about old-growth grasslands' resilience to strong anthropogenic disturbances presents a challenge to implementation of efficient conservation and restoration projects and jeopardizes their success.

Assessment of the natural resilience, i.e. both resistance and recovery (sensu [START_REF] Hodgson | W at do you mean, 'resilient'?[END_REF], of an altered ecosystem should help to determine whether active restoration is necessary and should provide useful information for planning adequate restoration actions [START_REF] Bradshaw | The use of natural processes in reclamation -advantages and difficulties[END_REF][START_REF] Prach | Spontaneous Succession versus Technical Reclamation in the Restoration of Disturbed Sites[END_REF][START_REF] Prach | Four opportunities for studies of ecological succession[END_REF]. System recovery is possible only if the system resists disturbance within its limits. If the system is disturbed beyond tipping points, however, recovery may then require modifications of the physical environment or manipulation of the vegetation [START_REF] Whisenant | Repairing damaged wildlands: A process-priented, landscape-scale approach[END_REF]. Vegetation recovery will be slow or absent when alteration of the soil's chemical and physical properties generates inappropriate abiotic conditions at the degraded site (i.e. limited nutrient availability, low water availability) [START_REF] Wong | Ecological restoration of mine degraded soils, with emphasis on metal contaminated soils[END_REF][START_REF] Yuan | Soil Formation and Vegetation Establishment on the Cliff Face of Abandoned Quarries in the Early Stages of Natural Colonization[END_REF]. Road construction or roadside gravel extraction, for example, alters abiotic conditions [START_REF] Barbosa Np De | Distribution of nonnative invasive species and soil properties in proximity to paved roads and unpaved roads in a quartzitic mountainous grassland of southeastern Brazil ( rupestrian fields )[END_REF].

Depending on the intensity of the disturbance, the vegetation and the seed bank in the incumbent soil can be either destroyed or severely altered. The lack of target species in the remaining seed bank or among surviving individuals [START_REF] Wilson | Chapter 19. Prairies. In: Handbook of ecological restoration[END_REF][START_REF] Bakker | Constraints in the restoration of ecological diversity in grassland and heathland communities[END_REF][START_REF] Bakker | Seed banks and seed dispersal: important topic in restoration ecology[END_REF]) also delays vegetation recovery. In the absence of an internal species pool, the seed supply for the recovery of degraded areas depends mainly on seed dispersal from surrounding sites via the seed rain [START_REF] Campbell | Determining the immigration potential of plants colonizing disturbed environments : t e case o milled eatlands in Quebec[END_REF][START_REF] Shu | Natural Colonization of Plants on Five Lead/Zinc Mine Tailings in Southern China[END_REF][START_REF] Bakker | Seed banks and seed dispersal: important topic in restoration ecology[END_REF].

However, grassland species may disperse poorly and at a low rate [START_REF] Oster | Agriculture , Ecosystems and Environment Plant colonization of ex-arable fields from adjacent species-rich grasslands : T e im ortance o dis ersal vs . recruitment ability[END_REF][START_REF] Bischoff | Dispersal and establishment of floodplain grassland species as limiting factors in restoration[END_REF]; in such cases, the natural recovery process of species-rich grasslands is very slow [START_REF] Buisson | The implications of seed rain and seed bank patterns for plant succession at the edges of abandoned fields in Mediterranean landscapes[END_REF]. Finally, although spontaneous recovery can occur, especially where environmental conditions are moderate [START_REF] Prach | The Role of Spontaneous Vegetation Succession in Ecosystem Restoration : A Pers ective[END_REF][START_REF] Prach | Spontaneous Succession versus Technical Reclamation in the Restoration of Disturbed Sites[END_REF], is it probable in cases of strong anthropogenic degradation of old-growth grassland species?

Campos rupestres are old-growth grassland (Veldman et al. 2015a;Fernandes 2016), considered as OCBILs (old climatically-buffered infertile landscapes) [START_REF] Silveira | Ecology and evolution of plant diversity in the endangered campo rupestre: a neglected conservation priority[END_REF] and part of the Cerrado domain. They occur between 800 m to 2 000 m altitude, primarily along the Espinhaço mountain range in south-eastern Brazil. Campos rupestres surround headwaters of important watersheds in Brazil [START_REF] Callisto | Water Resources in t e Ru estrian rasslands o t e Es in a o Mountains[END_REF]) and sustain a huge biodiversity [START_REF] Silveira | Ecology and evolution of plant diversity in the endangered campo rupestre: a neglected conservation priority[END_REF]. Whereas seed bank and seed rain generally play a main role in ecological restoration, little is known about the seed bank or seed rain of Brazilian grasslands, including campo rupestre (but see [START_REF] Medina | The potential of natural regeneration of rocky outcrop vegetation on ru estrian ield soils in ' Serra do Ci ó ', Brazil[END_REF], and information about campo rupestre recovery is scarce. Thus, nothing is known about the reliability of residual seed bank or seed dispersal to recover campo rupestre vegetation after a major anthropogenic disturbance.

In this study, we assess campo rupestre vegetation recovery after an anthropogenic disturbance: gravel extraction. As with other old-growth grasslands, we expect campo rupestre recovery to be very slow. To ascertain whether site conditions or low dispersion of target species favor or hamper spontaneous recovery of degraded areas, we compare soil conditions, seed bank and vegetation composition in two co-occurring undisturbed herbaceous reference communities of campo rupestre presenting different soil types-stony and sandy grasslands-and situated within two types of degraded area: one with sandy substrate and one with stony substrate.

Methods

Study area

The study took place in the southern portion of the Espinhaço Range, approximately 100 km northeast of Belo Horizonte, in the state of Minas Gerais, Brazil (19° 15′-25′ S and 43° 30′-40′ W). The study area is within the Environmental Protected Area of Morro da Pedreira, the buffer zone of the Serra do Cipó National Park. Campos rupestres are composed of a mosaic of species-rich primary grasslands and scattered rocky outcrops with evergreen shrubs and sub-shrubs [START_REF] Giulietti | Espinhaço range region: eastern Brazil. In: Centre of plants diversity: a guide and strategy for their conservation[END_REF]Le Stradic et al. 2015a;[START_REF] Silveira | Ecology and evolution of plant diversity in the endangered campo rupestre: a neglected conservation priority[END_REF]) They represent the main vegetation type in the region. Their high plant biodiversity comprises 14.7 % of the entire Brazilian vascular flora and includes numerous endemic species [START_REF] Giulietti | Espinhaço range region: eastern Brazil. In: Centre of plants diversity: a guide and strategy for their conservation[END_REF][START_REF] Echternacht | Areas of endemism in the Espinhaço Range in Minas Gerais[END_REF][START_REF] Silveira | Ecology and evolution of plant diversity in the endangered campo rupestre: a neglected conservation priority[END_REF]Fernandes 2016). Campos rupestres are fire-prone ecosystems (Le [START_REF] Stradic | Regeneration after fire in campo rupestre: Short-and long-term vegetation dynamics[END_REF]), but they are not grazed. They are constrained ecosystems with shallow, nutrient-poor and highly acidic soils [START_REF] Benites | Soils associated with rock outcrops in the Brazilian mountain ranges Mantiqueira and Espinhaço[END_REF]Le Stradic et al. 2015a) and a five-month dry season with significant water shortage. Both sandy and stony grasslands are the main herbaceous communities in the campos rupestres of the study area (Le Stradic et al. 2015a); we therefore consider these two grassland types as the reference ecosystem.

The study area presents a seasonal tropical altitudinal climate, with an annual average temperature of 21.2 °C [START_REF] Madeira | Reproductive phenology of sympatric taxa of Chamaecrista ( Leguminosae ) in Serra do Cipo[END_REF]. The average annual rainfall is ca. 1622 mm, mainly concentrated during the rainy season between November and April. The dry season extends from May to October [START_REF] Madeira | Reproductive phenology of sympatric taxa of Chamaecrista ( Leguminosae ) in Serra do Cipo[END_REF].

In 2002, the road MG010 was asphalted, a process during which small quarries were exploited for soil, sand and gravel extraction and were also used to park machinery.

Vegetation and upper soil horizons were destroyed. This degradation was not followed by restitution of the soil horizons, leaving the soils altered and composed of several kinds of substrate, including sandy and stony substrate. These degraded areas are surrounded by reference campo rupestre.

To evaluate the recovery of campo rupestre vegetation following such anthropogenic degradation, we analyzed soil characteristics, seed bank composition and vegetation composition in 2010 (eight years after the last degradation in 2002), at six degraded sitesthree sites consisting of sandy substrates (DSa) and three of stony substrate (DSt)-and in ten reference areas: five sandy grasslands (Sa) and five stony grasslands (St).

Soil samples

To assess soil characteristics, we randomly collected three soil samples from each of the six degraded sites and from each of the ten reference grasslands, once during the wet season (February) and once again during the dry season (July) (n = 2 seasons × 3 samples × around 1 m in diameter, at 10-cm depth, using a hand trowel. Samples were dried and sieved through a 2-mm mesh sieve prior to analysis. On the fine fraction (<2 mm), we performed chemical soil analyses (i.e. total N, P, K, pH, organic C, Mg 2+ , Ca 2+ , Al 3+ ): Phosphorus (P) and Potassium (K) in mg/dm 3 ; Nitrogen (N) and Organic Carbon (C org ) in dag/kg; Magnesium (Mg 2+ ), Aluminum (Al 3+ ), and Calcium (Ca 2+ ) in cmolc/dm 3 . P, N and K were analyzed with the Mehlich 1 extraction method; Ca 2+ , Mg 2+ , Al 3+ with 1 mol/L KCl extraction; and C org followed the Walkley-Black method. Analyses were conducted at the soil laboratory of Viçosa Federal University, Viçosa, Minas Gerais, Brazil. Soil analysis followed the recommendations of EMBRAPA (1997).

Seed banks

To evaluate seed banks, we randomly collected five 1-liter soil samples from each of the six degraded sites and each of the ten reference grasslands (n = 5 samples × 16 sites) at the end of the dry season (September); fruit production peaks between April and July (personal observation). Each sample consisted of ten pooled sub-samples, randomly collected within an area of around 2 m in diameter, at 5-cm depth to overcome seed bank heterogeneity, using a hand trowel. Samples were washed with water on sieves with 4-mm and 200-µm mesh sizes to remove 1) plant fragments and stones and 2) the finest soil fraction (clay and silt), respectively. The remaining seed-bearing soil was spread in a thin layer on trays (25 cm × 35 cm) on compresses placed over a 3-cm thick layer of vermiculite (a neutral substrate). Control trays (n = 3) (made of compresses over vermiculite) and controls of the finest soil fraction (<200 µm) (n = 3) (made of the finest fraction spread out on compresses over vermiculite) were also prepared in order to 1) control which species could colonize the greenhouse and contaminate samples and 2) ensure that no seed <200 µm was lost by sieving. No germination was found in the finest soil fraction or in any of the control trays. All trays were kept in a greenhouse, were regularly moved, and were watered every two days. On a weekly basis, emerging seedlings were identified and removed, or were replanted in pots for later identification. This was done to minimize competition within the trays and to reduce susceptibility to the emission of allelopathic substances. We monitored seed germination until one month passed with no new emergences. We then dried and lightly plowed the samples before initiating a second germination period; this procedure is a well-known technique for stimulating additional germination [START_REF] Roberts | Seed banks in soils[END_REF].

Vegetation survey

We compared the plant community composition of the degraded sites to that of the reference grasslands. In January 2010, we surveyed the vegetation in three sandy (Sa) and three stony (St) reference grasslands, as well as in the six degraded sites (DSa and DSt).

Sixteen plots in Sa, St and DSa, and twenty-four plots in DSt were surveyed to record (1) the list of species and (2) the percent cover of each species, visually estimated from the vertical projection of all aerial plant parts. The plots at all sites measured 40 cm × 40 cm (0.16 m 2 ).

Further in the manuscript, we consider the target species-all species occurring in reference grasslands-and non-target species, which occur in degraded areas but not in the reference campo rupestre. The latter group includes ruderal species that commonly grow in altered areas and along roadsides.

Statistical analysis

To compare soil chemical composition between the different types of soil substrate and between seasons, we performed two-way ANOVAs for each chemical element. For Al 3+ , we checked normality and variance homogeneity and applied the log transformation (Sokal & Rohlf 1998). To test for differences among soil substrate and between seasons, TukeyHSD post-hoc tests were performed using values from each season separately when seasonal difference was considerable, and using all values (i.e. data from the two seasons pooled together) when there was no significant seasonal difference.

We ran generalized linear mixed models (glmer in the R package lme4) with a Poisson error distribution, a log-link function, and random effect for sites [START_REF] Crawley | The R Book[END_REF] to compare the species richness and the number of emerged seeds in the seed banks of the different areas.

We calculated a mean dissimilarity matrix, using Jaccard index (meandist in the R package vegan) based on species presence/absence data, to assess the plant composition dissimilarity between and within the seed banks of DSa, DSt, Sa, and St. We also performed an ANOSIM (anosim in the R package vegan) for analysis of dissimilarities.

We compared the mean vegetation cover in the reference and degraded areas, using Kruskal-Wallis test followed by pairwise comparisons between group levels with Bonferroni corrections. Mean species richness in both the reference grasslands and degraded sites were examined using generalized linear models (GLM) with a Poisson distribution.

Dissimilarities between vegetation composition in the reference grasslands and the degraded sites were assessed using Adonis, an ANOVA-style analysis. Adonis (i.e.

Multivariate ANOVA based on dissimilarities) performs a multivariate analysis of variances using distance matrices to test the differences in group means and performs permutation tests to inspect the significance of the differences observed [START_REF] Oksanen | Vegan: community ecology package[END_REF]. The Adonis function determines whether the groups consistently differ in their community composition.

Adonis analyses were performed using Bray-Curtis dissimilarity to calculate distance matrices based on vegetation data (quadrat × species abundance matrices); its output values range from 0 and 1, tending towards 1 as the dissimilarity between plant communities increases [START_REF] Bray | An ordination of the upland forest communities of southern Wisconsin[END_REF]. Non-metric multidimensional scaling (NMDS), which produces an ordination based on a distance or dissimilarity matrix, was used to represent the dissimilarity between reference and degraded areas according to plant composition.

All statistical analyses were performed in software R Version 3.2.1 (R Core Team 2015), using stats, vegan [START_REF] Oksanen | Vegan: community ecology package[END_REF]) and lme4 [START_REF] Bates | Fitting linear mixed-effects models using lme4[END_REF] packages.

Results

Soil characteristics

Soil composition varied greatly between the reference grasslands and both types of degraded sites (Fig. 1, Table S1). Main nutrient content at the degraded sites was markedly depleted compared to the reference grasslands, where N, C org , P and K concentrations were generally higher and soils were more acidic (Fig. 1). Degraded sites showed slightly lower Al 3+ values than the reference grasslands, and Mg 2+ values were higher in stony grasslands than in the other areas. Degraded stony sites and reference stony grasslands showed a huge variation in Ca 2+ content (Fig. 1). P, pH and C org varied seasonally, with higher P and lower pH values during the dry season (Fig. 1, Table S1). Only the P content varied among soils, owing to interactions between soil type and season (Figure 1, Table S1). Coarse fraction in degraded sandy and stony areas did not differ from undisturbed sandy and stony grasslands, respectively (Table S2), and soil structure was mainly conserved among both degraded (Table S2) and reference areas.

Seed bank in reference and degraded areas

Based on seedling emergence, seed banks in both undisturbed reference grasslands and degraded sites were generally poor in species and in numbers of seeds (Fig. 2). No significant differences were found for species richness between seed banks of reference grasslands and degraded sites (glmer procedure z=1.73, p=0.08, Fig. 2a). Degraded sites had significantly higher numbers of seeds than the reference grasslands (glmer procedure z=2.91, p<0.01, Fig. 2b), but the amount of seeds in samples from degraded sites varied widely (from 0 to more than 50 seeds), which made post-hoc tests difficult to interpret (Fig. 2b). Seed bank composition showed high dissimilarity between all sites (ANOSIM statistic R=0.378, p<0.001, Table S3).

Vegetation composition in reference grasslands and degraded sites

Eight years after the disturbance, degraded sites presented bare ground over more than 70% of their area, especially the degraded sites with sandy substrate (Fig. 3). Vegetation cover in all degraded sites was significantly lower than in reference grasslands ( 2 =147.81, p<0.001, Fig 3). Species richness in degraded sites was also much lower than in reference grasslands, with less than 5 species per quadrat (40 cm × 40 cm). In contrast, reference grasslands presented between 12 and 16 species per quadrat (GLM procedure with p <0.001, Fig. 3). Vegetation composition also differed greatly between the reference grasslands and the degraded sites (Adonis F=34.36 R 2 =0.35, p<0.01, Table S4). NMDS was performed to represent the distance matrix in an ordination and illustrate these dissimilarities (Fig. 4).

Reference grasslands were quite similar in term of species composition, containing numerous species characteristic of campo rupestre grassland, such as Diplusodon orbicularis, Lagenocarpus alboniger, Mesosetum exaratum, Tatianyx arnacites, Vellozia epidendroides, Xyris pilosa, among others (Fig. 4). Conversely, degraded sites showed greater heterogeneity in term of species composition, with no consistency among substrate type (Fig. 4), and contained ruderal species, including either Andropogon bicornis or Zornia reticulata. A few species found on the reference grasslands-e.g. Polygala paniculata, Declieuxia fruticosa, Chamaecrista papillate, and especially the two Poaceae, Echinolenea inflexa and Mesosetum loliiforme-managed to establish only at the degraded sites with stony substrate (Fig. 4).

Discussion

The present study demonstrates that campo rupestre did not recover after severe anthropogenic disturbance, despite being particularly resilient to disturbances such as fire [START_REF] Neves | Campo rupestre recém-queimado na Chapada Diamantina, Ba ia, Brasil : lantas de rebrota e sementes, com es écies endêmicas na rocha[END_REF][START_REF] Stradic | Regeneration after fire in campo rupestre: Short-and long-term vegetation dynamics[END_REF]. Eight years after gravel extraction, bare ground still dominated the degraded sites, and species composition remained very different from undisturbed reference grasslands, despite their presence in the immediate surroundings (within 20-200 m). Some characteristic species from campo rupestre, like Poaceaae (e.g.

Tatianyx arnacites, Mesosetum exaratum, Homolepis longispicula), Cyperaceae (e.g.

Lagenocarpus rigidus subsp. tenuifolius, Lagenocarpus albo-niger, Bulbostylis paradoxa),

Velloziaceaea or Eriocaulaceae, did not recolonize the degraded areas, although large populations of them occurred in adjacent areas (see Le Stradic et al. 2015a). Altered abiotic conditions in degraded sites, a low capacity of campo rupestre plant communities to form seed bank and, probably, a low dispersal ability collectively explain the degraded campo rupestre areas' failure to recover, as detailed hereafter.

Site conditions

In degraded areas, the depletion of the main soil nutrients, N, P and K, can sometimes hamper vegetation establishment, as they are essential elements for plant growth. In our case, soil structure in degraded areas remained quite similar to those in the reference areas, but gravel extraction severely altered site conditions relative to the reference areas, and soils did not recover after degradation. The reference grasslands are oligotrophic, with low phosphorus and potassium supply [START_REF] Benites | Soils associated with rock outcrops in the Brazilian mountain ranges Mantiqueira and Espinhaço[END_REF][START_REF] Silveira | Ecology and evolution of plant diversity in the endangered campo rupestre: a neglected conservation priority[END_REF]Le Stradic et al. 2015a); hence plant species are already adapted to constrained environmental conditions [START_REF] Negreiros | CSR analysis of plant functional types in highly diverse tropical grasslands of harsh environments[END_REF])-they have developed efficient systems that minimize nutrient loss and optimize resource acquisition, and they are able to accumulate reserves [START_REF] Oliveira | Ecophysiology of Campos Rupestres Plants[END_REF][START_REF] Oliveira | Mineral nutrition of campos rupestres plant species on contrasting nutrient-impoverished soil types[END_REF][START_REF] Abrahão | Convergence of a specialized root trait in plants from nutrient-impoverished soils: phosphorus-acquisition strategy in a nonmycorrhizal cactus[END_REF]. We therefore expected plant species from reference grasslands to establish, even in sites with non-optimal conditions. Indeed, an experimental restoration project aiming to reintroduce species in a degraded area showed that some campo rupestre shrub species were able to survive and reproduce in these kinds of degraded environments when transplanted there [START_REF] Gomes | .5 years monitoring of shrub species translocation in degraded Neotropical mountain grassland[END_REF][START_REF] Stradic | The role of native woody species in the restoration of Campos Rupestres in quarries[END_REF]). These species have therefore been identified as potential candidates for restoration projects.

Poor seed banks in reference grasslands

Seed banks in undisturbed reference grasslands are poor in seeds and species, compared to other campo rupestre habitats such as rocky outcrops or peat bogs [START_REF] Medina | The potential of natural regeneration of rocky outcrop vegetation on ru estrian ield soils in ' Serra do Ci ó ', Brazil[END_REF]. In European grasslands, [START_REF] Bekker | Soil seed banks in European grasslands: does land use affect regeneration perspectives?[END_REF] noted that species usually associated with poor nutrient conditions were relatively scarce in the seed bank. The fivemonth dry season can also lead to unfavorable environmental conditions for seed bank formation, since wetter sites typically contain a larger number of seeds in mountain communities [START_REF] Funes | Edaphic patchiness influences grassland regeneration from the soil seed-bank in mountain grasslands of central Argentina[END_REF][START_REF] Medina | The potential of natural regeneration of rocky outcrop vegetation on ru estrian ield soils in ' Serra do Ci ó ', Brazil[END_REF]. Perennial species are dominant in campo rupestre (Le Stradic et al. 2015a;[START_REF] Silveira | Ecology and evolution of plant diversity in the endangered campo rupestre: a neglected conservation priority[END_REF], indicating that depleted seed banks may also be associated with a low quantity of annuals. However, in German grasslands, [START_REF] Hölzel | Assessing soil seed bank persistence in flood-meadows : T e searc for reliable traits[END_REF] found that a large proportion of perennial species had a strong tendency for seed accumulation in the soil. Almost all species in campo rupestre are resprouters after fire (Le [START_REF] Stradic | Regeneration after fire in campo rupestre: Short-and long-term vegetation dynamics[END_REF].

Those species usually develop specialized underground storage organs (USOs) that securely store carbohydrates (e.g. starch) and water for long periods of time, enabling them to resprout from dormant buds or root systems [START_REF] Overbeck | Adaptive strategies in burned subtropical grassland in southern Brazil. Flora -Morphology, Distribution, Functional Ecology of Plants 202[END_REF][START_REF] Fidelis | Does disturbance affect bud bank size and belowground structures diversity in Brazilian subtropical grasslands?[END_REF][START_REF] Maurin | Savanna fire and the origins of the 'underground orests' o A rica[END_REF]Veldman et al. 2015a). While in some cases, resprouters present low seed production and low fecundity in comparison to non-sprouting species [START_REF] Lamont | Are seed set and speciation rates always low among species that res rout a ter ire, and w y ?[END_REF][START_REF] Lamont | Fitness and evolution of resprouters in relation to fire[END_REF], this is not always true for Cerrado resprouter species. However, it has been demonstrated that the seeds of several species in campo rupestre are dormant, unviable or empty (Le Stradic et al. 2015b;[START_REF] Dayrell | Phylogeny strongly drives seed dormancy and quality in a climatically buffered hotspot for plant endemism[END_REF]. Considering all these parameters (i.e. the marked dry season, the large numbers of perennial species, and large number of resprouters), most grassland species from campo rupestre do not seem to form seed banks, though some species produce seeds capable of persisting in soil over time, such as some Velloziaceae [START_REF] Garcia | Long-term persistence of Velloziaceae species in the soil seed bank in campo rupestre vegetation, Brazil[END_REF]. We suggest that regeneration via the seed bank is very limited; resprouting remains the primary method of recovery after a disturbance like fire (Le [START_REF] Stradic | Regeneration after fire in campo rupestre: Short-and long-term vegetation dynamics[END_REF], and the bud bank may replace the seed bank in these ecosystems [START_REF] Fidelis | Does disturbance affect bud bank size and belowground structures diversity in Brazilian subtropical grasslands?[END_REF] when soils are intact.

Limited seed dispersal

At degraded sites, the probably small seed banks (see details above) were removed by gravel exploitation. The seeds found in these areas eight years after disturbance thus rely only on seed dispersal from standing vegetation already established on site or from the surroundings. Seed banks in degraded sites present a higher number of seeds in comparison to the reference grasslands, but these seed banks are usually from ruderal species. In campo rupestre, some species do not produce fruits regularly, especially Poaceae species (Le Stradic 2012), which reduces considerably the pool of species able to reach degraded sites. Likewise, seeds of some target species, such as Tatianyx arnacites, Lagenocarpus rigidus subsp. tenuifolius or Rhynchospora riedeliana, occurred sporadically in seed banks of reference grasslands but were absent in the seed banks of degraded sites. Furthermore, eight years after destruction, communities in degraded sites present numerous non-target and ruderal species, but almost no target species despite campo rupestre being a hotspot of biodiversity [START_REF] Silveira | Ecology and evolution of plant diversity in the endangered campo rupestre: a neglected conservation priority[END_REF]Fernandes 2016), which implies that dispersal of target species may be very limited. In climate-stable grasslands such as campo rupestre, perennial plants can be extremely long-lived and present lower dispersal and colonization potentials (Veldman et al. 2015a;[START_REF] Hopper | OCBIL theory: towards an integrated understanding of the evolution, ecology and conservation of biodiversity on old, climatically buffered, infertile landscapes[END_REF]. The environmental constraints of campo rupestre should favor reduced dispersal to ensure establishment in safe sites [START_REF] Hopper | OCBIL theory: towards an integrated understanding of the evolution, ecology and conservation of biodiversity on old, climatically buffered, infertile landscapes[END_REF]. In the open physiognomies of campo rupestre, such as sandy and stony grasslands, most species (e.g. Poaceae, Cyperaceae, Xyridaceae, Eriocaulaceae, or Velloziaceae) disperse unassisted, and only a few species produce fleshy fruits that are dispersed mainly by birds [START_REF] Guerra | Mutualistic Interactions Among Free-Living Species in Rupestrian Grasslands[END_REF]. Consequently, post-disturbance plant communities are composed largely of non-target and ruderal species, which establish by taking advantage of the soil modifications and high proportion of bare soil [START_REF] Hobbs | Disturbance , Diversity , and Invasion : Im lications or Conservation[END_REF][START_REF] Stradic | Comparison of translocation methods to conserve metallophyte communities in the Southeastern D.R. Congo[END_REF][START_REF] Shea | Community ecology theory as a framework for biological invasions[END_REF][START_REF] Hansen | The influence of disturbance and habitat on the presence of non-native plant species along transport corridors[END_REF]. Therefore, a collateral effect of soil modification is the introduction of competition from non-native and/or ruderal species, which may further limit establishment of native species.

Time is definitively fundamental to the assemblage of old-growth grasslands (Veldman et al. 2015a), a fact not often recognized because the evidence of grassland plant longevity is usually underground. Even in conditions that favor establishment, with undisturbed ecosystems in the surroundings acting as sources of propagules, the assembly of plant communities similar to the original ones will take centuries (Veldman et al. 2015a;[START_REF] Redhead | The natural regeneration of calcareous grassland at a landscape scale: 150 years of plant community re-assembly on Salisbury Plain, UK Fraser, L, editor[END_REF][START_REF] Hirst | The resilience of calcareous and mesotrophic grasslands following disturbance[END_REF]). In the case of a strong anthropogenic disturbance, it is unlikely that old-growth grasslands will recover by themselves. Rather, human intervention is necessary to rapidly reestablish the main species. Strategies include modification of soil abiotic conditions and the introduction of species through seed sowing, seedling transplantation or vegetation mat translocation. Bulk topsoil transfer allows for the transfer of seeds, propagules and soil microorganisms that are present in the native soil. The technique is commonly used to rehabilitate mines and quarries [START_REF] Rivera | The fate of herbaceous seeds during topsoil stock iling : Restoration otential o seed banks[END_REF]Koch 2007), but it is more successful in temperate grasslands than in tropical grasslands [START_REF] Stradic | Comparison of translocation methods to conserve metallophyte communities in the Southeastern D.R. Congo[END_REF]). In our case, the poverty of the seed bank in reference campo rupestre areas implies that a technique such as bulk topsoil transfer would have limited efficacy in reestablishing campo rupestre herbaceous vegetation in degraded areas, as has been demonstrated for other oldgrowth grasslands (Le [START_REF] Stradic | Comparison of translocation methods to conserve metallophyte communities in the Southeastern D.R. Congo[END_REF].

Figure 1: Box-and-whisker plots (including the extreme of the lower whisker, the lower hinge, the median, the upper hinge and the extreme of the upper whisker for each group) of the different chemical soil parameters, from soils collected in 5 sandy grasslands (Sa), 5 stony grasslands on pooled values of both seasons when there are no seasonal differences, according to Table S1, and performed on values from each season separately when there are seasonal differences, according to Table S1. In this last case, capital letters are results for the rainy season, and lowercase letters are results for the dry season.

Supporting Information:

Table S1: Results of the two-way ANOVAs performed for chemical soil parameters, according to soil substrate (i.e. sandy grasslands, stony grasslands, degraded sandy substrate and degraded stony substrate), for the two seasons (i.e. wet and rainy season) (n=96). ns: nonsignificant difference, *: significant difference with P<0.05, ***: significant difference with P<0.001.

Table S2: Mean and standard error values of soil texture, according to soil substrate: sandy grasslands, stony grasslands, degraded sandy substrate and degraded stony substrate).

Table S3: Mean dissimilarity matrix (using Jaccard index) of the seed bank composition between the degraded areas with stony substrate (DSt) and sandy substrate (DSa) and reference grasslands: the sandy (Sa) and the stony (St) grasslands, based on the matrix of species presence-absence data. The diagonal gives the averages within classes. Index values closer to 1 indicate greater dissimilarity between seed banks. Table S4: Mean dissimilarity matrix (using Bray-Curtis index) of vegetation composition between the degraded areas with stony substrate (DSt) and sandy substrate (DSa) and reference grasslands: the sandy (Sa) and the stony (St) grasslands based on the matrix of species percentage cover data. The diagonal gives the averages within classes. Index values closer to 1 indicate greater dissimilarity between seed banks.

Figure 2 Figure 3 Figure 4 :

 234 Figure 2: a) Number of species presenting emerged seeds per 1 L of soil, and b) number of emerged seeds per 1 L of soil in the seed banks of the reference grasslands (sandy [Sa] and stony [St] grasslands) and the degraded areas (with sandy substrate [DSa] and with stony substrate [DSt]). Different letters indicate significant differences according to the GLM results. Bars stand for standard error.

  (St), 3 degraded areas with sandy substrate (DSa) and 3 degraded areas with stony substrate (DSt), during the dry season (light grey) and the rainy season (dark grey). See Table1for statistical tests. Letters indicate significant differences according TukeyHSD tests (p < 0.05) performed

	a	b	c	d	a	A	b	B	c	C	c	C	a	A	b	B	c	C	a	C	a	A	b	A	c	B	d	B
	Sa	St	DSa	DSt	Sa	St	DSa	DSt	Sa	St	DSa	DSt	Sa	St	DSa DSt
	a	a	ab b	ac a			b	c		a		b		a		b		a	b	a	a
																												Dry
																				3 )								Rainy
	Sa	St	DSa	DSt	Sa	St	DSa	DSt	Sa	St	DSa	DSt	Sa	St	DSa DSt

Acknowledgements

We thank Megan King for English revision and Kathrin Kiehl and two anonymous reviewers for their useful comments. S. Le Stradic received postdoctoral support from grant #2016/13232-5 São Paulo Research Foundation (FAPESP). This work was also supported by the Conselho Nacional de Pesquisa (CNPq) [CNPq 561883/2010-6], by the Société Française d'Ecologie (Bourse de terrain SFE) for seed bank study, RTP CNRS-CEMAGREF "Ingénierie Ecologique" [Ecological Engineering] SAVER -SAVanna Ecological Restoration, Reserva Vellozia, the Ministère Français des affaires étrangères et européennes (EGIDE) [EGIDE 2009/657176K].


Gilles Pijaudier-Cabot

Khalil Haidar

Mirvat Omar

Ahmed Loukili

Non local damage models with evolving internal length: motivations and applications to coupled problems

Keywords: non local damage, internal length, coupled problems

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

INTRODUCTION

In quasi-brittle materials, fracture exhibits a finite size process zone. Macro-cracking is the result of progressive material damage in which micro-cracks appear first in a rather diffuse way and then coalescence occurs in order to form the crack. The size of the resulting fracture process zone (FPZ) is not dependent on the structural size, provided it does not interfere with the boundaries of the considered body. It is controlled by local heterogeneity, and by the state of stress as well. From the modelling point of view, the description of the FPZ has to involve the introduction of an internal length in the governing equations. It can be in the form of a characteristic length which is related to the length of the process zone, or in the form of an internal length in non local constitutive relations.

In most existing proposals, the internal length is a constant parameter. Still, there are some theoretical indications that suggest that the internal length should change in the course of the fracture process: with the help of micromechanics, [START_REF] Bazant | Nonlocal Damage Theory based on Micromechanics of Crack Interactions[END_REF] arrived at the conclusion that when the interactions between cracks and voids develops in the course of failure, the weight function entering in the calculation of the non local variable controlling damage should change as well. Recent experiments carried out at R&DO on model cementitious materials with controlled initial porosity, i.e. initial damage, have shown that the size of the fracture process zone changes with the amount of voids in the material. Acoustic emission (AE) analyses exhibit clearly an increase of the fracture process zone with initial damage.

The aim of this contribution is firstly to examine the correlation between the width of the fracture process zone observed with AE and the internal length in non local constitutive relations. Secondly our purpose is to consolidate these experimental observations in a modified non local damage model with evolving internal length. The correlation between the width of the FPZ and the internal length of the material obtained from inverse analysis of size effect tests is discussed. The consequences on the inception of strain localisation are also considered. The width of the localisation zone increases with damage and is stabilised, as opposed to the original model where it decreases.

Finally, extensions of this model to ageing resulting from an increase of material porosity, to creep-damage interaction, and to hydromechanical effects are discussed.

EXPERIMENTS ON MODEL MATERIALS

The experimental program has been designed in order to measure the mechanical characteristics of mortar specimens with a controlled microstructure [START_REF] Haidar | Correlation Between the Internal Length, the Fracture Process Zone and Size Effect in Mortar and Model Materials[END_REF]. This control was achieved by adding inclusions of weak mechanical characteristics (polystyrene beads) in a mortar matrix.

All test specimens were made with a mix which consists of ordinary Portland cement CPA-CEMI 52.5, polystyrene beads, normal density fine sand with a maximum size of 2 mm, a superplasticizing agent (Glenium 51) and water. Expanded polystyrene spheres of 3 -7 mm mean diameter were used as aggregate in the mix design. Expanded polystyrene consists essentially of air. Four different mixes of densities 2.0 -1.8 -1.6 and 1.4, having polystyrene content g of 13 -22 -31 and 39 % respectively, were achieved in addition to the reference material (mortar without inclusions). All mixes have a cement/sand ratio of 0.46 and a water/cement ratio of 0.4. For the bending tests, four different sizes of geometrically notched concrete specimens were used. The depths were D = 40 , 80 , 160 and 320 mm while the thickness was kept constant for all the specimens b = 40 mm. The length to depth ratio was L/D = 8:3 and the span to depth ratio was l/D = 2.5 for all specimens. One notch of depth D/6 and thickness 1.5 mm (same for all dimensions) was placed in each bending specimen by putting steel plates in the moulds before casting.

Size effect tests

The size effect tests followed the guidelines established by RILEM (1990). The tests were notch opening controlled with a constant CMOD rate of 0.1 µm/s for D = 40 -80 mm, 0.20 µm/s for D = 160 mm, and 0.25 µm/s for D = 320 mm. Figure 1 shows the response of medium size specimens (D=40mm) for each material density. Note that the deflection at peak is almost independent from the density of the material. The material density influences still the mechanical behaviour of beams; the lower the density, the lower the stiffness and the peak load.

These data are going to be interpreted with the help of Bazant's size effect law [START_REF] Bazant | Fracture and size effect in concrete and other quasibrittle materials[END_REF]. This theory is here restricted to the dependence of the nominal stress at failure σ N on the characteristic dimension D of 2D geometrically similar specimens. This dependence is described by the approximate formula:

0 / with 1 d D Bf t N = + = β β σ (1)
where f t is the tensile strength of the material, a 0 is a characteristic size that corresponds to a change of mechanisms between plasticity phenomena and fracture mechanics, and B is a material parameter which is a function of the geometry of the specimen and applied load. where F is the maximal load and L is the length between supports. The fracture energy G f , defined as the energy release rate required for crack growth in an infinitely large specimen, is also calculated (see [START_REF] Bazant | Fracture and size effect in concrete and other quasibrittle materials[END_REF].

It is found that the fracture energy G f shifts from the value 88.5 N/m for the reference material to 52.30 N/m for the material density 1.4, a decrease of 41%. In figure 2, size effect results are presented in a log-log diagram only for the two extreme densities (1.4 and 2.3) for more clarity. The larger the beam, the lower the relative strength. It can be noticed that the failure of the beams with polystyrene (density = 1.4) tends to adhere more to strength of material than to fracture

Acoustic emission analysis

AE analysis was performed on specimens of size (40×160×428 mm 3 ) and for three different material densities (2.3, 2.0 and 1.8). Three piezoelectric transducers (resonant frequency of 150 kHz) were used. Transducers were placed around the expected location of the process zone to minimize errors in the AE event localisation program. The accuracy of the technique ranged from 4

± mm for the reference mortar to 10

± mm for the lighter material tested (density 1.8).

The cumulated locations of acoustic events throughout a test are shown in Figure 3: the plotted points indicate the detected AE sources over a window of observation, centered at the notch, of width 130 mm and covering the beam depth. In the same figure, we have plotted the observed crack path that appeared after the test on the lateral surface of the specimen.

The major aim of the AE analysis is to obtain an experimental characterisation of the FPZ. More specifically, it is the width of the FPZ which is the quantity of interest since it is related to the internal length in continuum models (see e.g. [START_REF] Mazars | From damage to fracture mechanics and conversely: a combined approach[END_REF] and to the parameter d 0 obtained from Bazant's size effect analysis (Le [START_REF] Bellégo | Calibration of Non Local Damage Model from Size Effect Tests[END_REF]). An useful approach, well suited to measure the crack band width, is to divide the specimen into an array of rectangular elements and to count the AE events located within each element. A grid of size 1×1 cm is used here. The cumulative number of events, i.e. the sum over the entire record during the experiment, is plotted as a function of its horizontal position x for various vertical positions y over the depth of the specimen. Then, the crack band width is defined as the length of the segment of a horizontal straight line placed at 20% of the maximum number of counts (Nb max ), which intersects the average distribution of AE events (see [START_REF] Haidar | Correlation Between the Internal Length, the Fracture Process Zone and Size Effect in Mortar and Model Materials[END_REF] for more details). These values are about 50, 67 and 85 mm for the material densities 2.3, 2.0 and 1.8 respectively. We have also studied the case where the horizontal straight line intersects the vertical axis at the value = 10 % of Nb max , and we have observed that the evolution of the width of the FPZ, as a function of the polystyrene content g, is the same. Figure 4 shows the evolution of the width of the FPZ defined according to this criterion with the mass density of the specimens. On the same graph, the evolution of d 0 , of the fracture energy G f , of the tensile strength f t , and of the Young's modulus E are also plotted. Note that there is a very good agreement between the evolution of d 0 and the evolution of the width of the FPZ. This technique allows the determination of the shape of fracture process zone in its final stage, but incremental counts (in between two loading stages) provide also the evolution of the FPZ as the failure process develops. Such an evolution of the width of the FPZ is shown in figure 5. The width of the FPZ enlarges in the course of damage progression. Furthermore, the width is larger for the porous material compared to the reference one (without inclusions).

Figure 5. Evolution of the width of the fracture process zone v.s. the applied load for the two material densities. The load on the horizontal axis is increasing and then decreasing in the post peak regime.

Correlation with the internal length

We are going now to compare the experimental quantities determined in the previous section, namely the width of the FPZ and the parameter d 0 , with the internal length in a continuum model. The non local version of the isotropic damage model is used (see for instance [START_REF] Mazars | From damage to fracture mechanics and conversely: a combined approach[END_REF]. c l is the internal length of the non local continuum.

This internal length is obtained with the help of inverse finite element analysis, following the procedure described by Le [START_REF] Bellégo | Calibration of Non Local Damage Model from Size Effect Tests[END_REF]. The calibration procedure is based on a simultaneous fit of the numerical and experimental load deflection curves for the four sizes of specimens. Figure 6 shows the fits obtained for the reference material. The internal lengths and the others model parameters obtained as a result of these fits are reported in Same as for the acoustic emission tests we also measured the width of the FPZ obtained in the numerical analyses. It is 75 mm for the reference material, 120 mm for material density 1.8, and 139 mm for the lowest material density. These values are 40 percent greater than the experimental ones but the ratio between the computed and measured widths of the FPZ is constant whatever the mass density of the material as shown in Fig. 7. In the same figure, we have plotted also the evolution of Bazant's size effect parameter d 0 and of the internal length with the mass density of the specimens. The respective variations of these parameters are very similar, which is quite remarkable. This is also in good agreement with the result obtained by [START_REF] Bazant | Nonlocal Continuum Damage, Localization Instability and Convergence[END_REF], where the width of the zone of localized damage was shown to be proportional to the internal length of the material.

SIMPLIFIED MICROMECHANICS

The objective of the foregoing simplified analysis is to obtain qualitative expressions of non local effects induced by the presence of cracks in an elastic, homogeneous material (for more details see [START_REF] Pijaudier-Cabot | Non Local Damage Model with Evolving Internal Length[END_REF].

Consider an infinite isotropic two-dimensional solid subjected to a remote uniform stress field σ ∞ . Our purpose is qualitative and we shall consider for more simplicity σ ∞ as isotropic. Under this simplification, the considered problem is essentially one-dimensional, the strain and stress being volumetric. This solid contains microcracks caused by the loading history that are distributed in the material arbitrarily. Each crack induces a modification of the local stress and strain fields. In order to evaluate this perturbation, we assume that the microcracks are far enough from each others. Under this assumption, the induced remote stress and strain fields due to a crack are similar to those generated by a circular void. Therefore, cracks are going to be replaced by circular voids in the foregoing derivations. The calculation of the perturbation stresses and strains between the voids uses the superposition theorem. Note that cracks or voids are far from each others and that the perturbation stresses are computed far from them. We look at a material that has been slightly damaged only.

We may decompose this problem into two sub-problems:

• Sub-problem I: the solid is considered without any inclusion. It is subjected to the remote tensile volumetric stress σ ∞ .

• Sub-problem II: inside each void, a distribution of normal pressures is applied.

Superposition of these two sub-problems provides the distribution of the stress inside the medium containing voids. In the n problems of a circular void S i (i = 1 -n) of diameter a i in an elastic matrix, the remote traction σ ∞ is transformed into distributed normal forces P i = -(σ ∞ . n i ) acting inside each void where n i is the outward normal vector to the inner void surface Γ i . The effect of the pressure inside the voids S j on void S i is written as the sum of the p ij (i ≠ j), where p ij represents the normal pressure at the imaginary location of S i produced by S j :

2 2 ij j j ij r a P p × - ∝
(3) ij r being the distance between the centers of void i and void j. Since the voids are sufficiently far from each others, we have:

ij j ij n i j j ij i i r a l l P P = + ≈ ≠ = with 1 ) ( 1 2 (4)
On each contour Γ i of each voids we define:

i i P - = σ (5)
where i σ is the volumetric stress that equilibrates the normal pressure applied inside void i, to which the effect of interaction is added in order to equilibrate the remote stress ∞ σ on the void surface. Let us now evaluate the stress acting in the material, between the voids. According to the superposition scheme, the resulting local stress field at each point k x of the isotropic medium is the sum of the contributions due to each internal pressure inside each void plus the remote field:

) ( ) ( ) ( 2 i i ik k k x l x x ∞ ∞ + ≈ σ σ σ (6)
This equation is typically non local and the voids produce a stress amplification. At each material point, this amplification depends on the distance to the void considered, on the remote stress, and on the square of the radius of the void a i . Eq. ( 6) is very similar to the one derived by [START_REF] Bazant | Nonlocal Damage Theory based on Micromechanics of Crack Interactions[END_REF], with a more simple influence function here.

We are going now to derive the local strain field with a view to the expression that controls the growth of damage locally. Because the material in between the voids is elastic, we have:

+ = = ∞ ∞ i i ik k k k K x l K x K x x ) ( ) ( ) ( ) ( 2 σ σ σ ε (7)
where K is the bulk stiffness of the isotropic elastic medium. We can see here that the strain in the material is modified due to the voids. Same as for the stress, there is a non local amplification. Our goal is to recover an expression of the strain that is similar to the quantity that controls damage in continuum relations. For this, we need first to define such a constitutive relation. We use again the isotropic damage model:

(

)

) ( ) ( 1 ) ( k k k x x d K x ∞ ∞ - = ε σ (8)
Substitution in Eq. ( 7) yields:

( ) ( ) ∞ ∞ - + - = i i i ik k k k x x d l x x d x ) ( ) ( 1 ) ( ) ( 1 ) ( 2 ε ε ε (9)
It may be interesting to further modify Eq. ( 9) in order to exhibit the correction to the remote strain due to the presence of the voids. For this, we divide Eq. ( 9) by ) 1 ( d -, which is possible because damage is small. We obtain after some simplifications:

( ) ( ) ∞ ∞ ∞ + = i i ik i k k x r x f x x ) ( ) ( ) ( 2 ε ε ε ε (10)
Non local effects appear only when voids are present. They should grow when the number of voids increases. Function f(ε ∝ ) is a monotonically increasing function of the local strain, or on the local value of damage (see [START_REF] Pijaudier-Cabot | Non Local Damage Model with Evolving Internal Length[END_REF].

MODIFIED NON LOCAL MODEL

In the original non local damage model, the width of the FPZ is related to the internal length. According to bifurcation analyses (see e.g. [START_REF] Mazars | From damage to fracture mechanics and conversely: a combined approach[END_REF] it is proportional to the internal length. The experimental data presented in section 2 show that the internal length should increase in the course of damage. Furthermore, micromechanics shows that non local effects increase with damage. That can be captured considering that the internal length should increase in a non local model. Before modifying the original non local damage model accordingly, let us first recall the main equations. The stressstrain relation is:

kl ijkl ij d ε σ Λ - = ) 1 ( (11)
where σ ij and ij ε are the components of the stress and strain tensors respectively (i,

j, k, l ∈ [1, 3]), ijkl Λ
are the initial stiffness moduli, and d is the scalar damage variable. For the purpose of defining damage growth, the equivalent strain is introduced:

= + = 3 1 2 ~i i ε ε (12)
where + . is the Macauley bracket and i ε are the principal strains. In the non-local damage model, the variable ε which enters in the equations governing damage growth is:

Ω Ω - = - = ds s x x V ds s s x x V x r r ) ( ) ( with ) ( ) ( ) ( 1 ) ( ψ ε ψ ε (13)
where Ω is the volume of the structure, We look now for an enhancement of this model which accounts for the main characteristics of Eq.( 10) of the micromechanical model. According to Eq. ( 10) and at a given point x, the non local influence of a void located in its neighbourhood at coordinate z depends on the value of the scalar function 13) should be weighted following the same principle. There are several possibilities for capturing such an effect in the above non local model. One is to modify the value of the internal length in the weight function directly in order to capture the increase of the weight: On this plot, it can be observed that the width of the localised modes is increasing, at least in a first regime where the damage zone forms. This is consistent with the experimental observations in Fig. 5, as opposed to the results obtained with the original model with fixed internal length.

- - = - )) ( ( 4 exp )) ( , (

CLOSURE -APPLICATIONS TO COUPLED PROBLEMS

A first application to coupled problems deals with the chemo-mechanical case. More precisely, we intend to investigate the case of calcium leaching which produces an increase of porosity of the material, assuming that it is homogeneous, made of a single phase, which is a rather crude simplification of cement paste and mortar. The micromechanical model can be adapted in order to account for the initial porosity of the material. Eq. ( 6) becomes:

) ( ) ( ) ( ) ( j 2 2 j jk i i ik k k x l x l x x ∞ ∞ ∞ + + ≈ σ σ σ σ (17)
where the last term is the perturbation stress due to each initial void j. The derivation of the continuum model follows the same steps as in section 3, under the same assumptions and considering that the initial voids in the model material are sufficiently far from each others. The continuum constitutive relation which accounts for the initial porosity is chosen as

ε σ K V d ) 1 )( 1 ( - - =
where V is damage due to the initial porosity. This model is similar to the one devised by [START_REF] Gérard | Coupled Diffusion-Damage Modelling and the Implications on Failure Due to Strain-Softening[END_REF] among others, for chemo-mechanical damage. The strain governing damage growth (Eq. 10) becomes:

( ) ( ) ∞ ∞ ∞ ∞ + + = j j jk j i i ik i k k x r x V x r x f x x ) ( ) ( ) ( ) ( ) ( 2 2 ε ε ε ε ε (18)
An enhanced non local model can again be devised for materials with an initial distribution of voids such as those used in the experiments in section 2. One possibility is a subsequent modification of the weight function:

0 ) ( . ) , ( c c l V f V l + + = β ε α ε (19)
where β is an additional constant which accounts for the variation of internal length due to the initial material porosity. We can see here that an increase of the internal length is expected. This is consistent with experimental observations on model materials with controlled porosity (Fig. 7).

A second application is hydro-mechanical problems. Here, the voids or cracks are assumed to be filled with water. The water pressure is superimposed to the stress inside the voids and the interaction between voids is modified. Eq. ( 6) may be rewritten as:

( ) + + ≈ ∞ ∞ i i i ik k k x p x l x x ' ) ( ' ) ( ' 2 σ σ σ (20)
Note that the stress ' σ is now the effective stress.

The fluid pressure contributes to a part of the total applied stress and, in addition, it increases the interactions between voids. Eq.( 10 A third application is the case of creep-damage interaction. Eq. ( 6) remains unchanged but the local constitutive relation is time dependent:

( )

) ( ) ( 1 ) ( ) ( k k k x x d t K x ∞ ∞ - = ε σ (23)
The bulk modulus K(t) is a secant modulus that can be computed from visco-elastic relations. Eq. ( 10) becomes

( ) ( ) + = ∞ ∞ ∞ i i k i ik i k k x x t K x t K r x f x x ) ( ) , ( ) , ( ) ( ) ( 2 ε ε ε ε (24)
and one can see that the interactions depends on the ratio between the secant moduli at each point. If the rate of loading is larger at point x k than at point x i , then it is expected that this ratio is less than 1 and the interaction decreases. Consequently, an apparent decrease of the internal length is expected. The corresponding non local model with evolving internal length remains to be devised. One may think about a rate effect on the evolution of l c as suggested by size effect tests (see [START_REF] Bazant | Fracture and size effect in concrete and other quasibrittle materials[END_REF].

Finally, let us stress that the above qualitative discussion about the influence of porosity, internal pressure, and creep on the internal length has to be correlated with experimental results and probably with a less simplistic micromechanical analysis before a proper evolution of the internal length is implemented. Experimental data for the chemomechanical case are available from the experiments presented in this paper, with a model material only. Other type of experiments exhibiting the variation of the FPZ due to creep, internal fluid pressure, or chemo-mechanical effects remain to be performed.

Figure 1 .

 1 Figure 1. Influence of density on structural behavior, average load-deflection curves for different material density on 40 × 40 × 107 mm3 beams.

σ

  N is calculated according to the classical formula for a beam of unit thickness :

  the corresponding data shift right on the size effect plot. It means that the material becomes more ductile as the density decreases (increasing porosity).

Figure 2 .

 2 Figure 2. Bazant's size effect curve: calibration for material density 2.3 and 1.4.

Figure 3 .

 3 Figure 3. Cumulative location of AE events (material density 2.3).

Figure 4 .

 4 Figure 4. Evolution of fracture properties with polystyrene content.

Figure 6 .

 6 Figure 6. Prediction of the response of mortar beam with the material density 2.3.

Figure 7 .

 7 Figure 7. Evolution of d 0 , FPZ (experimental), FPZ (numerical) and l c with polystyrene content.

  internal length of the non local continuum.

  bifurcation analysis has been performed taking into account this modification of the non local model. The variation of the wavelength of localised modes is shown in Fig. 8.

Figure 8 .

 8 Figure 8. Variation of the admissible wavelength (mm) of the localised modes according to the original and enhanced damage models.

  devise a corresponding non local continuum model in which the internal length is a function of internal pressure: p) is positive and increases with increasing pressure.

Table 1 .

 1 Table 1 for all the mass densities. Set of model parameters resulting from optimised fits.

	At 4.61 10 -5 0.79 density lc (mm) κ 0 2.3 34.4	Bt 9836
	1.8	51.5	4.66 10 -5 0.65	9220
	1.4	64.2	4.79 10 -5 0.52	7893

ACKNOWLEDGMENTS

Financial support from the french ministry of research under the ACI Jeunes Chercheurs and from the partnership between Electricité de France and the R&DO group through the MECEN project are gratefully acknowledged.


F Z Aklouche

K Loubar

A Bentebbiche

S Awad

M Tazerout

Experimental investigation of the equivalence ratio influence on combustion, performance and exhaust emissions of a dual fuel diesel engine operating on biogas fuel

Keywords: Biogas, dual fuel engine, combustion, pollutant emissions, equivalence ratio

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

Experimental investigation of the equivalence ratio influence on combustion, performance and exhaust emissions of a dual fuel diesel engine operating on synthetic biogas fuel

Introduction

The development of internal combustion engines and the process of reducing pollutant produced by fuel combustion have become mandatory requirements for propulsion systems designers. One of the main objectives is to find the best way to minimize the emissions without considerably modify the engine's mechanical structure while maintaining the same performance. One of the proposed solutions is the method of injection of diesel fuel and the use of diverse gaseous fuels like biogas, natural gas, etc.

As a result of the gradual depletion of fossil oil and the environmental degradation, the utilization of gaseous fuel from biomass attracts the attention of the researchers. Thus, the use of some alternative gaseous fuels in the diesel engine increases worldwide. Biogas is an alternative fuel produced through a biological process. In the absence of oxygen (anaerobic condition), the methanization reaction starts spontaneously when organic matter is in a tepid environment, where it decomposes to form a gas mixture called biogas. Raw materials like industrialized waste, agricultural and biomass present an important potential for the generation of biogas but are underutilized [START_REF] Rasi | Trace compounds affecting biogas energy utilization a review[END_REF][START_REF] Demirbas | Biofuels sources, biofuel policy, biofuel economy and global biofuel projections[END_REF][START_REF] Frijns | The potential of (waste) water as energy carrier[END_REF]. However, the biogas composition varies according to parameters such as humidity, gas pockets and variations of the waste location [START_REF] Elsayed | Effect of VS organic loads and buckwheat husk on methane production by anaerobic co-digestion of primary sludge and wheat straw[END_REF].

Because of the increasing demand to reduce the pollutant emissions of existing technologies of internal combustion engine (ICE), several researches have been carried out investigating new approaches to achieve this goal. However, amongst several studies which were realized, the conversion of the diesel engine into a dual fuel (DF) engine, so as to use the alternative fuel, showed interesting results. In this mode, gaseous fuel is injected into the inlet manifold where it is mixed with air. After that, the gaseous mixture is entered into the combustion chamber where the pilot fuel, which has an important cetane number, is directly injected, and then ignites to initiate the combustion [START_REF] Abhishek | Effect of compressed natural gas dual fuel operation with diesel and Pongamia pinnata methyl ester (PPME) as pilot fuels on performance and emission characteristics of a CI (compression ignition) engine[END_REF][START_REF] Ryu | Effects of pilot injection pressure on the combustion and emissions characteristics in a diesel engine using biodiesel-CNG dual fuel[END_REF]. It is noted that biogas is a recommended fuel for engines which have a big compression ratio taking advantage of its important octane number allowing higher thermal efficiency. It was also reported that with minor modifications of the diesel engine, the biogas could be used [START_REF] Van Mitzlaff | Engines for biogas[END_REF]. In fact, a compression ignition engine running in conventional mode can be just altered into DF mode by branching a gas blender to its intake manifold. Moreover, a fuel test system must be placed to adjust the flow rate of the injected diesel fuel [START_REF] Bhaskor | Effect of compression ratio on performance, combustion and emission characteristics of a dual fuel diesel engine run on raw biogas[END_REF]. Also, it was suggested that the engine operating in DF mode running in biogas can be used to reduce the quantity of the diesel injected and at the same time diminish the compromise between NOx and smoke [START_REF] Bhaskor | Effect of compression ratio on performance, combustion and emission characteristics of a dual fuel diesel engine run on raw biogas[END_REF][START_REF] Barik | Investigation on combustion performance and emission characteristics of a DI (direct injection) diesel engine fueled with biogas-diesel in dual fuel mode[END_REF][START_REF] Barik | Experimental investigation on the behavior of a DI diesel engine fueled with raw biogas-diesel dual fuel at different injection timing[END_REF][START_REF]Effect of carbon dioxide on the performance of biogas/diesel dual-fuel engine[END_REF][START_REF] Bedoya | Exploring strategies for reducing high intake temperature requirements and allowing optimal operational conditions in a biogas fueled HCCI Engine for power generation[END_REF].

In diesel engines, nearest the injection of the diesel, the air temperature is around 553K.

However, in dual fuel mode, under these conditions, the biogas cannot ignite without the presence of a little quantity of pilot fuel to raise the temperature up to a temperature of about 1087K [START_REF] Sahoo | Clean development mechanism potential of compression ignition diesel engines using gaseous fuels in dual fuel mode[END_REF]. Furthermore, it has also been observed that, the dual fuel engine requires an extended combustion duration and at the same time an over long ignition delay [START_REF] Kyunghyun | Effects of pilot injection timing on the combustion and emissions characteristics in a diesel engine using biodiesel-CNG dual fuel[END_REF][START_REF] Barik | Simultaneous reduction of NOx and smoke in a dual fuel DI diesel engine[END_REF][START_REF] Abhishek | Effect of compressed natural gas dual fuel operation with diesel and Pongamia pinnata methyl ester (PPME) as pilot fuels on performance and emission characteristics of a CI (compression ignition) engine[END_REF]. In addition, it was noticed that the ignition delay can be shortened with the use of a fuel possessing a great stage of dissolved oxygen, and a high cetane number. Also, a reduction of the emission of exhaust can be observed [START_REF] Xiangang | Diesel engine gaseous and particle emissions fueled with diesel-oxygenate blends[END_REF].

Various gaseous fuels (methane, propane, CNG, LPG, hydrogen) can be used to power the diesel engine operating in DF mode while maintaining engine efficiency, and reducing exhaust emissions [START_REF] Karim | A review of combustion processes in the dual fuel enginethe gas diesel engine[END_REF][START_REF] Carlucci | Experimental investigation and combustion analysis of a direct injection dual-fuel diesel-natural gas engine[END_REF]. Furthermore, the reduction of some exhausts emissions and the improvement of the engine efficiency can be achieved by the optimizing of certain parameters influencing the engine, such as, substitution ratio, injection timing, engine loads [START_REF] Sayin | Effects of injection timing on the engine performance and exhaust emissions of a dual-fuel diesel engine[END_REF], and inlet air temperature [START_REF] Papagiannakis | Study of air inlet preheating and EGR impacts for improving the operation of compression ignition engine running under dual fuel mode[END_REF]. Moreover, it was noticed by Makareviciene et al. [START_REF] Makareviciene | Performance and emission characteristics of biogas used in diesel engine operation[END_REF] that the combustion performance was better with variation of injection timing.

Srinivasan et al [START_REF] Srinivasan | Cyclic combustion variations in dual fuel partially premixed pilot-ignited natural gas engines[END_REF] found that DF (natural gas/diesel) engine could participate to minimize carbon dioxide emission by reason of the smallest carbon-hydrogen ratio. The natural gas may decrease greatly both NOx emission and soot [START_REF] Lounici | Towards improvement of naturel gas-diesel dual-fuel mode: an experimental investigation on performance and exhaust emissions[END_REF][START_REF] Abdelaal | Combustion and emission characteristics of a natural gasfueled diesel enginewith EGR[END_REF], which is complicated to attain in conventional mode. In addition, for various advantages of natural gas, it may be used like an additional fuel to operating in DF mode [START_REF] Abdelaal | Combustion and emission characteristics of a natural gasfueled diesel enginewith EGR[END_REF]. That is why former studies showed that the use of the biomethane as a fuel for vehicles is preferable for the energy production [START_REF] Henham | Combustion of simulated biogas in a dual fuel diesel engine[END_REF].

Additionally, dual fuel mode using biodiesel as pilot fuels [START_REF] Awad | Experimental investigation on the combustion, performance and pollutant emissions of biodiesel from animal fat residues on a direct injection diesel engine[END_REF][START_REF] Khiari | Experimental investigation of pistacia lentiscus biodiesel as a fuel for direct injection diesel engine[END_REF][START_REF] Tarabet | Experimental investigation of DI diesel engine operation with eucalyptus biodiesel/naturel gas under dual-fuel mode[END_REF][START_REF] Kezrane | Experimental assessment of performance and emissions maps for biodiesel fueled compression ignition engine[END_REF] shows a lowering of particulate emissions with the increasing of load [START_REF] Tarabet | Experimental investigation of DI diesel engine operation with eucalyptus biodiesel/naturel gas under dual-fuel mode[END_REF]. This was explained by the important combustion temperature and enabling combustion amelioration. Luijten and Kerkhof [START_REF] Luijten | Jatropha oil and biogas in a dual fuel CI engine for rural electrification[END_REF] have replaced the diesel by the Jatropha oil to ignite the DF engine operating with biogas. A reduction of about 10% of the brake thermal efficiency was observed. Similar observation was reported by other researchers using different pilot fuels (karanja methyl) [START_REF] Barik | Investigation on performance and exhaust emissions characteristics of a DI diesel engine fueled with Karanja methyl ester and biogas in dual fuel mode[END_REF].

Papagiannakis et al [START_REF] Papagiannakis R G, Rakopoulos | Emission characteristics of high speed, dual fuel, compression ignition engine operating in a wide range of natural gas/diesel fuel proportions[END_REF] obtained the effects of the amount of natural gas on NOx emissions.

The results showed that the augmentation of natural gas mass ratio has a good effect to minimize NOx emissions.

On the other hand, the effect of the biogas composition in DF mode was studied by Daouk et al [START_REF] Daouk | Experimental investigation and combustion analysis of biogas with different compositions in dual fuel diesel engine[END_REF]. They noted that the biogas containing 70% methane (by volume) and about 30% carbon dioxide has advantages in terms of emissions compared to the conventional mode.

Also, the study of the performance of dual fuel (biogas-diesel) was established by Lounici et al [START_REF] Carlucci | Experimental investigation and combustion analysis of a direct injection dual-fuel diesel-natural gas engine[END_REF], where a good knock resistance was observed from measured torque at the knock onset.

It was reported by several researchers that the high levels of THC emissions produced by DF combustion is considered as a disadvantage of this mode. In fact, it was achieved in other works that the hydrocarbon emission in normal diesel mode was lower than that in dual fuel operation, with about 6000 ppm [START_REF] Wannatong | Combustion and knock characteristics of natural gas diesel dual fuel engine[END_REF][START_REF] Papagiannakis | Combustion and exhaust emission characteristics of a dual fuel compression ignition engine operated with pilot diesel fuel and natural gas[END_REF]. In spite of the fact that, in DF mode, the THC emissions were decreased as engine load increases, but the value of hydrocarbon emission was even more important by about 2000 ppm [START_REF] Liu | Effects of pilot fuel quantity on the emissions characteristics of a CNG/diesel dual fuel engine with optimized pilot injection timing[END_REF] and 2.5 times [START_REF] Imran | Natural gas fueled compression ignition engine performance and emissions maps with diesel and RME pilot fuels[END_REF] in DF mode with natural gas. Thus, the need to get a method to diminish the THC emissions on a DF mode emerges.

Various methods were used in DF engine (NG/diesel) to reduce the THC without lowering the thermal efficiency, such as using injection timing [START_REF] Sun | Combustion performance and stability in dual fuel engine with different pilot diesel injection timing[END_REF], gas recirculation burning [START_REF] Zhou | Effect of hot exhaust gas recirculation on the combustion characteristics and particles emissions of a pilot-ignited natural gas engine[END_REF], raising the quantity of pilot fuel [START_REF] Liu | Effects of pilot fuel quantity on the emissions characteristics of a CNG/diesel dual fuel engine with optimized pilot injection timing[END_REF], etc.

Previous studies focused mainly on the use of natural gas for engines running in DF mode with respect to biogas. There are fewer studies about the biogas as a high potential alternative source of energy for compression ignition engines. Moreover, these studies stated that the use of biogas can be limited by the high levels of pollutant emissions, especially unburned hydrocarbon. Thus, the main objective of the present study is to investigate the use of biogas in CI engine and to propose a technique to reduce the pollutant emissions without any drawbacks on the performance of engine at high load. The proposed technique is based on varying the total equivalence ratio using a throttle valve to adjust the air mass flow rate.

Materials and procedure

Biogas used in engine test

In general, the composition of biogas fuel is ranging from 50% to 70 % (by volume) for methane and 30% to 50% for carbon dioxide. In this study, CH 4 and CO 2 , stored separately in pressurized bottles, were used in the engine test with a percentage of 60% and 40%

respectively. The biogas used was prepared using a computer controlled mixer.

In the beginning, the engine is operated only on diesel fuel to prepare the engine (warm up and stabilize). After that, the engine is switched to dual fuel mode. The synthesized gaseous fuel passes through a line to the intake manifold after mixing. Close to the compression process ending, the flow rate of the pilot fuel injected into the combustion chamber is maintained constant to cover ten percent of the power output. After that, by increasing only the gaseous fuel flow (biogas), the power output is more rises. The compositions of primary fuel and diesel fuel used for this study are shown in table 1. function in a speed range of 0 to 2500 rpm, capable of generating a power up to 7.4kW. It includes a dynamometer, a particle analyzer, an exhaust gas analyzer and a gas supply system to feed the engine when it is operating in dual fuel mode. The fig. 1 shows the engine test scheme.

Fig. 1. Experimental setup scheme.

Using AVL software, the data was registered and analyzed from 100 cycles. A sampling interval of 0.2 crank angle (CA) is considered to obtain the combustion parameters. More details about the acquisition system; sensors precision and uncertainty calculation could be found in our previous works [START_REF] Lounici | Towards improvement of naturel gas-diesel dual-fuel mode: an experimental investigation on performance and exhaust emissions[END_REF][START_REF] Tarabet | Experimental investigation of DI diesel engine operation with eucalyptus biodiesel/naturel gas under dual-fuel mode[END_REF].

Through the tests, the energy input under dual fuel operation (diesel pilot fuel+biogas) was kept constant; this energy is allows to produce about 80% of the full load under conventional mode. The percentage energy substitution rate (PES) of biogas was kept constant (60%) for the different total equivalence ratios studied. The total equivalence ratio and the biogas percentage energy substitution rate are determined as following:

PES=( LHV B )/( LHV B + LHV D ) (1) ɸ=( AFR B-th + AFR D-th )/( ) (2)
Where , and (kg/h) are the mass flow rates of biogas, diesel and air respectively. The calibration of the engine test bench was done according to the instructions given in the manufacturer catalog. The brake torque is measured from the dynamometer control system for a given operating condition. Parameters, such as the pressure cylinder, the flow rates of diesel, biogas and air are registered to analyze the engine efficiency.

Analysis combustion model

In order to examine the combustion process in both modes, the heat release rate (HRR) must be determined. The HRR can supply valuable information for understanding the engine operating. It is calculated analytically by applying and the first law of thermodynamics and the law of ideal gas. Using the variation of the cylinder volume and the recorded value of the cylinder pressure, the following expression is used to obtain the HRR [START_REF]Internal combustion engine fundamentals[END_REF].

] [ 1 1 ] [ 1         d dP V d dV P d dQ d dQ d dQ W net C       (3)
Where

 d dQ net is the net HRR,  d dQ C
is the rate of heat released by the fuel combustion and

 d dQ W
is the heat transfer rate through the cylinder wall obtained from the Woschni's correlation [START_REF]Internal combustion engine fundamentals[END_REF]. P is the cylinder pressure. γ is the ratio of specific heats. V represents the combustion chamber volume; it depends on the crank angle (θ) and the geometric parameters of the engine. The cylinder volume V is obtained by the following equation:

                         2 2 sin 2 2 1 2 cos 1 1 C L Cr Cr V V d (4)
where V d , C r , L and C are respectively the displacement volume, the compression ratio, the connecting rod length and the stroke.

Results and discussion

Combustion characteristics

The results shown below are discussed for a percentage energy substitution rate (PES) of 60%. The effect of the variation of total equivalence ratio was studied for the engine dual fuel (biogas/diesel) at high load. To diagnose combustion behavior, it is important to analyze the cylinder pressure history, which is obtained by the cylinder pressure data. The cylinder pressure data is used to plot the curves of cylinder pressure and the evolution of heat release rate (HRR), for the different total equivalence ratios with respect to crank angle. The incylinder pressure, ignition delay and net HRR for the conventional diesel and dual fuel (DF) operating modes at a constant engine speed of 1500 rpm are shown below for 80% of load. A comparison was done between the results of the conventional and DF engine mode.

Cylinder pressure

Fig. 2 shows the evolution of the cylinder pressure versus crank angle at various total equivalence ratios. As shown in fig. 2, the highest peak of cylinder pressure, of 86 bars, is noticed for the conventional diesel mode, which occurs 5.4 after TDC. However, as the total equivalence ratio increases, the evolution, as well as the peak, of cylinder pressure of dual fuel operation decreases. A minimum peak of cylinder pressure of 63 bars is observed at ϕ=0.7; it represents a reduction of about 26% in comparison to conventionel mode. In addition, it can be shown that the evolution of cylinder pressure also decreases even during the compression stage. Indeed, the reduction of the intake air flow, reduces the volumetric efficiency which reduces the in cylinder pressure. Fig. 2. Cylinder pressure variation with crank angle for both modes, for different equivalence ratios (ϕ).

Ignition delay

The ignition delay (ID) can be defined as the crank angle (CA) interval between two points.

The first point is the start of injection, and the second is the beginning of combustion. The combustion of biogas in DF mode undertakes a much complex process compared to that of diesel. Fig. 3 shows the plot of the ID evolution versus ϕ for DF mode (PES 60%) compared to conventional mode. It can be seen that the ID of DF is greater than the conventional mode for all studied cases. In addition, the ID increases as ϕ increases. The value of the ignition delay varies between 3.8 and 7.6 for ϕ ranging from 0.35 to 0.7. The reasons of the prolongation of ID are the reduction in the oxygen concentration, as the ϕ increases, and the diminution of the charge temperature [START_REF]Internal combustion engine fundamentals[END_REF] due to lower pressure as discussed previously (fig. 2). On the other hand, this extension can also be caused by the specific heat capacity of biogas which is high.

Furthermore, as reported by Wei Lijiang et al [START_REF] Wei | A review on natural gas/diesel dual fuel combustion, emissions and performance[END_REF], the addition of biogas into the cylinder can delay the auto-ignition of pilot fuel because of the coupling between free radicals. In fact, the gaseous mixture (air/biogas) goes through a pre-ignition reaction over the compression phase.

This chemical reaction affects the ignition of the pilot fuel, due to the formation of energetic radicals. Hence, the prolongation of ID can also be referred to chemical factors. Fig. 3. Ignition delay variation with ϕ.

Heat release

Fig. 4 shows the evolution of the heat release rate (HRR) versus the crank angle (CA) for conventional and dual-fuel (DF) modes at different total equivalence ratios. As shown in fig. 3, the combustion process, is divided into three phases namely: ignition delay, premixed phase (rapid combustion), and the diffusion combustion. At the beginning, one can visualize a negative heat release over the first phase which is explained by the vaporization of diesel fuel accumulated. As the combustion starts, the HRR takes positive value and increases until the peak of the second phase. This is followed by the diffusion combustion which is controlled by the (fuel-air) gaseous mixture. From fig. 4, the peak of HRR increases with the increasing of ϕ. Furthermore, the DF combustion start later with a few degrees of CA compared to the conventional mode due to the extension of ID as explained previously. The maximum and the minimum values of premixed peak of HRR for DF mode are 70 J/deg CA and 43 J/deg CA corresponding to ϕ of 0.7 and 0.35, respectively. In addition, the minimum of HRR of 36.7

J/deg CA is recorded in the case of conventional mode, which takes place at 8.8 °CA before TDC. Furthermore, at 0.35, 0.45, 0.55 ϕ, the diffusion combustion of DF mode is similar to that in conventional mode. This can be interpreted by the augmentation of ϕ of the gaseous mixture, owing to the rise of combustion temperature. Also, as ϕ increases the combustion process enhances and the second phase is reinforced as result of the good mixture concentration (fig. 5), which gives a highest flame speed of gaseous mixture (biogas/air).

Combustion duration

Fig. 6 presents the evolution of the combustion duration with respect to total equivalence ratio. The combustion duration is presented in terms of crank angle. It is defined as the duration between the instance where the HRR takes positive value and the instance at which 90% of the net heat is released [START_REF]Internal combustion engine fundamentals[END_REF]. The combustion duration decreases as ϕ rises. It varies from 20.5 to 12.2 CA when ɸ varies from 0.35 to 0.7 respectively. As known, at high ɸ the burning velocity of biogas is higher than that at low ɸ [START_REF]Internal combustion engine fundamentals[END_REF], which consequently reducing the combustion duration, the same observation was achieved by Debabrata Barik et al [START_REF] Debabrata | Effects of diethyl ether (DEE) injection on combustion performance and emission characteristics of Karanja methyl ester (KME)-biogas fueled dual fuel diesel engine[END_REF].

Fig. 6. Variation of combustion duration versus ϕ.

Engine performance

The evolution of the brake thermal efficiency (BTE) for DF operation and conventional diesel engine with ϕ are shown in fig. 7. It can be calculated by the following expression:

Ƞ eff =P eff /( LHV B + LHV D ) (7)
Where P eff (kW) is the brake power. The BTE in dual fuel (DF) mode increases with increasing equivalence ratio (fig. 7). Else, the BTE for the DF mode is higher than that of conventional mode for all the cases studied. For instance, the BTE of the engine operating in DF at ϕ=0.7 is better than that of diesel mode by about 19%. Indeed, as known, at high load, the BTE is improved when more biogas is provided to the cylinder. Regarding DF mode, the BTE increases with about 13% as ϕ increases. In fact, at high ϕ gaseous mixture (biogas/air) became more homogeneous. This is beneficial factor to have a complete combustion and limits misfires cases, which reduce THC emissions as it is shown in the next section and improve the BTE.

Exhaust emissions

In this part, the evolution of pollutant emissions was analyzed for different ϕ at 60% PES. In DF mode, the concentration of soot in the exhaust gas is very low at high load; a similar observation was reported by Lyes Tarabet et al [START_REF] Tarabet | Experimental investigation of DI diesel engine operation with eucalyptus biodiesel/naturel gas under dual-fuel mode[END_REF]. Therefore, the evolution of soot is not presented in this study.

The variation of total unburned hydrocarbon (THC) related to the variation of ϕ is plotted in fig. 9. As shown in fig. 9, the concentration of THC emissions under DF mode is much important than that in conventional mode. On the other hand, it can be observed that THC emissions in DF mode decrease significantly with the augmentation of ϕ. Indeed, changing ϕ from 0.35 to 0.7 results in a THC emissions decrease of about 77%. This reduction can be particularly explained by the decrease of dilution of air/biogas mixture, which provides a good condition of fast flame propagation of biogas-air mixture. On the other hand, as stated previously the rich mixture leads to a better combustion process due to higher temperatures in the combustion chamber and limits misfires cases. Fig. 11 shows the evolution of the carbon monoxide emissions (CO) with ϕ. It may be noticed that as the ϕ increases the concentration of the CO emissions decreases about 58%. This is again the result of the better flame propagation leading to a more complete combustion due to the rich mixture. However, it can be also observed that, although the concentration of CO emission decreases with increasing ϕ, the concentration of these pollutants is still twice that of the conventional mode. Fig. 12 shows the evolution of the carbon dioxide with increasing ϕ. It can be observed that at high ɸ, the difference between the concentrations of CO 2 for both modes is about 7%. The specific emission of CO 2 (g/kWh) decreases about 14% with the augmentation of ϕ in the case of DF mode. Indeed, as discussed previously, the increase of ϕ induces an improvement of combustion process resulting in higher CO 2 concentrations (%Vol.) in the exhaust gas.

However, in the same time, the power output increases since the BET is becoming higher and thus resulting in lower specific emission (g/kWh) when increasing ɸ.

Conclusion

In the present work, an experimental investigation was conducted to study the effects of equivalence ratio (ϕ) variations on the combustion characteristics, performance and exhaust emissions of a dual fuel (DF) diesel engine operating on biogas fuel at high load (80% of full load). The experiments were performed with a fixed energy input to the engine while the percentage energy substitution (PES) was kept constant (60%). ϕ was varied from 0.35 to 0.7.

The results led to the following conclusions:

-The peak of in-cylinder pressure under DF mode was lower than that observed for conventional mode for all the cases studied. Also, the peak of in-cylinder pressure decreased as ϕ increases for DF operation.

-Under DF mode, as ϕ increases, the ignition delay became longer and the heat release rate gave higher peak for the premixed phase.

-Concentrations of THC, CO, CO 2 and NOx were reduced with about 77%, 58%, 14% and 24% respectively when ϕ was varied from 0.35 to 0.7.

-The BTE was improves by about 13% with increasing ϕ under DF mode. Moreover, at ϕ=0.7, the BTE is higher than that of conventional mode by about 19%.

F

  .Z. Aklouche, Khaled Loubar, A. Bentebbiche, Sary Awad, Mohand Tazerout To cite this version: F.Z. Aklouche, Khaled Loubar, A. Bentebbiche, Sary Awad, Mohand Tazerout. Experimental investigation of the equivalence ratio influence on combustion, performance and exhaust emissions of a dual fuel diesel engine operating on synthetic biogas fuel. Energy Conversion and Management, 2017, 152, pp.291-299. 10.1016/j.enconman.2017.09.050. hal-01731269

  AFR B-th and AFR D-th (MJ/kg) are the theoretical air fuel ratios of biogas and diesel respectively. LHV B and LHV D are the lower heating values of biogas and diesel respectively.The injection timing of diesel fuel is fixed at 13°CA before top dead center (TDC). During dual fuel operation, ɸ was varied by adjusting the air flow rate using a throttle valve.However, for conventional diesel mode, the engine tests were conducted under wide open throttle (WOT) condition.

Fig. 4 .

 4 Fig.4. Heat release rate (HRR) with crank angle for different ɸ.

Fig. 5 .

 5 Fig.5. Evolution of the premixed burned mass fraction versus ϕ.

Fig. 7 .

 7 Fig.7. Evolution of the BTE with ϕ.

Fig. 8 .

 8 Fig.8. Evolution of the BSFC with ϕ.

Fig. 9 .

 9 Fig.9. Variation of THC emissions versus ϕ.

Fig. 10

 10 Fig.10 indicates the evolution of NOx emissions versus ϕ. From this figure, a decrease of 24%

Fig. 10 .

 10 Fig.10. Variation of NOx emissions with different ɸ.

Fig. 11 .

 11 Fig.11. Evolution of CO emissions with various ϕ.

Fig. 12 .

 12 Fig.12. Variation in CO 2 emissions with different ϕ.

Table 1

 1 Diesel fuel and biogas properties.

	Component	Primary fuel (Biogas)	Pilot fuel (diesel)
	Chemical Composition	60% CH 4 , 40% CO 2	C 12 H 26
		(V/V (%))
	Cetane number	-	49
	Density (kg/m 3 )	1.33	840
	Stoichiometric air fuel ratio	6.04	14.60
	LHV (MJ/kg)	17.65	42

2.2. Engine test and procedure

In this study, the engine tests were carried out in the laboratory of Energy of Ecole des Mines de Nantes. It consists of a single-cylinder engine LISTER-PETTER, which is made to

Acknowledgments

The authors are very thankful to all the technicians in the laboratory of Ecole des Mines de Nantes for their help and for kind collaboration in this study.