Thomas Barnay
email: barnay@u-pec.fr

Sandrine Juin
email: sandrine.juin@ined.fr

Renaud Legal
email: renaud.legal@sante.gouv.fr

Audrey Baillot

Magali Dumontet

Cermes

Disparities in taking sick leave between sectors of activity in France: a longitudinal analysis of administrative data 1

Keywords: sick leaves, health insurance, government policy, longitudinal data, fixed-effects, conditional maximum likelihood I13, I18, I38, J24

The main objective of this study is to analyse the effect of the professional environment on sick leaves. The professional context is approximated by the sector of activity. The database used -Hygie (2005)(2006)(2007)(2008) -allows taking individual heterogeneity into account thanks to the longitudinal dimension. Sick leave probability is estimated through a fixed effects logit model and the duration (number of days absent due to sickness) is estimated through a fixed effects Poisson model. The results show that sectors of activity differ in sick leave duration rather than in the occurrence. Indeed, taking into account individual heterogeneity and differences in health status and wages reduces the variability in sick leave probability between sectors by half. On the other hand, the sector remains decisive in explaining sick leave durations. This residual variability may refer to unobserved differences in working conditions, in the generosity of daily sick pay benefits or in job insecurity.

Introduction

French health expenditures on daily sick pay benefits (see annex 6.1) paid by the National Health Insurance Fund for Salaried Workers, rose to 6.8 billion euros in 2010. On the macroeconomic level, the main drivers in daily sick pay benefits' dynamic are relatively well known: the salary level (price effect), the employment environment including unemployment (volume effect), the proportion of workers over 50 years in the Labour force (health effect), and also the intensity of sickness absence control policy by the public authorities. By contrast, on the microeconomic level, the study of determinants is still insufficient, although it is a major issue in terms of French public policies (the role of work conditions, the social cost of absenteeism, the optimal level of coverage…). Taking sick leave should essentially be due to a bad health status [START_REF] Ose | Working conditions, compensation and absenteeism[END_REF]. Nevertheless, other factors can intervene such as medical's prescriptions, the employees' moral hazard behaviour [START_REF] Allen | An empirical model of work attendance[END_REF][START_REF] Brown | The Economics of Absence: Theory and Evidence[END_REF], the role of collective agreements or again the work demands forcing some employees to take sick leave or inversely, to be present despite bad health status.

This study falls within empiric publications on sick leaves and proposes, in the French case, to sharply analyze the microeconomic determinants. More precisely, it endeavours to estimate the net effect of the professional context on the individual disparities in the occurrence and the duration of sick leaves after controlling composition effects.

It is important to isolate the professional context effect -which is relative to characteristics of the professional environment (work conditions, sick leave benefits…) from composition effects -which relate to the individuals' personal characteristics (age, gender, salary level, health status…) and environmental determinants -which relate to the non-professional environment (provision of care characteristics, unemployment rate…). Indeed, in terms of public policies, the effects of the professional context will not require the same answers as those pertaining to composition effects. For instance, a sector of activity distinguished by a particularly high claim rate could involve incentive measures aiming to improve work conditions. Conversely, a given category of employees presenting atypical rates of sick leave could suggest targeted actions focussed on prescribers. Moreover, social contributions that fund daily sick pay benefits paid by the Health insurance solely depend upon the individual's salary level: the rules for funding sick leave ignore the possible effect due to the professional context and hardly encourage companies to anticipate sick leaves. It is therefore interesting to estimate the extent to which the professional context explains sick leave disparities.

Several levels of analysis are permitted in order to analyse the effects of the professional context such as the company or the sector of activity… This study chooses to understand the professional context at the sector of activity level. There were two reasons this choice was made. First, in the absence of being able to observe the levels of sick leave coverage in each company, the sector of activity enables us to approach this compensation level. Indeed, beyond mandatory compensation for sick leaves paid by the Health insurance, there exists an optional compensation provided for through collective bargaining which is highly dependent upon the branch of activity. Second, the sector of activity also enables taking gaps in working conditions into account.

This study was carried out using a panel of over 400,000 employees in the private sector on whom we had access to much administrative information: consumption of medical care, sick leaves, retrospective information on professional careers, etc.

From a methodological point of view, it is not easy to isolate the net effect of the professional context, due to the problems linked to unobserved individual heterogeneity, potentially correlated to the professional context. For instance, if a company recruits unhealthy people, but whose health status is not correctly observed, we could assign the professional context what is indeed a composition effect. Having access to panel data gave valuable answers to the problems of endogeneity. The empirical strategy consists in using changes in sectors on an individual level to estimate the net effect of the professional context: it fully exploits the longitudinal dimension of the data. The effect of the professional context is analysed both in terms of the occurrence of sick leaves and in terms of the duration thereof.

The article is organized as follows: part 2 proposes a critical review of publications pertaining to sick leave; part 3 presents the database and methodology used; part 4 presents the main results obtained. Finally, the last part is devoted to discussion and the conclusion.

Review of the literature

Many papers have endeavoured to empirically study the determinants of sick leave. Two types of determinants can be identified: individual and contextual.

The individual determinants

Socioeconomic characteristics play a large role. Thus, women generally take longer and more frequent sick leaves than do men [START_REF] Chaupain-Guillot | Les absences au travail : une analyse à partir des données françaises du Panel européen des ménages[END_REF][START_REF] Halima | Sick Leaves: Understanding Disparities Between French Departments[END_REF][START_REF] Halima | Duration of Sick Leave, Income and Health Insurance: Evidence from French linked employer-employee data[END_REF]Frick and Malo, 1008;Livanos et al., 2010). They are thus more sensitive to economic incentives (compensation system effect) and are more influenced by unemployment [START_REF] Henrekson | The effects on sick leave of changes in the Sickness Insurance system[END_REF][START_REF] Ose | Working conditions, compensation and absenteeism[END_REF]. Moreover, the length of sick leaves increases with age, without actually making them more frequent (Chaupain-Guillot and Guillot, op. Cit). This surprising result can be partially explained by the existence of a healthy worker effect: employed seniors are healthier than those who are not employed [START_REF] Barnay | In which ways do unhealthy people older than 50 exit the Labour Market in France?[END_REF]. Having young children increases the probability of a sick leave (Chaupain-Guillot and Guillot, op. cit.). Education, rarely studied, seems to decrease sick leave: the later an individual starts their career (high education and human capital levels), the shorter the sick leave (Ben [START_REF] Halima | Duration of Sick Leave, Income and Health Insurance: Evidence from French linked employer-employee data[END_REF].

Health status is equally a determining factor. A degradation of the health capital could lead to sick leave by making the individual unable to work. In addition, careful management of health capital can suppose forms of preventive sick leaves to prevent more damaging consequences on the individual's occupational status [START_REF] Grossman | On the Concept of Health Capital and the Demand for Health[END_REF]. Chaupain-Guillot and Guillot (op. cit.) demonstrated that a person suffering from a chronic disease or disability has a higher probability of taking sick leave. Furthermore, Ben Halima and Regaert (op.cit.) highlight that an individual with an Acute chronic disease (ACD)5 has longer sick leaves. Additionally, [START_REF] Case | Broken down by work and sex: how our health declines[END_REF] explain that manual workers self-report to be in the poorest health status.

Finally, concerning individual characteristics linked to employment, several theoretical mechanisms underlie sick leaves. In the Shapiro-Stiglitz efficiency wage model (1984), the individuals, whose utility positively depends upon wages and negatively upon effort, would be less inclined to be voluntarily absent (shirking model) when the probability of finding a new job is lower. Thus, the critical wage (the minimum wage satisfying the non-shirking condition) is an increasing function of the expected utility associated with unemployment. Ben Halima and Regaert (op.cit.) demonstrate a negative relationship between wages and the length of sick leaves (in which case leisure is considered to be a normal good) by controlling those individuals with ACD while Chaupain-Guillot and Guillot (op. cit.) indicate that the impact of wages on the probability of absence in men is negative, corroborating the shirking model. As concerns the type of work contract, a permanent contract increases the probability of returning to work (Ben Halima and Regaert, op.cit.). Women with fixed-term contract have a lower probability of being absent (Chaupain-Guillot and Guillot, op. cit.). In the economic theory, absenteeism results from a work-leisure trade-off in a neoclassical model of labour supply [START_REF] Allen | An empirical model of work attendance[END_REF][START_REF] Brown | The Economics of Absence: Theory and Evidence[END_REF]. Within this framework, sick leaves could correspond to the differential between the contractual number of hours and the desired number of hours. For instance, women working part time (ensuring a better balance between family and professional lives) have a lower probability of absence (Chaupain-Guillot and Guillot, op. cit.).

The contextual determinants

Based on [START_REF] Shapiro | Equilibrium unemployment as a worker discipline device[END_REF], it is commonly argued that labour market uncertainty has a negative impact on absenteeism (in other words, absenteeism is countercyclical) but empirical evidences have to be more nuanced. We can assume that the unemployment rate constitutes a worker discipline device and employees may fear to lose their job if they report sickness. Nevertheless, the duration of sick leave is determining. Thus, [START_REF] Ose | Working conditions, compensation and absenteeism[END_REF] found that short-term absences (shorter than 3 days) do not depend on the unemployment rate while long-term absences do. [START_REF] Livanos | Unemployment, Labour Market Flexibility and Absenteeism: A Pan-European Study[END_REF] showed that a higher proportion of dependents persons (inactive and unemployed individuals) decreases sickness absence, probably because of the increasing pressure active people may experience.

The geographic context is equally important. For instance, interaction effects on the local neighborhood level play a role on the utilization of the Swedish sickpay insurance (Lindbeck et al., 2011). In France, Ben [START_REF] Halima | Sick Leaves: Understanding Disparities Between French Departments[END_REF] highlight that sick leave county6 disparities subsist even after controlling composition effect into counties. These county gaps could notably be due to an unequal access to healthcare across the territory.

Econometric work on sickness absence little studied sector of activity and this variable has, to our knowledge, never been a dedicated study on panel data. Nonetheless, there seems to exist that which could be called a sector of activity effect. Thus, the probability of sick leave seems to be higher in the public sector than in the private sector (Chaupain-Guillot and Guillot, op. cit.). More recently, Ben Halima and Regaert (op. cit.) showed that relative to the commercial sector, employees in the sectors of healthcare and social work, industry, construction, finance, real-estate, transportation and communication take shorter sick leaves, contrary to those in the hotel and catering sector. These inter-sectoral gaps can be explained by differences in employment characteristics, work conditions and sick leave coverage between sectors. As concerns the generosity of the insurance coverage, it has been demonstrated that a generous compensation system increases the number of sick leaves and their duration [START_REF] Henrekson | The effects on sick leave of changes in the Sickness Insurance system[END_REF]Frick and Malo, op. cit.). Moreover, the intensification of sickness absence's checks by health insurance, which has reduced the moral hazard, seems to reduce the probability of taking sick leaves, at least in the short term (Ben Halima et al., op. cit.). As for work conditions, [START_REF] Afsa | Le rôle des conditions de travail dans les absences pour maladie : le cas des horaires irréguliers[END_REF] show that a high percentage of absenteeism in unskilled workers is, in fact, due to irregular working hours. Chaupain-Guillot and Guillot (op. cit.) reveal that a person unsatisfied with their work has a higher probability of absenteeism. Moreover, the positive relationship between the company's size and the probability of absence due to illness (Ben Halima et al., op. cit.;[START_REF] Ose | Working conditions, compensation and absenteeism[END_REF] seems to confirm the importance of work conditions (nevertheless, this positive relationship could also reveal differences in verification policies or individual effort within the company).

In reference to this short review of publications, our study attempts to analyse the intersectoral disparities in terms of probability and duration of sick leave. To what extent are they explained by the differences between the individuals composing the sectors (in this case, we refer to composition effects)? What part does the sectoral context play?

Method 3.1. Data

The Hygie panel 2005-2008 (Information System on Daily Sick Pay Benefits) is the first French database enabling a simultaneous study of health, work and company factors intervening in sick leaves of private sector employees. It was built by matching data from the French Pension insurance and the statutory National Health insurance. We thus know the identity of the insured persons, their professional trajectories, the last establishment in which they worked and their retirement information. The French Health insurance provides data on individual healthcare consumptions, sickness benefits as well as information relative to accidents at work and occupational diseases. Our sample is composed of 414,185 employees in the private sector (working or unemployed), aged between 22 and 60 in 2008 and having contributed to the general Pension scheme at least once over the course of their lives and living over the entire period from 2005-2008 (cf. annex 6.2, table A for the descriptive statistics).

Almost 20 % of the individuals had at least one period of sick leave in 2008 and the majority had only one (table B in annex). These sick leaves were characterised by a median number of 16 sickness absence days (days cumulated in 2008) and a median amount of 352 € in daily sick pay compensation benefits paid. Half of the employees belong to four of the sixteen sectors of activity studied (table C in annex): real estate, renting and business activities (18 % of the sample); manufacturing industry (14 %); commerce (14 %) and health and social work (8 %).

Variables used

The sectoral context

The sector of activity constitutes this study's variable of interest. It is understood according to the French Classification of Economic Activities (National Institute of Statistics, 2003), which describes 16 sectors of activity. The geographic context here is controlled throughout the individual's region of residence. This variable acts as a control and will not be analysed as such. Finally, the temporal heterogeneity is taken into account by introducing annual indicators.

Individual / composition effects

The observable sociodemographic characteristics are age and gender. However, the Hygie database gives no information on either the family composition or the level of education. The health status is approximated using ACD as well as by the annual medical consumption in the previous year (reimbursement by the compulsory Health Insurance for general practitioners and specialists, reimbursement for medication and number of hospital days in the private sector 7 ). The use of lagged variables linked to health consumption enables establishing a causality link and avoids the simultaneity of taking sick leave and the health consumption associated therewith 8 . Furthermore, we chose reimbursement by compulsory Health Insurance rather than the total expenditure so as to not falsify the results by introducing charges exceeding the statutory fees widely practiced by specialists that are not necessarily linked to any health need. Finally, having access to general practitioners and specialists was added in order to take into account substitution and complementarity effects that exist between these two types of expenditures 9 .

A priori, many sometimes conflicting hypotheses can explain the relationship between medical consumption in t-1, state of health and sick leaves. A high medical consumption in t-1 could characterise those individuals in poor health at the time t-1 and who we may assume remain in poor health in t 10 . It must be noted that this proxy of the state of health remains imperfect. First, this is an objective variable that does not reflect as largely upon the state of health as do subjective variables such as the perceived state of health or functional limitations. Also, this variable reflects a past state of health: the ideal would have been to have information on healthcare at the time the sick leave occurred, but the data does not allow this. Finally, it should be noted that medical consumption is multi-factorial and is linked in particular to socioeconomic characteristics (income, insurance coverage, socio-professional category) and to healthcare access (density). It is thus appropriate to control for these variables.

The individual work factors retained in the analysis are: the capped gross annual salary quintile in t-1, the fact of working part-time or full-time, the declaration of an accident at work or occupational sickness (AT-MP) in t-1. The income quintile is lagged for one period so as to take the potential impact of a sick leave on an individual's salary into account. The AT-MP are likely to influence the behaviour of taking sick leaves insofar as they reflect an effect of the state of health. Moreover, the pricing for AT-MPs could incite some establishments not to declare them and to instead pass them off as sick leaves. Additionally, unemployment is introduced here at the individual level through an indicator signalling those individuals in the sample having been unemployed for at least a quarter over the year before the study. The individual unemployment variable is lagged for a period as the data does not allow us to distinguish whether an episode of unemployment in t occurred before or after a sick leave. So 7. The Hygie database does not have data pertaining to public hospitalisation. 8. Data on consumption, added annually, does not allow us to distinguish between consumption having occurred before or after the sick leave. 9. This medical consumption is introduced on a scale of 1:10 so as to avoid problems of software convergence. 10. The results will allow testing this hypothesis. An alternative would be considering that the individuals having had access to healthcare in t-1 are in better health in t than those not treated in t-1 (prevention behaviour). However, this could be access to expensive specialised care that is not necessarily essential (wealth effect superior to degraded state of health effect) from whence the necessity to control for the income level.

as to take into account the specific case of sick leaves for the unemployed, a second indicator tags those individuals having had an episode of unemployment in t.

Methodology

So as to study the determinants of the occurrence of sick leaves, the probability of having taken at least one sick leave over the year is estimated (logit model). The duration is learned through the number of sick days cumulated throughout the year (Poisson model). This estimation of the duration of sick leaves relates to all individuals and not uniquely those who took sick leaves. Consequently, at the interpretation stage, results on sick leave duration must be linked to those on the probability. The longitudinal utilisation of the Hygie panel enables to control for the unobserved individual heterogeneity and thus avoiding the attribution of unobserved individual effects to the sectoral context.

In studying the crossed phenomena between sectors of activity and taking sick leaves, we assume that some unobserved individual characteristics are correlated to the explanatory variables. We thus chose a fixed effects model rather than a random effects specification that does not require an independence hypothesis between the terms of individual heterogeneity and the explanatory variables [START_REF] Wooldridge | Econometric Analysis of Cross Section and Panel Data[END_REF]. We estimate a fixed effects logit for the probability of sick leave and a fixed effects Poisson model for duration. Within the framework of these non-linear fixed effect models, the estimation by maximum likelihood is not convergent due to the problem of incidental parameters. The solution consists of basing the likelihood function on a conditional distribution of data that is no longer dependent in terms of individual heterogeneity . This conditional maximum likelihood estimator uses the distribution conditional to and [START_REF] Chamberlain | Analysis of Covariance with Qualitative Data[END_REF] for the fixed effect logit; [START_REF] Hausman | Econometric Models for Count Data with an Application to the Patent-R&D Relationship[END_REF] for the fixed effect Poisson model). Moreover, we should clarify that, by construction, the fixed effects specification does not allow an estimation of the effect of variables fixed in time at the individual level. For instance, the gender effect will not be present in the econometric results. It is, however, controlled for throughout the term of individual heterogeneity that captures all the constant variables -observed or not -in the temporal dimension. This constraint on fixed effects seems to bear little importance on this study insofar as the sector of activity varies over time for some individuals (this inter-sectoral mobility concerns approximately 10% of the individuals from one year to the next 11 ).

In summary, the estimation strategy consists of taking changes in sector of activity at an individual level and seeing whether they explain the sequences of daily sick pay compensation benefits at an individual level, whilst controlling for the unobserved individual heterogeneity fixed in time (see boxed text 3).

11. These proportions of inter-sectoral mobility concern the mobility between sectors of which the titles are reported, it is higher when the mobility between a missing sector and a reported sector is also considered (15 %, 16 % and 23 % respectively).

Boxed text 3. The models -Probability of sick leave (fixed effects Logit)

The fixed effects logit model is based on the following equation: represents the model's latent variable.

is a binary variable equal to 1 if individual i has taken sick leave over the year t and 0 if not.

represents the explanatory variables introduced (besides sector of activity), is the individual heterogeneity term and the error term that follows a logistic law.

-

Expected duration of sick leave (fixed effects Poisson Model)

The Poisson model is based on the hypothesis according to which the sick days are independently and identically distributed. Moreover, it assumes there is equality between expectation and variance in the number of sickness absence days conditional to the explanatory variables. While these hypotheses appear to be very restrictive in cross-section, they are less restrictive on longitudinal data. In fact, individual heterogeneity, which is added to other explanatory variables, allows us to explain a portion of the over-dispersion of the variance relative to expectation as well as a part of the correlation of residual terms in time. The Poisson model assumes that:

The Poisson law's parameter is such that .

The explained variable corresponds to the number of sick days, represents the explanatory variables (besides sector of activity) and the individual heterogeneity term.

Results

This section first provides descriptive statistics pointing out inter-sectoral disparities in sick leaves as well as the differences between employees from one sector to another. Then, the fixed effects regressions allow to disentangle the relative shares of i) individual variables introduced (composition effects) and ii) differences in sectoral context in the explanation of inter-sectoral disparities. The descriptive statistics relate to all sectors besides fishing, a sector for which only seventeen observations are available. The fixed effects regressions are run on all sectors of activity but only eight sectors will be analysed in this article, notably due to the low number of observations for some atypical sectors or a lack of homogeneity in some groups of sectors 12 .

Descriptive statistics: great inter-sectoral disparities in sick leaves

The descriptive statistics bring to light the existence of disparities between sectors of activity as much so in the frequency level as in the duration of the sick leaves (see table D in annex).

The proportion of individuals having taken sick leave at least once in 2008 thus varies from 10 % in agriculture to 25 % in the manufacturing industry while the average length of sick leave (cumulated number of sickness absence days in 2008) ranges between 3 days for extraterritorial activities and "agriculture, hunting, forestry" to 12 days in the health and social work sectors. In addition to these absolute gaps, some atypical sectors differentiate themselves, such as in the health and social work sectors where sick leaves appear to be both highly probable and longer.

Nevertheless, these inter-sectoral disparities can both be due to differences in individual characteristics (sociodemographic characteristics, health status, individual factors linked to employment) and in the sectoral context between employees in different sectors 13 . The proportion of women is, for instance, particularly high in health and social work (78 %). The median age varies between 34 in real estate, renting and business activities to 42 in extractive industries. The median reimbursement for general practitioners from the compulsory National Health Insurance in 2007 varied between 31 euros for agriculture and 107 euros for health and social work.

Concerning the variables linked to employment, in 2007, 23 % of employees working in the sectors of real estate, education and community, social and personal services experienced a period of unemployment while for extractive industries and financial activities, this proportion is 4 % and 6 % respectively. Part time is common in the hotels and restaurants sector (24 %) and the health-social work sector (31 %) while it is rarer in the sectors of construction (4.5 %) and the extraction industry (3 %). Finally, the salary level fluctuates noticeably depending upon the sector. Some sectors, like construction and real estate have both low wages and high salaries. Other sectors appear to group the highest salaries of the sample (industry, financial activities, production and distribution of electricity gas and water) or, on the contrary, the lowest salaries (hotels and restaurants, education).

The inter-sectoral disparities in sick leaves decrease after taking composition effects into account

Chart I infra enables a comparison of inter-sectoral disparities in probability and duration of sick leaves i) in raw statistics and ii) in fixed effects regressions controlling for composition effects, the geographical context and the macroeconomic context.

12. The "fishing", "agriculture, hunting and forestry", "extractive industries" and "extraterritorial activities" sectors are not represented in the charts as the estimates were too imprecise due to a low number of observations and a low intraindividual variability. This can be explained by the fact that these sectors are generally associated with special social security schemes or very specific activities. Also, the "education", "public administration" and "production and distribution of electricity, gas and water" sectors, for which we dispose of very few elements for interpretation; and the "community, social and personal service activities" within which there is only relative homogeneity are not commented on.

Statistics not integrated herein. Available upon request.

The duration and probability of sick leaves are based at 100 for the manufacturing industry. This normalisation allows us to reason in percentages and on a similar scale for variations in probability and duration.

Only the sectors of construction, hotels-restaurants and real estate significantly distinguish themselves from the others as concerns their impact on individual probability for taking sick leave, everything else being equal. Taking individual, macroeconomic and geographic effects into account thus enables us to noticeably decrease the inter-sectoral disparities in terms of probability of sick leave. However, although they have been reduced, the gaps in duration of sick leave remain significant. Thus, the individual effects appear to be dominant in the choice of taking sick leave or not while the sectoral context (coverage of sick leaves, characteristics of employment and work conditions) appears to be dominant in the duration of sick leaves 14 .

So as to quantify the relative shares of individual effects and of sectoral context in the disparities in sick leave between sectors, it is interesting to compare the raw variance with the variance after regression for both probability and duration of sick leaves. Initially, the variance between the eight sectors represented graphically is higher for duration than for proportion of sick leaves: 224 as compared to 177. After controlling for individual characteristics, the macroeconomic and geographic contexts, the inter-sectoral variance on the duration of sick leave level changed to 155 and that associated with probability was reduced to 95. The variables introduced in our model enable us to reduce the inter-sectoral variability of the probability of sick leave by practically half (precisely 46% reduction in the variance) and the variability between sectors in terms of duration of sick leave by almost one third (precisely 31% reduction in the variance). The remaining share is attributable to the sectoral context.

14 Let us note here that the estimates on duration of sick leaves concern the individuals whether they take sick leave or not; they can thus mask a gap in the probability of sick leave. However, the fact that most sectors do not significantly differ from one another in terms of probability of taking sick leave leads us to believe that the disparities in duration brought to light by the Poisson model stem from a "duration of sick leave in case of sick leave" effect rather than a taking sick leave effect.

Chart I -Inter-sectoral disparities in sick leaves: comparison between descriptive statistics (2008) and fixed effects estimations (2006-2008)

Reading: the fixed effects regressions indicate that working in the construction sector diminishes the probability of sick leaves by 27 % and the duration of the sick leave by 39 % relative to the manufacturing industry.

(1) Some sectors are not represented here due to important imprecision in the estimations (lack of observations and individual variability). For these sectors, refer to annex 6.3 for the estimations.

(2) It is necessary to set an average individual for the probability of taking sick leave so as to compare the sectors of activity. This individual works full time, has not been unemployed in t-1 nor in t, has not has any accident at work or occupational disease in t-1 and does not have any ACD. His annual salary is within the sample's third quintile, his medical consumption is equal to the sample's median and he resides within the Pays de la Loire region.

(3) For the duration of sick leave, the comparisons between sectors are independent of the choice of the average individual. Concerning the probability of taking sick leave, taking a leave for accident at work or occupational disease, having an ACD, a high salary level and not having been unemployed over the current (or past) year appear to favour taking sick leave. Consistent with the empirical literature, the age has no significant effect on the probability of taking sick leave. Degradation of health on the current date or past date plays a decisive role on the duration of the sick leave. Chronic Disease, a high medical consumption in t-1, having an accident at work or an occupational illness in t-1 favour an increase in the duration of sick leave.

Suffering from an ACD multiplies the duration of the sick leave by four, for example (see results of panel estimations, annex 6.3).

Discussion

The intension of this study was to define the net effect of the professional context, identified at the level of the sector of activity, in individual disparities in taking sick leaves. Let us first remember that this study does not allow a normative approach on the legitimacy of sick leaves. More generally, measuring the efficiency of expenditures on Daily Sick Pay Benefits is delicate. In fact, sick leaves can be "voluntary" or "involuntary" (linked to individual health status and working conditions; [START_REF] Ose | Working conditions, compensation and absenteeism[END_REF]. Distinguishing the former from the later is extremely complicated, since the employee's effort level and prevention behaviour regarding sick leave is neither observable by the employer nor by the insurer. In the same manner, the prevention level regarding professional risks or promotion of health at work (e.g. adaptation of the workplace) implemented by the employer are imperfectly observable.

Our results indicate that professional context effects are massive: they explain over half of the inter-sectoral disparities in terms of occurrence of sick leaves and two thirds of inter-sectoral disparities in terms of duration. Moreover, inter-sectoral gaps in terms of sick leaves remain high -especially when it comes to estimating the duration of the sick leave -and this despite individual, macroeconomic and geographic control variables.

As regards the occurrence of sick leaves, three sectors, Construction, Hotels-restaurants and Real estate remain subject to significantly less frequent sick leaves 15 . In other words, employees in the Construction sector, notably, do not appear to have equal access to sick leaves, for a given set of individual characteristics. Potentially, workers safety (work conditions, coverage…) could limit these disparities in access to sickness benefits. Great inter-sectoral disparities remain between the duration of sick leaves with a similar hierarchy.

An in-depth study of the sectoral characteristics could clarify these residual gaps. The structure of the size of the companies according to the sector is doubtlessly a key variable. Sectors characterised by large companies could propose higher quality coverage and a more organised job security. The atomicity of the real estate sector could, for instance, explain the shorter sick leaves in this sector.

Nevertheless, the importance of the professional context brought to light by our study questions the current rules for funding sick leaves that do not take into account the professional context effect. In the French regulatory context, the exercise enables highlighting transfers between sectors of activity occurring through social contributions and daily sick pay benefits. Indeed, we can point the fact that the benefits paid in cases of accidents at work and occupational diseases are funded via company contributions that are dependent upon the claim rate. On the contrary, social contributions that fund sickness benefits are solely dependent upon the individual's salary level: compulsory French Health insurance rules funding sick leaves thus do not take the professional context into consideration. Moreover, the compulsory scheme intervenes as of the fourth day of sickness absence and companies are not legally bound by the law to be responsible for the three days waiting period (although, in practice, the majority do so). In the end, there are few incentives for the companies to lower the number of short sick leaves in France.

Our results invite a reflection on a possible transfer of benefits as of the first days to the companies. These transfers would, in principle, be likely to associate the companies with regulating sick leaves by creating incentives for bettering work conditions. However, there will very probably be numerous consequences (among which, incentives on presenteeism), which are difficult to understand ex ante.

Annexes

Health insurance and sick leaves in France

There exist three main Social security plans in France, the General scheme, the Agricultural scheme and the scheme for self-employed persons alongside which exists an ensemble of special employee schemes. Our study concerns the employees of the General scheme, which insures four out of five people in France and funds 75 % of healthcare expenditures. This General Social security scheme is composed of 4 branches (sickness, family, accidents at work and occupational diseases, old-age pension) and is funded through contributions from employers and employees and, more recently, by taxes following the introduction of the General Social Contribution in 1991 and the Contribution for the Reimbursement of the Social Debt in 1996. Here, we are interested in the sickness branch (called Health insurance) that covers sickness, maternity, disability and death, and more specifically sick leaves.

Coverage of sick leaves by Health insurance:

In cases of sick leave, the insured person receives daily sick pay benefits starting on day four of the inability to work (there is a three days waiting period) and for three years maximum if they worked for the minimum number of hours or contributed a sufficient salary during the period preceding their sick leave (this condition becomes stricter for sick leaves lasting over 6 months).

The daily sick pay benefits correspond to a fraction of the daily salary calculated using the average gross salary of the three months preceding the sick leave (12 months in case of seasonal or irregular work) and within the Social security ceiling (2 574,40 euros on January 1, 2013). This fraction is equal to 50 % of the salary and increases to 66.66 % as of the 31 st day of sick leave for employees with more than three dependent children. In the case of unemployment, the insured person can also receive sick pay benefits. The unemployment benefits are then interrupted and differed.

Other than the compensation paid by the national Health insurance, employers are required by law (1978 and 2008) to pay a salary supplement to employees on sick leave having worked for the company for over a year. The amount and the duration of this benefit are equally linked to years of service. Finally, there exists a third level of compensation: optional branch agreements contracted by companies. -141,252.45 -5,730,128.8 Reading:

Descriptive statistics (2008)

-***: significance at the 1% level; **: 5% level; *: 10% level.

-Interpretation of the incident rate ratio coefficients: "having had a long-term illness multiplies the duration of the sick leaves by 4.112".

  Field: employed persons in the private sector, 23-60 years of age, years 2006-2008. Source: Hygie database (national Pension insurance and national Health insurance data).

Table A -Individual characteristics, work-related factors, health status and place of residence (N=414,185)

 A

		Average	242.0
	Access to private hospitalisation (%) in t-1	6.4
	Number of days of private hospitalisation in t-1 for those resorting to it	1 st	quintile	1
		value
	Individual characteristics	2 nd quintile	1
	Average age in 2008 (years) Proportion of women (%)	value 40.8 value 48.8 3 rd quintile	1
	Work-related factors	Average	4.4
	Proportion of individuals having been unemployed for at least one quarter in t-1 (%) Region of residence (in percentage of the sample)	14.7
	Annual salary (€) in t-1 (2007) Alsace	1 st 2.9	quintile	6509
	Aquitaine	value 4.7
	Auvergne	2 nd quintile 2.1	15790
	Bourgogne	value 2.4
	Bretagne	3 rd quintile value 4.6	21271
	Centre	4 th 3.9	quintile	29554
	Champagne-Ardenne	value 2.0
	Employment contract Corse	Full time 0.4	69.9
	Franche-Comté	Part time 1.8	16.8
	Ile-de-France	Not reported 13.3 20.7
	Proportion of individuals having had an accident at work or occupational Languedoc-Roussilon	3.3 3.7
	disease in t-1 Limousin	1.0
	Health status Midi-Pyrénées	4.2
	Proportion of individuals with an acute chronic disease (%) Nord-Pas-de-Calais	8.7 6.3
	Access to a general practitioner and/or specialist (%) in t-1 Basse-Normandie	83.8 2.2
	(Compulsory) Health insurance reimbursement for generalist and/or specialist (€) in t-1 for those resorting to them Haute-Normandie	1 st value 3.0	quintile	42.5
	Pays de la Loire	2 nd quintile 5.6	104.9
	Picardie	value 3.1
	Poitou-Charentes	3 rd quintile 2.5	234.0
	Lorraine	value 3.4
	Provence-Alpes-Côte d'Azur	Average 7.4	202.1
	Drug consumers (%) in t-1 Rhône-Alpes	82.2 10.0
	Health insurance drug reimbursement (€) in t-1 for those consuming drugs Abroad	1 st value 0.01	quintile	21.1
	French Overseas Departments and Territories	2 nd quintile 2.3	60.8
	Region not reported	value 0.1
		3 rd quintile	178.3
		value

Field: people working in the private sector, 25-60 years of age, in 2008. Source: Hygie database (national Pension insurance and national Health insurance data).

Table B -Sick leaves in the total sample (N=414,185)

 B Field: people working in the private sector, 25-60 years of age, in 2008. Source: Hygie database (national Pension insurance and national Health insurance data).

	Proportion of individuals having taken at least one sick leave	18.57
	over the year 2008 (%)
	Number of sick leaves taken among those individuals having	Quart1 Quart2 Quart3 Average
	taken at least one sick leave in 2008	1	1	2	1.4
	Total number of sick days in 2008 among those individuals	Quart1 Quart2 Quart3 Average
	having taken at least one sick leave	7	16	45	45.5
	Amount of sick pay benefits paid by Health insurance to	Quart1 Quart2 Quart3 Average
	individuals having taken sick leave in 2008 (€)	104.2	352.8 1253.0 1430.6

Table C -Distribution of the sample (%) by sectors of activity (N=414,185)

 C

	Agriculture, hunting, forestry	0.07
	Fishing	0 (17 individuals)
	Extractive industries	0.11
	Manufacturing	14.45
	Production and distribution of electricity, gas and water	0.28
	Construction	4.49
	Trade; repair of vehicles and personal and household goods	13.58
	Hotels and restaurants	3.79
	Transport, communication	4.74
	Financial intermediation	2.78
	Real estate, renting and business activities	17.94
	Public administration	7.37
	Education	1.91
	Health and social work	8.27
	Community, social and personal service activities	3.17
	Extraterritorial organizations and bodies	0.03
	Not reported	17.02
	Total	100
	Reading: 14.43% of the individuals in the sample work in the manufacturing industry.
	Field: people employed in the private sector, 25-60 years of age, in 2008.
	Source: Hygie database (national Pension insurance and national Health insurance data).

Table D -Proportion and duration of sick leaves by sector of activity

 D

	Extractive industries	21.1		8.5
	Manufacturing Production and distribution of 6.3. Panel estimations	25.2		10.4
	electricity, gas and water	20.1		7.7
	Construction	18.3 Conditional Logit model (individual fixed effects)	Conditional Poisson model 7.2 (individual fixed effects)
	Trade; repair of vehicles and personal and household goods	20.2 Probability of taking at least one sick leave over the year	Expected duration of sick leave 9.3 (cumulated number of sick
	Hotels and restaurants	16.0 (marginal coefficients).	8.9 days); notation in incidence rate
	Transport; communication	23.8	10.1 ratio.
	Financial intermediation Age (ref. ]20; 30 years of age])	20.7		8.4
	Real estate, renting and business ]30; 40]
	activities	15.3		6.7
	Public administration	15.6		7.8
	Education	13.8		6.4
	Health and social work	22.7		11.7
	Community, social and personal
	service activities	14.5		7.0
	Extraterritorial organization and
	bodies	11.6		3.2
	Sector of activity	Proportion of individuals having	Average duration of sick
		taken sick leave at least once in	leave for the ensemble of
		2008		individuals in the sector
		(%, N=414,185)		(N=414,185)
	Agriculture, hunting, forestry	10.3		3.0

In France, the costs of 30 Acute chronic diseases (ACD) are fully paid by the social security.

France counts 101 counties across 22 regions.

Provided that abusive sick leaves are equally distributed across sectors of activity.

Reading: in 2008, 25.2% of individuals working in the manufacturing industry took at least one sick leave; the total average days of sick leave in this sector was 10.4. Field: people working in the private sector, 25-60 years of age, in 2008. Source: Hygie database (national Pension insurance and national Health insurance data).

Acknowledgements


Wei-Kang Song

Yu-Jun Cui
email: cui@cermes.enpc.fr

Anh Minh Tang

Wen-Qi Ding

Thanh Danh

W.-K Song

Y.-J Cui

W.-Q Ding

Experimental study on water evaporation from sand using environmental chamber

Keywords: soil water evaporation, environmental chamber, Fontainebleau sand, soil surface suction évaporation de l'eau du sol, chambre environnementale, sable de Fontainebleau, succion

Large-scale evaporation experiments were conducted on bare sand using an environmental chamber. Four different atmospheric conditions and various drying durations were imposed on the soil sample. Atmospheric parameters (air flow rate, relative humidity, and temperature) and response of the soil (volumetric water content, temperature, and soil suction) were both monitored simultaneously. Notably, the temperature and matric suction at the soil surface were monitored using an infrared thermometer and high-capacity tensiometer, respectively. The results show that the air and soil temperatures depend on the evaporation process and atmospheric conditions. In addition, volumetric water content in the near-surface zone is strongly affected by the evaporation process and changes linearly over depth. The evaporation rate is strongly dependent on the air conditions.

Introduction

Soil water evaporation at the air-soil interface is an important water cycle and energy exchange process, which causes many problems in various fields: soil degradation in arid areas with a high evaporation rate [START_REF] Xue | Maximum surface temperature model to evaluate evaporation from a saline soil in arid area[END_REF], soil salinization in arid and semi-arid regions (e.g., [START_REF] Shimojimaa | Salinization owing to evaporation from bare-soil surfaces and its influences on the evaporation[END_REF][START_REF] Zarei | Modeling transient evaporation from descending shallow groundwater table based on Brooks-Corey retention function[END_REF][START_REF] Xue | Maximum surface temperature model to evaluate evaporation from a saline soil in arid area[END_REF], damage of buildings and geotechnical constructions due to water loss [START_REF] Cui | Water balance and evapotranspiration monitoring in geotechnical and geoenvironmental engineering[END_REF][START_REF] Corti | Simulating past droughts and associated building damages in France[END_REF][START_REF] Corti | Drought-induced building damages from simulations at regional scale[END_REF], etc. This shows the importance of investigating the mechanisms of soil water evaporation. On the other hand, the study of this process has significant practical benefits in various fields: estimating the amount of water loss in the assessment of soil management technologies in agriculture [START_REF] Qiu | An improved methodology to measure evaporation from bare soil based on comparison of surface temperature with a dry soil surface[END_REF], predicting evaporation flux in design of soil cover of mine tailings [START_REF] Wilson | Soil evaporative fluxes for geotechnical engineering problems[END_REF][START_REF] Wilson | Coupled soil-atmosphere modelling for soil evaporation[END_REF][START_REF] Wilson | The effect of soil suction on evaporative fluxes from soil surfaces[END_REF][START_REF] Yanful | Measurement of evaporative fluxes from candidate cover soils[END_REF], investigating the long-term performance of moisture-retaining soil covers [START_REF] Yang | Water balance during evaporation and drainage in cover soils under different water table conditions[END_REF][START_REF] Yanful | Modeling and measurement of evaporation in moisture-retaining soil covers[END_REF], designing evapotranspirative cover systems for waste containment and mining sites [START_REF] Cui | Water balance and evapotranspiration monitoring in geotechnical and geoenvironmental engineering[END_REF], classifying landfill sites according to climatic water balance [START_REF] Blight | Solar heating of the soil and evaporation from a soil surface[END_REF], etc. Moreover, the investigation of soil water evaporation is also an important issue in geotechnical engineering [START_REF] Cui | Simulating the water content and temperature changes in an experimental embankment using meteorological data[END_REF][START_REF] Cui | Experimental and numerical investigation of soil-atmosphere interaction[END_REF].

For bare soils, the water evaporation process is controlled by both atmospheric conditions and soil conditions [START_REF] Wilson | Soil evaporative fluxes for geotechnical engineering problems[END_REF][START_REF] Wilson | Coupled soil-atmosphere modelling for soil evaporation[END_REF][START_REF] Van De Griend | Bare soil surface resistance to evaporation by vapor diffusion under semiarid conditions[END_REF][START_REF] Qiu | An improved methodology to measure evaporation from bare soil based on comparison of surface temperature with a dry soil surface[END_REF]. Regarding the atmospheric conditions, it appears that evaporation rate is sensitive to wind speed at the beginning of the process when the soil surface is wet [START_REF] Kondo | A model and experimental study of evaporation from bare-soil surfaces[END_REF][START_REF] Yamanaka | A modified surface-resistance approach for representing bare-soil evaporation: Wind tunnel experiments under various atmospheric conditions[END_REF], whereas increasing wind speed results in a reduction of evaporation rate when the soil surface is dry [START_REF] Yamanaka | A modified surface-resistance approach for representing bare-soil evaporation: Wind tunnel experiments under various atmospheric conditions[END_REF]). An increase in relative humidity decreases the evaporation rate and vice versa [START_REF] Yamanaka | A modified surface-resistance approach for representing bare-soil evaporation: Wind tunnel experiments under various atmospheric conditions[END_REF]) -evaporation ceases when the vapor pressure at the soil surface becomes equal to that of air [START_REF] Yanful | Measurement of evaporative fluxes from candidate cover soils[END_REF]. The evaporation rate determined from the field meteorological data was found higher at lower relative humidity, higher wind speed, higher air temperature, and stronger solar radiation [START_REF] Cui | Field simulation of in situ water content and temperature changes due to ground-atmospheric interactions[END_REF][START_REF] Cui | Water balance and evapotranspiration monitoring in geotechnical and geoenvironmental engineering[END_REF]. Furthermore, the field daily evaporation rate was also found to be dependent on the atmospheric conditions: a high net radiation results in high latent heat flux and hence high evaporation rate; thereby, most evaporation takes place during daytime [START_REF] Blight | Interactions between the atmosphere and the Earth[END_REF][START_REF] Aluwihare | Measurement of evaporation on bare soil and estimating surface resistance[END_REF]. As far as soil conditions are concerned, the evaporation rate is dependent on the soil texture [START_REF] Wilson | Soil evaporative fluxes for geotechnical engineering problems[END_REF][START_REF] Wythers | Bare-soil evaporation under semiarid field conditions[END_REF], initial water content [START_REF] Wang | Wind tunnel experiments on bare soil evaporation[END_REF], hydraulic conductivity [START_REF] Wilson | Coupled soil-atmosphere modelling for soil evaporation[END_REF]) and water retention capacity [START_REF] Yanful | Measurement of evaporative fluxes from candidate cover soils[END_REF]. In addition, the drainage condition and water table level also significantly affect the process of evaporation [START_REF] Yang | Water balance during evaporation and drainage in cover soils under different water table conditions[END_REF].

Basically, soil surface temperature and suction are two essential parameters controlling soil water evaporation. However, these two parameters have scarcely been investigated experimentally, in particular the soil surface suction.

In the present work, a large-scale compacted Fontainebleau sand sample (1000 mm in length, 800 mm in width, and 300 mm in height) was subjected to four evaporation tests in an environmental chamber under various controlled atmospheric conditions (i.e., different values of air relative humidity, temperature, and air-flow rate) and with a steady water table. Air conditions and the response of soil parameters were monitored during the tests, including soil surface temperature and matric suction using an infrared thermometer and high-capacity tensiometer, respectively. The recorded data allow better understanding of the soil water evaporation mechanisms on one hand and further theoretical and numerical analyses on the other.

Materials

The soil studied is the Fontainebleau sand, with a specific gravity of 2.64. The values of its minimum and maximum unit masses are 1.39 and 1.75 Mg/m 3 , respectively. The effective grain size, D 10 , is 0.14 mm and the coefficient of uniformity, C u =D 60 /D 10 (where D 60 and D 10 are the particle sizes for which 60% and 10% of the sample are finer than D 60 and D 10 , respectively), is 1.6 (Delfosse- [START_REF] Delfosse-Ribay | Shear modulus and damping ratio of grouted sand[END_REF]). The grain size distribution curve determined by sieve analysis is shown in Fig. 1.

Testing apparatus

The evaporation tests were carried out in a large-scale environmental chamber setup (see Fig. 2). This setup includes an environmental chamber (i.e., an transparent acrylic tank with 800 mm internal width, 1000 mm internal length, and 895 mm height), a wind supply unit, an air collection unit, a water supply unit, and a data-logging system. Upon initiation of the evaporation test, the wind supply unit supplies an air stream with a controlled air-flow rate, temperature, and relative humidity to the chamber. The air collection unit collects the moist air passing through the chamber and records its temperature and relative humidity. The water supply unit can control the water level during evaporation. The datalogging system records all the results from different sensors. It is noted that the evaporation rate can be determined by changes in absolute humidity and air flow rate. Furthermore, various sensors with different applications were installed at different locations of the soil sample and the chamber. More specifically,

• five soil moisture sensors (ThetaProbe (ML2x)) for recording changes in soil volumetric water content were buried at different depths of the soil sample; • six resistance temperature detectors (PT1000) for measuring soil temperature were also buried inside the soil sample over its depth; • five thermistors monitoring air temperature were fixed at different heights above the soil surface; • six humidity sensors (T3111 transmitter) were also placed at different locations of the chamber for monitoring of air relative humidity and temperature; • an infrared thermometer (Pyropen-D) was used to measure the soil surface temperature; • five high-capacity tensiometers were installed at different depths for the sake of matric suction measurement; • a flowmeter (MAS-3120) and anemometer (Testo 435-2) were used to measure air flow rate and wind speed, respectively.

The details of the sensors used are presented in Table 1. A sketch of the sensor arrangement is shown in Fig. 3. More details of this environmental chamber and the sensors used can be found in [START_REF] Song | Development of a largescale environmental chamber for investigating soil water evaporation[END_REF].

Testing methodology

The dry Fontainebleau sand was compacted in 50 mm thick layers in the environmental chamber (Fig. 4a). A soil layer of 300 mm total thickness was compacted at a dry unit mass of 1.7 Mg/m 3 . During the compaction, various sensors were installed in the soil: six PT1000 sensors were installed every 50 mm (i.e., 25, 75, 125, 175, 225, and 275 mm depths) and two ThetaProbe sensors were buried at 125 and 225 mm below the soil surface. The other three ThetaProbe sensors were buried after soil saturation in the first 60 mm below the soil surface (i.e., 25, 40, and 55 mm depths) (Fig. 4b). Five thermistors were fixed at different elevations (i.e., 80, 185, 275, 380, and 465 mm heights) along one inside wall of the chamber (Fig. 4c). Three relative humidity sensors (T3111 transmitter) were installed at the soil surface and at various heights (50 and 275 mm heights), allowing air relative humidity to be monitored (Fig. 4c). An anemometer was fixed at 50 mm above the soil surface for the measurement of wind speed. Note that the chamber cover was sealed with silicon to ensure air-tightness. For relative humidity at the inlet, outlet, and in the laboratory, three other relative humidity sensors were fixed in a plastic cell at the inlet, in the air collection unit, and outside the chamber. The infrared thermometer was fixed on the cover to monitor the soil surface temperature (Fig. 4d).

Subsequent to soil compaction and sensor installation, the soil column was saturated through the water tank connected to the bottom of chamber. After saturation, the water level in the tank was lowered to a level close to the bottom of the soil layer and was kept constant during the tests. Meanwhile, four high-capacity tensiometers, constructed in-house, for soil matric suction measurement within a range of 1.5 MPa were installed on two sides of the wall at different depths (i.e., 25, 77, 173, and 276 mm below the soil surface) and one tensiometer was placed at the soil surface allowing the measurement of near-surface suction. This type of tensiometer is composed of a porous ceramic stone with an air-entry value of 1.5 MPa, a specially designed strain gage glued on a diaphragm, and a very thin water reservoir (0.1 mm thick) between them (Cui et al. 2008a;[START_REF] Muñoz-Castelblanco | The water retention properties of a natural unsaturated loess from northern France[END_REF]. Prior to use, the tensiometer needs to be saturated in a saturation cell with de-aired and distilled water under a pressure as high as 4 MPa (Cui et al. 2008a). Meanwhile, the calibration is completed during this saturation process. More details about this tyoe of tensiometer can be found in Cui et al. (2008a), [START_REF] Tang | Calibration of the osmotic technique of controlling suction with respect to temperature using a miniature tensiometer[END_REF][START_REF] Muñoz-Castelblanco | The water retention properties of a natural unsaturated loess from northern France[END_REF].

The tests were conducted under various controlled air conditions. The compressed air in the laboratory was used and its pressure was controlled using a regulator. The air flow was measured by a flowmeter to an accuracy of ±1.5% over a working range of 500 L/min. It was then heated in a heating tube to a temperature controlled by a temperature regulator. The temperature and relative humidity of this heated air were measured by a T3111 transmitter before being diffused in the chamber (i.e., inlet) through an air distributor (i.e., a perforated metal tube). After crossing the chamber (i.e., outlet), the air was gathered and the temperature and relative humidity were measured again. For control of the water table, it was necessary to adjust its level regularly by adding water into the tank.

Four soil water evaporation tests were conducted at various constant air rates and heating tube temperatures (see Table 2). Note that the heating tube temperature was much higher than that in the chamber, as can be seen later from the results. Tests 1 and 2 were carried out at similar air flow rates (185 L/min for test 1 and 172 L/min for test 2), but different temperatures in the heating tube (50 °C for test 1 and 200 °C for test 2). Tests 3 and 4 were conducted at the same lower air flow rate (130 L/min) and different heating tube temperatures (50 °C for test 3 and 200 °C for test 4).

The duration of tests 3 and 4 was much longer (17.5 days for test 3 and 30 days for test 4) than the 11.5 day duration of tests 1 and 2. Note that the dry unit mass of sand is assumed to be unchangeable (1.7 Mg/m 3 ) during the four evaporation tests.

Determination of the evaporation rate is based on the water vapor balance, as follows:

(1)

E a ϭ (86 400)Q(H a-outlet Ϫ H a-inlet )/( w A)
where E a is the actual evaporation rate (mm/day); Q is the air flow rate through the chamber (L/s), H a-outlet and H a-inlet are the absolute humidity (Mg/m 3 ) at the outlet and inlet, respectively; w is the density of water (Mg/m 3 ), and A is the area of the evaporative surface exposed in the chamber (m 2 ). The absolute humidity (H a ) is calculated using eq. ( 2):

(2) H a ϭ 0.622e a /(1000RT a ) where e a is the vapor pressure (Pa), R is the gas constant (287.04 J/(kg•K)), T a is the air temperature (K), 0.622 is the ratio of the molecular weight of water to that of dry air. The vapor pressure, e a , is determined by eq. ( 3)

(3) e a ϭ e sat H r /100

where e sat is the saturated vapor pressure (Pa) and H r is the air relative humidity (%).

The saturated vapor pressure (e sat ) is deduced from eqs. ( 4) and ( 5) [START_REF] Brutsaert | Evaporation into the atmosphere: theory, history, and applications[END_REF] (4)

e sat ϭ (101 325) exp(13.3185t R a Ϫ 1.9760t R a 2 Ϫ 0.6445t R a 3 Ϫ 0.1299t R a 4 ) (5) t R a ϭ 1 Ϫ 373.15/T a
Note that this method was also used by Mohamed et al. ( 2000) and [START_REF] Aluwihare | Measurement of evaporation on bare soil and estimating surface resistance[END_REF].

Results and discussion

Air flow rate

Figure 5 depicts the variations of air flow rate versus elapsed time during the four drying tests. It can be seen that some fluctuation as high as ±5 L/min exist around a constant average value in test 1 (Fig. 5a), test 2 (Fig. 5b), and test 3 (Fig. 5c). The larger fluctuation in test 4 (Fig. 5d) was due to a technical problem related to the compressed air system in the laboratory. It is noted that the corresponding average wind speeds at 50 mm above the soil surface are 0.5, 0.46, 0.34, and 0.34 m/s in tests 1, 2, 3, and 4, respectively.

Air temperature

Figure 6 shows air temperatures at the inlet and outlet of the chamber as well as in the laboratory, the inlet temperature being the highest. When the heating tube temperature is high (i.e., 200 °C in tests 2 and 4, see Figs. 6b and6d), the laboratory temperature is lower than the outlet one. By contrast, when the heating tube temperature is low (i.e., 50 °C in test 1s and 3, see Figs. 6a and6c), the phenomenon is reversed.

Evolutions of air temperature at different elevations in the chamber are presented in Fig. 7. Note that the positions with similar air temperatures are termed as "other heights". On the whole, at the same heating tube temperature, the higher the air flow rate the lower the air temperature in the chamber. Indeed, the air temperature in test 3 (17.5 to 21.5 °C, see Fig. 7c) at 130 L/min air flow rate is higher than that in test 1 (16 to 20.5 °C, see Fig. 7a) at 185 L/min. The same trend can be observed when comparing test 2 to test 4 (see Figs. 7b and7d). Furthermore, at a similar air flow rate, the air temperature increases over time when the heating tube temperature is as high as 200 °C (i.e., tests 2 and 4). However, when the heating tube temperature is as low as 50 °C (i.e., tests 1 and 3), the air temperature declines initially, and then goes up and down. Compared to the temperatures at inlet (see Fig. 6), the temperatures in the chamber vary in the same fashion (see Fig. 7), indicating that the air temperatures inside the cham-ber are strongly influenced by the inlet temperature. It is also observed that air temperature shows a sharp increasing trend by the end of test 3 and in the middle of tests 2 and 4.

The inlet temperature is one of the controlled parameters in the four tests (see Fig. 6). Its values (i.e., 22, 24, 47, and 56 °C) depend on both the heating tube temperature and air flow rate. Indeed, when the air flow rate is similar, a high heating tube temperature produces high inlet temperature (e.g., the inlet air temperature in test 4 is higher than in test 3). When the heating tube temperature is fixed, the inlet temperature is higher at a lower air flow rate (e.g., the inlet air temperature in test 3 is higher than in test 1). In addition, the temperature drops from inlet to outlet. This suggests that the soil water evaporation in the chamber is an energyconsuming process. Inside the environmental chamber, the air adsorbs energy from hot air, leading to an increase of its temperature (see Fig. 7). As water vaporization consumes energy and cools the surrounding medium, the temperature of air close to the soil surface (i.e., 80 mm height) is affected and exhibits the lowest value. Under low heating tube temperatures (see Figs. 7a and7c), water evaporation consumes more energy than air heating, thereby cooling both air and soil. Consequently, air temperatures decrease during the first 0.5 and 0.7 days in tests 1 and 3, respectively (see Figs. 7a and7c). At high heating tube temperatures (see Figs. 7b and7d), the energy from hot air allows both water evaporation and air heating. Therefore, the air temperature exhibits a gradual increase in tests 2 and 4, exceeding the laboratory temperature.

Soil temperature

Evolutions of soil temperature at different positions are presented in Fig. 8. The positions with similar temperatures are termed as "other depths". Two distinct evolutions can be identified: the soil temperatures show a gradual increase at high heating tube temperatures (i.e., tests 2 and 4, see Figs. 8b and8d), while at low heating tube temperature (i.e., tests 1 and 3, see Figs. 8a and8c) a decrease is observed at the beginning. In addition, soil temperatures at high air flow rates are lower than that at low air flow rates when the heating temperature is the same. Indeed, at a heating tube temperature of 50 °C the temperature values vary from 10.5 to 18 °C in test 1 at 185 L/min (see Fig. 8a) while they change within the range 13-20.5 °C in test 3 at 130 L/min (see Fig. 8c). A similar phenomenon is observed in tests 2 (see Fig. 8b) and 4 (see Fig. 8d), both at a 200 °C heating tube temperature, despite the unstable imposed air flow in test 4. Furthermore, the soil surface temperature is the lowest at low heating tube temperatures (i.e., tests 1 and 3) while it is the highest at high heating tube temperatures (i.e., tests 2 and 4). The soil temperature at different depths increases quickly by the end of tests 1 and 3 (see Figs. 8a and8c, respectively) or in the middle of tests 2 and 4 (see Figs. 8b and8d, respectively), especially at the soil surface. In addition, the evolution of soil temperatures follows the one of air temperatures.

The evolutions of soil temperature are also evaporation dependent (see Fig. 8). Indeed, comparison with the evolutions of air temperature (see Fig. 7) shows that the changes of soil and air temperatures are similar (i.e., both of them decrease at the initiation of evaporation, and then go up and down), suggesting that the energy for evaporation is supplied by both air and soil at low heating tube temperatures. At high heating tube temperatures (i.e., tests 2 and 4), soil temperatures are elevated as air temperatures because the high temperature air flow provides more energy than required for water evaporation. Furthermore, the soil temperatures decrease after the initiation of evaporation and then increase along with the decline of evaporation rate at low heating tube temperatures (Figs. 8a and8c). A similar trend was observed in the column drying test conducted by [START_REF] Wilson | Soil evaporative fluxes for geotechnical engineering problems[END_REF] and [START_REF] Wilson | Coupled soil-atmosphere modelling for soil evaporation[END_REF] and in the column evaporation test under controlled air conditions performed by [START_REF] Yanful | Measurement of evaporative fluxes from candidate cover soils[END_REF].

Air-soil temperature profile

To further analyze the evolutions of temperature inside the chamber, the recorded air and soil temperatures are used to establish the air-soil temperature profiles (Fig. 9). The highest air temperature is observed at the elevation corresponding to the level of air inlet (i.e., air distributor). The air temperature decreases from this position to the position close to the chamber cover and it also declines from this position to the soil surface. The temperature at the soil surface is the lowest value under low heating tube temperatures (see Figs. 9a and9c) while this phenomenon is not observed in the case of high heating tube temperatures (see Figs. 9b and9d). On the other hand, the soil temperatures increase progressively over depth under low heating tube temperatures (see Figs. 9a and9c) while it decreases under high heating tube temperatures (see Figs. 9b and9d). Note that the temperatures inside the soil column (i.e., below 25 mm depth) are similar for the four tests. Two sharp but quite opposite temperature gradients are observed between the 80 mm height, soil surface, and 25 mm depth under low heating tube temperatures. By contrast, only one temperature gradient is identified under high heating tube temperatures. Note that the initial soil temperature distribu-tion at the beginning of evaporation in different tests can also be identified from the profiles: for test 1, the soil temperature at the surface is 13.7 °C; it increases to 17.6 °C at 25 mm depth, and to 18.1 °C at 275 mm depth. For test 2, it decreases from 18.8 °C at the soil surface to 18.4 °C at 275 mm depth. For test 3, it increases The observed results can be explained as follows. At the beginning of the evaporation process, the water at the soil surface firstly evaporates and the lowest temperature appears in this location (e.g., tests 1, 3, and 4). Further evaporation leads the soil surface to become dry and the evaporation front progresses into a deeper position; that is, the lowest temperature position is deeper. During this evaporation process, the water loss increases soil resistance to evaporation, thus decreasing the evaporation rate. The energy consumed by evaporation also declines. As a result, more energy is available for increasing soil and air temperatures. This explains the quick increase of soil and air temperatures when the evaporation rate is low (e.g., in tests 2, 3, and 4) or when the evaporation duration is long. Therefore, we can deduce that if longer drying is allowed in test 3, the lowest temperature will not be at the soil surface.

Air relative humidity

The changes of air relative humidity in the chamber are presented in Fig. 10. All values at various elevations decline over time. Relative humidity at the soil surface presents the highest value while the one at the inlet shows the lowest. Furthermore, values at the outlet, at 50 mm, and 275 mm height are very similar. In general, the evolution of relative humidity at various positions except the inlet can be divided into three stages: (i) initial decrease stagethe relative humidity decreases slowly in the first 10 days under low heating tube temperatures, and in the first 6 to 8 days under high heating tube temperatures; (ii) quick decline stage; and (iii) stabilization stage with a quite low decrease rate. All these three stages appear clearly in test 4 (see Fig. 10d). The first two stages appear in tests 2 and 3 (see Figs. 10b and10c) while only the first stage appears in test 1 (see Fig. 10a). For test 1, the imposed air relative humidity at inlet is low and keeps a constant value around 6.5% while the outlet air relative humidity decreases from 46% to 33% over time. The imposed relative humidity at the inlet is around 1.5%, 3.5%, and lower than 1% in tests 2, 3, and 4, respec-tively, whereas the corresponding values at the outlet vary from 33% to 12.4%, 50% to 20%, and 35% to 8%, respectively. Note that the surface relative humidity does not correspond exactly to the surface position but at 5 mm above the soil surface due to the dimensions of the sensor.

The values of air relative humidity at different elevations clearly reflect the evaporation process. Because of water evaporation from the soil, the air relative humidity near the soil surface is higher than at other elevations (see Fig. 10). This relative humidity difference is sustained when water supply for evaporation is sufficient (e.g., from t = 0 to 9 days in test 3). Along with the evaporation process, the soil surface resistance to evaporation increases and the amount of water vapor entering the air decreases. Thus, the relative humidity difference at different elevations decreases. Eventually, water evaporation will cease when the soil vapor pressure becomes equal to that of the surrounding air [START_REF] Yanful | Measurement of evaporative fluxes from candidate cover soils[END_REF]. On the other hand, from the evolutions of relative humidity, the effects of air temperature and air flow rate on evaporation can also be observed: at similar air flow rates, the higher the heating tube temperature the lower the relative humidity inside the chamber. At the same heating tube temperature, a lower air flow rate gives rise to only a slightly higher relative humidity.

Soil volumetric water content

The changes of volumetric water content are shown in Fig. 11. As expected, the volumetric water content in the near-surface zone (i.e., from soil surface to 60 mm depth) firstly decreases in all tests, followed by a decrease at 125 mm depth, while the value at 275 mm depth remains unchanged. Taking test 1 as an example, the volumetric water content in the soil surface zone declines from 29.3% to 8.9% at 25 mm depth and from 31.7% to 13.8% at 55 mm depth. In a deeper zone at 125 mm depth, the value is constant in the first 9.5 days, and then decreases from 31.4% to 28.6% at the end of the test. However, the value at 275 mm depth remains 34.5%. Note that the volumetric water content at a saturated state is 35.6%. The evolution of volumetric water content in the near-surface zone also follows three stages: (i) a decrease with The evolutions of volumetric water content at various depths are depicted by Fig. 12. This contour map allows visualization of the drying advance in the soil column. On the whole, all contour lines go into a deeper position over time except the 35% line. Furthermore, the lower the water content the later the line appears.

For instance, in test 1, the 30% contour line is at 25 mm depth in the beginning; its depth increases quickly and reaches 110 mm in the first 3.5 days. It continues to increase at a very low rate, but at t = 11 days it increases sharply and reaches 150 mm at the end of the test. The contour line of 30% almost remains constant at 110 mm depth from t = 3.5 to 11 days, suggesting that water loss occurs only in the zone above this depth. In terms of variation of volumetric water content, it decreases from 30% to 25% in the first 1.2 days at 25 mm depth, decreases to 20% at t = 3.2 days, to 15% at t = 5.2 days, and to 10% at t = 10 days. At the end of the test, it becomes lower than 10%. Similar observations can be made for the other tests.

The profiles of volumetric water content for different tests are shown in Fig. 13. A clear water loss can be observed due to evaporation. In general, a linear relationship between water content and depth in the near-surface zone (i.e., 25, 40, and 55 mm depths) can be observed. Moreover, this linear relationship also develops toward deeper zones. Indeed, in test 3 (see Fig. 13c)t h e linear relationship exists at three positions, i.e., 25, 40, and 55 mm depths, with a slope of about 0.23%/mm. This relationship also exists from 25 to 225 mm depth at t = 17.5 days. It is noted that the volumetric water content distribution over depth at the beginning of the four evaporation tests can also be observed: for test 1, the volumetric water contents at 25, 40, and 55 mm depths are 29.3%, 33%, and 32%, respectively. The values in the deeper zone (below 55 mm depth) increase over depth from 32% to 35.6%. For test 2, the values of volumetric water content increase from 25.4% at 25 mm depth to 34.4% at 225 mm depth. For test 3, the volumetric water content values also increase from 24.8% at 25 mm depth to 34.1% at 225 mm depth. For test 4, the values increase from 23.1% at 25 mm depth to 34% at 225 mm depth. The volumetric water content at the soil bottom in the four tests is close to the saturated value, 35.6%.

Basically, soil water evaporation results in a decrease of water content. In the tests performed, the volumetric water content in the near surface zone declines quickly at the initiation of evaporation and then decreases gradually. Furthermore, the deeper zone starts to lose water only when the evaporation lasts a long time (see Fig. 11). This phenomenon can be explained by the evolution of soil resistance to evaporation (van de Griend and Owe 1994; [START_REF] Wythers | Bare-soil evaporation under semiarid field conditions[END_REF]. A similar decreasing trend was observed by [START_REF] Wythers | Bare-soil evaporation under semiarid field conditions[END_REF] in their field evaporation experiment on loams.

The results of volumetric water content from the four tests show that the evaporation from bare soil occurs mainly in the near surface zone (e.g., within a depth of 55 mm). This agrees with the observation by [START_REF] Wythers | Bare-soil evaporation under semiarid field conditions[END_REF]. Furthermore, the evolution at deeper positions suggests that the bottom soil will become dry if the evaporation continues and if there is no water table. The contour map (see Fig. 12) clearly indicates this trend. Note that the linear relationship of soil water content in the near-surface zone (see Fig. 13) can be used for determining the surface water content by extrapolation.

Matric suction

The evolutions of suction over time are presented in Fig. 14 for the four tests. It can be observed that suction increases over time for all positions, indicating the progress of the evaporation process. It also decreases over depth, with the value on the soil surface being the highest. In test 1, only the suctions at the soil surface (i.e., 5 mm depth), 77 mm depth, and 276 mm depth are monitored. The soil surface suction grows in the beginning from 13 to 240 kPa at t = 8 days, and reaches the limit of the tensiometer (1.5 MPa) 1 day later. The suctions at the other two positions are nearly the same, and the tensiometer at 77 mm depth fails due to cavitation after 8 days. In test 2, suction at the soil surface (i.e., 10 mm depth) increases quickly from 14 kPa at t = 0 days to 46 kPa at t = 8 days, and reaches the limit of the tensiometer (1.5 MPa) a few hours later. At 77 mm depth, the suction is slightly higher than at 173 mm depth. The lowest matric suction is found at 276 mm depth. In test 3, suctions were recorded at the same positions as in test 1, and the data in the first 0.7 days was not recorded. The suction at soil surface (i.e., 10 mm depth) grows from 5 to 22 kPa. The value at 77 mm depth is higher than at the bottom (i.e., 276 mm depth). For test 4, the surface suction (i.e., 10 mm depth) varies from 17 to 67 kPa during the first 17.5 days. The values at 20 and 25 mm depths were measured in this test and the tensiometers reached their limits at t = 13 and 17.7 days, respectively. The lowest suction is observed at the bottom and the value at 173 mm depth is close to the bottom one. Note that the suction measurement was disturbed from t = 2.1 to 2.7 days due to some technical problems. The tensiometers at 173 and 276 mm depth did not work correctly during this test and stopped the measurement many times, thus the data are lost for the first 1.2 days at 173 mm depth and no data were recorded after 16.5 days at 276 mm depth.

The profiles of soil suction are shown in Fig. 15. For all the tests, a clear decrease over depth can be identified, with the largest gradient in the surface zone. For test 1, the gradient from the soil surface to 77 mm depth varies from 0.2 kPa/mm at the beginning to 1.5 kPa/mm at t = 6 days. For test 2, the gradient from the soil surface to 7 mm depth increases from 0.2 kPa/mm at the beginning to 0.5 kPa/mm at t = 8 days. The gradient from the soil surface to 77 mm depth increases from 0.05 kPa/mm at the beginning to 0.2 kPa/mm at t = 17.5 days in test 3. For test 4, the gradient from the soil surface to 25 mm depth increases from 0.7 kPa/mm at the beginning to 2.4 kPa/mm at t = 16 days. On the other hand, the matric suction distribution over depth at the initiation of evaporation can be identified: for test 1, the suctions decrease over depth and their values at the soil surface (5 mm depth), 77 mm depth, and 276 mm depth are 13, 1.7, and 1 kPa, respectively. For test 2, the suction values at the soil surface (10 mm depth), 77, 173, and 276 mm depths are 13.5, 4.6, 2.6, and 1.8 kPa, respectively. For test 3, the values at the soil surface (10 mm depth), 77, and 276 mm depths are 5.2, 1.8, and 0.6 kPa, respectively. For test 4, the values at the soil surface (10 mm depth), 20, 25, 173, and 276 mm depths are 17.6, 9.1, 6.5, 3.8, and 0.9 kPa, respectively.

The increasing suction in the soil suggests a gradual water loss during evaporation (see Fig. 14). The decrease of suction over depth corresponds to the increase of volumetric water contentthe surface soil loses water quickly during evaporation resulting in a sharp increase in suction (see Figs. 14 and 15). The increase of suction gradient in the surface zone during evaporation (see Fig. 15) confirms that water loss at the soil surface is quicker than in deeper zones. Note that the measurement of soil surface suction is essential in theoretical analysis of evaporation [START_REF] Wilson | The effect of soil suction on evaporative fluxes from soil surfaces[END_REF][START_REF] Aydin | Test of a simple model for estimating evaporation from bare soils in different environments[END_REF]. The measurements done in this study provide useful information in this regard, but it is worth noting that they were done slightly below the soil surface, and in addition the suction values were limited to 1.5 MPa.

Soil water retention curve and unsaturated hydraulic conductivity

Figure 16 presents the soil-water retention curve of Fontainebleau sand obtained from the four evaporation tests with simultaneous measurements of suction and volumetric water content at various depths during the drying process. In the determination, for each level of soil suction measurement (see Fig. 14), the corresponding volumetric water content was determined based on the volumetric water content profile (see Fig. 13). Figure 16 Figure 17 shows the unsaturated hydraulic conductivity of Fontainebleau sand determined by the instantaneous profile method based on the profiles of volumetric water content (Fig. 13) and the profiles of suction (Fig. 15). For more details about the instantaneous profile method, refer to the work of Cui et al. (2008b) and [START_REF] Wang | Hydraulic conductivity and microstructure changes of compacted bentonite/ sand mixture during hydration[END_REF]. A large data scatter is observed. However, on the whole, the unsaturated hydraulic conductivity is found to decrease with the increase of matric suction. Note that different symbols in Fig. 17 represents the data obtained from different evaporation tests.

Actual evaporation rate

Based on the air temperature and relative humidity at inlet and outlet as well as the air flow rate, the actual evaporation rate can be calculated using eq. ( 1). The results are shown in Fig. 18 for all four tests. In general, the evaporation rate under low heating tube temperatures (tests 1 and 3) is lower than under high heating tube temperatures (tests 2 and 4). On the other hand, the evaporation rate at high air flow rate (tests 1 and 2) is higher than at low air flow rate (tests 3 and 4). In addition, for tests 2, 3, and 4, three stages can be identified: (i) nearly constant or slightly decreasing evaporation; (ii) a sharp decline; and (iii) stabilized or very slightly decreasing evaporation. Note that only one stage exists for test 1. Comparison between the variations of actual evaporation rate and those of relative humidity (Fig. 10) shows that they are com-patible: an initial-decrease stage for relative humidity corresponds to a high evaporation rate; a quick-decline second stage for relative humidity corresponds to an evaporation rate reduction; a final stabilization stage with a very low decrease rate for relative humidity corresponds to a low-rate evaporation.

For test 1, the initial water content was higher than for the other three tests, and therefore the constant evaporation stage lasted longer. The effect of air flow rate on evaporation can be also identified: at the constant evaporation stage, the 172 L/min air flow rate in test 2 resulted in a nearly 2.2 mm/day evaporation rate while the 130 L/min air flow rate in test 4 led to an evaporation rate of 2 mm/day. The effect of air temperature appears more significant than the effect of air flow rate, especially during the constantevaporation stage. For instance, at a similar air flow rate (i.e., 185 L/min in test 1 and 172 L/min in test 2) but different air temperatures (i.e., 16 to 20.5 °C in test 1 and 24 to 29 °C in test 2), the evaporation rate ranges from 1.5 to 2.1 mm/day in test 1 whereas it ranges from 2.0 to 2.3 mm/day in test 2. Similar observations can be made from tests 3 and 4: the evaporation rate in test 3 has an average value of 1.7 mm/day while this value is 2 mm/day in test 4.

Conclusions

Four soil water evaporation tests were carried out on Fontainebleau sand with a stable water table in a large-scale environmental chamber, with varying air temperature, air flow rate, and test duration. Both air parameters (air flow rate, temperature, and relative humidity) and soil parameters (temperature, water content, and suction) were monitored. The following conclusions can be drawn based on the results obtained.

1. The air temperature inside the chamber is affected by both the heating tube temperature and air flow rate. The air temperature in the chamber is nearly constant when the temperature in the heating tube is low, but increases when the temperature in the heating tube is high. Furthermore, the air temperature is also affected by the soil water evaporation process. 2. Soil temperature is strongly affected by the air conditions. When the temperature in the heating tube is high, the soil temperature is increased and the heat energy for evaporation is solely from the hot air. By contrast, when the air temperature is low, the energy for evaporation comes from both air and soil. The evaporation process also influences the soil temperature: when the evaporation rate is low, the energy consumed by evaporation decreases, thus soil temperature increases by heat from hot air. 3. Relative humidity in the chamber decreases during the evaporation progress. The relative humidity in the chamber is lower at higher heating tube temperatures. The large increase at the outlet of the chamber represents water evaporation from the soil. In other words, evolution of the relative humidity in the chamber is an indicator of evaporation progress. 4. Volumetric water content in the near-surface zone is strongly affected by the evaporation process and exhibits a linear relationship with depth. The change of water content in the surface zone is related to the evolution of soil resistance to evaporation. 5. Soil suction decreases over depth and increases over time. This is consistent with the volumetric water content changes. 6. Evaporation rate is strongly affected by the air conditions especially at the initial constant-evaporation rate stage. At higher heating tube temperatures, the evaporation rate is higher. At a higher air flow, the evaporation rate was also found to be higher.

The test data obtained allowed the mechanism of water evaporation from bare sand to be revealed. They can be also used for the validation of numerical models dealing with water transfer under the effects of both soil temperature and soil suction. Most importantly, these data can be used to verify existing models for soil water evaporation or to develop new ones. From a practical point of view, these kinds of models are helpful in determining the soil surface conditions (water vapor flux, suction, temperature). When these conditions are known, common numerical models for unsaturated soils can be used to predict changes in soil temperature, soil suction, soil water content, etc. In other words, the models for soil water evaporation are essential when dealing with the interaction between the atmosphere and soils.

Fig. 1 .

 1 Fig. 1. Grain size distribution curve of Fontainebleau sand (data from Delfosse-Ribay et al. 2004).

Fig. 2 .

 2 Fig. 2. Experimental set-up with the environmental chamber.

Fig. 4 .

 4 Fig. 4. Soil compaction and sensor installation: (a) soil compaction, (b) ThetaProbe installation in the zone of 60 mm depth, (c) T3111 transmitter and thermistor installation, and (d) infrared thermometer installation.

Fig. 5 .

 5 Fig. 5. Variations of air flow rate: (a) test 1, (b) test 2, (c) test 3, and (d) test 4.

Fig. 6 .

 6 Fig. 6. Evolutions of air temperature at inlet and outlet of the chamber as well as in the laboratory: (a) test 1, (b) test 2, (c) test 3, and (d) test 4.

Fig. 7 .

 7 Fig. 7. Evolutions of air temperature at different elevations: (a) test 1, (b) test 2, (c) test 3, and (d) test 4.

Fig. 8 .

 8 Fig. 8. Evolutions of soil temperature at different positions: (a) test 1, (b) test 2, (c) test 3, and (d) test 4.

Fig. 9 .

 9 Fig. 9. Profiles of air-soil temperature: (a) test 1, (b) test 2, (c) test 3, and (d) test4.

Fig. 10 .

 10 Fig. 10. Evolutions of air relative humidity at different positions in the chamber: (a) test 1, (b) test 2, (c) test 3, and (d) test 4.

Fig. 11 .

 11 Fig. 11. Evolutions of volumetric water content at different depths: (a) test 1, (b) test 2. (c) test 3, and (d) test 4.

Fig. 12 .

 12 Fig. 12. Contour map of evolutions of volumetric water content at different times: (a) test 1, (b) test 2, (c) test 3, and (d) test 4.

Fig. 13 .

 13 Fig. 13. Profiles of volumetric water content: (a) test 1, (b) test 2, (c) test 3, and (d) test 4.

Fig. 14 .

 14 Fig. 14. Evolutions of matric suction at different positions: (a) test 1, (b) test 2, (c) test 3, and (d) test 4.

  also shows

Fig. 15 .

 15 Fig. 15. Profiles of matric suction at different times: (a) test 1, (b) test 2, (c) test 3, and (d) test 4.

Fig. 16 .

 16 Fig. 16. Soil water retention curve obtained from the four evaporation tests.

Fig. 17 .

 17 Fig. 17. Unsaturated hydraulic conductivity versus matric suction, determined by the simultaneous profile method.

Fig. 18 .

 18 Fig. 18. Evolutions of actual evaporation rate: (a) test 1, (b) test 2, (c) test 3, and (d) test 4.

Table 1 .

 1 Specification of the sensors used.

	Sensor	Manufacturer	Parameter measured	Range	Accuracy	Position	Number
	High-capacity	ENPC	Matric suction	0-1.5 MPa	-	Soil surface and	5
	tensiometer					chamber wall
	T3111 transmitter	Elcowa	Relative humidity	0%-100%	±2.5%	Chamber wall, wind	6
						supply unit, and
						air collection unit
			Temperature	-30-+150 °C	±0.4 °C	Chamber wall, wind	6
						supply unit, and
						air collection unit
	ThetaProbe (ML2x)	Delta-T	Volumetric water	0%-100%	±1.0%	Soil	5
			content
	PT1000	Correge	Temperature	0-100 °C	±0.3 °C	Soil	6
	Thermistor (DO-35)	Radiospare	Temperature	-40-+250 °C	±1.0%	Chamber wall	5
	Infrared thermometer	Calex	Temperature	-20-+250 °C	±1.0%	Chamber cover	1
	(Pyropen-D)
	Flowmeter (MAS-3120)	Kobold	Air flow	0-500 L/min	±1.5% full scale	Wind supply unit	1
	Anemometer	Testo	Wind speed	0-20 m/s	±(0.03 m/s + 5%	50 mm above soil
	(Testo 435-2)				measured value)	surface

1 Fig.

3

. Sketch of arrangement of the sensors.

Table 2 .

 2 Test program.

			Temperature	Test
	Test	Air flow	in heating	duration
	number	rate (L/min)	tube (°C)	(days)
	1	185	50	11.5
	2	172	200	11.5
	3	130	50	17.5
	4	130	200	30

Can. Geotech. J. Vol. 51, 2014 Published by NRC Research Press Can. Geotech. J. Downloaded from www.nrcresearchpress.com by DOCUMENTATION RECHERCHE on 02/07/14 For personal use only.

Published by NRC Research PressCan. Geotech. J. Downloaded from www.nrcresearchpress.com by DOCUMENTATION RECHERCHE on 02/07/14 For personal use only.

Acknowledgements

The authors are grateful for the financial support from the China Scholarship Council (CSC) and Ecole des Ponts ParisTech.