Mickael Le Vern
email: mickael.le-vern@univ-eiffel.fr

Andry Razakamanantsoa

Frédéric Murzyn

Frédérique Larrarte

Véronique Cerezo

Study on a test track of dust resuspension induced by a vehicle

Keywords: Dust re-suspension, Vehicle traffic, Unpaved road, Test track

An experimental campaign was carried out on a test track to assess resuspension of dust by vehicle traffic. Two vehicles were driven on a road covered by four different types of particles representing a wide range of fine soils. Each test consisted of running one of the vehicles at a given speed (30, 45 or 60 km.h -1 ) over one of the type of particles previously spread on the road at a given mass per unit area (200, 400 or 600 g.m -2 ). The concentration of resuspended particles was measured by suction of the dust plume behind the rear tire using a particle counter. The influence of physical (type and quantity of particles, vehicle geometry) and mechanical (vehicle speed, tire/surface interface, dynamical behavior) parameters on particle lift are discussed. In terms of particle mass concentrations, results indicate that doubling the vehicle speed leads to 1.5 to 5.7 times higher PM10 emissions. The lift of fine clay particles is 2 to 9 times more important than that of coarser soils. Significant differences are also observed between the emissions of the two vehicles, pointing out the key role of ground clearance and mud flaps in particles resuspension. It is believed that the present results may be extended to earthworks sites where solutions are expected to reduce dust emissions without watering.

Introduction

Dust emissions lead to a reduction of visibility and the worsening of air quality [START_REF] Pope | Health effects of fine particulate air pollution: Lines that connect[END_REF][START_REF] Baddock | A visibility and total suspended dust relationship[END_REF]. This phenomenon occurs during the circulation of cars and haul trucks on unpaved roads and earthworks runways [START_REF] Kuhns | Big Bend Regional Aerosol and Visibility Observational (BRAVO) study emissions inventory[END_REF][START_REF] Muleski | Particulate emissions from construction activities[END_REF]. The particles on the surface of the road can be re-suspended by the passage of a vehicle due to the shear stress at the tire/road interface combined with the 3D turbulent flow generated in the wake [START_REF] Gillies | Guide français pour la Réalisation des remblais et des couches de forme. IFSTTAR-CEREMA[END_REF][START_REF] Kuhns | Effect of Soil Type and Momentum on Unpaved Road Particulate Matter Emissions from Wheeled and Tracked Vehicles[END_REF]. This problem is also present on paved roads due to non-exhaust emissions including tire, brake and road related wear [START_REF] Hussein | Factors affecting non-tailpipe aerosol particle emissions from paved roads: On road measurements in Stockholm, Sweden[END_REF][START_REF] Hichri | Understanding the behavior of fine particles at the tire/road interface[END_REF].

Studies on unpaved roads (USEPA, 1995;[START_REF] Etyemezian | Vehicle-based road dust emission measurement: I-methods and calibration[END_REF][START_REF] Gillies | Guide français pour la Réalisation des remblais et des couches de forme. IFSTTAR-CEREMA[END_REF][START_REF] Kuhns | Effect of Soil Type and Momentum on Unpaved Road Particulate Matter Emissions from Wheeled and Tracked Vehicles[END_REF] have shown that dust emissions are dependent on vehicle weight and speed as well as on the silt content (% of particles < 75 µm) of the road. These roads are built from compacted soils that degrade as vehicles travel, resulting in the accumulation of particles on the surface (Le Vern et al., 2020a;[START_REF] Vern | Experimental assessment of dust emissions on compacted soils degraded by traffic[END_REF]. However, no study has investigated dust emissions as a function of the level of degradation of the unpaved road surface yet. Similarly, [START_REF] Gillies | Guide français pour la Réalisation des remblais et des couches de forme. IFSTTAR-CEREMA[END_REF] found that vehicle type did not influence emissions. Nevertheless, the use of accessories to control particle lift (such as mud flaps) has not been studied to date.

The main objective of this study is to analyze the effect of the level of surface degradation of an unpaved road on the dust emission. The degradation is characterized by the dust loading on the surface, i.e. the mass of particles per unit area. Different amounts of particles had been poured on a test track before vehicles were driven on it. Several types of particles were studied in order to identify the convenient parameter governing dust lift. The effect of vehicle type and mud flaps on this phenomenon is also studied. For this purpose, a light passenger car and a 4x4 equipped with mud flaps were driven at different speeds over the particles. An analysis of the mechanical parameters of tire/surface contact is also performed by means of a dynamometric wheel fitted to the passenger car.

The results of the study apply to the topic of unpaved roads but can be extended to the problem of particulate contamination of asphalt roads.

The methodology used for this study is described in the second part of this paper, followed by a presentation of the results and a discussion. This paper ends with the different conclusions that can be drawn from the experiments.

Methodology

Vehicles used and dynamometric wheel

Two vehicles were used during the tests: a Renault Clio III and a 4x4 Ford Ranger. The first one was chosen because it is one of the best-selling cars in Europe and is representative of small passenger cars. The 4x4 is much more massive (unladen weight of about 2 tons against 1 ton for the Clio) and has larger dimensions. Moreover, it is more likely to be used on unpaved roads and earthworks runways. Figure 1 shows these two vehicles. The Clio has about half the ground clearance of the 4x4 (120 mm vs. 229 mm). From a dimensionless point of view, the ratio of ground clearance to empty height (H/G as shown in Figure 1) is also different between the two vehicles (0.08 for the Clio and 0.13 for the 4x4).

The Clio was also instrumented with a Kistler RoadDyn S625 dynamometer wheel. This device was mounted on the right front wheel of the vehicle (see its location in Figure 3-a). It allows the continuous measurement of longitudinal, vertical and transverse forces and torques applied to the wheel using Wheatstone bridge-mounted strain gauges. Its acquisition frequency is 100 Hertz.

Particles under study

In previous studies about dust generation during vehicle traffic on unpaved roads, there is often only one geotechnical criterion for characterizing the soil: the percentage of particles smaller than 75 µm (USEPA, 1995;[START_REF] Etyemezian | Vehicle-based road dust emission measurement: I-methods and calibration[END_REF][START_REF] Gillies | Guide français pour la Réalisation des remblais et des couches de forme. IFSTTAR-CEREMA[END_REF][START_REF] Muleski | Particulate emissions from construction activities[END_REF][START_REF] Kuhns | Effect of Soil Type and Momentum on Unpaved Road Particulate Matter Emissions from Wheeled and Tracked Vehicles[END_REF]. The United Soil Classification System designates this percentage as the "silt content". Results have shown that the higher the silt content, the more dust will be emitted, all other things being equal. For this study we have chosen to work with particles having approximately the same percentage below 75 µm. Thus, we will be able to verify if this criterion is sufficient to characterize particle lift (if so we will measure similar dust emissions with the different soils) or if it is required to take into account other geotechnical parameters.

Four types of particles were used for the tests: a clay mixture composed with montmorillonite and illite (cosmetic green clay CATTIER) and three silty soils sampled from different earthwork sites in Europe: Val d'Europe and Strasbourg in France, Marche les Dames in Belgium. These soils have been selected because they have similar silt contents (between 95 and 100%) but their other geotechnical properties differ, as shown in Figure 2. In this Figure, the Liquid Limit and Plastic Limit are parameters that quantify the cohesion of the soil. They have been measured according to ISO 17892-12:2018(ISO, 2018). Together with the granulometric properties (passing at 2 µm and 75 µm), they allow the classification of the particles. In Figure 2, we present their classification according to the American Society for Testing Material standard (ASTM, 2017) and the French Guide for road earthworks (GTR, 2000).

Experimental protocol

In order to ensure particles being free of moisture during the tests, they were previously dried in an oven at 105°C for 24 hours. They were then sieved to break up any aggregates and packed in plastic bags. Before each test, the particles were spread homogeneously on the track along two lines each 3 m long and 0.3 m wide and spaced apart from each other by a distance corresponding to the spacing between the two tires of the vehicle (1.47 m for the Clio and 1.56 m for the 4x4). The width of the lines was chosen to be greater than the width of the vehicle tires (20 cm for the Clio and 25 cm for the 4x4). The length was chosen for practical reasons related to the quantities of particles available. Three quantities of particles per unit area were tested: 200, 400 and 600 g.m -2 . These quantities correspond to three distinct soil degradation states (low, medium and high) highlighted in a previous study (Le [START_REF] Vern | Experimental assessment of dust emissions on compacted soils degraded by traffic[END_REF]. The two lines were delimited by markings on the ground on which wooden frames were placed. The necessary quantity of particles was poured into these frames and then spread evenly with a brush. A weather station was on the side of the road to measure temperature, relative humidity as well as wind speed and direction. The tests took place after 9 days without precipitations, under conditions of relative humidity ranging from 50 to 80% and temperature ranging from 17 to 25°C. Figure 3 shows the experimental layout. Each test consisted in running one of the two vehicles at a predefined speed (30, 45 or 60 km.h -1 ) over one type of particles previously poured on the ground at a given mass per unit area (200, 400 or 600 g.m -2 ). The speed of 30 km/h corresponds to the traffic conditions generally imposed when the risk of dust is important (especially on construction sites). The speed of 45 km/h is a speed frequently reached in cities or on construction sites. Working at 60 km/h allows to study the effect of doubling the speed compared to 30 km/h. The test track was made of asphalt concrete to ensure that the vehicle blew away only the particles that had been poured on the surface. Conducting the tests on an unpaved road would not have controlled this parameter. This experimental configuration makes it possible to extend the results obtained to the problem of particle emission due to contaminations of asphalt mixes. These contaminations nevertheless generate smaller quantities of particles than those studied here.

During the tests, an optical particle counter measured the concentrations of suspended dust by particle aspiration directly behind the right rear tire of the vehicle. It is a dust analyzer PALAS Fidas Mobile equipped with a pump that sucks the particles contained in the ambient air. These particles pass through a beam of LED light which is then scattered at an angle that depends on the size of the particle (Mie scattering theory). The estimation of the particle size is performed with a photomultiplier that measures the scattered light. Combined with a counting algorithm, the mass concentration of particles per unit volume (µg/m 3 ) can be estimated.

Figure 4 shows the two vehicles (Figure 4-a for the Clio III and 3-b for the 4x4) as well as the installation of the particle counter in the 4x4 (Figure 4-c). For these measurements, the inlet of the suction pipe for particle aspiration was located in the median plane of the right rear wheel, 30 cm from the rear edge of the tire and 20 cm above the ground (Figure 4d). The distance between the pipe and the tire was the same for the measurements with the Clio III, except that the pipe was 10 cm above the ground. These pipe positions are related to practical considerations due to the vehicles' geometry.

After each test, the particles remaining on the ground were blown to the sides of the road using a leaf blower. A manual sweep of the road was also performed to ensure that the particles in the asphalt voids were removed. A total of 47 tests were carried out over three days by varying the different parameters (vehicle type and speed, particle type and mass per unit area). Table 1 shows all the tests carried out. Not all the possible configurations of parameters could be tested for practical reasons of time and quantity of particles available. Some configurations were tested several times for two reasons:

-To check the repeatability of the measurements by performing the same test twice in a row;

-To highlight the effect of meteorological parameters on dust emission by performing the same test in the morning and afternoon. The particle counter provides the evolution of the concentration of the different classes of particles (PM10, PM4, PM2.5 and PM1) at a data rate of 1 Hertz. We did not analyse particles beyond PM10 because it is the upper limit of the apparatus. Moreover, particles larger than 10 µm have high deposition velocities [START_REF] Petroff | Development and validation of a size-resolved particle dry deposition scheme for application in aerosol transport models[END_REF] and therefore fall rapidly to the ground, within 100 meters from their emission source [START_REF] Veranth | Vehicle-generated fugitive dust transport: analytic models and field study[END_REF]. They are also much less hazardous to health than the finest particles [START_REF] Autrup | Ambient air pollution and adverse health effects[END_REF].

Figure 5-a shows an example of particle concentration measured during a test performed with the 4x4 at 30km/h on 400g/m² of Val d'Europe silt particles. Figure 5-b presents the parameters that are taken into account in the present study for each curve, namely: the area under the curve, the maximum value and the mean value. The area under the curve is determined by the trapezoidal method and allows the definition of an "emission coefficient" φ given in μg.s.m -3 . The mean value is assessed by considering the measurements between the beginning of the concentration rise before the peak and the return to a "normal" concentration (defined as the average of the PM10 concentrations measured between two tests, i.e. 10 µg.m -3 ). It is arbitrarily considered that the peak concentration begins when the "normal" concentration is exceeded by a factor of 100 (that is PM10 concentration larger than 1000 µg.m -3 ) and ends when it falls below 10 µg.m -3 . According to this procedure, it is possible to highlight the moment when the vehicle is driving over the particles.

As the tests were carried out under subisokinetic conditions, the measurements underestimated the concentrations of the finest particles [START_REF] Wilcox | Isokinetic flow and sampling[END_REF][START_REF] Belyaev | Techniques for collection of representative aerosol samples[END_REF]. We therefore focus our analysis on the coarsest particles, i.e. PM10 concentrations. Moreover, it is the range of particles generally studied in the literature on dust emissions on unpaved roads (USEPA, 1995;[START_REF] Etyemezian | Vehicle-based road dust emission measurement: I-methods and calibration[END_REF][START_REF] Gillies | Guide français pour la Réalisation des remblais et des couches de forme. IFSTTAR-CEREMA[END_REF][START_REF] Kuhns | Effect of Soil Type and Momentum on Unpaved Road Particulate Matter Emissions from Wheeled and Tracked Vehicles[END_REF].

Analysis of dynamometric wheel measurements

The dynamometric wheel allows real-time measurement of the forces and moments applied to the right front wheel of the Clio III. In the context of the study, the influencing parameters on the lift of the particles are:

-The longitudinal force Fx which characterizes the friction between the tire and the road;

-The vertical force Fz which characterizes the action of the vehicle weight in the tire/road contact mechanics;

-The moment My which also characterizes the tire/road friction.

The vertical force Fz did not vary much during the tests (Fz ≈ 3750 N±3%) since the masses of the Clio and its driver were always the same. In addition, the road smoothness was of good quality and the speed of the vehicle was constant so the dynamic variations were attenuated by the shock absorbers. The parameter Fz is therefore not taken into account in the analysis.

Results and discussion

Repeatability of the results

Some configurations were tested several times to check the repeatability of the results (the acronyms are those used in Table 1):

-The SS-60km/h-200g/m²-Clio configuration was reproduced twice -The SMD-60km/h-200g/m²-Clio configuration was reproduced four times -The SMD-60km/h-400g/m²-Clio configuration was reproduced twice -The GC-60km/h-200g/m²-Clio configuration was reproduced twice Repeatability tests were done at 60 km/h because this is the speed for which there are the most disturbances and a priori the most lifted particles. For each configuration, the average value is determined for PM10max, φ and PM10mean. The minimum and maximum values are also considered. The average gap for each configuration is given by equation (1):

𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎_𝑎𝑎𝑎𝑎𝑔𝑔(%) = 𝑉𝑉𝑎𝑎𝑉𝑉𝑉𝑉𝑎𝑎 𝑚𝑚𝑚𝑚𝑚𝑚 -𝑉𝑉𝑎𝑎𝑉𝑉𝑉𝑉𝑎𝑎 𝑚𝑚𝑚𝑚𝑚𝑚 𝑉𝑉𝑎𝑎𝑉𝑉𝑉𝑉𝑎𝑎 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 × 100 (1)
Figure 7 shows the corresponding results.

Figure 7: Average gaps for the repeatability tests

The overall average gap is 47% for PM10max, 19% for φ and 26% for PM10mean. The large deviations observed for the peaks of concentration are due to the very strong dependence of this parameter on the particle aspiration kinematics. Indeed, their distribution in a dust plume is chaotic and more or less particles can be recorded at the same time in the particle counter. Thus, for the same dust plume, the concentration peak can vary significantly depending on the location of the aspiration. Therefore, it is more relevant to look at the evolution of the amount of particles sucked up as a function of time. As such, the parameter φ appears to be the most appropriate to characterize the dust plume generated. It is also the parameter with the best repeatability.

The observed variations are not due to the wind as it has no effect on the particles directly behind the vehicle tires. On the one hand, the wind speeds were low during the tests (between 2 and 9 km/h). On the other hand, it was visually observed during the experimental campaign that the effect of the wind appears several seconds after the particles are suspended, when they have reached a certain height (about 1 meter). Below this height, it is the aerodynamic phenomena related to the wake of the vehicles that entrap the particles, particularly in the counter-rotating vortices generated behind the wheels [START_REF] Mercker | On the simulation of road driving of a passenger car in a wind tunnel using a moving belt and rotating wheels[END_REF].

Some tests were carried out both in the morning and in the afternoon with a strong variation in relative humidity (about 80% in the morning and 60% in the afternoon). However, small differences were observed for dust emissions between these tests (less than 8% for the φ parameter). This suggest that relative humidity does not appear to be a parameter influencing the lift of particles directly behind the tire for the presenting tests. Indeed, the vehicle was running on the dry particles few minutes after they were poured on the ground while moisture exchanges take hours or even days to take place between dry particles and the atmosphere [START_REF] Ravi | On the effect of moisture bonding forces in airdry soils on threshold friction velocity of wind erosion[END_REF].

In the following, the results are presented with error bars that take into account the average gaps that were defined above.

Emission coefficients

For the sake of brevity, we focus the analysis on the parameter with the best repeatability: the emission coefficient φ.

Figure 8 shows its evolution as a function of the vehicle speed and of the particle concentration for the Clio III tests.

Overall, it appears that an increase in speed leads to an increase in φ. For the same concentration of particles on the ground, doubling the speed of the Clio III (from 30 to 60 km/h) leads to a multiplication of the emission coefficient by a factor ranging from 1.5 (for green clay at 400 g.m -2 , Figure 8 Figure 9-a shows that the emission coefficient φ is particularly correlated with the percentage of particles smaller than 2 µm (R²=0.77) and with the vehicle speed (R²=0.60). The variables Fx and My are highly correlated with each other (R²=0.78) since they represent the same physical phenomenon. The correlation is not 100% because the Fx measurement is noisy due to slip-free rolling conditions. According to the Principal Component Analysis theory, the F1 and F2 axes allow to define the plane that maximizes the dispersion of the experimental data in order to visualize the cloud of results as well as possible. The circle of correlations is such that the abscissa axis F1 is highly correlated to Fx and My (correlations of 94% and 91% respectively). The F2 axis is highly correlated to φ (R²=0.93). Thus, the analysis of the observations on these two axes (Figure 9-b) does not allow to conclude about the effect of the parameters Fx and My on the coefficient φ for concentrations of 200 g/m² and 400 g/m². Indeed, the clouds of the blue and red symbols are too scattered. For the highest concentration (600 g/m², black symbols in Figure 9-b), a decreasing trend of φ appears when Fx and My increase. This is probably a phenomenon of aggregation of the particles caused by the tire. Indeed, the tire compacts the bed of particles as it rolls over it, forming aggregates that are then torn off by shear force (Le [START_REF] Vern | Experimental assessment of dust emissions on compacted soils degraded by traffic[END_REF]. The greater the shear forces, the more numerous these aggregates are. Many of them have sizes greater than 10 µm and are therefore not measured by the particle counter (hence the decrease of the parameter φ which only takes into account PM10). This mechanism seems to appear when the quantity of particles on the ground is large and is particularly marked for coarser particles (silts from Strasbourg and Marche les Dames). This phenomenon of aggregation has been previously highlighted for soil degradation by vehicles (Le [START_REF] Vern | Experimental assessment of dust emissions on compacted soils degraded by traffic[END_REF].

Figure 10 shows the emission factors as a function of vehicle speed and particle concentration for the Ford Ranger 4x4 tests. By analyzing Figures 8 and 10, it can be seen that the orders of magnitude of the emissions are lower for the tests with the 4x4 compared to those carried out with the Clio. Since the 4x4 is more massive, one could theoretically have expected a higher generation of particles. This is not the case because semi-rigid mud flaps were present behind the tires of the 4x4 (visible in Figure 4-d). They may prevent dust resuspension. It can be seen that the average difference between the emissions of these two vehicles is all the greater the lower the clay content of the particles. The effect of mud flaps seems to be more marked for coarse particles than for very fine particles.

For confirmation, it would be necessary to carry out the tests with the same vehicle with and without mud flaps.

Figure 11: Emission coefficients: gap between Clio and 4x4 tests calculated using equation (1)

Virtual Conference "Transport and Air Pollution" Graz, 2021

In general, Figures 8 and10 show different dust emissions depending on the type of particle. However, the particles used in the study have almost the same percentages of particles below 75 µm (between 95% and 100%). It is therefore evident that this parameter, although often used in the literature, is not sufficient to characterize the dust emission related to vehicle traffic. Figures 9 and 11 suggest that the percentage of particles below 2 µm would be a more relevant parameter to quantify the lift of particles.

Conclusions

In this study, the dust emissions linked to the traffic of a Renault Clio III and a Ford Ranger 4x4 were studied. Four types of particles (green clay, silt from Val d'Europe, silt from Strasbourg and silt from Marche les Dames) were poured on a test track at different mass per unit area (200 g/m², 400 g/m² and 600 g/m²). Vehicles were driven over the particle beds at different speeds (30, 45 and 60 km/h) and the concentrations of suspended dust were measured directly behind the tire of the vehicle. Weather conditions were measured on the roadside.

The results of the study lead to the following conclusions:

-To quantify the lift of particles, it is not relevant to consider only their silt content (% < 75 µm). The percentage of particles < 2 µm seems to be a more appropriate parameter.

-Although it is often the sole data considered in the literature, the weight of the vehicle is not a sufficient criterion to characterize its dust emission potential. It appears from this study that the impact of accessories such as mud flaps behind the tires could be significant. Vehicle aerodynamics is also a relevant criterion that needs to be taken into account.

-The effect of vehicle speed on dust emission is not a linear process. Indeed, doubling the speed can lead to a multiplication of the emission coefficient by a factor of 5.7. The effect of speed depends on the type of vehicle and the type of particles.

-The results suggest that a phenomenon of particle aggregation by the tire may appear. It seems to be all the more marked as the concentration of particles on the ground is important. This phenomenon would be characterized by the suspension of coarser particles (larger than 10 µm). The measurement of the particle size distribution of all suspended aerosols would be necessary to validate this hypothesis.

Figure 1 :

 1 Figure 1: Dimensions of the two vehicles

Figure 2 :

 2 Figure 2: Particle size distributions and geotechnical properties of the soils

Figure 3 :

 3 Figure 3: Experimental layout of the tests on the track (diagram not to scale)

Figure 4 :

 4 Figure 4: Vehicles used for the experiments: a) Renault Clio III and b) 4x4 Ford Ranger; On-board measurements with c) installation of the particle counter in the 4x4 and d) suction of particles directly behind the tire.

Figure 5

 5 Figure 5: a) Evolution, for one of the tests, of the particle concentrations measured behind the tire as a function of time; b) Highlighting, for the PM10 curve, of the parameters considered in the study

Figure 6 -

 6 Figure 6-a shows an example of the evolution over time of the vehicle speed, Fx and My for one of the tests (Clio driving at 45 km/h over 200g/m 2 of Marche les Dames silt particles). The figure shows the total duration of a test characterized by an evolution of the vehicle speed in three phases: acceleration, steady speed and then deceleration. During the acceleration and deceleration phases, the parameters Fx and My undergo significant variations due to gear changes and braking. For the analysis, the average values of these parameters (Fxmoy and Mymoy) are taken into account during the

Figure 6 :

 6 Figure 6: (a) Time evolution, for one of the tests, of the vehicle speed (green curve), the longitudinal force (blue curve) and the vertical moment (red curve) applied to the vehicle wheel. Curves (b) and (c) show respectively a zoom on the evolutions of the longitudinal force and the vertical moment during the passage of the vehicle on the particles.

  -a) to 5.7 (for Strasbourg silt at 200 g.m -2 , Figure8-c).

Figure 8 :

 8 Figure 8: Emission coefficients for the Clio tests with particles of (a) green clay, (b) silt from Val d'Europe, (c) silt from Strasbourg and (d) silt from Marche les Dames For the same speed of the vehicle, an increase in the concentration of particles on the ground can lead to a decrease in the emission coefficient. Indeed, it is observed for the tests at 60 km/h on the Val d'Europe silt (Figure 8-b), for the tests at 30 and 60 km/h on the Strasbourg silt (Figure 8-c) and for the tests at 45 and 60 km/h on the Marche les Dames silt (Figure 8-d).It cannot be explained by the weather conditions as they do not affect the measurements as indicated in the previous section. To get a better understanding of the processes involved, a Principal Component Analysis (PCA) integrating the longitudinal force Fx and the vertical moment My is performed (Figure9).

Figure 9 :

 9 Figure 9: Principal Component Analysis of the Clio tests. a) Circle of correlations for the variables and b) visualization of the tests in the correlation space. Each test is designated by: Type of particles-vehicle speed-concentration

Figure 10 :

 10 Figure 10: Emission coefficients for the 4x4 tests with particles of (a) green clay, (b) silt from Val d'Europe, (c) silt from Strasbourg and (d) silt from Marche les Dames In order to quantify the difference in dust emissions between the two vehicles, Figure 11 shows the comparison of the coefficient φ corresponding to the tests with the Clio and those with the 4x4. The gaps are calculated using equation (1).It can be seen that the average difference between the emissions of these two vehicles is all the greater the lower the clay content of the particles. The effect of mud flaps seems to be more marked for coarse particles than for very fine particles.For confirmation, it would be necessary to carry out the tests with the same vehicle with and without mud flaps.

Table 1 :

 1 Configurations of the tests

	Vehicle	Particles*	Speed	Concentration	Vehicle	Particles*	Speed	Concentration
			30 km/h	400 g/m²			30 km/h	400 g/m²
				200 g/m²			45 km/h	400 g/m²
		GC	60 km/h	400 g/m²		GC		200 g/m²
				600 g/m²			60 km/h	400 g/m²
			30 km/h	400 g/m²				600 g/m²
				200 g/m²			30 km/h	400 g/m²
		SVE	60 km/h	400 g/m²				200 g/m²
	Clio III	SS	30 km/h 45 km/h	600 g/m² 200 g/m² 400 g/m² 200 g/m² 400 g/m²	4x4 Ford Ranger	SVE SS	60 km/h 30 km/h 45 km/h	400 g/m² 600 g/m² 400 g/m² 400 g/m² 200 g/m²
				200 g/m²			60 km/h	400 g/m²
			60 km/h	400 g/m²				600 g/m²
				600 g/m²			30 km/h	400 g/m²
			30 km/h	200 g/m² 400 g/m²		SMD	60 km/h	400 g/m² 600 g/m²
			45 km/h	200 g/m²			* GC: Green Clay
		SMD		400 g/m²		SVE: Silt from Val d'Europe
				200 g/m²		SS: Silt from Strasbourg
			60 km/h	400 g/m²		SMD: Silt from Marche les Dames
				600 g/m²
	2.4 Data processing
	2.4.1 Analysis of particle counter measurements

Acknowledgement

The authors would like to express their gratitude to the Fédération Nationale des Travaux Publics (grant number RP2_E18101) and the Région Pays de la Loire (grant number GHPAI3) for their financial support. Special thanks to Ouardia Sediki, Erwann Rayssac, Sébastien Buisson and Daniel Bodenes for their help during the experiments.


Antoine Clément

Didier Gourc
email: didier.gourc@mines-albi.fr

Daouda Kamissoko
email: daouda.kamissoko@mines-albi.fr

François Marmier
email: marmier@unistra.fr

Antoine Clement
email: antoine.clement@mines-albi.fr

Francois Marmier

Didier

François Marmier

An original approach to assess the robustness of road freight transport plannings based on a dynamic risk identification

Keywords: risk identification, robustness, decision making, danger, daily schedule, road freight transport

Introduction and motivation

Many organisational and planning works have been done under implicit assumptions such as the stability of the context and the availability of all information at the time of planning. They consider that the execution will proceed according to what has been planned. This hypothesis is far from being true in the real world. Particularly, road freight transport (RFT) remains uncertain and fraught in the execution of the deliveries as unexpected events can arise all along the tour: activities can take longer to execute than planned caused for instance by traffic jam which can perturb driving activities, vehicles break down, drivers unavailability [START_REF] Ghezail | Analysis of robustness in proactive scheduling: a graphical approach[END_REF][START_REF] Goren | Robustness and stability measures for scheduling: single-machine environment[END_REF][START_REF] Hu | Real-time traffic jams prediction inspired by Biham, Middleton and Levine (BML) model[END_REF].

As a consequence, a schedule perceived as good assessed without considering potential disturbances can become, during its execution, worse than expected or planned. However, the preliminary evaluation of the quality of the plan is a complex activity. The stakes and the objectives can be various and sometimes antagonistic [START_REF] Woodruff | Ecosystem services in urban planning: comparative paradigms and guidelines for high quality plans[END_REF][START_REF] Hersperger | Evaluating outcomes in planning: indicators and reference values for Swiss landscapes[END_REF][START_REF] Avril | Automation and complacency: insights from a planning task in the transportation domain[END_REF]. The criteria for measuring the quality of a planning are different according to experience and knowledge brought by the decision maker: limitation of the amplitude of the rounds, balance of the working time between the drivers, CO 2 emission, cost of the schedule, economic profitability, health and safety of driver [START_REF] Govaere | Smart planningapproaching the characteristics of a valid, balanced transport round[END_REF].

In most works, authors do not necessarily take into account the impact of process disturbances and schedules often lack of robustness face to hazards [START_REF] Mingers | Problem structuring methods in action[END_REF]. In recent years the number of work on robustness has increased significantly. This term is used in more and more field (Clément et al., 2018a) and especially in the field of planning [START_REF] Davenport | A Survey of Techniques for Scheduling with Uncertainty[END_REF][START_REF] Fischer | Robust planning and disruption management in roll-on roll-off liner shipping[END_REF][START_REF] Thaman | Green cloud environment by using robust planning algorithm[END_REF]. [START_REF] Clément | Robustesse, résilience: une brève synthèse des d éfinitions au travers d'une analyse structurée de la littérature[END_REF] proposed a comparison of the definitions of robustness and resilience through a structured analysis of the literature. Robustness describes generally the ability of a system to perform well under different conditions or scenarios [START_REF] Rebekka | Proactive-Reactive, Robust Scheduling and Capacity Planning of Deconstruction Projects under Uncertainty[END_REF]. It can be also defined as the (desired) insensibility of a system under different uncertain or non-anticipated events. A schedule is qualified as robust if its performance varies little under the influence of unexpected events.

Several authors [START_REF] Davenport | A Survey of Techniques for Scheduling with Uncertainty[END_REF][START_REF] Herroelen | Project scheduling under uncertainty: survey and research potentials[END_REF] divide schedule robustness into two classes: solution robustness and quality robustness. Solution robustness is defined as the insensitivity of the schedule to perturbations, and quality robustness aims to evaluate the insensitivity of the schedule performance. As an example of quality robustness in the project domain, [START_REF] Hazır | Robust scheduling and robustness measures for the discrete time/cost trade-off problem[END_REF] define project robustness as the insensitivity of activity start times of a schedule to variations of input data. They propose to use slack-based measures to assess project schedule robustness. In their works, [START_REF] Demeulemeester | Robust project scheduling[END_REF] propose to measure the robustness schedule through the expected makespan and the service level (the project completion probability).

For robustness evaluation, several performance criteria can be used to compare alternative solutions. Face to the diversity of domains concerned by robustness scheduling, authors have proposed several examples of operational criteria to assess the robustness of a schedule according to multiple domains: worldwide airport network [START_REF] Xiaoqian | Robustness analysis metrics for worldwide airport network: a comprehensive study[END_REF], aging domain: magnitude of deviation from the original state and time to peak value [START_REF] Ukraintseva | Resilience versus robustness in aging[END_REF], machine scheduling [START_REF] Ghezail | Analysis of robustness in proactive scheduling: a graphical approach[END_REF][START_REF] Gören | Robustness and Stability Measures for Scheduling Policies in a Single Machine Environment[END_REF], project management [START_REF] Hazır | Robust scheduling and robustness measures for the discrete time/cost trade-off problem[END_REF].

In the same perspective, Rebekka (2017) listed a lot of aggregated criteria to evaluate the robustness such as: mean, (empirical) variance or standard deviation, relative regret values or decision rules (maximin-rule, maximax-rule, minmax-rule) when sequential decisions have to be performed face to several scenarios [START_REF] Rebekka | Proactive-Reactive, Robust Scheduling and Capacity Planning of Deconstruction Projects under Uncertainty[END_REF]. The indicators proposed by [START_REF] Schatteman | Methodology for integrated risk management and proactive scheduling of construction projects[END_REF] focus on the difference between the baseline schedule and the realised schedule. It can also be proposed to measure the weighted sum of the differences between their respective activities' start times or the number of activities that are delayed by the occurrence of unexpected events during the plan execution. These metrics concern an a posteriori evaluation, which is done after the execution of the schedule.

As in the work of [START_REF] Schatteman | Methodology for integrated risk management and proactive scheduling of construction projects[END_REF], many other contributions are interested in the measure of a posteriori robustness, after the tour is finished or at least after the occurrence of the disturbance. In this context, some works focus on reactive scheduling, which focus on the generation of repairing strategies after a baseline schedule has become unfeasible [START_REF] Rebekka | Proactive-Reactive, Robust Scheduling and Capacity Planning of Deconstruction Projects under Uncertainty[END_REF][START_REF] Herroelen | Project scheduling under uncertainty: survey and research potentials[END_REF]. Reactive scheduling' approaches address modifying, repairing, improving of the baseline schedule after unexpected events occurred. The dynamic context of schedule can induce several modifications that could have negative impacts on the global performance of a company on quantitative dimensions (return on investment: ROI) and also on managerial aspects. As a consequence, regular modifications of the baseline can be disturbing for team members and drivers.

Transport systems are constantly subjected to disturbances [START_REF] Andersson | A method for measuring and valuing transport time variability in logistics and cost benefit analysis[END_REF]) which can have a negative impact on the different activities of the transport system. As identified in several papers [START_REF] Andersson | A method for measuring and valuing transport time variability in logistics and cost benefit analysis[END_REF][START_REF] Mattsson | Vulnerability and resilience of transport systemsa discussion of recent research[END_REF][START_REF] Rodrigue | The Geography of Transport Systems[END_REF][START_REF] Rodrigue | Transportation and disasters[END_REF][START_REF] Leobons | Assessing urban transportation systems resilience: a proposal of indicators[END_REF], disruptions in the transport system can be various. [START_REF] Mattsson | Vulnerability and resilience of transport systemsa discussion of recent research[END_REF] propose a useful distinctions between internal and external cause of disruption and between accidental events and intentional interferences. Table 1 lists some examples of causes of disruptions according to several authors [START_REF] Andersson | A method for measuring and valuing transport time variability in logistics and cost benefit analysis[END_REF][START_REF] Mattsson | Vulnerability and resilience of transport systemsa discussion of recent research[END_REF][START_REF] Rodrigue | The Geography of Transport Systems[END_REF][START_REF] Rodrigue | Transportation and disasters[END_REF][START_REF] Leobons | Assessing urban transportation systems resilience: a proposal of indicators[END_REF] implemented in the categorisation proposed by [START_REF] Mattsson | Vulnerability and resilience of transport systemsa discussion of recent research[END_REF]. The risk of disturbances in the road freight transport can be very variable in terms of frequency and magnitude. [START_REF] Andersson | A method for measuring and valuing transport time variability in logistics and cost benefit analysis[END_REF] propose a classification of disturbances composed of four main types: system killers, catastrophic events, expected risks and contingencies. The two first types system killers and catastrophic events refer to disturbances with large magnitude and for which there is limited capacity to manage. The expected risks induce small consequences on the transport system but are relativity common, so the planners generally anticipate their occurrence when they design the plan. The contingencies are less frequent and the consequences can be more or less important. For these disturbances, there are no plans but it is often possible to manage these disturbances. We consider the contingencies can be classified in two categories: risk that can be identified and listed and those who are totally unpredictable for which occurrence mechanisms are not known, 'black swans' in the word of [START_REF] Taleb | The Black Swan: The Impact of the Highly Improbable[END_REF]. For those who are identifiable and due to the relative high level of consequences of the disturbances of contingencies type we consider that it is necessary to develop mechanisms for anticipating and assessing those impacts on transport system and particularly on plans produced. The aim is to give planners information on the ability of the plan produced to provide correct transport services to users. The problem addressed is to aid the planners to choose a schedule, among all those allowing the delivery of goods to clients that satisfies as well as possible the objectives of the company in terms of economic, environmental and health and safety indicators while maintaining a good probability to respect the customers' requirements despite possible disturbances. As we saw above, several works in the literature review address reactive scheduling problem.

In this paper, we propose an alternative way, which is based on proactive scheduling approach. Our objective is mainly to design schedules that are able to maintain good performances, as expected by the planner and the company manager, even if one or more disturbances occurs during the execution. To achieve this goal, we propose a methodology to generate several schedules with their assessment according to a list of predetermined indicators, including an indicator of robustness.

We propose a preliminary list of the usual hazards in the field of road freight transport. This list is organised by category according to the origin of the dangers:

• Resources, including: a humans, as for example drivers, warehouse clerk, customer site manager: unavailability, absence, delay b means, as for example vehicle, road infrastructure: breakdown, unavailability (the previous round is not finished) c additional equipment's, as for example loading equipment, parking zone: unavailability, breakdown.

• Infrastructures, as road infrastructure: bursting point, faulty.

• Weather conditions: heavy rainfall, snowy episode, strong winds, snow-covered, flooding, ... which can lead to risks of saturation of roads or closing of roads.

For this, after a preliminary dangers identification, an automatised process based on the planned schedule is proposed to identify and characterise the risks that can arise during the execution of the tour. Then, the robustness evaluation is performed by a risk simulation process which consists in applying the risk scenarios to the initial schedule in order to analyse the whole consequences of risk occurrence. For each scenario identified, several KPI's are evaluated. Finally, these results are proposed to the planners who are now able to choose the best schedule thanks to the explicit knowledge of the robustness of each plan. This article deals with a vehicle routing problem in road freight transport, in the literature several indicators are used to characterise a schedule. [START_REF] Patier | Une méthode d'enquête du transport de marchandises en ville pour un diagnostic en politiques urbaines[END_REF] and [START_REF] Meier | Key performance indicators for assessing the planning and delivery of industrial services[END_REF] offer a list of indicators that focus on economic (cost, duration, number of km, …) and ecological (CO 2 , energy consumption, ...) aspects of planning. The optimisation models used for vehicle routing problems often aim to minimise one of these indicators such as delivery cost, comprising the transportation cost, total duration of the rounds or carbon footprint [START_REF] Vidal | A concise guide to existing and emerging vehicle routing problem variants[END_REF][START_REF] Liu | Green vehicle routing optimization based on carbon emission and multiobjective hybrid quantum immune algorithm[END_REF][START_REF] Konstantakopoulos | Vehicle routing problem and related algorithms for logistics distribution: a literature review and classification[END_REF].

Unlike optimisation algorithms, our aim is not to produce the best schedule but to provide complementary indicators to help the planner to select a schedule compliant with the planner's daily objectives. Our work focuses on the robustness evaluation of the solutions. In addition to classical indicators such as the cost or the duration of a schedule, our model provides robustness indicators measuring the possible influence on the delivery time of disturbances that could occur during the delivery process.

This paper is organised as follows. Section 2 describes our general approach to generate plan's tour and to assess the robustness. Section 3 focuses on the robustness evaluating step of our general approach and describes the model proposed to assess the robustness of a daily schedule. In Section 4, we illustrate the proposed approach and the developed models with a case study and discuss the results. Finally, Section 5 provides a conclusion and some suggestions for future work.

Approach overview

This holistic approach aims to help planners choose the best plan based on the company's goals. The overall process of the proposed approach is presented in Figure 1. It is composed by two steps briefly detailed in this section:

• step identifying and modelling dangers

• step evaluating daily schedules robustness.

Step identifying and modelling dangers

This step is carried by human expertise. It consists of manually identifying the various dangers that may be present and modelling them in a danger portfolios. A portfolio corresponds to a structured list of hazards to be described on a model of danger dedicated. This model, as structured description of a hazard, is part of the contributions of this paper which is presented in Subsection 3.1. It makes possible to identify risks and evaluate their impacts on road freight transport plans. In addition, this step is a data collection step, the frequency of realisation is low compared to the realisation of a daily schedule. The off-line and on-line activities are asynchronous, the off-line activity is performed once and then updates are performed, while on-line activity is daily.

Step evaluating daily schedules robustness

When selecting a schedule, the planner seeks to compare a number of schedules (ds) using different indicators (KP I). The indicators are mainly economic or environmental. The objective of this step is to provide a schedules' robustness indicator (KP R) to aid the planner to select a daily schedule. This step is done in three parts. First, there is the identification of risks. From the danger portfolio and the different schedules selected, this step generates the risks that will impact the schedules. The second part simulates risk scenario by simulating all possible risk combinations. The last part corresponds to the implementation of the robustness KPI.

Figure 1 Proposal of approach to assess the robustness of planning A specific and original simulation approach based on multiple scenario simulator permits to assess the impact of potential risks on the characteristics of the tour. Our contribution on robustness indicator, the elementary characteristics used and the formulation of the aggregated robustness indicator, is detailed in Subsection 3.2.

Assessing the robustness of daily schedule with danger

First, in Subsection 3.1, we develop our model of danger dedicated to identifying risks and evaluating risk impacts on road freight transport plans. The proposed model underlies the danger modelling devoted to the activity 'identifying and modelling danger' as presented in Figure 1. Then, in Subsection 3.2, we detailed the evaluation step of the approach, presented in Figure 1, with the robustness KPI proposed.

Modelling of the concept of danger

Before presenting in detail the danger model, we define the basics of the planning model in the road freight transport and the activities that compose it.

Model of planning in road freight transport

To set up the danger model, the planning model studied is essential. A schedule corresponds to a set of tours carried out by resources (vehicle and driver). A couple, vehicle-driver, will realised a set of activities to satisfy all customer requests. These activities can be classified according to four types:

• Moving activity that represents the driving phase between two sites/places.

• Activity on site (loading/unloading) that illustrates the manipulation of goods.

• Starting activity and ending activity that takes into account the preparation of the vehicle before starting the tour and for closing the tour.

• Waiting activity that materialises a buffer of time when a driver arrives at the deliver site before the required hour. This buffer is necessary because sometimes clients do not accept to get the goods before the hour of the appointment. In these cases, the driver has to wait for the hour of appointment.

Each activity is characterised by a start time, a duration, a location and a type presented above. The planning model being described, it is possible to recommend the danger model

The model of danger in road freight transport

Based on the definitions identified in the literature review and inspired by the work of [START_REF] Desroches | La gestion des risques: principes et pratiques[END_REF], we define the danger (see Figure 2) in road freight transport planning' system as any source of potential damage, harm or adverse effects on an element, which can be something or someone, of the system under study. The exposure of an element to a danger combined with a trigger induces a risk, which is characterised by a probability of occurrence and potential effects on the system or elements of the system. Risk concept is a central point of our approach for assessing the robustness indicator, detailed risk definition is given in [START_REF] Marmier | A decision-making tool for assess feasibility of risky NPD projects under the constraint of limited resources[END_REF], [START_REF] Nguyen | A decision-making tool to maximize chances of meeting project commitments[END_REF] and Marmier et al. (2014b).

Figure 2 The risk design scenario, inspired from [START_REF] Desroches | Le management des risques par l'analyse globale des risques[END_REF][START_REF] Desroches | La gestion des risques: principes et pratiques[END_REF] As presented in Figure 2, a dangerous situation da is generated by two concepts:

• danger, corresponding to the overall description of a hazard

• context, corresponding to the environment description which is characterised by a danger zone (dz) and a time window (tw).

A danger zone (dz) defines "any space within and/or around machinery in which a person can be exposed to a hazard". 1 We propose to specify the danger zone with a Geographic Information System (GIS) by zoning the area where the danger is identified.

A time window (tw) represents the period where the danger could be present and where elements or systems staying in the danger zone could be impacted by a risk induced by this danger. The time window can be expressed by temporal expressions with days and hours. For example, every Monday between 7h30 and 8h30. As proposed by [START_REF] Gani | Formal modeling and analysis of home care plans[END_REF] and [START_REF] Bastide | Plas'O'Soins: a software platform for modeling, planning and monitoring homecare activities[END_REF], a user centred specification language tailored to express RFT plans using high level abstractions was implemented.

A risk, characterised by an event and its consequences on the RFT system, is modelled by three concepts: a dangerous situation (da), a trigger (tg) and the exposed system (es).

The trigger (tg) lists the triggering factors that could initiate the transformation of a danger to a risk. The exposed system (es) able to list the elements of the system, something or someone that may be concerned by risks induced by this danger. In the context of tour plan, this attribute allows to specify which type of activity of a tour may be impacted by this risk. For example, the risk of traffic jam may, induced by the danger 'intensification of road traffic', occurs during a drive activity between two sites and can impact the same driving activity. Occurring of risk can be observed during the execution of a task (for example, during a driving activity) and the impacts could modify the execution of the same or another task. Modifications could concern, for example, the delay of the activity.

The combination of three concepts (a dangerous situation da, a trigger (tg) and the exposed system (es)) generate new risk attributes such as: probability estimator and impact estimator. Probability estimator (pe) is an expression, or a function, that defines the probability value of the risk induced by this danger for a specific situation. So, this expression is based on the elements of the danger's context in order to generate the specific probability value of the risk. For example, on a road connection, the probability to meet a traffic jam depends on the day (holidays period versus work period, Monday versus Tuesday, ...) and on the hour (hour in the morning when workers are going to their office versus middle of the morning, ...).

Impact estimator (ie) is an expression dedicated to specify the level of impacts of the risk induced by this danger for a specific situation. As the probability estimator, the impact estimator is based on context' elements. [START_REF] Fertier | A situation model to support collaboration and decision-making inside crisis cells, in real time[END_REF] indicate that a danger brings risks on each stake in its perimeter. Several expressions can be developed according to the diversity of impact' types: delay, cost, tiredness, safety, CO2 emissions, ... For the same example that above, the value of the impact 'delay' depends on the hour the vehicle cross the road connection.

It is important to note that a risk can modify a task of a tour, and potentially modify its attributes. The meta model, presented in Figure 3, gives a global view of all these concepts and their relationships. We focus our study on the dangers that are relied to the road freight planning system.

For this, we express the fact that the dangers we study involve at least one element of the road freight planning system.

In Figure 4, an illustrative example for danger modelling is proposed. It concerns the description of the danger 'traffic jam' which is related to a road connection between the road A15 and N184. The attributes are fulfilled and specify that this danger could occur each day of the working days (from Monday to Friday) specially on the periods 7h30-8h30 and 17h-18h30. The probability estimator (F Prob B A15-N184) is illustrated in Table 2. In each cell of this table (couple day-hour period), a level of probability for the risk 'traffic jam' is given according to a 4-level intensity scale (no risk, moderate, high, very high). These estimations are performed by planners with the help of drivers that are in charge of the deliveries in these zones. A similar table is proposed to specify the impact in delay. Finally, this danger impacts only the driving activity from one site to the next because it concerns moving activities (F move). Thus, for each driving activity crossing this geographical zone during one of the periods mentioned, an induced risk must be created and assigned to that driving activity with the specified characteristics. We explicit this risk instantiating mechanism in the next subsection.

Daily schedules robustness assessment

This section aims to present the approach proposed to assess robustness indicator of daily schedules selected by the planner. The process, used to realise the step 'evaluating delay schedules robustness' of the global approach, is composed of three stages.

Based on the dangers identified and modelled, the first stage consists in automatically identifying and generating risks that will disturb the execution of the daily schedules (Subsection 3.2.1). The second stage aims to simulate the whole scenarios of risks and to measure the impacts of the risks on the deliveries plan (Subsection 3.2.2). And then, in the third stage, the robustness indicators are calculated to help planners choosing the daily schedule to execute (Subsection 3.2.3).

Risk identification based on the dangers' definition

Based on the portfolio of dangers and the plan activities, which are part of the daily schedule definition, we propose an instantiating mechanism to create the tour' risks and to assign them to the inherent activities. In this work, we adopt the risk definition presented in [START_REF] Nguyen | A decision-making tool to maximize chances of meeting project commitments[END_REF]. Risk is defined as an event, which has occurrence characteristics (for example, the probability of occurrence) and consequence characteristics on the schedule objectives (for an example, the impacts if the event occurs). The increase of the duration of the task impacted is an illustration of a risk impact.

The instantiating mechanisms, including the identification of risks and then the creation of associated risks, are specified respectively in Algorithms 1 and 2. Algorithm 1 develops the mechanism enabling the identification of a risk. When an activity a is performed inside a context of danger (i.e., inside the danger zone, the period where the danger is present, ...) an associated risk must be created. So, this process able to identify a list ER of risks R i , (i = 0, ..., n), where n is the number of risks.

Algorithm 2 gives details of the risk creating process and information used to fulfil the risk attributes. A risk R i is characterised by several attributes, the two first able to define the activity where the risk can occur task source and the task that is impacted by the occurrence of the risk task impacted. The probability of the risk, designed by proba(R i ), is the probability that the event related to R i happens. The impact of the risk is measured on two dimensions, respectively cost CI(R i ) and duration DI(R i ).

These probabilities and impacts are also named initial probability and initial impact. Their valuation is obtained by the use of the estimators pe and ie that are modelled in the dedicated danger.

At the end of this stage, all dangers of the portfolio, identified during humane activity, has been analysed and the induced risks are assigned to activities of the daily schedules.

Algorithm 1 Identifying and creating risks associated to a daily schedule ds 1: for all da ∈ D do ◃ For all the dangers identified 2:

for all a ∈ ds do ◃ For all the activities in ds r.impact ← l.ie(a) ◃ Use of the impact estimator ie 8: end procedure

As an example, we illustrate in Figure 5 a projected schedule with estimated hours which is programmed for Monday. Based on the danger specified in Figure 4 and Table 2, the instantiating process generates a specific risk that is illustrated in Table 3. This risk relates to the task 'moving to site B' because this driving activity passes through the road link A15-N184 during a period of heavy traffic. The probability of occurrence of this risk is very high and, if it occurs, the consequences will be materialised by an increase of 25 minutes in the duration of the activity 'moving to site B'.

Simulating risk scenario in daily schedules

Nguyen et al. ( 2013) proposed the method ProRisk, supported by a software tool that assists in modelling and evaluating the impact of risks on project activities and project KPI. In this work, dedicated to a project context, the KPI's proposed concerns cost and duration of the activities. The authors define the concepts of risk scenario, treatment scenario and project scenario. This method has been applied in several domains for aiding decision makers dealing with uncertainty: satellites design projects (Marmier et al., 2014b), new product development projects [START_REF] Deniaud | A risk management approach for collaborative NPD project[END_REF][START_REF] Marmier | A risk oriented model to assess strategic decisions in new product development projects[END_REF][START_REF] Marmier | A decision-making tool for assess feasibility of risky NPD projects under the constraint of limited resources[END_REF], construction projects (Marmier et al., 2014a). ProRisk is now integral part of the platform RIOSUITE. 2 The ProRisk methodology aims to generate all the possible combinations of identified risks to assess the global impacts on the whole process. The assessment framework is based on the evaluation of risk scenario. A risk scenario ScR for a specific process corresponds to the combination of s, with s = 0, ..., n risks occurring during the daily schedule studied and n -s risks no occurring. It exists several possible combinations. For example, a process with k risks leads to 2 k risk scenarios. ScR s , (s = 1, ..., 2 n ) is one possible implementation with k risks (0 ≤ k ≤ n). We consider a particular risk scenario noted ∅. It corresponds to the situation where there is no risk occurring, all the hazards have been avoided. The total number of risk scenarios, presenting k risks is equal to n!/k(n-k)!.

We have chosen to implement and upgrade this framework in the domain of RFT robustness assessment. So, we extended it to make possible to consider the assessment of daily schedules. For this, a first stage simulates risk impacts on a tour level t, i.e., a process, and then, an aggregated phase calculates indicators on the daily schedule level ds. A daily schedule ds is composed of r tours.

A risk can have an impact on the strong constraints and thus make a scenario become not feasible but it also simply affect the indicators without modifying its feasibility. Based on these appraisals, we implement an analysis process allowing to generate all possible scenarios and calculate the indicators characterising each scenario. The aim is, first, to determine the probability of occurrence of risk scenario s in the tour j noted proba j (ScR s ) = p s j . This probability of the scenario depends on the combination of risks in this scenario. The probability of this risk scenario represents the probability that the events related to this risk scenario occur and other risks do not occur, the expression is developed equation (1).

proba j (ScR s ) = i=1 { proba(R i ), if R i ∈ ScR s 1 -proba(R i ), if R i / ∈ ScR s (1)
Beside the occurrence probability of a scenario, we characterise each scenario by other indicators. Very typically, the time and cost indicators are mobilised to effect this characterisation. Thus, for each identified scenario, its duration and its cost are calculated. The expression of the cost calculation for a tour level is shown in equation ( 2). The cost of the project scenario j considered under the risk scenario ScR s is named CI j (ScR s ) = CI s j . It includes the cost of tasks C(T a ) which constitute the initial planning process, impacts of occurrence risks, i.e., risks present in ScR s , on the process tasks and the global cost GC initial (R s ) of occurring risks. GC initial (R s ) is the aggregation of risk impacts on the cost criterion. This includes a fixed portion of the total cost (materials, tools, parts, etc.) and indirect costs depending on the duration of action of each possible impact of risk.

CI j (ScR s ) = t ∑ i=1 CI(T i ) + ∑ Ri∈ScRs GC initial (R i ) (2)
Similar functions have been developed to calculate the values of the other indicators, as those concerning duration characteristics. Calculation of the tour's duration (DI j (ScR s ) = DI s j ) characteristics compels to take into account the graph structure of activities and the PERT algorithm.

It is important to note that 'wait' activities play the role of buffer in planning. That is, if a risk increases the duration of an activity, and the delivery time can not be changed then if there is an activity 'wait' the delay generated by the risk will be absorbed either totally by reducing this activity (if the delay is less than the duration of the activity Wait) or partially by limiting the delay. The other wait activities of the process will decrease the delay if there are any left.

Calculating robustness KPI

In the RFT domain, meeting delivery deadlines is considered as a crucial issue for customer satisfaction. Therefore, we focus our robustness KPI on measuring the ability to deliver goods in accordance with customer requirements. Characterising the robustness of a daily schedule through a single number may be quite restrictive [START_REF] Ghezail | Analysis of robustness in proactive scheduling: a graphical approach[END_REF], therefore we choose to consider several indicators to take into account all the dimensions of the robustness.

Based on the risk scenario assessments, produced by the previous stage, we first characterise robustness dimensions at a tour level. In the second stage, we propose robustness KPI's at a daily schedule level.

At a tour level, we propose to measure three characteristics:

• T M axDelay t : The maximum delay of the deliveries of the tour t that need to add for comply with the client's requirements [equation ( 3)]

• T M inSat t (x): The minimum number of deliveries of the tour t that comply with the client's requirements for all risk scenarios with a margin of x minutes [equation ( 4)].

• T P robRespect t (x): Probability of a tour to meet all customer requirements in terms of delivery times with a margin of x minutes [equation ( 5)]. [START_REF] Clément | Premières pistes pour évaluer la robustesse, aux risques, de plannings de tournées de transport routier de marchandises[END_REF]Clément et al. ( , 2018a) ) proposed a robustness indicator based on the calculation of a global probability for a tour to be compliant with all the customer requirements.

In this work, we propose a new probability indicator introducing acceptable lateness x for the client in the delivery activity. Thanks to the two measures, presented above (T M axDelay t , T M inSat t ), and the knowledge of risk probabilities, we construct a KPI measuring the probability of meeting customer requirements in terms of delivery times with a margin of x minutes (T P robRespect t (x)). T N umDel t corresponds to the number of delivery present in the tour t. T P robRespect t (x) is the robustness indicator, T M inSat t (x) and T M axDelay t are actionable data for the robustness indicator. The activable data are indicators which for us vary according to the delay on a delivery accepted. They are intended to allow the planner to make his schedule more robust to satisfy his customers.

T M axDelay

t = max s⊂1..2 n [delay(ScR s )] (3)
T M inSat t (x) = min s⊂1..2 n N umberOf DeliverySatisf ied(ScR s ) T N umDel t (4) T P robRespect t (x) = n ∑ s=1 proba t (ScR s ) * { 1, if delay(ScR s ) ≤ x 0, else (5)
with 2 n the number of risk scenarios, and proba t (ScR s ) the probability of the risk scenario s of the tour t. At a daily schedule, similar measures are proposed:

• SM axDelay ds : The maximum delay of the deliveries of the daily schedule ds that need to add for comply with the client's requirements [equation ( 6)],

• SM inSat ds (x): The minimum number of deliveries of the daily schedule ds that comply with the client's requirements [equation ( 7)].

• SP robRespect ds (x): The probability of a daily schedule to meet all customer requirements in terms of delivery times with a margin of x minutes [equation ( 8)].

SP robRespect ds (x) is the robustness indicator, SM inSat ds (x) and SM axDelay ds are actionable data for the robustness indicator at daily schedule level.

SM axDelay

ds = max t⊂DS T M axDelay t (6) SM inSat ds (x) = ∑ t⊂DS T M inSat t (x) * T N umDel t ∑ t⊂DS T N umDel t (7) SP robRespect ds (x) = ∏ t⊂DS T P robRespect t (x) (8)
The use of the robustness indicator and the two actionable data are described during the computational study. These three elements are intended to allow the planner to make a compromise between the various solutions that are proposed. The validation of our model was carried out by a panel of planners during one week of planification. The schedules produced by the planners have been evaluated with the robustness indicators. At the same time the system proposes others schedules qualified by the robustness indicators we proposed. This experiment has allowed planners to validate the pertinence of the indicators. On this basis, they improve their own schedules. In the next section, we pursue the demonstration with a simplified version of a daily schedule of this experiment.

Computational study

In this section, we apply the proposed framework to a real-world case. Then, we present the experimental results and discuss the interest of our approach, its limits and the future developments.

Data

The use case presented corresponds to the half-day planning of a real company. All data have been anonymised for reasons of confidentiality. The planner must plan 25 orders, and own 15 vehicles and 15 drivers. An order is described by the site where it must be delivered, the quantity of pallet to be delivered as well as the delivery time. The delivery time is a fixed hour. The delivery points are presented on the map Figure 6. Other attributes describing the site or the order are used to calculate financial, economic and health and safety indicators. A vehicle is described by its type of energy, its pallet capacity (4, 6, 8, 10 pallets), its CO 2 emission... Drivers are described for example by their type of driving license, the number of hours worked... In the identification step, the experts identified three hazards described in Table 6. Road 1 is the axis between site 1 and site 6. Route 10 is the axis allowing to leave the site 10 caused by a one-way street. Period in the journey are identified to distinguish specific values of probabilities and impacts of the potential risks according the phase of the day. For example, the probability to have a high circulation on road 1 is more important between 5h and 10h (40%) than between 0h and 5h (5%). In a similar manner, the impact of this perturbation is more important between 10h and 16h (+15 minutes) than between 21h and 24h (+5 minutes). The detailed values are presented in Table 7.

In order to illustrate our proposition, risks used in this use case are independent. This means that the presence of one risk on a schedule does not affect the probability or impact of others risks.

Results and discussion

Once the data set is complete, for this use case, 56 schedules are produced by an external planning module. This module generates solutions respecting a list of constraints imposed by the planner such as for example the respect of the delivery time or the use of specific vehicles (vehicle with tailgate, electric vehicle, ...). They are labelled ds 1 to ds 56 . These schedules are then evaluated according the three indicators financial, environment and H&S. The results are presented in Figure 7. Each bullet corresponds to a schedule. A first comparison is made by the planner to select a smaller number of schedules. It can exclude schedules that do not meet his financial goals using a threshold. In this example, the planner fixed the financial threshold at e4,000. In the same way, he put a threshold on the indicators environment and H&S so as to preserve only the schedule which seems to him to satisfy its objectives. The environment indicator is between 20,500 and 21,700 gram of carbon dioxide and for the health and safety indicator it is between 100 and 135 for this example.

After this analysis only five daily schedules are kept for the study of robustness (ds 27 , ds 32 , ds 34 , ds 46 , ds 48 ). The evaluation of these schedules is presented in Table 8.

Subsequently, the robustness indicators will be calculated on the different schedules selected. Tables 9 and 10 correspond to the details of the calculations carried out for the three robustness indicators on the whole tour of the planning ds27 and by aggregation of the schedule ds27. Table 9 corresponds to the robustness value for a delay accepted of 0 minute (x = 0) and Table 10 corresponds to the robustness value for a delay accepted of 10 minutes (x = 10). The schedule ds27 is composed of 11 tours (t1 to t11). The three dangers (d1, d2 and d3) generated risks (R1, R2 and R3) on the schedule. The risk R1 impacts the tour t8, R2 impacts t5 and R3 impacts t2. For example, if the customer is very demanding and does not accept a single minute late, the planner will be interested in SP robRespect(0) and SM inSat(0). By viewing the graphs present in Table 13, schedules ds27, ds32, ds34, ds46 and ds48 have a probability SP robRespect(0) low (less than 0.42, Table 11). So it is difficult to select these schedules because the planner knows that all deliveries will be not satisfied. If the planner can not negotiate with his customer he will then choose the solution that has the highest probability of respect SP robRespect(0), the highest satisfaction SM inSat(0) and the lowest delay SM axDelay to satisfy his customer.

[0h-5h] [5h-10h] [10h-16h] [16h-21h] [21h-24h] [0h-5h] [5h-10h] [10h-16h] [16h-21h]
For the case of a compliant customer accepting 10 minutes late, schedules ds32 and ds34 can be implemented without any problem because SM axDelay is less than 10 minutes (Table 12). Other schedules (ds27, ds46 and ds48) can have some deviation. For the values of the ds27 schedule SP robRespect(10) ds27 = 0.6 and SM inSat(10) ds27 = 0.96. This schedule shows the planner that despite the 10 minutes delay, all customers are not satisfied only 96% (SM inSat(10) ds27 ) and that the probability that all goes well is 60% (SP robRespect(10) ds27 ) .

Depending on the values of 'x' the schedules will be considered as risk taking acceptable by the planner both on the probability indicator that for the delivery percentage satisfied in the most catastrophic scenario. Because it is difficult to select a scenario with a high probability of success (SP robRespect(x)) if the percentage of delivery satisfied can be very low (SM inSat(x)). This means that there is a small risk that a lot of customers will be unsatisfied because their delivery is not delivered on time. Conversely, if the probability of success is low (SP robRespect(x)) and the percentage of delivery satisfied is high (SM inSat(x)) this means that a very small number of customers are likely to not be delivered on time. The indicator SM axDelay flag allows you to give a quick value of the number of minutes that the planner has to negotiate with the client so that his schedule runs without any worries.

If the delay accepted by the client is not sufficient for a schedule to run correctly, the planner makes either a compromise using the indicator or actionable data presented or he can select other schedules to assess their robustness.

These robustness indicators allow the planner to see the different problems that may impact his schedule and their consequences give him the means to be able to anticipate the negotiations with the customer on possible delay so that his panning can meet both the requirements of his company and that of customers.

Conclusions

The road freight transport sector plays a crucial role in the economic balance of a country. Moreover the constraints and the client requirements become more and more important. At the same time, the delivery process frequently encounters many disruptions that make it more difficult for planners to meet customer deliveries. In this context, many research works focused on reactive scheduling methods to aid planners when disturbances occurred. As an alternative way, this paper proposes to take into account disturbances as soon as the design of the tour and to give planners the opportunity to select a solution knowing its capacity to respect clients' requirements despite possible disturbances.

Firstly, this paper proposes a model of danger allowing to model the knowledge of the planners in terms of hazard situations which could impact the delivery process.

Secondly, this paper proposes three indicators to assess RFT plannings. The first one gives the estimated probability that the daily schedule could meet all customers' requirements. The last two, SM axDelay and SM inSat, are actionable data. They give planners information on how to improve the robustness of the planning evaluated (SP robRespect). Lastly, this paper provides an original approach to assess these robustness indicators. The approach is based on a dynamic mechanism of risk identification which used a danger instantiating mechanism. Then, the impacts of the identified risks on the activities of the plans are assessed through a risk scenario simulator labelled RIOSUITE.

Our proposal uses as an input a schedule which can be generated either manually or by a commercial tool when it can be exported in a neutral and/or compatible format with the one used by our module. This approach hypothesises that activities' duration are considered without taking into account the potential impacts of risks. However, if the planner has planned extra time on some activities to anticipate the impacts of potential risks, during the robustness evaluation process he can deactivate, from the risk portfolio, the risks that are associated with this extra time. The tool offers the possibility to select which risks the planner wants to consider in the schedule analysis.

For any planner who has little experience (in planning, new delivery area, …), the system makes it possible to give an assessment of the level of robustness of the planning currently being designed and retain expertise on risks that can impact planning.

Further research should be done on finding ways to improve the risk model and the scenario simulator in order to take into account possible dependencies between risk occurrences. Nowadays, the proposal considers all the risks as independent. However, it is also necessary to consider that a specific risk could induce disturbances on two or more tours, as an example a risk of traffic jam that can impact several tours in the same time.

Figure 3

 3 Figure 3The danger and risk meta model

Figure 4

 4 Figure 4 Illustration of the danger 'traffic jam' (see online version for colours)

if

  Context of Realisation(a) ∩ Context(da) ̸ = ∅ then impacted ← a ◃ this risk could occur on task a 6: r.probability ← l.pe(a) ◃ Use of the probability estimator pe 7:

Figure 5

 5 Figure 5 Illustration of a projected schedule with estimated hours (see online version for colours)

Figure 7

 7 Figure 7 Three-axis representation of evaluation of daily schedules (KPI) (see online version for colours)

Table 1

 1 Categorisation of disruptions causes to transport system according to[START_REF] Mattsson | Vulnerability and resilience of transport systemsa discussion of recent research[END_REF]

		Accidental event	Intentional interference
		Mistakes and accidents causes by staff or users,	Labour market conflict, sabotage,
		technical failures,	incorrect planning done deliberately
		components that break down,
		faulty constructions,
	Internal	overload, driver or warehouse man accident, object loss,
		unavailability of manutentionary equipments,
		staff not available to receive the shipment,
		warehouse is full,
		planning mistake due to inattention
		the unloading area is occupied by other vehicles,
		Natural phenomena including various degrees of	Pranks,
	External	weather and natural disasters, traffic jam due to heavy traffic, accident infrastructure failure,	sabotage, theft, terrorist actions of war, traffic jam due to congestion,
		infrastructure maintenance	sports events, cultural events, riots

Table 2

 2 Illustrative example of the probability estimator F Prob B A15-N184

		7h30-8h30	17h-18h30	other hours
	Monday	Very high	Very high	No risk
	Tuesday	High	High	No risk
	Wednesday	High	High	No risk
	Thursday	High	High	No risk
	Friday	Very high	Very high	No risk
	Other days	No risk	Moderate	Moderate

Table 3

 3 Extract of the risk description

	Name	Traffic jam Moving to site B
	Task concerned	Moving to site B
	Probability	Very high
	Task impacted	Moving to site B
	Impact on duration	+25 mn

Table 4

 4 Matrix of daily schedule assessment with risk impact

	Tours in ds	∅	ScR1	...	ScRs	...	ScR ?
	t1				CI s 1 ; DI s 1
	...
	tj				CI s j ; DI s j ; p s j
	...
	tr				CI s r ; DI s r

Table 5

 5 List of orders Map of the delivery points (see online version for colours)

	Order Id.	Delivery site	Delivery time	Quantity (pallets)
	Order 1	Site 1	7h15	3
	Order 2	Site 2	7h00	2
	Order 3	Site 3	8h00	3
	Order 4	Site 4	7h15	3
	Order 5	Site 5	5h30	2
	Order 6	Site 6	8h15	3
	Order 7	Site 7	7h30	2
	Order 8	Site 8	7h15	2
	Order 9	Site 9	6h30	3
	Order 10	Site 10	6h00	3
	Order 11	Site 11	6h00	2
	Order 12	Site 12	7h00	3
	Order 13	Site 13	6h30	2
	Order 14	Site 14	7h30	3
	Order 15	Site 15	5h00	3
	Order 16	Site 16	6h45	3
	Order 17	Site 17	6h45	3
	Order 18	Site 18	8h30	2
	Order 19	Site 19	5h00	2
	Order 20	Site 20	6h45	2
	Order 21	Site 21	7h30	2
	Order 22	Site 22	7h30	2
	Order 23	Site 23	8h00	3
	Order 24	Site 24	7h30	2
	Order 25	Site 25	6h30	2
	Figure 6

Table 6

 6 Description of dangers

	Id	Name of danger	Task concerned	Localisation
	d1	High circulation road 1	Move	Road 1
	d2	Absence of customer 13	Act. site	Site 13
	d3	High circulation road 10	Move	Road 10

Table 7

 7 Characterisation of the probability and impact of the dangers

	Probability
	Id

Table 8

 8 Evaluation of planningTables11 and 12present the values of robustness indicators for each daily schedule. Table11considers a margin x equal to 0 and Table12considers a margin x equals to 10.

	Daily schedule	Fin. (e)	Env. (gCO2)	H&S
	ds27		3,601	21,684	131
	ds32		3,961	21,397	123
	ds34		3,702	21,558	119
	ds46		3,589	20,655	126
	ds48		3,712	21,145	123
	Table 9 Robustness indicators (for x = 0) detailed for each tour of ds27
		T N umDel	T P robRespect(0)	T M inSat(0)	T M axDelay(min)
	t1	3	1	1	0
	t2	4	0.7	0.5	12.77
	t3	2	1	1	0
	t4	2	1	1	0
	t5	3	0.5	0.5	1.8
	t6	2	1	1	0
	t7	2	1	1	0
	t8	2	0.6	0.5	8.1
	t9	1	1	1	0
	t10	2	1	1	0
	t11	2	1	1	0
		SN umDel	SP robRespect(0)	SM inSat(0)	SM axDelay(min)
	ds27	25	0.21	0.84	12.77

Table 11

 11 Robustness indicators with x = 0

	Daily schedule	SP robRespect(0)	SM inSat(0)	SM axDelay(min)
	ds27	0.21	0.84	12.77
	ds32	0.35	0.92	8.32
	ds34	0.21	0.88	8.32
	ds46	0.42	0.92	22.37
	ds48	0.42	0.92	12.77
	Table 12 Robustness indicators with x = 10
	Daily schedule	SP robRespect(10)	SM inSat(10)	SM axDelay(min)
	ds27	0.6	0.96	12.77
	ds32	1	1	8.32
	ds34	1	1	8.32
	ds46	0.7	0.96	22.37
	ds48	0.7	0.96	12.77
	These table are not enough to be able to make a choice. The planner can look at the
	evolution of the functions SP robRespect(x) and SM inSat(x) for different values of
	x. The SP robRespect(x) and SM inSat(x) functions of the schedules (ds27, ds32,

ds34, ds46 and ds48) are presented in their respective columns of Table

13

. These functions allow him to see according to the delay that he can negotiate with the customer what would be the best planning.

Table 13

 13 Schedules evaluation of ProbRespect(X) and Minsat(X) (see online version for colours)

	SP robRespect(X)	SM inSat(X)
	ds27
	ds32
	ds34
	ds46
	ds48

Acknowledgements

This work is part of the research project Smart Planning (ANR-16-CE26-0017), project funded by the ANR (French National Agency of Scientific Research). We would like to thank all the industrial partners of the project for their implication in the project.

project selection. He develops his research work especially in relation with the industry (pharmaceutical sector and transport sector).