Alice Guille Des Buttes
email: alice.guille-des-buttes@ifsttar.fr

Bruno Jeanneret
email: bruno.jeanneret@ifsttar.fr

Alan Keromnes

Serge Pelissier

Luis Le Moyne

Optimizing Fuel Consumption and Pollutant Emissions of a Spark Ignition Engine for Eco-driving Applications

Keywords: driving, pollutant emissions, dynamic programming, air/fuel ratio

The transportation sector is a major contributor to both air pollution and greenhouse gas emissions. While optimizing fuel consumption reduces CO2 emissions, it can increase fuel-rich operation and cause higher HC and CO emissions. A simplified emissions model is thus introduced in order to account for the impact of air/fuel ratio on both the exhaust concentration of regulated pollutants and the catalyst efficiency. This model is used to solve the eco-driving problem with dynamic programming and a weighted objective function. An emission-centered and a consumption-centered scenario are compared on various driving cycles and with several time constraints. The optimal driving style in terms of emissions shows a substantial decrease in CO and HC while consumption stays relatively stable and NOx emissions slightly increase.

I. INTRODUCTION

The transportation sector is a major contributor to both air pollution and greenhouse gas emissions. Researchers and manufacturers have thus been working on the design of vehicle components to improve their aftertreatment capabilities and energy efficiency. For a given design, emission levels and fuel consumption still vary across the operating range [START_REF] Heywood | Internal Combustion Engine Fundamentals[END_REF]. Therefore, the vehicle's performance strongly depends on the driver's choice of gears and speed trajectory [START_REF] Ericsson | Independent driving pattern factors and their influence on fuel-use and exhaust emission factors[END_REF]. Ecodriving attempts to determine the optimal driving style for a specific vehicle on a predefined trip.

Many publications on ecodriving focus on minimizing fuel consumption, which is proportional to CO 2 emissions. However, previous work by Mensing [START_REF] Mensing | Ecodriving: an economic or ecologic driving style?[END_REF] showed that such strategies can increase other pollutant emissions because they encourage the use of high engine loads. To address the tradeoff between emissions and consumption, Mensing reduced operation in this unfavorable region by introducing an arbitrary penalty factor. Johansson also recommended avoiding highload areas in an experimental study on ecodriving style [START_REF] Johansson | Impact of ecodriving on emissions and fuel consumption, a pre-study[END_REF].

The aim of our work is to provide a more systematic approach to this optimization problem by including a simplified emissions model in an ecodriving method based on dynamic programming.

The following section introduces the model used to evaluate the impact of air/fuel ratio (AFR) on exhaust composition and catalytic converter efficiency in high-load ranges. Next, the optimal driving style for a given trip is determined with dynamic programming. Finally, the resulting trade-off between fuel consumption and emissions is discussed.

II. MODELS

A. Vehicle model

This work focuses on the behavior of spark ignition engines. The engine is studied in the context of a standard powertrain, which includes an internal combustion engine (ICE), followed by a clutch, a gearbox, and a final drive reduction (FD), as seen in Fig. 1.

The vehicle's motion is modeled on the longitudinal axis, where the projection of Newton's second law [START_REF] Heywood | Internal Combustion Engine Fundamentals[END_REF] expresses the relation between the powertrain's traction force (F t ), the aerodynamic drag (F aero ), the rolling resistance (F roll ) and the acceleration force given by the mass of the vehicle (m), the equivalent mass of the rotating parts (m rot ), and the acceleration (a).

F t = (m + m rot ) • a + F aero + F roll (1)
The aerodynamic drag given by ( 2) is proportional to the air density (ρ), the body's cross sectional area (A) and drag coefficient (C D ) and the square speed of the vehicle (v).

F aero = 1 2 • ρ • A • C D • v 2 (2)
The rolling resistance is given by (3) where g is the standard acceleration due to gravity, c 0 the constant rolling resistance coefficient, and c 1 is the quadratic rolling resistance coefficient. The transmission is composed of a final drive (with a ratio k F D and an efficiency η F D ) and a gearbox (with a ratio k GB and an efficiency η GB ). Equation ( 4) expresses the engine's torque (T eng ) as a function of the transmission parameters, the traction force and the tire radius (R tire ).

F roll = m • g • (c 0 + c 1 • v 2 ) (3)
T eng = F t • R tire η F D k F D • η GB k GB (4)
In order to identify the engine's operating point, the engine speed (ω eng ) also has to be defined as given by [START_REF] Kean | Effects of vehicle speed and engine load on motor vehicle emissions[END_REF].

ω eng = v • k F D • k GB R tire (5)
B. Spark ignition engine 1) Fuel consumption: knowing the engine's operating point (see vehicle models) and assuming a quasi-static relationship, the fuel consumption ( ṁf ) can be computed from a lookup table, as expressed in [START_REF] Guzzella | Introduction to Modeling and Control of Internal Combustion Engine Systems[END_REF]. The table is obtained from test-bench measurements on a 1.6-liter gasoline indirect injection engine and the corresponding engine efficiency is shown as map of speed and torque (Fig. 2).

ṁf = ṁf (ω eng , T eng ) (6)
It can be observed on the map (Fig. 2) that in the low-load ranges, efficiency increases with torque as the relative weight of friction decreases. However, efficiency decreases again in high-load ranges (contour lines closing on themselves). This phenomenon coincides with the high emissions measured by Mensing on an ecodriving cycle in [START_REF] Mensing | Ecodriving: an economic or ecologic driving style?[END_REF], which appear as red dots in Fig. 2. This can be attributed to a change in the chemical composition of the air/fuel mixture.

In gasoline engines, fuel can be injected in excess with respect to the stoichiometric combustion ratio in high-load ranges [START_REF] Kean | Effects of vehicle speed and engine load on motor vehicle emissions[END_REF]. This has several advantages: as fuel vaporization lowers the gas temperature at intake, it increases its density and draws a higher mass of mixture in the cylinder. Fuelrich conditions also decrease the exhaust temperature, lowering stress on the engine [START_REF] Guzzella | Introduction to Modeling and Control of Internal Combustion Engine Systems[END_REF]. However, this strategy causes incomplete combustions, which are detrimental to the overall energy efficiency and lead to unburned hydrocarbons (HC) and CO emissions.

2) AFR and pollutant emissions: in this paper, we assume that the mixture is stoichiometric up to 85% of the maximum torque, as it is the limit of the high-emissions zone identified in [START_REF] Mensing | Ecodriving: an economic or ecologic driving style?[END_REF]. The relative AFR (φ) then increases with the load. It can be expressed as a static function of the engine speed and torque [START_REF] Vinot | Fuel consumption vs pollutant emission trade-off for hybrid electric vehicle. an application of the pontryagins minimum principle[END_REF]. The corresponding map for the relative AFR is shown in dashed lines in Fig. 2. The quasi-static approach assumes that the engine's AFR control compensates for transients due to fuel pooling in the intake manifold.

φ = φ(ω eng , T eng ) (7)
The pollutant concentrations ([S] with S = CO, HC, NOx) before the catalyst are then interpolated based on typical values of the AFR for spark ignition engines as in [START_REF] Guzzella | Introduction to Modeling and Control of Internal Combustion Engine Systems[END_REF] (see Fig. 3). Each pollutant's mass flow ( ṁS ) is given by [START_REF] Shaw | A simplified coldstart catalyst thermal model to reduce hydrocarbon emissions[END_REF]. It depends on the concentration of the respective species and the flow of gas out of the engine ( ṁg ). As the composition of the mixture is given by the AFR, the flow of gas can be determined from the fuel consumption, the relative AFR and the stoichiometric AFR (ψ S ).

ṁS = ṁg • [S](φ) = ṁf • (1 + ψ S φ ) • [S](φ) (8)
Finally, tailpipe emissions strongly depend on the threeway catalyst, which removes more than 90% of the regulated pollutants in its nominal working conditions: stoichiometric AFR and above light-off temperature [START_REF] Vinot | Fuel consumption vs pollutant emission trade-off for hybrid electric vehicle. an application of the pontryagins minimum principle[END_REF]. Since our study focuses on the influence of the AFR in high-load ranges, we assume perfect thermal efficiency. The capacity of the catalyst to store oxygen in order to maintain stoichiometric AFR in the short term is also neglected. The catalyst efficiency (η cata ) can thus expressed as a Wiebe function of AFR according to Shaw's approach in [START_REF] Shaw | A simplified coldstart catalyst thermal model to reduce hydrocarbon emissions[END_REF] (see Fig. 3). The tailpipe mass flow for each pollutant is then given by [START_REF] Mensing | Optimal energy utilization in conventional, electric and hybrid vehicles and its application to eco-driving[END_REF].

ṁS = ṁf • (1 + ψ S φ ) • [S](φ) • (1 -η cata (φ)) (9)

III. OPTIMIZATION METHOD

A. Optimal control problem

Ecodriving consists in optimizing gear choice and velocity trajectory for a given trip. We have applied the algorithm developed by Mensing during her PhD studies [START_REF] Mensing | Optimal energy utilization in conventional, electric and hybrid vehicles and its application to eco-driving[END_REF]. Gear choice is the result of an instantaneous optimization: the gear which results in the lowest cost is chosen for each time-step. On the other hand, acceleration is the controllable input to be optimized. This can be formulated as an optimal control problem where acceleration is the control variable (u(t) = a(t)).

The state vector of the system (x) can be described by two variables: speed and distance (x(t) = [v(t), d(t)]) which are submitted to the dynamics given by [START_REF] Maamria | Which methodology is more appropriate to solve eco-driving optimal control problem for conventional vehicles[END_REF].

v(t) ḋ(t) = 0 0 1 0 v(t) d(t) + 1 0 a(t) (10)
In order to study pollutant emissions and fuel consumption, the cost function to be minimized is a weighted sum of both during a time window (T ). Equations ( 1) to ( 9) define consumption and pollutant mass flows as a function of the control variable and state vector, the objective function can thus be written as [START_REF] Hooker | Optimal driving for single-vehicle fuel economy[END_REF]. In order to compare the various pollutants, the corresponding Euro 4 emission limit (S lim ) are introduced as a scaling factor.

J = T 0 ṁf (u(t), x(t)) + α S ṁS (u(t), x(t)) S lim dt (11)
The problem's constraints describe the predetermined trip. They consist of speed limits, initial and final velocity, as well as total trip distance and time. The maximum allowable speed is given as a function of distance.

This optimization is usually performed using dynamic programming or the Pontryagin Minimum Principle [START_REF] Maamria | Which methodology is more appropriate to solve eco-driving optimal control problem for conventional vehicles[END_REF]. We used dynamic programming, which can be computation intensive but allows an easier integration of constraints.

This ecodriving method was introduced by Hooker in [START_REF] Hooker | Optimal driving for single-vehicle fuel economy[END_REF] and it is based on the iterative solving of a graph built by discretizing the vehicle's state variables. In order to account for the constraints in time, distance and speed, Hooker used a 3-dimensional approach with time as one of the three state variables. However, further developments in [START_REF] Monastyrsky | Rapid computation of optimal control for vehicles[END_REF], [START_REF] Mensing | Optimal energy utilization in conventional, electric and hybrid vehicles and its application to eco-driving[END_REF], and [START_REF] Maamria | Which methodology is more appropriate to solve eco-driving optimal control problem for conventional vehicles[END_REF] chose only two state variables (distance and velocity) and included the time constraint in the objective function in order to speed up calculation. As we chose the same approach, the discrete-time objective function is given by [START_REF] Monastyrsky | Rapid computation of optimal control for vehicles[END_REF] where ∆t k is a variable time-step.

J = k ṁf,k ∆t k + α • k ( ṁCO,k CO lim + ṁHC,k HC lim + ṁNOx,k N Ox lim )∆t k + β • k ∆t k (12)
The trade-off between fuel consumption and pollution is investigated by varying the weighting factor α. For each value of α, the parameter β is determined with a bisection method in order to fulfill the time constraint.

B. Simulation parameters

Our vehicle model is based on a Peugeot 308, with typical values for a compact car : The main results of this study are presented with speed constraints extrapolated from the urban driving cycle of the ARTEMIS program (see Fig. 4). The total trip time for the optimization is only 710 seconds as idle periods have been cut (their speed profile is already fixed). The corresponding fuel consumption and emissions are added after the graph has been solved.

As highlighted in [START_REF] Maamria | Which methodology is more appropriate to solve eco-driving optimal control problem for conventional vehicles[END_REF], the results of dynamic programming depend on the state variables' discretization step. We have chosen a distance step of 2 meters and a speed step of 0.01 meters per second, as further refining didn't have a significant impact on the results.

IV. RESULTS AND DISCUSSION

A. Simulated emissions

While the simulated speed profile does not match the standard (New European Driving Cycle), we could have expected emissions similar or higher than the limit as our cycle is quite dynamic. However, for all the tested scenarios (pollutant weighting factor α ∈ [0, 0.5]), simulated HC are lower than the limit and NOx emissions are significantly lower than the associated standard (see Fig. 5). This is consistent with the fact that our emissions model does not account for the coldstart period where the catalyst efficiency is close to null. The impact of this phase can be great in the case of HC, as mentioned in [START_REF] Shaw | Coldstart engine combustion modelling to control hydrocarbon emissions[END_REF]. On the other hand, CO levels are the closest to the limit, which suggests that the model offers a better description of CO formation mechanisms. This matches with Andrianov's observations [START_REF] Andrianov | A physics-based integrated model of a spark ignition engine and a three-way catalyst[END_REF] that CO concentrations are weakly dependent on all tested variables other than AFR.

CO and HC are mainly emitted during short acceleration bursts as a series of spikes (see Fig. 6) which correspond to high-load fuel-rich operation. In our model, these phases have a very adverse effect on CO and HC as high exhaust concentrations coincide with low catalyst efficiency. Recent measurements by Zhu [START_REF] Zhu | Experimental study on combustion and emission characteristics of turbocharged gasoline direct injection (gdi) engine under cold start new european driving cycle (nedc)[END_REF] show that while AFR has a lesser effect on HC emissions, CO is indeed emitted in short spikes which match fuel-rich operation.

B. Emissions vs consumption

In our emissions model, the choice of a weighted objective function has a significant impact on emissions. While fuel consumption stays stable (see table II), HC and CO sharply decrease and reach an asymptotic value with the increase of the weighting factor α (see Fig. 5). The NOx emissions slightly increase as their behavior is antagonistic with regards to the AFR but they stay significantly below the standard value. We can compare two extreme scenarios.

CO (g/s)

Fig. 6. Ecodriving cycles and CO emissions for the identified scenarios

• In the fuel-centered scenario, the objective function only considers the fuel consumption (α = 0).

• In the pollutant-centered scenario, the emission term has a high weighting factor (α > 0.3). It can be observed in Fig. 6 that both scenarios have almost overlapping speed profiles. They both implement the same strategy in order to reduce the fuel consumption as illustrated on Fig. 7 where we zoom on a sequence between two stops. The optimal solution alternates between acceleration phases (P1 in white), stabilized speed (P2 in yellow), slow deceleration (P3 in blue) and fast deceleration (P4 in green).

In the acceleration phases (P1), high gears are chosen in order to increase the torque (and lower the engine speed) to take advantage of the increase in efficiency of the engine in higher torque regions. In the slow deceleration phases (P2), the engine is disconnected from the wheels and the vehicle's speed is a result of its inertia. The engine consumes some fuel to maintain its slowest speed but the ratio between average velocity and fuel consumption is still advantageous. In the fast deceleration phases (P3), the engine is connected to the wheels and functions as a brake. The injection is then cutoff and there is no fuel consumption. Finally, the stabilized speed phases (P4) actually show an oscillating behavior around a mean speed by alternating between acceleration and slow deceleration. The resulting fuel consumption is lower than maintaining the equivalent cruising speed by taking full advantage of the engine efficiency and of the vehicle's inertia.

This last strategy leads to very frequent disengaging of the engine which is not very realistic and the oscillating behavior might be uncomfortable for the user. A more realistic driving style could be proposed by grouping all the decelerating phases and all the accelerating phases together. The optimality of this solution could be investigated by introducing a penalty for frequent gear change in the current algorithm. While excursions in the fuel-rich zone still occur for the pollutant-centered scenario in the dynamic phases in order to meet the time constraint, the decrease in CO and HC is obtained by reducing the load. In the fuel-centered scenario, the maximum load is very close to 100% (99.9%). In the pollutant-centered scenario, the load does not exceed 87% of the highest torque (85% being the start of the fuel-rich zone). This is achieved thanks to a change in acceleration and gear shifting strategy for the acceleration phases. Such a behavior is shown in Fig. 8 where we zoom on a dynamic phase. The pollutant-centered scenario displays a lower acceleration (lower resulting speed) and the choice of a higher gear is delayed in order to keep the torque within acceptable bounds. This strategy successfully reduces the CO spike.

While the CO and HC emissions are significantly reduced, the fuel consumption stays stable. This suggest that several paths lead to a similar fuel consumption with different acceleration strategies, which introduces a degree of freedom to optimize the emissions.

Finally, NOx emissions increase by 3% in the pollutantcentered scenario. This is not surprising as NOx formation mechanisms requires high temperatures [START_REF] Guzzella | Introduction to Modeling and Control of Internal Combustion Engine Systems[END_REF] and fuel in excess lowers it. Furthermore, while CO and HC oxidation in the catalyst is less efficient in rich conditions, NOx reduction is improved. The effect of AFR on NOx is thus inconsistent with the one it has on the other species.

C. Effect of trip constraints

In order to validate the previous results on several missions, we will study the impact of the trip's arrival time and the chosen cycle on fuel consumption and pollutant emissions in the following sections.

Table III shows the emissions and pollution results for the pollutant-centered scenario, when the total trip time is reduced by 10% and by 20%. Table IV corresponds to the relative difference between the pollutant-centered and the fuel-centered scenario for each arrival time.

In table III, we observe that the consumption increases when the trip time is shorter, as expected. This trade-off between arrival time and consumption has already been studied in literature [START_REF] Javanmardi | Effect of trajectory optimization parameters on energy consumption and co2 emissions for a gasoline powered vehicle[END_REF] [START_REF] Mensing | Optimal energy utilization in conventional, electric and hybrid vehicles and its application to eco-driving[END_REF]. Table IV shows that for all trip times, the consumption increases for the pollutant-centered scenario. The increase is more substantial for a reduced trip time as there is less freedom to choose the speed profile. However, the maximum fuel consumption increase that we have observed is still less than 2% which is relatively stable.

Table III displays an increase in CO as the travel time decreases. This is due to increasingly dynamic phases which require high loads and fuel in excess. The impact of travel time on HC is less pronounced but the same trends still hold. A trade-off between emissions and travel time is thus revealed, as previously described with fuel consumption. In table IV, there is always a significant decrease in CO between the pollutant-centered scenario and the fuel-centered scenario. This is expected as CO emissions are the closest to the standard limit and thus have the largest impact on the sum of normalized emissions. Minimizing the pollution term is thus closely related to the minimization of CO emissions. As mentioned earlier, HC emissions present a behavior similar to that of CO, with a less pronounced impact as the decrease in catalyst efficiency for CO is significantly steeper (Fig. 3).

The response of NOx emissions to AFR is inconsistent with the one it has on CO and HC. Furthermore, the modeled emissions for this pollutant are low, which makes the relative differences quite sensitive to even small changes in values. A trade-off between emissions and consumption for this particular pollutant is not observed for the arrival times that we studied (see table III). A more complete model would need to be built in order to conclude as to the trends for this pollutant as it depends on a large number of other parameters, such as spark timing, engine speed, and intake conditions [START_REF] Andrianov | A physics-based integrated model of a spark ignition engine and a three-way catalyst[END_REF].

Table V shows the emissions and pollution results for the pollutant-centered scenario, for the previously introduced urban ARTEMIS cycle (ARTURB), the extra-urban ARTEMIS cycle (ARTROUT) and the urban hyzem cycle (HYZURB). Table VI corresponds to the relative difference between the pollutant-centered and the fuel-centered scenario for each driving cycle. It can be observed that the results are very similar for each driving cycle, with a significant impact on HC and CO while consumption and NOx stay relatively stable.

V. CONCLUSION

This paper discusses the trade-off between pollutant emissions and fuel consumption in ecodriving for gasoline engines, which is affected by the torque management.

Ecodriving cycles can involve high loads as they allow the driver to satisfy the travel time constraint with little decrease in the engine efficiency. However, they can lead to higher CO and HC emissions as they are associated to fuel-rich combustion. In order to predict and minimize pollutant emissions, we introduced a simplified model describing the effect of air/fuel ratio on tailpipe emissions.

Its use in a weighted objective function to solve the ecodriving problem with dynamic programming allowed us to identify a fuel-centered and a pollutant-centered scenario. The latter showed great potential for emissions reduction with a relative decrease as high as 55% for CO and 16% for HC while fuel consumption stayed stable. Pollutant emissions decreased thanks to a change in acceleration and gear shifting strategy in the dynamic phases which resulted in lower engine torques. Small excursions in the fuel-rich zone still occurred especially in the case of shorter travel times, resulting in a trade-off between trip time and pollutant emissions.

Further work will focus on refining the emissions model to account for the influence of other parameters such as power demand, spark timing and intake conditions on HC and NOx concentrations. The dynamics of the air/fuel ratio can also be studied by modeling the oxygen storage in the catalyst or fuel pooling in the intake manifold (indirect injection). This work could also be extended to take the cold start period into account in order to optimize the light-off of the catalytic converter in the context of pollutant-centered ecodriving.

This approach could also be applied to hybrid electric vehicles, with an additional degree of freedom concerning the torque split between the electric machine and the internal combustion engine. This involves adding an additional dimension in the dynamic programing graph, leading to a complex and computation intensive resolution. In this context, a Hamiltonian formulation might be more appropriate, as long as the expression of the various adjoint states can be derived.

Fig. 1 .

 1 Fig. 1. Standard powertrain schematic

Fig. 2 .

 2 Fig. 2. Engine efficiency and CO emissions (measures) -AFR (model)

Fig. 3 .

 3 Fig. 3. Data input for the emissions model

Fig. 4 .

 4 Fig. 4. Speed constraints extrapolated form ARTEMIS urban cycle

Fig. 5 .

 5 Fig. 5. Emission ratios as a function of weighting factor α

Fig. 7 .Fig. 8 .

 78 Fig. 7. Analysis of the strategy to reduce fuel consumption

TABLE III FUEL

 III CONSUMPTION AND EMISSIONS FOR VARIOUS ARRIVAL TIMES

		T	0.9T 0.8T
	Fuel (L/100km)	5.8	6.4	8.2
	CO (g/km)	0.5	0.6	0.8
	HC (g/km)	0.06	0.06	0.08
	NOx (g/km)	0.03	0.02	0.03
	TABLE IV
	RELATIVE DIFF. BETWEEN SCENARIOS FOR VARIOUS ARRIVAL TIMES
		T	0.9T	0.8T
	Fuel (L/100km)	+0.1%	+0.3%	+1.6%
	CO (g/km)	-55%	-18%	-96%
	HC (g/km)	-16%	-2%	-79%
	NOx (g/km)	+3%	-25%	+44%


Jean-Loup Madre

Yves D Bussière

Richard Grimal

A life Expectancy-Period-Cohort model to project private car fleet and traffic applied to France

Keywords: Individual motorization, use of the automobile, life expectancy, demographic and economic factors, prospective

In most industrialized countries, after decades of gradually slowed growth, car traffic stagnated in the 2000s. This phenomenon has been attributed not only to conventional economic factors (stagnation of incomes, upward volatility in fuel prices) and to re-urbanization linked to metropolisation, but also to demographic factors (ageing of the population, longer life cycle stages leading in particular to delay the passage of the driving license in the younger generations). The economic recovery, albeit rather slow, and a significant drop in the price of oil in 2014 favored a certain revival of traffic growth in several countries (U.S.A., Germany, France, ...); but what about the structural factors and how to predict medium-term developments? We have already dealt with these questions via Age-Period-Cohort models, and more often Age-Cohort (AC). In view of the over-determination generated by the mechanical link between these three factors, we propose a Life Expectancy-Period-Cohort model (EPC); indeed, by replacing age by life expectancy at this age and at each date, the model can be directly estimated keeping the three components, while making this approach more consistent with the extension of life cycle stages (longer studies, women having their children in their thirties, postponement of retirement age, ...). Period effects are specified by introducing the income of the household and a fuel price index as explanatory variables. The results are compared with those of various previous models.

The scope is the adult population (i.e., of driving age), considering three phases for automobile behavior: -to pass the driver's license, -to be the main user of a vehicle, -to ride (annual mileage) or frequency of use of the vehicle.

Once the model is estimated on the data of the Parc-Auto Kantar-SOFRES 1994-2016 panel survey, an example of medium-term (horizon 2030) projection of the annual mileage is presented, being aware that in the long term the technical innovations (autonomous vehicle, electric and hybrid engines) and organizational evolution (car sharing, carpooling, ...) are likely to fundamentally change the conditions of use of the car.

Introduction

After expanding rapidly in the 1960s and 1970s, growth in car driving per capita slowed in the early 2000s in a number of industrialized countries. Is it an interruption in long term growth due to economic circumstances (high fuel price, then recession)? a peak due to saturation? a turning point before a long-term decline? (Goodwin, 2010-11). This "peak car travel" has been attributed both to structural factors (population ageing, new generations less addicted to automobile, metropolisation i.e. more and more people living in large urban areas, etc.) and to economic factors (lower income growth, upward volatility of fuel price, etc.).

Most papers on this phenomenon [START_REF] Litman | Evaluation of Public Transit Benefits and Costs. Best Practices Guidebook[END_REF][START_REF] Millard-Ball | Are We Reaching Peak Travel? Trends in Passenger Transport in Eight Industrialized Countries[END_REF][START_REF] Newman | Peak Car Use': Understanding the Demise of Automobile Dependence[END_REF]Kenworthy, 2011, Madre et al., 2012) are based on data collected before 2010. However, at least in the US, Germany and France, car traffic has notably increased since 2015 [START_REF] Cgdd | Les comptes de transport en 2016 -Tome 1 -54º rapport de la Commission des comptes des transports de la Nation[END_REF] as well as in Canada (e.g. in Montreal). Is it only a short-term phenomenon due to a cheaper fuel since 2014? Are structural (mainly demographic) factors still active for moderating the growth of car traffic? These questions will be investigated using the data of Parc-Auto Kantar-SOFRES panel survey for France from 1994 to 2016, using a new demographic approach, (i.e. the Life Expectancy-Period-Cohort model proposed by d [START_REF] Albis | Intergenerational inequalities in standards of living in France[END_REF]. We will investigate the behavior of successive cohorts and their impact on traffic growth, being aware that the context is quite specific, i.e. the most numerous cohort in the U.S. is the millennial generation, while in France it is that born in the 1960's at the end of the baby-boom, because of less immigration and of a lower fertility rate, even if, except Ireland, it is in France that the fertility rate is the highest in Europe.

After a literature review (section 2), our individual based nested approach (holding a driving license / being the main user of a car / annual mileage) is presented (section 3). Then, a descriptive analysis is given (section 4). Follows estimations of different models, with comparison of forecasts for the annual mileage per adult (section 5). Finally, a conclusion (section 6).

Literature Review

The Australian Bureau of Infrastructure, Transport and Regional Economics, which has compiled long timeseries for 25 countries, explains the slowing down of car driving per capita as a reflection of fuel prices and economic activity, as well as a time-related saturation effect for which a deeper understanding is needed (BITRE, 2012). A comprehensive analysis of global transport demand trends over the next 40 years was presented by the JTRC/ITF in May 2011 in Leipzig (OECD/ITF, 2011 and 2013) and regularly updated in "Outlooks" (see ITF website).

Most papers on this topic were focused on economic factors taking into account changes in behavior (economic growth and fuel price), but the demographic factors were neglected for explaining peak car [START_REF] Mannering | A Dynamic Empirical Analysis of Household Vehicle Ownership and Utilization[END_REF][START_REF] Hensher | The demand for vehicle use in the urban household sector: theory and empirical evidence[END_REF][START_REF] Goodwin | Elasticities of road traffic and fuel consumption with respect to price and income : A review[END_REF][START_REF] Pirotte | Déterminants du traffic des véhicules légers et élasticités: une approche spatiale sur données regionals françaises[END_REF].

During the diffusion of private cars, successive generations of men and women have increased their motorization along their life cycle. However, car ownership and use is specific for each generation cohort [START_REF] Gallez | Modèles de projection à long terme de la structure du parc et du marché de l'automobile, sous la direction de Jean-Loup Madre et François Gardes[END_REF][START_REF] Dargay | Car Ownership Dynamics Seen Through the Follow-Up of Cohorts: Comparison of France and the United Kingdom[END_REF][START_REF] Dejoux | Projection of the daily travel of an ageing population: The Paris and Montreal case, 1975-2020[END_REF]. Recent cohorts have grown in a society where the private car tends to become an individual good because of the diffusion of driver's license [START_REF] Roux | Transition de la motorisation en France au XXème siècle[END_REF]. Age cohort modelling has already allowed to anticipate phenomena such as decreasing car ownership of the inhabitants of the City of Paris starting in 1990, which has spread to inner suburbs in the 2000's [START_REF] Bussière | Vers la saturation ? Une approche démographique de l'équipement des ménages en automobile dans trois régions urbaines[END_REF]. Using continuous data, the introduction of period effects shows the influence of income growth and fuel price on peak car [START_REF] Berri | Étalement urbain, contexte économique et croissance de la circulation automobile des ménages en France: projections à l'horizon 2020[END_REF]. [START_REF] Bastian | Peak car? Drivers of the recent decline in Swedish car use[END_REF] explain the peak car in Sweden by GDP and fuel price. They conclude that most of the aggregate trends in car distances driven per adult, as much as 80% over the years 2002 to 2012 with elasticities higher among urban populations and in municipalities with high density, low average income and high share of foreign born residents. They stress the importance of accurate predictions of economic growth and fuel prices for accurate transport forecasts. Also, price elasticities tend to increase at high price levels and during periods of rapid price increases [START_REF] Bastian | Explaining 'peak car' with economic variables[END_REF]. A vast review of econometric literature concerning mainly aggregate time-series in developed countries showed that income elasticities tend to be greater than price by a factor 1.5-3 and long-run elasticities are greater than short-run elasticities by a factor of 2-3 [START_REF] Goodwin | Elasticities of road traffic and fuel consumption with respect to price and income : A review[END_REF].

A study of over 15 developed countries, then extended to 14 additional countries, shows a decrease, in the past 25 years, in the percentage of young people with a driver´s license, but an increase for older people (Sivak & Schoettle, oct. 2011). Data on Paris region confirm these tendencies with a threshold around 2001 and a significant growth in mobility by car by the retired population (Courel & Bouleau, April 2013).

Other authors argue that the observed trends in car use imply a paradigm shift in what constitutes a good city [START_REF] Newman | Peak Car Use': Understanding the Demise of Automobile Dependence[END_REF] as well as a series of other factors as road congestion and travel time in the cities [START_REF] Metz | Saturation of Demand for Daily Travel[END_REF].

Using Family Expenditure and Travel Surveys for different points in time, Yoann [START_REF] Démoli | The social stratification of the costs of motoring in France (1984-2006)[END_REF] shows the influence of socio-professional characteristics, in particular the differences between white collars from public and private sectors. Through qualitative surveys conducted in Lyon and Montreal, [START_REF] Ortar | The decline of car use. A long-lasting effect? French and Canadian young adults´relationship with mobility[END_REF] show, in the context of a longer access of young adults to be autonomous, that acquiring a license is less important than leaving their parents' household and having a job; environmental consciousness is emerging when a longer upper education period is present ; finally, the younger generation plans much less to move towards outer suburbs, but prefers to remain in a dense built environment, offering much more multimodal opportunities (bike and car sharing, public transport, etc.), but where car use is more and more considered as a costly constraint.

Based on the National Travel Surveys 1995-2009, conducted continuously in the Netherlands, and on qualitative surveys conducted at only one point in time, KiM (2014) makes the hypothesis that Dutch people will not have less cars, but will have them later, a tendency confirmed -the number of private cars went up by 15% between [START_REF] Noble | Why are some young people choosing not to drive ?[END_REF]and 2015(KiM, 2016)).

According to a longitudinal analysis of the 2003-2013 American Time Use Surveys [START_REF] Garikapati | Activity patterns, time use, and travel of millennials: a generation in transition?[END_REF](Garikapati et al., ), compared to recent generations: millennials (born between 1979(Garikapati et al., and 2000) ) are found, in early adulthood, to travel less, own fewer cars, have lower driver's licensing rates, and use alternative modes more. Older millennials are showing activity-time use patterns similar to their prior generation counterparts as they age, although some differences persist, particularly in time spent as a car driver. But to what extent will it still be the case as millennials move through various phases of their life cycle? Millennials appear to exhibit a lag in adopting the activity patterns of predecessor generations due to delayed lifecycle milestones (e.g., completing their education, getting jobs, marrying, and having children) and lingering effects of the economic recession, suggesting that car travel demand could resume growth in the future. Chatterjee, K., [START_REF] Chatterjee | Young People's Travel -What's Changed and Why? Review and Analysis[END_REF] recall that the downward trend for young adults in UK began approximately 25 years ago, explained by differences in life circumstances (demographics, living and socioeconomic situation, precarious economic situation, rise in motoring costs), in contrast with baby boomers who represented rapid and prolonged growth in driver´s license holding, car ownership and car use. They predict only a modest change towards greater car ownership for millennials in the next 10-15 years, and only for those who secure stable, full-time employment. [START_REF] Circella | What Affects Millenials´ Mobility? PART1: Investigating the Environmental Concerns, Lifestyles, Mobility-Related Attitudes and Adoption of Technology of Youn Adults in California[END_REF][START_REF] Circella | What Affects Millenials´ Mobility? PART II: Investigating the Environmental Concerns, Lifestyles, Mobility-Related Attitudes and Adoption of Technology of Youn Adults in California[END_REF]) in a study based on an online survey in California to a sample of 2,400 residents, including millennials show the importance of changes in attitudes and that the differences associated with the location where the respondents live are remarkably larger than differences observed among age groups: urban dwellers consistently report stronger pro-environmental policy attitudes than non-urban residents; urban millennials are heavy adopters of technology, smartphone apps in particular, and on average use these services more often for various purposes, including accessing information about the means (or combination of means) of transportation to use for a trip, finding information about potential trip destinations (e.g. a café, or a restaurant), or navigating in real time during a trip; large differences are also observed in the adoption of shared mobility across both age groups and urban vs. non-urban populations; not surprisingly, millennials tend to adopt these technological services more often than Gen Xers (i.e. born in the 1970s), particularly in urban areas. -They further analyzed the relationships between accessibility and the adoption of multiple modes of transportation (multimodality, and/or intermodality) among the various sub-segments of the population. For this analysis, they classified millennials in two groups of independent and dependent millennials based on their living arrangements and household composition. In fact, the residential location where dependent millennials live has likely been the result of their parent`s choices, and not of the millennials themselves. Accessibility and multimodality are usually positively correlated. Dependent millennials are found to make the most of their built environment potential, either due to individual choices, or the presence (or lack) of travel constraints. They are less likely to be mono-drivers and more likely to be multimodal commuters, even if they often live in neighborhoods that are less supportive of such behaviors. Independent millennials more often choose to live in accessible locations and tend to adopt non-motorized and multimodal travel options more often. The model for millennials compared to the model for other generations explains the lowest amount of variance in the data. A finding which signals the higher heterogeneity and variation among the members of this group, and the increased difficulty in explaining their behaviors through the estimation of econometric and quantitative models.

Laitian [START_REF] Zhong | Carless or Car Later? Declining Car ownership of millennial households in the puget sound region[END_REF] from a study in the Puget sound region in Washington state explains most of the decline of driving since the mid-2000s by socioeconomic factors, reduction of car ownership due to location, especially in compact neighborhoods. [START_REF] Stapleton | Peak car and increasing rebound: A closer look at car travel trends in Great Britain[END_REF] shows results for Great Britain, which are consistent with the claim that economic recovery and low fuel prices could encourage renewed traffic growth -particularly since the income short-term elasticity of car travel is found to be significantly larger than the price elasticity. These results also suggest that the rebound effect from improved fuel efficiency averaged 26% over this period -which is consistent with the literature. [START_REF] Bastian | Explaining 'peak car' with economic variables[END_REF] show that the traditional variables GDP and fuel price are sufficient to explain the observed trends in car traffic in all the countries included in their study (USA, France, UK, Sweden, Australia, Germany). Price increases in the early 2000s has been underappreciated in many studies. They remind us that:

¨finding correlations between variables in times series does not prove causality, of course, so we should be precise with what our conclusion is. The logic is this: if economic variables could not explain recent downward trends in aggregate car use, then that would have meant that the trends must have been caused by something else, and this ''something else" could be changes in lifestyles and attitudes. What we show is simply that the first part of this syllogism is not true: economic variables can in fact explain these recent trends. Of course, this does not rule out the existence of alternative explanations (this is true for any econometric model); nor does it imply that there are no changes in lifestyles or attitudes (of course there are), or that other variables do not affect travel patterns as well (of course they do). However, we can conclude that economic variables are sufficient to explain the aggregate trends in car use¨.

Barbara [START_REF] Noble | Why are some young people choosing not to drive ?[END_REF] shows that in Great Britain young people aged up to 24 with full car driving licences has been falling since about 1993 and that for those aged 25-29 there appears to be a more recent fall for young men and around 2002/04 a small decrease in the 30-34 age group. But in this age group licence holding continued to increase, though still lower than among men. Among other factors, the main cause of the decrease of licence holding is the cost of driving and the increased difficulty to pass the driving test. She mentions falling rates in Sweden, Norway, USA and Finland but no evidence of falling rates in Denmark, Netherlands and West Germany.

In Switzerland [START_REF] Rérat | A decline in youth licensing: a simple delay or the decreasing popularity of automobility?[END_REF], as in several western countries, the proportion of young people aged between 18 and 24 who have a driving licence fell from 70.7% in 1994 to 58.7% in 2010, before increasing slightly to 61.0% in 2015 [START_REF] Ofs | Comportement de la population en matière de transports: Résultats de micro-recensement mobilité et transports 2015 Office fédéral de la statistique et[END_REF]. Between 1994 and 2015, there was a very slight decrease among people aged 25-44 (88.9% vs. 87.8%) and a 10-point increase among those aged 45-64 (79.5% vs. 89.8%). There are significant changes among people aged 65-79 (50.6% vs. 79.0%) and those aged over 80 (from 19.7% to 45.0%). These increases of nearly 30 points are explained by the arrival in these age groups of women who have had greater access to cars than in previous generations. Thus, since 2005, there are proportionately more people in their 60s and 70s who have a driving licence than young adults. The symbolic meaning of the car that may declining. Rérat identifies four main factors explaining these tendencies: 1-complex administrative and pedagogical steps to obtain the driver´s licence, 2-age, mainly 18 years old, the difference being not significant at the age of 22, 3-possession of a public transport pass, 4-the residencial context: fewer licences in large or medium cities. Ages seems the determinant factor and, overall, young adults get their licences later and a catch-up effect occurs.

There is no consensus on the causes of peak travel except that it is multifactorial, and on whether it will persist. The final issue will depend of a combination of factors: demography, urban density, income, price, policies, technology, accessibility, mentalities. We don´t pretend to be able to take into account all these factors but propose a demographic approach which takes into account at national level, population growth, changes in behavior through generations, as well as period effects represented by real income per consumption unit and fuel price.

Data and Methodology

An individual based approach

The household is the traditional sampling unit for surveys. However, a household-based approach doesn't allow a clear understanding of individual's behavior, especially for young adults, who play a crucial role for peak car; they experience a longer and longer transition from the household of their parents to their own one.

Our analysis is based on 23 waves of TNS-SOFRES Parc-Auto panel survey (from 1994 to 2016). For comparability, a datafile of adults (individuals 18 or more years old, i.e. old enough to have a driving license in France) has been built from the household files, which contain a description of up to 6 adult members of the household; from 2004 to 2006 they are directly extracted from the datafile of individuals, which introduces a slight heterogeneity for this short period. The resulting datafile contains 284,286 observations (i.e. individuals*years). The analysis has been broken down into 16 age brackets (from "18-22 years old" to "93-97 years old"), which allows a detailed analysis of the life cycle.

A nested approach from driving license holding to annual mileage

Car use at an individual level has been split into three rather independent steps [START_REF] Grimal | L´auto-mobilité au tournant du millénaire : une approche emboîtée, individuelle et longitudinale[END_REF] : -Driving licence holding. -Car ownership, i.e. the proportion of individuals holding a driving licence, who are the main user of a car; in the rare case of a vehicle with 2 or 3 main users, only the car with the highest annual mileage is retained; -

The annual mileage of the car. -Thus, car use, i.e. the average annual mileage per adult, is the product of license holding, by individual motorization per license owner, by annual mileage per car.

4-Descriptive analysis

We will start by analyzing each component of automotive behavior by cohort along the period of their life cycle for which the 1994-2016 data is available. This is synthetized through the estimation of Age-Cohort models (see [START_REF] Dejoux | Projection of the daily travel of an ageing population: The Paris and Montreal case, 1975-2020[END_REF][START_REF] Bussière | Vers la saturation ? Une approche démographique de l'équipement des ménages en automobile dans trois régions urbaines[END_REF].This simplified model relies on the hypothesis that there is a constant lag between different cohorts along their life cycle for their automotive behavior (e.g. % of driver`s licence owners or annual mileage per adult). A dummy variable for the years 2004 to 2006 is introduced to take into account the slight heterogeneity of data for this period; in fact, this dummy is significant only for driving licence holding and for the proportion of main users among licence owners. Then, forecasting issues will be discussed according to the hypothesis that can be made on the gap between the different cohorts in the future.

Driver's licence

Towards the end of life cycle, the proportion of driving licene holders seems to decline in each cohort (Table 1) but very late in the life cycle. If we average 5 cohorts of people born between 1974 and 1993, we observe a peak at 33-47 years with 94% and then diminishes very slowly. It is still at 88% between 63-67 years and remains at 68% between 88-92 years. This is mainly due to a longer life expectancy of women; indeed, those born during the first half of the XXth century had notably less often a driving licence than men. If we considered separately each gender, we would observe that there are quite few significant declines of licence holding at old age : in the cohort 1918-21, from 78 years onward 90% of men have their licence, while 60% of women have it around 80 and only 55% around 90. However, almost no women loose their licence, while for men the maxima of cancelled licenses is around 30, 60 and 85 years old, but never exceeds 1% of individuals in each age bracket.

At an early stage of life cycle (i.e. in the 18-22 years bracket following the minimum age to be licensed), the licence rate is minimal (56%) for the individuals born during the late 1980's (cohort 1986-89), but notably higher for those born in the early 1990's (66% for the cohort 1990-93), with no more significant difference between genders. For the cohort 1986-89, the licence rate has increased rapidly, reaching 85% around 25 years old. Between 23 and 27 years, women have a higher rate than men since the cohort 1982-85 (86% for women, compared to 81% for men). Between 25 and 30 years old, the increase of licence rate is lower for people born during the early 1970's than for those born later. Around 35 years old, there are few significant differences between the cohorts born in the 1960's and 1970's, with a slightly higher rate for men.

The Age-Cohort model (explained in Box 1) shows that after 30 years old, the rate of driving licence owners is not significantly different by gender, from 96% for men, and from 88% for women (up to 75 years old; in all age groups until 88-92 the rate of driving licence owners is high for both men (up to 97% in 28-32 for men) and women (up to 93% for the same age group) and very slightly higher for men, from 3% to 7.5% until the age of 87 and rises at the ages of 88 an over (Table 2).

Concerning cohort effects, men born before the 1920's are significantly less licensed than those born later, while it is before the 1940's for women with a larger gap (Table 1). Men born after 1980 are significantly less licensed, while this phenomenon is less marked and appears later for women.

Finally, up to the cohort 1986-89, there is an important decrease of the proportion of licensed people between 18 and 22 years (Table 3). But when getting older, these cohorts tend to catch up with previous cohorts. This shows that in some instances the trajectories of each cohort may diverge and makes questionable the simplified hypothesis used in the Age-Cohort Model that the trajectories of each cohort are parallel all along the life cycle.

Box 1 : Age-Cohort Model For a demographic analysis, three inter-related dimensions have to be considered: •Age for identifying different stages in the life cycle, •Cohort, considering that people borna round the same date share a similar experience, •Period, i.e. socio-economic factors influencing everyone at the same time (e.g. fuel price) -date of observation.

Unfortunately : PERIOD (date) = COHORT (birth year) + Age -which makes model identification problematic. However, making the hypothesis that curves are parallel for successive cohorts, a "profile-type" can be computed from observations collected for a long enough period of time:

Car ownership -main user of a car

For young adults (18-22 years) the proportion of licence holders who are the main user of a car (Table 3), is increasing from 34% for those born around 1975 to 56% for those born in the late 1980's, but drops to 47% for those born in the early 1990's. The rate of main users per adult along the life cycle is low in the 18-22 age group, doubles for the 23-27 which reflects the financial capacity to own a car (Table 4), then is rather flat until the early 60´s and then diminishes significantly with ageing. For the most recent generations, there seems to be a kind of compensation between a low licence rate and a high proportion of people having their own car among licensed individuals. But around 35 years old, the differences between adults born in the 1960's and 1970's are much smaller. Does it mean that the following generations will catch up with them when they will reach 35 years? According to the Age-Cohort model (Table 2), more than 80% of licensed men (resp. 67% for women are the main user of a car when they are between 35 and 75 years old. There are almost no cohort effects for men except a slight one for extreme generations, which is negative for the individuals born before 1920 and positive for those born in the 1980's. For women, it varies widely from over -30 points for those born till the 1920's to over +30 points for those born in the 1980's (Table 2b). Thus, for the most recent generations, there is a kind of compensation between a low licence rate and a high proportion of people having their own car among licensed individuals.

Car use

For each age bracket, with almost no significant exception, the annual mileage per car is decreasing when considering more recent generation cohorts (Table 2). For example, the 18-22 years had an annual mileage of 13,023 km for those born in 1974-1977 and of 10,711 for those born in 1990-1993, a diminution of 18%. In the age groups where the mileage was the highest, 23-27 years, the annual mileage was 16,800 km for those born in 1970-1973 and of 13,600 km for those born in 1986-1989, a reduction of 19% (Table 5). This may be partly due to a higher fuel price after 2005 as well as changes in travel habits.

The resulting annual km per adult according to age is bell shaped, with a flat maximum moving slightly from the mid-twenties to the early fifties (Table 6). People born in the 1920's and before drive less, as well as those born in the 1990's, while the maximum is observed for those born from the 1960's to the early 1980's according to the Age-Cohort model. These changes correspond clearly to delayed steps in the life cycle for the most recent generations. For instance, more than 80% of the 18-22 years lived with their parents (i.e. were more than 20 years younger than the head of household), and less than 70% were students among those born in the late 1970's, while it is less than 60% (and more than 80%) for those born in the 1980's.

Forecasting the annual mileage per adult

Forecasting using fixed behavior by age with an Age-Cohort model

Demography is an important factor explaining peak car travel. Indeed, we have just shown that the curve of drivers' mobility according to age is bell shaped. A straightforward combination of fixed mobility by age group at date t° with the evolving number of inhabitants suggests that the demographic transition (i.e. a slower growth of the number of inhabitants with population ageing) implies a slow decrease of the annual mileage as car driver per adult.

Whatever trends in socioeconomic transformation in the country and users' expectation and preferences towards using cars, the choice of the reference date t° shows some influence: indeed, because of a generation effect, the mobility of the elderly is higher nowadays than it was before (e.g. people 68 to 72 years old drove 2,300 km annually in 1984-86, 5,000 km in 1994-96, 5,700 km in 2004-06 and 6,000 km in 2014-16).

Table 7 summarizes various projections with the Age-Cohort model and the Life Expectancy-Period Cohort model. The resulting forecast of the annual mileage driven by the whole population for 2032 compared to 2007 is a decrease of 8.3% with the 1984-86 reference, while it is only around 5% with a reference period after 2000. Figure 1 illustrates projections up to the horizon 2057 even though uncertainties of the future diminishes reliability in long term forecasting.

The Age Cohort model combines life cycle and generation effects. For car ownership, it gives a flat maximum around 2040 for the average number of main users per adult, and around 2050 for the total number of vehicles. For the annual mileage per adult, it shows a cohort coefficient increasing till the generation born around 1970, then a decrease. For forecasting, we made two simulations :

-"constant lag" means that we have maintained for "future generations", the coefficient of the cohort born in the early 1990's (i.e. the most recent cohort surveyed), -"reversed lag" means that we have extrapolated an increase of the generation coefficient after that of the cohort 2000-04, symmetrically to the decrease observed for previous generations, assuming that the generation gap could increase after its minimum observed around 1990.

Between 2007 and 2032, there is not much difference between these simulations (-8% for "constant lag" vs. -7% for "reversed lag"). Between 2007 and 2032, there is not much difference between these simulations (-8% for "constant lag" vs. -7% for "reversed lag").

Forecasting using the Life Expectancy-Period-Cohort (EPC) model

Taking into account longer stages in the life cycle (i.e. not only the perception that death will occure later but also that more time is available at each stage of life cycle), shown in the literature review as well as in the descriptive analysis, the Life Expectancy-Period-Cohort model see Box 2) seems quite attractive. Moreover, contrary to Age-Period-Cohort, it is not subject to collinearity problems for estimation (d'Albis and Badji, 2017) -see Box 1.

Box 2 : Life Expectancy-Period-Cohort Model Let us take the example of KMA as dependent variable, which is the annual mileage of the car at date t for which the individual i (at age a and date t) is the main user; KMA=0 when this individual is not the main user of a vehicle.

•KMA(i,t) = aLE(a,t) + ble(a,t)² + cGN + Dcuinc(i,t) + EPFUEL(t) With : -LE, the Life Expectancy of the individual at the date t when he/she is surveyed, deduced from his/her age; -LE² to take into account that the curve of annual mileage as a function of age is bell shaped, with a maximum for individuals in their forties; -dummy variables -(GN: Generation: BF: Before; AF: After) -GNBF1955 to GN1995 for cohorts (GNBF1955 for individuals born before 1955, GN196579 for those born between 1965 and 1979,…, GNAF1989 for those born after 1989); the reference cohort, for which the coefficient is set to 0, corresponds to individuals born from 1955 to 1964 ; quinquennial cohorts have been grouped in order to obtain coefficients which are significantly different from one another.

-And for period effects, the economic variables:

-* CUINC, real income of the household per consumption unit, -* PFUEL, the national index of fuel price, taking inflation into account (2015=100).

Table 7 compares provisional forecasting results with both models. The Age-Cohort model gives for the period 2007-2032 a fall in km/adult ranging from -8.3% to -5.2% depending of the fixed behavior hypothesis chosen which reflects the observed tendencies of fall of car use without price effects.

The LEP model gives quite different results with a 13% increase of the annual mileage per adult between 2007 and 2032; it is only +8.5% when keeping the real fuel prices of 2007 constant instead of taking for 2032 its value of 2016 which was 4% lower after the drop in 2014. Indeed, the economic factors have a strong influence. Neutralizing them after 2017 by keeping fuel price and income constant, it appears that demographic factors have a positive influence till about 2030, which is due to cohort effects (the life expectancy effect is negative). Combined with a stagnation in population growth, total traffic saturates after 2032. Table 8 gives the estimation of coefficients for average km per adult in the EPC model.

In a further research we could diversify scenarios including various price variations in both models to estimate its influence versus demographic factors

Comparison between forecasts obtained from different methods (Figure 1)

Driver`s license holding for young adults (aged 18 to 22), whose decline was the first advanced signal of peak car travel in Great Britain in the 1990's [START_REF] Noble | Why are some young people choosing not to drive ?[END_REF], seems to have reached a minimum after 2010 in France for the generation cohort born in the late 1990's. But the proportion of license owners being the main user of their car has compensated the differences between successive cohorts, resulting in a quite uniform distribution by age of the annual mileage per adult, despite an increasing proportion of students and individuals living with their parents in the new generations of young adults.

What consequences can be derived from the behavior of the younger generation-cohorts in terms of forecasting? Postulating a fixed behavior by age, we obtain quite similar results for the period 2007 to 2032 (-8% based on 1980's behavior vs. -5% based on behaviors observed after 2000). Using the Age-Cohort model and maintaining for future generations the lag observed for the cohort 1990-1994, a slight downward trend (-8% between 2007 and 2032) is obtained for the annual mileage per adult, and a slightly positive trend (+5% on the same period) for car traffic (total number of kms driven) till a flat maximum after 2032. Supposing that after a minimum reached for the cohort born in the 1990's, the lag for new (not yet observed) cohorts increases, reaching for the individuals that will be born around 2025 the lag observed for those born around 1970, the annual mileage per adult is still decreasing (-7% between 2007 and 2032), and it is only after 2030 that the rate of decrease is halved (-6% between 2032 and 2057) compared to that obtained with a constant lag (-3% on the same period).

In the life Expectancy-Period-Cohort model we added economic factors and consequently the model gives less stable forecasts because it exhibits a strong influence of these factors (mainly fuel price), which can explain the renewal of traffic growth since 2015. Maintaining constant the generation lag of people born in the 1990s, shows that its demographic components have a positive effect till about 2030, unlike a simple Age-Cohort model.

Scenarios with both methodologies show that, even in the case of younger generations catching up with their predecessors, the annual mileage per adult would hardly resume growth because of a rapidly increasing proportion of old drivers, with lower mobility, due to population ageing.

CONCLUSIONS

In a context of longer stages of life cycle (having a job and children later, retiring at older age), it makes sense to replace age by life expectancy among the three components of an Age-Period-Cohort model; moreover, this approach avoids the collinearity between these components. Indeed, in the context of volatility of economic factors (income growth and fuel price), it is important to take into account their impact as period effects, at least in the medium term.

For forecasting, the specification adopted here which should be improved, is flexible enough to allow: -

In the long run, to take into account the saturating effect of demographic factors using the life expectancy forecasts at each age up to 2060 delivered by the Institut national de la statistique et des études économiques (INSEE), and based on hypothesis on generation gaps for cohorts whose automotive behavior

has not yet been surveyed; a conservative hypothesis consists in keeping the coefficient estimated for the cohort born in the 1990s.

-

In the medium term, to build differentiated scenarios for income growth at different stages of the life cycle (e.g. slower growth at retirement age, as shown by the changes of taxation rate (contribution sociale généralisée -CSG) for retirement pensions in 2018.

-

To elaborate contrasted scenarios concerning fuel price at an aggregate level, and fuel efficiency for taking into account of rebound effects, possibly by age.

However, major uncertainty comes from changes in economic factors (mainly fuel price and a carbon tax) and political factors (restraints of car use) , and more research is needed for calibrating their influence in the context of major technical and organizational innovations (autonomous car, carpooling, short term car rental membership, rent a bike, new services, etc.). Moreover, spatial factors e.g. density, are not explicitly taken into account by our approach, despite of their important influence on automotive behavior. Let us suggest that they should be integrated by implementing the life Expectancy-Period-Cohort model separately on contrasted types of zones for which demographic forecasts are available (e.g. a longer life expectancy for the inhabitants of Paris region than for the rest of France as well as a higher supply of public transportation and consequently less private car use), then to aggregate the results. * years for which the file of adults has been built directly from the individuals', not from the households' datafile.

Figure 1 :

 1 Figure 1: FB: Fixed Behavior: ACCL Age-Cohort with Constant Lag: ACRL: Age-Cohort with reversed Lag; EPC: Life Expectancy-Period-Cohort model with constant lag.

Table 2a .

 2a Age-Cohort Models by Gender, 1994-2017

			Drivers' License Table 2b. Age-Cohort Models by Gender (continued) -Generation gap with the Reference Cohort 1960-1964 Main users/drivers' license Annual mileage/adult (km)
		Men	Women		Men		Women		Men		Women
	Age	Coef. Men	Std. Err. Drivers' License	Coef. Women	Std. Err.	Coef. Men	Main users/drivers' license Std. Err. Coef. Std. Err. Women	Coef. Men	Std. Err.	Annual mileage/adult (km) Coef. Std. Err. Women
	18-22 COHORT born	0.748	0.004	0.705	0.006	0.439	0.008	0.250	0.009	5954.08	182.78	1176.33	140.65
	23-27 in:	0.929	0.004	0.891	0.005	0.656	0.007	0.479	0.008	11353.00	168.54	6063.03	127.17
	28-32 1910-1914	0.970 -0.082	0.003 0.012	0.927 -0.336	0.005 0.018	0.785 -0.017	0.006 0.021	0.613 -0.583	0.007 0.031	13614.00 1869	141.82 494	7853.96 -3991	110.22 386
	33-37 1915-1919	0.968 -0.040	0.003 0.008	0.931 -0.375	0.004 0.014	0.810 -0.033	0.005 0.015	0.672 -0.472	0.006 0.024	13052.00 1348	120.43 360	8204.79 -4060	96.19 309
	38-42 1920-1924	0.967 -0.007	0.003 0.005	0.926 -0.260	0.004 0.008	0.815 0.027	0.005 0.009	0.712 -0.462	0.006 0.012	12176.00 2090	120.26 230	8393.03 -4128	95.89 181
	43-47 1925-1929	0.963 0.005	0.003 0.005	0.932 -0.224	0.004 0.007	0.829 0.036	0.005 0.008	0.727 -0.420	0.006 0.010	11856.00 2365	124.22 202	8404.25 -3985	96.71 156
	48-52 1930-1934	0.955 0.014	0.003 0.004	0.923 -0.150	0.004 0.006	0.809 0.039	0.005 0.007	0.754 -0.343	0.006 0.009	10877.00 2637	129.41 186	8080.17 -3390	99.31 142
	53-57 1935-1939	0.954 0.022	0.003 0.004	0.916 -0.092	0.005 0.006	0.824 0.046	0.006 0.007	0.742 -0.305	0.007 0.008	10389.00 2777	144.52 175	7120.36 -3011	108.73 133
	58-62 1940-1944	0.955 0.028	0.004 0.004	0.909 -0.043	0.005 0.006	0.846 0.029	0.006 0.007	0.727 -0.235	0.007 0.008	9449.60 2672	157.55 168	6223.74 -2419	119.55 127
	63-67 1945-1949	0.957 0.014	0.004 0.003	0.918 -0.035	0.005 0.005	0.859 0.016	0.007 0.006	0.741 -0.183	0.008 0.007	8698.57 1358	165.54 151	5868.35 -1876	125.66 115
	68-72 1950-1954	0.957 0.002	0.004 0.003	0.916 -0.020	0.006 0.005	0.851 -0.001	0.007 0.006	0.760 -0.105	0.009 0.007	7338.99 720	177.69 141	5571.10 -1302	134.75 109
	73-77 1955-1959	0.950 -0.004	0.004 0.003	0.902 0.006	0.006 0.004	0.828 -0.007	0.008 0.005	0.776 -0.037	0.010 0.006	5696.88 -186	194.58 130	5293.05 -459	148.53 103
	78-82 1960-1964	0.944 0	0.005 0	0.898 0	0.007 0	0.778 0	0.009 0	0.773 0	0.011 0	3806.81 0	221.94 0	5036.25 0	170.43 0
	83-87 1965-1969	0.937 0.005	0.007 0.003	0.871 0.006	0.010 0.004	0.665 0.000	0.012 0.005	0.743 0.057	0.015 0.006	2080.76 -479	286.40 130	4639.95 664	217.58 101
	88-92 1970-1974	0.909 0.000	0.011 0.003	0.748 0.016	0.015 0.005	0.524 -0.007	0.019 0.005	0.623 0.110	0.027 0.006	948.61 -1287	461.31 137	3959.19 1394	333.41 106
	93-97 1975-1979	0.894 -0.014	0.025 0.004	0.441 0.003	0.029 0.005	0.346 -0.007	0.045 0.006	0.424 0.133	0.069 0.007	1373.32 -1866	1067.18 154	2673.28 1574	624.35 119
	YEARS 2004-1980-1984 2006* 1985-1989	0.015 -0.035 -0.097	0.002 0.004 0.005	-0.020 -0.007 -0.043	0.003 0.006 0.007	-0.012 0.028 0.061	0.003 0.007 0.009	0.015 0.199 0.243	0.004 0.008 0.010	-215.58 -2185 -2686	83.537 172 212	81.0764 2195 2052	130 63.54004 156
	1990-1994	-0.064	0.006	-0.038	0.009	0.011	0.012	0.212	0.013	-3193	267	1640	201
	1995-1999	-0.105	0.008	-0.078	0.013	0.028	0.017	0.239	0.021	-3551	353	1437	293
	Adj. R²	0.946		0.866		0.818		0.647		0.549		0.414
			Source : Parc-Auto panel survey 1994-2017.

Table 4 .

 4 Main user of a car per adult along the life cycle by cohort(%), 1994-2015

	Age	18-22	23-27	28-32	33-37 38-42	43-47	48-52	53-57	58-62	63-67	68-72	73-77	78-82	83-87 88-92
	Individuals
	born in:
	All	30%	56%	69%	73%	73%	72%	69%	66%	63%	62%	58%	52%	46%	37%	26%
	1914-1917													32%	28%	15%
	1918-1921													39%	28%	15%
	1922-1925												49%	43%	40%	35%
	1926-1929											50%	48%	47%	38%
	1930-1933										57%	55%	51%	50%
	1934-1937									58%	59%	58%	58%
	1938-1941									60%	61%	64%
	1942-1945								62%	63%	66%	67%
	1946-1949							64%	64%	65%	68%
	1950-1953							65%	67%	66%
	1954-1957						69%	68%	71%
	1958-1961					67%	71%	74%
	1962-1965				70%	74%	76%	76%
	1966-1969			65%	71%	77%	78%
	1970-1973		53%	70%	75%	79%
	1974-1977	25%	53%	70%	76%
	1978-1981	30%	56%	74%
	1982-1985	32%	57%	69%
	1986-1989	32%	57%
	1990-1993	31%
	Source : Parc-Auto panel survey 1994-
	2015.

Table 5 .

 5 Annual mileage per vehicle along the life cycle by cohort(km), 1994-2015

	Age	18-22	23-27	28-32	33-37	38-42	43-47 48-52	53-57 58-62	63-67	68-72 73-77 78-82 83-87	88-92
	Individuals
	born in:
	All	11778	15512	15377	14851	14416	14349 13901	13106 12058	11319	10183 8874	7379	6099	5642
	1914-1917	.	.	.	.	.	.	.	.	.	.	.		7886	8066	6500
	1918-1921	.	.	.	.	.	.	.	.	.	.	.		7504	6004	3837
	1922-1925	.	.	.	.	.	.	.	.	.	.		9321	7648	5904	4577
	1926-1929	.	.	.	.	.	.	.	.	.		10391 9499	7473	5969
	1930-1933	.	.	.	.	.	.	.	.		11972	10587 8584	6983		.
	1934-1937	.	.	.	.	.	.	.		12770	12028	10399 8555		.	.
	1938-1941	.	.	.	.	.	.	.		13102	11924	10009		.	.	.
	1942-1945	.	.	.	.	.	.		14911 13012	11099	9682		.	.	.
	1946-1949	.	.	.	.	.		14880	13551 11505	10227		.	.	.	.
	1950-1953	.	.	.	.		15405 14785	12880 11040		.	.	.	.	.
	1954-1957	.	.	.		14813	14907 13342	11703		.	.	.	.	.	.
	1958-1961	.	.	.		15315	14605 13116		.	.	.	.	.	.	.
	1962-1965	.	.		15416	14428	13884 13447		.	.	.	.	.	.	.
	1966-1969	.		16648	15451	14069	12938		.	.	.	.	.	.	.	.
	1970-1973		16799	16213	14589	13839		.	.	.	.	.	.	.	.	.
	1974-1977	13023	16107	15341	14214		.	.	.	.	.	.	.	.	.	.
	1978-1981	12384	15657	14119		.	.	.	.	.	.	.	.	.	.	.
	1982-1985	12265	14661	14114		.	.	.	.	.	.	.	.	.	.	.
	1986-1989	11220	13607		.	.	.	.	.	.	.	.	.	.	.	.
	1990-1993	10711		.	.	.	.	.	.	.	.	.	.	.	.	.
	Source : ParcAuto panel survey 1994-2015.

Acknowledgments

We are grateful to the former Ministry of Transport for having funded the PREDIT project ANDEMO, as well as to the CEREMA which has sponsored the PhD thesis by Richard Grimal, which has inspired this paper. Grateful also to the University of Paris-Est and IFSSTAR of Marne-la-Vallée which financed a study intership of Dr. Bussière in Mayo 2017. We also thank, in Mexico, the CONACYT and the BUAP for their support.

(Preliminary versions of this paper have been discussed in an international seminar organized by the BUAP in Puebla in December 2016, as well as at the Rencontres Francophones Transport et Mobilité in Lyon and Journées de Méthodologie Statistique in Paris -June 2018).


Géraldine Villain
email: geraldine.villain@univ-eiffel.fr

Marie-Antoinette Alhajj
email: marie-antoinette.alhajj@univ-eiffel.fr

Sérgio Palma Lopes
email: sergio.palma-lopes@univ-eiffel.fr

Véronique Bouteiller
email: veronique.bouteiller@univ-eiffel.fr

Towards the Determination of Chloride Profiles by means of Resistivity Measurements in Reinforced Concrete

Keywords: Electrical Resistivity Tomography, NDT, Inversion, Durability, Reinforcement

).

Introduction

The preservation of our civil engineering infrastructure heritage is part of sustainable development initiatives and programs. Reinforced concrete (RC) structures exposed to de-icing salts and the marine environment may corrode through the action of chloride ions, water and oxygen. It has been shown that the methods for measuring the electrical resistivity of concrete are effective in alerting the potential corrosion risk [START_REF] Gowers | Measurement of concrete resistivity for assessment of corrosion severity of steel using Wenner technique[END_REF][START_REF] Andrade | The Use of Electrical Resistivity as NDT Method for the Specification of the durability of Reinforced Concrete[END_REF]. They are particularly sensitive to the moisture and chloride contents in concrete [START_REF] Saleem | Effect of moisture, chloride and sulphate contamination on the electrical resistivity of Portland cement concrete[END_REF]. Finally, electrical resistivity tomography methods also have the great advantage of investigating the concrete from the surface to the core in a non-destructive manner and of drawing as information the apparent resistivity. However, such data need to be inverted to obtain a resistivity profile with depth [START_REF] Loke | Rapid least-squares inversion of apparent resistivity pseudosections by a quasi-Newton method[END_REF][START_REF] Chouteau | An investigation on application of the electrical resistivity tomography method to concrete structures[END_REF][START_REF] Fares | Determining chloride content profiles in concrete using a resistivity probe[END_REF]. The calibration determines the conversion function to obtain the desired indicator: either the water content or the chloride content [START_REF] Fares | Determining chloride content profiles in concrete using a resistivity probe[END_REF]. But the presence of metal reinforcements disturbs the electric field and the measurement of apparent resistivities [START_REF] Sengul | Effect of embedded steel on electrical resistivity measurements on concrete structures[END_REF][START_REF] Presuel-Moreno | Numerical modeling of the effects of rebar presence and/or multilayered concrete resistivity on the apparent resistivity measured via the Wenner method[END_REF][START_REF] Garzon | Modification of four point method to measure the concrete electrical resistivity in presence of reinforcing bars[END_REF] and can prevent the inversion process, which is why the RILEM recommends to place itself at a distance from the reinforcements [START_REF] Polder | Test methods for on site measurement of resistivity of concrete-a RILEM TC-154 technical recommendation[END_REF]. The work of [START_REF] Alhajj | Accounting for steel rebar effect on resistivity profiles in view of reinforced concrete structure survey[END_REF] showed that it was possible to reproduce by finite elements modelling the effect of the reinforcements on the measurement of apparent resistivities.

The objective of this paper is to present the first results of the inversion programmed by [START_REF] Alhajj | A joint inversion technique of electric and electromagnetic measurements for the determination of water saturation profiles in concrete structures[END_REF] for reinforced and unreinforced slabs subjected to an imbibition of a saline solution in the laboratory. The first part presents the measurement method and summarizes the inversion procedure. The second part details the experimental program. The third one shows the measurement results and the monitoring of resistivity profiles over time in both reinforced and unreinforced slabs.

Method used for Non-Destructive Evaluation

The selected non-destructive evaluation (NDE) method is electrical resistivity tomography (ERT) because it is very sensitive to the water content and chloride content of concrete.

Electrical Resistivity Measurement Principle and Method

The electrical resistivity method used is based on the Wenner principle for 4 electrodes regularly spaced (spacing a). The current is injected by the 2 external electrodes and the potential difference measured between the 2 inner electrodes. The apparent resistivity is calculated from current and potential measurements and a geometric coefficient G [START_REF] Marescot | A general approach for DC apparent resistivity evaluation on arbitrarily shaped 3D structures[END_REF]. G is calculated by finite element modelling taking into account the geometry of the test body and the position of the electrodes. If the medium is homogeneous the apparent resistivity is equal to the «true» resistivity of the medium.

The device used was developed by [START_REF] Plooy | Development of a multi-ring resistivity cell and multi-electrode resistivity probe for investigation of cover concrete condition[END_REF]. It consists of 14 inline electrodes, 2cm-spaced. This allows the implementation of 26 Wenner configurations with 4 different spacings a=2 cm, a=4 cm, a=6 cm and a=8 cm. The larger is the spacing, the larger the volume examined from the surface. The raw results correspond to apparent resistivities at each level of spacing. They give information about the presence of a gradient in concrete.

Inversion Process

The inversion of these raw results allows to obtain a resistivity profile according to the depth. [START_REF] Loke | Rapid least-squares inversion of apparent resistivity pseudosections by a quasi-Newton method[END_REF] notably developed an inversion algorithm for a discrete, multi-layer material model. The resulting RES1D software is free of access and gives good results for unreinforced concrete slabs. However, the presence of metal reinforcements alters the current lines in the reinforced concrete slabs, thus influencing apparent resistivity measurements. This influence can be quantified by finite element modelling [START_REF] Alhajj | Accounting for steel rebar effect on resistivity profiles in view of reinforced concrete structure survey[END_REF]. It must be taken into account in the inversion process.

An inversion process has been developed and is presented at the DBMC 2020 Congress by [START_REF] Alhajj | A joint inversion technique of electric and electromagnetic measurements for the determination of water saturation profiles in concrete structures[END_REF]. In summary, the imposed initial true resistivity profile is continuous and follows a Weibull law with 4 parameters. The direct finite element model (Comsol Multiphysics®) calculates the modelled apparent resistivities. The least squares cost function between the modelled and the measured apparent resistivities is computed. A Levenberg-Marquardt algorithm minimizes this cost function in order to fit an estimated resistivity profile of the concrete. The iterative optimization algorithm is written in Matlab® linked with Comsol and is called "IFSTTAR inversion program" in the following. The finite element model may or may not take into account steel reinforcements present or not in concrete slabs. The resistivity profile obtained corresponds to the resistivity of the concrete material with a gradient of saline solution, independently of the conductive steel influence.

Experimental Program

A research project called APOS (Villain et al. 2015) aimed to compare embedded sensor results and non-destructive evaluations of reinforced concrete slabs submitted to chloride ingress in the initiation phase then in the corrosion phase (Bouteiller et al. 2018). The present study is limited to ERT in the initiation phase to evaluate chloride ingress in the cover concrete. The purpose of this section is to present the concrete formulation, the geometry of the slabs, their preconditioning and the chronology of the experimental program of this study.

Concrete and Slabs

 (%)
15.9 ± 0.7 Concrete is of type C30 containing ordinary Portland cement (Table 1). Its 28-day compressive strength equals 36.3±0.9 MPa and its porosity equals 15.9±0.7%. For this concrete, 10 slabs were casted to study the penetration of a saline solution of concentration [NaCl] = 35 g/L, close to that of the Atlantic Ocean. Among these slabs, we will study here 1 non-reinforced slab placed in salt solution (noted 13-NS), 2 slabs reinforced with carbon steel placed in salt solution (noted 14-CS and 15-CS), and 1 reinforced slab with stainless steels (noted 18-SS).

The dimensions of all the slabs are 90x75x13 cm. The reinforced slabs contain 1 single bed of rebars placed at 3 cm of depth, forming 4 meshes of 20x30 cm (Figure 2).

After casting, the moulds were removed at the age of 3 days. Then, the slabs were placed in a room first not ventilated for 3 months and then ventilated with fans for 6 months to accelerate drying. The side faces are protected by 2 layers of epoxy resin to keep transfers along the depth.

Imbibition Program

At the age of 9 months (T0 test time for imbibition process), the slabs were tested by nondestructive evaluation methods (NDT) and then placed in 1 to 2 cm of salt solution in pools, so that it can penetrate by imbibition on the reinforced side (Figure 3). At each test time, the slabs are removed from the salt solutions and subjected to NDT testing; then, they are put back in the pools. The chosen test times are about 1h, 4h, 1day, 2days, 7 days, 1 month, 4 months. Note that there can be differences between the slab for the out-of-water duration due to the numerous slabs and NDT methods. Here, we present the results of the first 4 test times (T1 to T4) which correspond to the imbibition of salt solution under temperature conditions of about 18-20°C. Moreover, at these early test times, the resistivity contrasts are higher and the ERT method gives thus the best results.

For each test time, the resistivity measurements were performed on the mesh AB23 along both diagonals (Figure 2), minimum twice, usually 3 or 4 times. The mean values are used for inversion.

Raw Results and Profiles of Resistivity versus Depth

The influence of the steel reinforcement on the apparent resistivity measurements is presented, first. Then, the inverted resistivity profiles are show in the 2 nd and 3 rd sub-sections.

Raw Results and Influence of Steel Rebars

Figure 4 shows the apparent resistivity measurements determined for 4 spacings of the Wenner configuration, for test times T1 to T4. The resistivity measurement was impossible at T0 because the slab surface was too dry. In Figure 4-a, corresponding to the non-reinforced slab 13-NS, at T1, the apparent resistivity is lower near the face in contact with the salt solution (a = 2 cm) than for larger spacings corresponding to higher volumes of investigation. Moreover, for later test times, the apparent resistivity decreases due to salt solution ingress into the concrete.

In Figure 4-b, corresponding to the reinforced slab for small spacing a = 2 cm, the apparent resistivity values are similar for both slabs, they decrease when the salt solution penetrates along time. But, for the other spacings, the larger are the spacings, the lower are the apparent resistivities. This is due to the steel rebar influence in accordance with literature results [START_REF] Polder | Test methods for on site measurement of resistivity of concrete-a RILEM TC-154 technical recommendation[END_REF]. This influence was quantified by a direct model using finite elements by [START_REF] Alhajj | Accounting for steel rebar effect on resistivity profiles in view of reinforced concrete structure survey[END_REF].

Resistivity Profiles versus Depth in the Unreinforced Concrete Slab

For each test time, the apparent resistivities obtained for the unreinforced slab (13-NS) are inverted:

• Firstly, by using the free-access software RES1D from Loke (2001); the resulting resistivity profiles are shown in Figure 5-a; • Secondly, by using the ISTTAR Program; the resulting resistivity profiles are shown in Figure 5-b and compared to the RES1D resistivity profiles. In Figure 5, the resistivity profiles show the salt solution ingress. Concerning RES1D (Fig. 5-a), the inversion process is very fast. Figure 5-b presents the results of both inversion programs which are in a good agreement especially at the 2 first test times. This can be explained by the ERT method, more informative about shallower volumes, thus less accurate for deeper volumes.

Resistivity Profiles versus Depth in Reinforced Concrete Slab with HA Carbon Steel and Stainless Steel

Then, for each test time, the apparent resistivities obtained for the reinforced slabs (14-CS, 15-CS and 18-SS) are inverted by using the same initial parameters as those used for the slab 13-NS. The inversion is performed with IFSTTAR program because it is not possible with RES1D.

Figure 6-a makes it possible to compare the resistivity profile obtained for unreinforced slab (13-NS) and reinforced slab (14-CS). Figure 6-b presents the resistivity profiles obtained for the 3 reinforced slabs.

The profiles in non-reinforced and reinforced slabs are very similar for T1, T2 and T3 (Fig. 6-a). The discrepancies between the profiles are of the same order of magnitude as the ones between the profiles of the 3 reinforced slabs (Fig. 6-b). This uncertainty can be due to the concrete material variations which influence the kinetics of the penetration of the salt solution. For the later test times, the discrepancies between all the curves increase. The uncertainty of the measurement method for a higher spacing is higher.

Moreover, the resistivity profile of the slab reinforced with stainless steel rebars (18-SS) is similar to the profiles of the 2 other slabs reinforced with carbon steel rebars (14 and 15-CS). The reinforcement is indeed in passive conditions in this study.

Conclusions and Further Developments

This paper presents the first results of an ERT inversion code tested on both reinforced and unreinforced slabs subjected to an imbibition of a saline solution in the laboratory. This study shows that it is possible to take into account the influence of steel reinforcement on the apparent resistivity measurements, to proceed to their inversion and obtain the "true" resistivity profiles. These profiles make it possible to monitor and evaluate the penetration of a salt solution (35 g/L) in the cover concrete.

Four slabs, either non-reinforced or reinforced with carbon or stainless steel rebars were submitted to the same imbibition process. The similar resistivity profiles obtained enable us to assess the uncertainty range due to both the concrete material variability and the ERT method itself. Indeed, the ERT uncertainty increases with high value of resistivity (it is higher for the dry core of slabs) and ERT give less information for larger volumes of investigation.

Note that carbon and stainless steel give similar resistivity results in passive conditions. However, to convert resistivity profiles into free chloride content profiles, calibration curves are needed, but they are not available at various water contents. Imbibition is a rapid process but more complex than diffusion in saturated conditions. This point has to be developed.

In further developments, non-destructive evaluations by ERT will be compared to embedded sensors in the concrete slab in view of structural health monitoring.

Figure 1 .

 1 Figure 1. Picture of the ERT testing device.

Figure 2 .

 2 Figure 2. Scheme of the reinforced concrete slab -a-Position of the ERT testing device -b-FE model.

Figure 3 .

 3 Figure 3. Scheme of the slab during the imbibition process in a pool filled with saline solution and showing the steel reinforcement.

Figure 4 .

 4 Figure 4. Apparent resistivity measurements for 4 Wenner configuration spacings -a-Unreinforced slab 13-NSb-Reinforced slab 14-CS.

Figure 5 .

 5 Figure 5. Inverted Resistivity profiles at test times T1 to T4, for the slab 13-NS -a-Inversion with RES1D -b-Inversion with "IFSTTAR program" (superimposed on the RES1D results).

Figure 6 .

 6 Figure6. Comparison of resistivity profiles corresponding to salt solution ingress in non-reinforced and reinforced concrete slabs -a-Slabs 13-NS and 14-CS (line with marks) -b-Slabs 14-CS, 15-CS and 18-SS.

  https://orcid.org/0000-0002-4478-034X Marie-Antoinette Alhajj: https://orcid.org/0000-0001-7711-5103 Sérgio Palma Lopes : https://orcid.org/0000-0001-7022-389X Véronique Bouteiller: https://orcid.org/0000-0003-1467-0622

Table 1 .

 1 Concrete mix design and properties.

	Aggregates 11.2/22.4	(kg/m 3 )	760
	Aggregates 6.3/10	(kg/m 3 )	320
	Sand 0-4	(kg/m 3 )	860
	Cement CEM I 52.5N CE CP2 NF St Pierre La Cour	(kg/m 3 )	305
	Total water	(kg/m 3 )	190
	Admixture AD Sika Prise SC2	(kg/m 3 )	0.7
	Water to cement ratio	Weff/C (-)	0.58
	Compressive strength at 28 days	Rcsat (MPa)	36.3 ± 0.9
	Saturated mean density	sat (kg/m 3 )	2332 ± 23
	Porosity (water saturation under vacuum)

Acknowledgements

The authors would like to thank all the team from the Regional Laboratory of de Saint-Brieuc (Cerema) in particular B. Thauvin, R. Queguiner, S. Pasquiet, P. Boulaire for the slab instrumentation and casting, as well as the slab survey during the experimental campaign. The authors are also grateful to the Ministry of Ecology MTES, IFSTTAR and Cerema for their financial support of the research project APOS.


Thomas Robert

Paul Leborgne

Georges Beurier

Raphaël Dumas

Personalized body

teaching and research institutions in France or abroad, or from public or private research centers.

Introduction

Personalized values of Body Segment Inertia Parameters (BSIP) are necessary to perform dynamic analysis of human movement (e.g. trajectory of the whole body centre of mass trajectory for stability analysis, joint torques / muscular forces estimations, etc.). BSIPs are usually estimated using regressions derived from anthropometric tables (AT) [1]. However, these tables are usually not adapted to atypical populations (children, elderly, obese persons, individuals with prostheses, etc.) that are classically of interest. An alternative consists in estimating BSIPs from segments' volumes assuming a uniform density. This alternative is of growing interest as: 1) it would be suitable even for populations with atypical body mass repartition; 2) 3D body shapes acquisition has recently became easier and cheaper thanks to the developments of low-cost 3D scanners [2]. However, there are still some issues to makes this measurement (3D point cloud of the external shape) usable in the context of movement analysis with minimal intervention. The main issue is the segmentation of the whole body external shape into body segments with relevant local coordinate systems (LCS) and anatomical landmarks (AL) [3].

Research Question

This study aims at proposing and evaluating a semi-automatic method (i.e. with minimal manual intervention), adapted to the human movement analysis framework, to estimate personalized BSIP from whole body 3D scanner images.

Methods

An experiment was conducted to compare BSIP from AT to those estimated from the volumetric approach. It consisted of a classical human motion capture experiment, to which a bodyscanning session was added. Nine subjects (6 M-3 F, 35±10 y.o., 171±10 cm and 84±7 kg) were equipped with 51 reflective skin markers, most of which located on specific AL. Subject' external shape was acquired in a standard standing posture in a 3D body scanner (SYMCADTM II by Telmat), resulting in a raw textured mesh of about 160000 nodes. Then several functional motions were recorded using a standard movement analysis set-up (optoelectronic system and fore plates). Experiments were approved by the French national ethical committee.

BSIP were estimated using both a volumetric approach and regression built on anthropometric tables. The volumetric approach primarily consisted in matching a template mesh, segmented and with identified ALs, onto the raw mesh of the subject's whole body shape. The template is a 50 th percentile male mesh of about 9000 nodes prepared with MakeHuman and Blender softwares. It was previously segmented into 15 bodies and 15 AL were manually identified and used to create the body LCSs, according to anatomical definitions [1]. Then, for each individual raw mesh, 15 anatomical landmarks of the template (a subset of the reflective markers located on subject's skin, i.e. easily identifiable) were manually identified. The template was then deformed on the individual raw mesh using a non-rigid transformation tool (mHBM software [START_REF] Yamakazi | Proc of 2 nd Int DHM Symp[END_REF]) that ensured a minimal distance between meshes and a match between template and target AL. It resulted in a structured, segmented and personalized mesh with identified AL. Then each segments mesh was isolated, transferred into its corresponding LCS and BSIP were estimated by volumetric computation assuming a homogeneous density [START_REF] Mirtich | [END_REF]. BSIP were also estimated using AT [1] and 3D coordinates of markers recorded during a 10 second static posture trial. BSIP obtained from AT and volumetric approach were compared. In addition, the whole body CM trajectory was estimated for static trials using BSIP from both volumetric and AT approaches and their projection were compared to the Centre of Pressure (CoP) measured by force plates.

Results

Estimated BSIP by AT or volumetric methods yielded to very similar results: difference on mass distribution below 2% of body weight, differences on CM location below 1cm in the frontal and lateral axis (up to 4 cm in the longitudinal axis for the thorax and abdomen). For static trials the volumetric approach yield to slightly smaller CM-CoP distances in the AP direction (about 50% less), in particular for persons with higher BMIs, i.e. volumetric approach improved whole body CM estimation for the person with "less normal" body mass repartition.

Discussion

We proposed a semi-automated method estimate personalized BSIP. This method is quasi-automated (one single manual operation: identifying the AL markers on the coloured raw mesh) and adapted to the human movement analysis framework. Further investigations would be required to properly assess this method. However, it seems a promising candidate to fill the lack of proper methodology to estimate BSIP, and thus to perform dynamic movement analysis, for populations that are poorly represented in anthropometric tables.