P-O Vandanjon

E Vinot

V Cerezo

A Coiret

M Dauvergne

M Bouteldja

Longitudinal Profile Optimization for Roads within an Eco-design Framework

Keywords: Energy, GWP, Road, Optimization, Dynamic Model

This paper proposes a methodology to optimize the longitudinal profile of roads according to either an energy consumption or Global Warming Potential (GWP) criterion calculated for both construction and operation phases. For the construction phase assessment, this methodology is based on a earthworks model that computes the geometric differences between the natural terrain and the longitudinal road profile and moreover uses environmental data validated with real experiments. The operation phase is assessed by simulating traffic over a ten-years period. Traffic simulations are based on vehicle dynamic models, also validated with real experiments. The optimization problem is set up in a finite dimensional optimization. A case study illustrates this methodology. By taking into account actual traffic measurements, the optimized profile decreases by 6 % the total primary energy consumption and by 8 % the GWP.

Introduction

In the future, according to the International Transport Forum (ITF) 2017 report for the Organization for Economic Cooperation and Development (OECD), GreenHouse Gas (GHG) emissions from transportation should increase by 60% between 2015and 2050[START_REF] Itf | ITF Transport Outlook 2017. Tech. rep[END_REF]). During this same period (2010 -2050), in order to maintain the global warming below 1.5 • C, experts from the Intergovernmental Panel on Climate Change (IPPC) advise keeping the GHG emissions from transportation constant [START_REF] Meyer | Climate Change 2014: Synthesis Report. Contribution of Working Groups I, II and III to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change[END_REF]. It has thus become necessary to explore new leads in order to achieve this objective of GHG emissions for 2050. This goal has stimulated recent developments in the assessment of the environmental impacts of road infrastructure within Life Cycle Assessment (LCA) and Life Cycle Costs (LCC) framework. An LCA analysis considers several steps in the life of road infrastructure: planning/design, construction, maintenance, operations and end-of-life. Most researches conducted on assessment have focused on the construction and maintenance phases since these steps are fully controlled by road builders and operators. Recent research however revealed that the operation phase can account for up to 97 % of the facility energy consumption and 95 % of its GHG emissions when considering a 30-years lifetime, which is common in road structure sizing (Jullien et al. 2015a). When comparing two infrastructure projects, the operation phase can become decisive. An accurate assessment of this phase is thus required.

In the automotive field, the road is often viewed as an invariant of the vehicle-infrastructuredriver system. Numerous studies have focused on limiting vehicle fuel consumption while investigating the benefits of vehicle enhancements or eco-driving behavior (for passenger cars: [START_REF] Kamal | Ecological Vehicle Control on Roads With Up-Down Slopes[END_REF], for trucks: [START_REF] Huang | Using 3d road geometry to optimize heavy truck fuel efficiency[END_REF]). Studies conducted on the influence of road characteristics on fuel consumption are not as prevalent [START_REF] Hammarström | Rolling resistance model, fuel consumption model and the traffic energy saving potential from changed road surface conditions[END_REF]) and mainly address rolling resistance [START_REF] Bryce | Ch. Analysis of rolling resistance models to analyse vehicle fuel consumption as a function of pavement properties[END_REF]. The seminal work by [START_REF] Webb | The effect of gradient on fuel consumption and speed of a road vehicle[END_REF] on the effect of longitudinal road grade on fuel consumption is interesting from a historical perspective.

Our approach here is different since this work focuses on the impact of road geometry on the operation phase energy demand. Such an approach is more widespread in the civil engineering field, where the road is considered as a design variable. The objective is generally minimizing the construction costs while maintaining satisfactory comfort and safety performances [START_REF] Chew | Simultaneous optimization of horizontal and vertical alignments for highway[END_REF]. National design guidelines summarize good practices and provide limitations for the geometric characteristics such as the Guide for Road Design from American Association of State Highway and Transportation Officials, Austroads (Association of Australasian Road Transport Agencies) or the French ARP and ICTAAL [START_REF] Aashto | A policy on geometric design of highway and streets[END_REF][START_REF] Setra | ICTAAL -French technical reference document for design of motorways in interurban areas, divided carriageway roads, with at least two lanes in the link sections[END_REF]). Nevertheless, classical design methods are mainly based on economical cost assessments from the seminal paper by [START_REF] Monge | Mémoire sur la théorie des déblais et des remblais[END_REF] to the more recent books in road design (e.g. [START_REF] Jha | Intelligent Road Design[END_REF]). Moreover, it appears that energy demand during the operation phase can indeed be taken into account but in a very simplistic way. In [START_REF] Jong | An evolutionary model for simultaneously optimizing three-dimensional highway alignments[END_REF], fuel consumption is estimated from both average running speed and longitudinal road slope using regression models. More recently, [START_REF] Kang | Applicability of highway alignment optimization models[END_REF] included fuel consumption in the vehicle operating costs which are derived from applying vehicle-mile ratios to the length of road infrastructure and certain traffic information (traffic flow, travel time, and speed). The approach proposed herein is more accurate since it uses vehicle dynamics models.

In the environmental field, road impacts are assessed to obtain a more general view and are mainly based on simplified statistical models. Along these lines, [START_REF] Ragione | The influence of road gradient in an integrated approach of real driving cycles and emissions factors model[END_REF], [START_REF] Sentoff | Implications of driving style and road grade for accurate vehicle activity data and emissions estimates[END_REF] and [START_REF] Wyatt | The impact of road grade on carbon dioxide (CO2) emission of a passenger vehicle in real-world driving[END_REF] highlighted the importance of taking into account longitudinal road slope in models that assess the environmental impacts. Nevertheless, longitudinal road slope is always considered as a constant input. More recently, [START_REF] Davey | Optimal road design through ecologically sensitive areas considering animal migration dynamics[END_REF] proposed optimizing road design based on the basis of ecological considerations.

In this work, we apply an optimization methodology for road energy demand based on a specific variable, namely the longitudinal road profile. This methodology includes vehicle simulations, which are based on accurate and sensitive dynamic models and engine models validated using real data. The present paper thus proposes an original approach, that establishes a strong link between the civil engineering and automotive fields.

After describing the methodology and assumptions introduced to establish the optimization process, the paper will present the framework for assessment of the construction and operation phases. Next, the optimization method will be detailed. Lastly, the method will be applied to a case study and a discussion of results will be provided .

Methodology

The methodology developed herein, called "Sloop" for slope optimization, lies within the Eco-design framework, which is viewed as an infrastructure design optimization process. The optimization criteria consist of the assessment-related outputs of each phase of the infrastructure life-cycle (see the green arrows in Figure 1 pointing to the optimization cell). Degrees of freedom of the optimization are design parameters. This assessment is based on the impacts (red arrows) or resource consumption (blue arrows) of each infrastructure life-cycle phase, with, maintenance feeding back into the operations phase. With respect to the environmental impact assessment, two life cycle phases are taken into account: construction and operations. The optimization criteria are selected among classical life-cycle environmental impact indicators. The degrees of freedom of this optimization process consist of geometric characteristics (longitudinal slope, cross-fall, radius of curvature), as well as with surface characteristics (texture in relation to rolling resistance) or materials. The adequacy of this type of approach has been demonstrated in comparing two variants for the case of High Speed Rail Line project [START_REF] Bosquet | Eco-design model of a railway: A method for comparing the energy consumption of two project variants[END_REF]. This study focuses on primary energy consumption and global warming potential (GWP) minimization. These indicators are robust, validated by the scientific community and standardized. The degree of freedom is the longitudinal profile of the road. The initial profile is provided by technical draftsmen. Sloop performs a local optimization around this initial profile. It is assumed that the optimized profile is not very different from the initial profile. Under this assumption, the maintenance phase is considered to be the same regardless of the longitudinal road profile. Similarly, the pavement layers are assumed to be the same for each profile. The construction phase is then primarily assessed by examining the earthworks, which are estimated by computing geometric variations between the natural terrain and the longitudinal profile. The operations phase is assessed by simulating traffic over a ten-years period (this choice of duration is discussed at the end of the paper).

Design

Life Cycle Analysis: System description

The environmental impact assessment is carried out according to the standardized life cycle analysis methodology (ISO 2006a,b). The objective therein is to obtain impact indicators values that correlate the earthmoving phase of a new road with the operations phase on the same road for a given period of time. The functional unit studied is defined so as "to enable the circulation of a certain level of vehicle traffic over a given road section for 10 years". Both the system and boundary conditions are described in Figure 2. Some processes are not considered in the global assessment since they produce the same impact independent of the longitudinal road profile under the assumption that the considered profiles are not too much different:

• Road pavement structure (i.e. layer composition and thickness);

• Road maintenance sequences;

• Construction of plants, machinery and vehicles used to build and transport materials;

• Construction of the vehicles traveling the given road section.

In this paper, only primary energy consumption and global warming potential are considered. Following [START_REF] Wang | Life-cycle assessment of airport pavement design alternatives for energy and environmental impacts[END_REF], the upstream part of energy and carbon footprint tied to fuel production is considered in both construction and operation phases of LCA. The indicator for 100-year global warming potential is calculated according to the IPCC 2007 method (IPCC 2007). Regarding the construction phase, life cycle inventories used for earthmoving impact assessments stem from the ECORCE M (ECO comparator applied to Road Construction and Maintenance) database. They are described in the tool reference manual (Jullien et al. 2015b). These inventories include the upstream part of energy and carbon footprint of fuel production. As far as the operation phase is concerned, only carbon dioxide emissions for the GWP are considered; these have been calculated from the fuel consumption data provided by VEHLIB (Electric Hybrid Vehicle Library) (Vinot et al., 2008a;[START_REF] Jeanneret | New hybrid concept simulation tools, evaluation on the toyota prius car[END_REF]. To ensure system homogeneity, the GWP and energy consumption tied to fuel production are added in and originate from the same source as the ECORCE M software.

Sloop methodology steps

The Sloop methodology steps are listed in Figure 3. Its core is a single-criterion optimization process. The following sections will detail the methodology in terms of energy minimization. The GWP minimization process is similar although not expressly developed herein.

Earthwork phase Operations phase

Vehicle traffic (Fuel consumption)

System boundary

Figure 2. System boundaries

For a given initial longitudinal profile, the earthmoving volume is computed from the original ground level (included in the Worksite Data box). From this volume, an assessment of primary energy costs for the construction phase can be calculated. Next, vehicle trajectories are simulated on this initial longitudinal road profile, and primary energy consumption for the entire operations phase is estimated. The global cost in energy is the sum of construction cost and operating cost. The first iteration of the optimization algorithm analyzes these costs by computing longitudinal profile slopes and then proposes a new longitudinal profile. The optimization cycle can thus continue until convergence on the optimized profile, i.e. the one minimizing energy demand. An assessment of both the construction and operation phases will be provided in the next two sections.

Construction phase Assessment

Hypothesis and assessment method

For every road infrastructure project, the designer proposes a longitudinal profile that takes into account the following:

• design rules based on safety considerations, more specifically sight distance and braking distance depending on the pavement skid resistance;

• quality of the natural soil for possible reuse as embankment instead of final deposit. In case of reuse, specific treatments may be necessary (e.g. by incorporating lime into the soil);

• equilibrium between cut and fill in order to minimize earthworks. Starting from this longitudinal profile, considered as the reference profile, a 3D model of the road sub-grade, which supports the pavement layers, is computed. The comparison between this reference profile and the natural soil requires an accurate assessment of earthmoving. Various longitudinal profiles therefore lead to significant differences in earthmoving quantities. At the same time, these longitudinal road profiles do not imply significant changes in the pavement layer size because their widths and lengths mainly depend on traffic levels. Consequently, road pavement layers have not been formalized in the optimization process. Earthworks can be broken down into the following operations: raw material extraction, transportation and deposit as fill (in the case of reuse) or storage as final deposit [START_REF] Capony | Monitoring and environmental modeling of earthwork impacts: A road construction case study[END_REF]. Any assessment of earthmoving quantities must therefore include an estimate of the fuel consumed by earthworks equipment (bulldozer, scraper, dump truck) during each task. Soil treatment needs to be quantified as well. These aspects are incorporated into the evaluation of energy consumption and GHG for the optimization process. To achieve this goal, earth movements are estimated from volume differences between the natural ground level and the current longitudinal profile The energy consumption and GHG emissions assessment is performed using the software ECORCE M, which features an extensive database pertaining to earthworks equipment [START_REF] Capony | Monitoring and environmental modeling of earthwork impacts: A road construction case study[END_REF]Jullien et al. 2015b).

Volume Computation

The longitudinal profile of the project, denoted Ps, and the natural soil profile, Pn, are altitudes relative to the distance x (also called the metric point); they are discretized every d meters. For each point on these discretized profiles, an altitude differential is computed and then multiplied by the road infrastructure width ,w ph , to obtain a surface area measure. In turn, this surface area is multiplied by the segment length, d, to yield a volume. Embankments with a given transverse slope, In conclusion, for each point on the discretized profiles, an elementary volume, V, is computed. The relevant equations are presented in the Appendix A for the simplest embankment cross-section, as illustrated in Figure 4, though volume computations for all cases described in Figure 5 have been performed. Global embankment volume, V e , and cut volume, V c , are the sum of the elementary volumes, V, along the discretized longitudinal profile.

Assessment of energy consumption and GHG emissions from the Volume Computation

With these calculated volumes, the environmental impacts can be assessed in terms of both energy consumption and GWP by taking into account raw material extraction, transportation between excavation and embankment, laying of materials, and quicklime treatment of natural soil. The energy consumption associated with the construction phase, denoted E c , is calculated with the following equations:

E c = e f × V e + e cnu × (V c -V e ) if V c ≥ V e (1) E c = e f × V e + E AddMat if V c < V e (2)
with e f and e cnu , being the energy consumption per cubic meter for the embankment and the cutting spread on the final deposit, respectively. e f = e extrac + e trans × Dist FC + e spread + e lime × r limeF

(3) e extrac is the energy consumed per cubic meter to extract the materials. e trans is the energy consumed to transport one cubic meter of materials over one kilometer. Dist FC is the average distance between cut and fill; this parameter depends on the site configuration. e spread is the energy consumed to spread one cubic meter of materials. e lime is the energy consumption associated with one cubic meter of quicklime. Lastly, r limeF is the quicklime rate of the treated embankment materials. E AddMat is the energy consumption due to required additional material in the event of a negative balance between fills and cuts (i.e. for a worksite with a materials deficit).

As far as GWP is concerned, the equations are set up similarly, i.e.:

GWP c = gwp f × V e + gwp cnu × (V c -V e ) if V c ≥ V e (5) GWP c = gwp f × V e + GWP AddMat if V c < V e (6)
with gwp f and gwp cnu , being the GWP per cubic meter for the fill and the cutting spread in a final deposit, respectively. The breakdown of environmental impacts is the same as for energy consumption with a set of consistent notations:

gwp f = gwp extrac + gwp trans × Dist FC + gwp spread + gwp lime × r limeF (7) gwp cnu = gwp extrac + gwp trans × Dist D + gwp spread + gwp lime × r limeC (8)
The optimization process includes E c and GWP c as cost components to be minimized.

Operation phase Assessment

Hypothesis and assessment method

The operation phase is assessed by considering a functional unit composed of a road section with various longitudinal profiles and traffic levels summed over a reference period. Environmental impact indicators are calculated by modeling traffic flows for ten years. A number of assumptions must be adopted regarding both the composition and evolution of traffic. A distribution of vehicles across several categories has been considered with the assignment of an average vehicle in each category for purposes of numerical simulations. Moreover, the evolution in the vehicle distribution is based on a French national study (CCFA 2017). The energy and GWP indicators are calculated via total fuel consumption over a ten-year traffic period. Special attention has been paid to the choice of vehicle fuel consumption model. Both gasoline and diesel engines have been considered in the simulations with various conversion factors. Lastly, total fuel consumption is calculated separately in both directions in order to consider the impact of the longitudinal profile, which does not have the same effect depending on travel direction (ramps and downhills).

Modeling considerations 4.2.1. Traffic

Traffic is modeled using different classes of vehicles from passenger cars to heavy vehicles. The number of vehicles in each class has been obtained through traffic flow measurements. The following classes are proposed in the present work:

Car: passenger cars;

Van: van with a Gross Combination Weight Rating (GCWR) less than 3.5 tons;

Mini-truck: Vans with a Gross Combination Weight Rating (GCWR) greater than 3.5 tons;

Truck: 2-rigid-axle heavy vehicles with a Gross Combination Weight Rating (GCWR) below 19 tons;

Articulated vehicle: 5-axle heavy vehicles with a Gross Combination Weight Rating (GCWR) of up to 44 tons (fully loaded). This type of vehicle however is not running fully loaded all the time. In fact, trucks can sometimes travel with a partial load and even if full, depending on the type of goods, the maximum available load might not be reached. To take into account these different load scenarios, this class has been separated into two sub-classes: 40-tons for almost fully loaded, and 25-tons for half-loaded vehicles. This choice is based on weight-in-motion data analyses carried out on the French national road network.

The vehicle sub-classes can also be defined by engine type. For passenger cars, both diesel and gasoline engines are considered, whereas for all other categories, only diesel engines are assumed.

For each class, a vehicle model has been parameterized to be representative of the average fuel consumption of the entire fleet. The technical characteristics of these classes and the composition of traffic are presented in Table 5. The vehicle speed is either the maximum legal speed or the maximum achievable speed, which means that vehicle speed actually depends on slope. For example, the truck speed may lie below the legal speed when traveling uphill and at the legal speed on downhill stretches, in using the engine brake and/or brake.

Vehicles

Several fuel consumption models are available in the literature. As an example, [START_REF] Hammarström | Rolling resistance model, fuel consumption model and the traffic energy saving potential from changed road surface conditions[END_REF] proposed a semi-analytical consumption model taking into account vehicle speed, rolling resistance force and geometric characteristics (transverse and longitudinal profiles). The objective therein was to estimate fuel consumption over an entire road network. The model is thus set at the macro scale and focuses on rolling resistance. The influence of longitudinal road slope is not fully analyzed. A parameter introduced, called RF (for Rise and Fall), serves to measure the total increase and total decrease in altitude (per distance traveled). This parameter can be viewed as an "absolute variation" of a function that describes the mathematical nature of this concept. Moreover, the model has been calibrated for just three types of vehicles: car, truck, and articulated vehicle.

It was decided in this study to use a customized model called VEHLIB (Vinot et al. 2008a;[START_REF] Jeanneret | New hybrid concept simulation tools, evaluation on the toyota prius car[END_REF], which is a Matlab/Simulink library developed at Ifsttar/LTE (Environment and Transportation Laboratory) to simulate all types of vehicles (from cars to articulated vehicles) and power-train architectures (from conventional to complex hybrid power-trains). It uses a modular cybernetic approach that allows for an easy exchange of vehicle components. According to this model, the vehicle is thus considered as a set of sub-systems. Modeling the vehicle therefore entails modeling its various units and the interactions taking place between them [START_REF] Vinot | A complete set of tools for hybrid vehicle design : from cybernetics model to hardware in the loop simulation[END_REF]). Simulating a vehicle requires defining a driving cycle, represented by a vehicle speed as a function of time and an altitude as a function of distance profile. Both the normalized cycles, e.g. NEDC (New European Driving Cycle) or WLTP (Worldwide harmonized Light vehicle Test Procedure), and a personally defined cycle can be used in this application. The VEHLIB model is mainly composed of the engine, clutch, gear-box, final gear and vehicle chassis sub-model. The vehicle chassis model comprises an aerodynamic model and a rolling resistance model. The fundamental dynamic principle is solved in order to proceed upstream from wheel effort to engine solicitation.

Figure 6 displays the general principles of the fuel consumption computation. Starting from the trajectory of the vehicle and the longitudinal profile, Vehlib simulates the vehicle. One simulation output is the fuel consumption. Direct calculations yield the primary energy consumption and the CO 2 emissions which is converted in GWP. In the following, the calculations for each step are presented.

Firstly, Newton's second law is applied to a vehicle described as a single degree of freedom model (see the car on Figure 6) in order to compute the tractive force F t developed by the wheels:

m × γ = F t -F r ( 9
)
where m is the vehicle's mass and γ is its acceleration. F r is the running resistance and is expressed as:

F r = 1 2 ρSC x v 2 + mg(C rr0 + C rr1 v) + mg sin(α r ) ( 10
)
Where ρ is the air density, S is the front vehicle area, C x is the drag forces coefficient, C rr0 et C rr1 are the tires rolling resistance coefficients, g is the acceleration of gravity and α r is the angle of the slope in radian. This quantity varies according to the profile.

As illustrated by the gears on Figure 6, knowing F t and v, the engine torque and angular speed (T e and ω e ) are then computed. We exhibit the equations only for the engine torque, equations for the angular speed are symmetric.

Knowing F t , the torque T w to be applied to the wheel is then:

T w = F t × R w (11)
where R w is the wheel radius.

Going upstream to the engine shaft considering the different gear ratios, the engine torque T e is then:

T e = T w k f g .k gb η f g .η gb i f T w > 0 (12)
where k f g and η f g are the gear ratio and efficiency of the final gear, k gb and η gb are the gear ratio and efficiency of the gear box. Fuel consumption is then calculated using specific fuel consumption maps (e.g. see Figure 7 for a 390kW diesel engine). VEHLIB has been validated with experimental data. For example, the map of the vehicle representing the truck class (2-rigid-axle heavy vehicle) (Figure 7) was calibrated with experimental measurements recorded by CEREMA-Lyon (France's National Center For Studies and Expertise on Risks, Environment, Mobility, and Urban and Regional Planning).

Lastly, the fuel consumption of the different type of vehicles (see section 4.2.1) are calculated in the two directions of circulation and summed to obtain fuel consumption due to the traffic for N year s years (here, N year s = 10). Knowing these quantities, the computation of both criteria GWP and primary energy is straightforward taking into account the boundaries of the LCA system which includes fuel production and supply (see Figure 2). We present the equations for the GWP

Diesel

Gasoline eqCO 2 in kg/l τ d2GWP =2.98 τ g2GWP =2.66 Primary energy in MJ/l τ d2Energy =38.3 τ g2Energy =34.1 during the operation phase, GWP o , since the equations for the primary energy are identical for their structure.

GWP o = N year s k=1 veh N vehk ( FC d1 + FC d2 2 )τ FC2GWP ( 13
)
where N year s is the number of years considered in the study, N vehk is the numbers of each type of vehicles composing the traffic for the year k (see section 4.2.1), FC d1 and FC d2 are the fuel consumption in each directions, and τ FC2GWP is the emission factor of one liter of fuel (its value is τ d2GWP for diesel and τ g2GWP for gasoline).

The emission factor coefficient is calculated adding the GWP of combustion and those by the fuel production part. For the combustion, it is derived from the combustion equation of a reference fuel in stoichiometric conditions:

CH 1.86 + 1.4625O 2 -> CO 2 + 0.925H 2 O (14)
where CH 1.86 is a hydrocarbon with a ratio hydrogen -carbon of 1.86 for diesel (respectively 1.89 for gasoline) according to the European norm (EU 2010). For the fuel production and supply part the emission factor comes from ECORCE M software (Jullien et al. 2015b). Table 1 summarizes the aggregate emission factors used in equation 13 for diesel and gasoline and for GWP and primary energy with consistent notations, described in Appendix B.

For the sake of clarity, we presented simplified equations. The simulation has to take into account some particular cases which complicate them. For example, going downhill if the slope is too steep, running resistance becomes a driving force in particular for trucks, and the equations are then modified to take into account the braking system (engine brake and mechanical brake). When going uphill, the engine limitations imply that the actual speed may be lower than the legal speed. This fact is simulated by Vehlib. Technical equations are moreover added for the choice of gear ratio.

Optimization method

Previous sections have described the energy consumption or Global Warming Potential (GWP) assessment of both the construction and operations phases of a road project according to the longitudinal road profile. This section will present the method implemented to identify the longitudinal profile that globally optimizes a criterion J, which designates either the primary energy consumption E or the GWP of a road project. J depends on the longitudinal profile Ps, i.e.: J(Ps) = J c (Ps) + J o (Ps) (15)

Since the optimal solution is a function, this problem becomes one of infinite-dimensional optimization. In this form, the solution to this optimization process cannot be directly applied by road designers. To overcome this obstacle, the longitudinal profile of a road is modeled as a sequence of straight lines linked by circular arcs. This sequence must follow stringent rules, as dictated by technical standards: such standards are specified in national guidelines, e.g. [START_REF] Aashto | A policy on geometric design of highway and streets[END_REF] for the United States or [START_REF] Setra | ICTAAL -French technical reference document for design of motorways in interurban areas, divided carriageway roads, with at least two lanes in the link sections[END_REF] for France. Moreover, infinite-dimensional optimization problems are difficult to solve.

For all these reasons, the previous infinite-dimensional optimization has been simplified into a finite-dimensional problem. The function Ps is parameterized as illustrated in Figure 8 and described by the following set of typical equations for road designers: C x k ,h k ,α k ,R k ,x k+1 ,h k+1 ,α k+1 (x) is the equation of the circle, with radius R k , that links straight line k to straight line k + 1. This circle is tangent to straight line k at the point with abscissa a k and is tangent to the straight line k + 1 at the point with abscissa b k . With these equations, the derivative of Ps(x) is continuous which is a mandatory condition to simulating vehicle dynamics models. Also, circular arcs are often used by road designers to "smooth" the profile. For this purpose, large radii (R k > 10, 000 m) are chosen, thus implying that the circular arcs cannot be neglected in the longitudinal profile model.

x k-1 x k+1 a k b k R k straigth line k with slope α k straigth line k+1 with slope α k+1 h k-1 h k+1 x k h k b k-1 a k+1
(x) = α k (x -x k ) + h k if b k-1 ≤ x < a k Ps(x) = C x k ,h k ,α k ,R k ,x k+1 ,h k+1 ,α k+1 (x) if a k ≤ x < b k Ps(x) = -α k+1 (x k+1 -x) + h k+1 if b k ≤ x < a k+1
The boundary conditions, i.e. the connection with the existing road, are managed by setting:

x 0 = x b , α 0 = α b , Ps(x 0 ) = Ps b , x n = x e , α n+1 = α e , x n = x e , Ps(x n ) = Ps e . α b
is the longitudinal slope of the existing road before x b , which is the beginning of the studied profile, α e is the longitudinal slope of the existing road after x e , which is the end of the studied profile.

The degrees of freedom in this parameterization are:

x k , α k , R k , with k varying from 1 to n -1 and R 0 , R n , α n .
The other variables can be obtained from the degrees of freedom. h k is computed in knowing

x k-1 , x k and α k . a k , b k are computed in knowing the equation of circle C(x k , h k , α k , R k , x k+1 , h k+1 , α k+1 ).
With this parametrization, infinite-dimensional optimization problem (Equation 16) becomes the following finite-dimensional problem. minimize

x k ,α k , R k , k=1...n-1 R 0 R n α n J(Ps) subject to Ps(x o ) = Ps o , Ps(x f ) = Ps f (18)
Since the chosen parameterization is commonplace for road designers, the initial profile, Ps 0 , is the longitudinal profile designed by them. One parameter of the optimization program n, i.e. the number of straight lines, is given by the road designers in order to adjust the profile to the natural soil. Its value is typically set by the initial profile. The degrees of freedom of the optimization program: x k , α k , R k are not completely independent of one another. For example, if the consecutive straight lines are parallel (i.e α k+1 = α k ), it is impossible to build a circular arc that joins them. Another constraint is that the beginning of the circular arc d k must lie after x k . Moreover, the assumptions of the methodology implies that the profile cannot be completely different from the initial profile. It means that the variations of the degrees of freedom are bounded. In summary, different technical constraints are added to the optimization protocol (Equation 18).

Application

In this section, the Sloop methodology is applied to a French road project in order to demonstrate its efficiency in defining a longitudinal profile that minimizes primary energy consumption or GWP. This road project had been carried out prior to our study. The actual road and alternative profiles delivered by Sloop are compared. Since the road actually exists, real traffic measurements have been performed to verify traffic estimations and recalibrate them as needed.

Description of the case study

The section is a 4.75 km long 2x2 lane road in the French national road network; its longitudinal slope varies from -2 % to 2 %. The same asphalt pavement mix has been laid over the whole section. All the technical data (earthworks, pavement structure) required to assess the energy demand and GWP during construction works were collected from the relevant road authorities.

Construction phase Parameters

During the construction phase, the energy consumption required and GHG emissions produced due to the tasks of extraction, spreading, transportation and treatment are described according to Equation. 1, 2, 5 and 6.

The calculations require identifying a number of parameters specific to this site. These values are: average distance between cut and fill (Dist FC = 1.132 km), average distance between cut and final deposit (Dist D = 0.869 km), average quicklime rate of the material treated for fill (r limeF = 1.04 %) and the quicklime rate for the final deposit, set at 0 % given the absence of treatment (r limeC = 0 %).This site features highly accurate values from dedicated experiments carried out in 2012 as part of the national TERDOUEST project (funded by the French National Research Agency). At most worksites, these parameters can be identified from mass diagrams. This particular site had a material surplus; for this reason, the parameters E AddMat and GWP AddMat are not used herein. Had such not been the case, then these parameters would be provided by life 2).

Simulation Parameters of the Operations phase 6.3.1. Traffic measurements

Assumptions regarding traffic evolution heavily influence the impact indicator values. In 1998 (origin of this project), traffic was estimated at 8,800 vehicles/day with 23 % heavy vehicles (i.e. the sum of mini-trucks, trucks and articulated vehicles -these classes have not been distinguished in this initial study), in both directions. Moreover, traffic growth was assumed to reach 12,820 vehicles/day by 2020. To verify the validity of these assumptions, traffic data were collected in 2016 by CEREMA Lyon over a two-week period. Two counting devices with radars were installed in order to record the number of vehicles and their type and speed in both directions (see Figure 9 for the location of these devices).

As an initial finding, the measurements showed that the level of traffic is equivalent in both directions, and it was decided to apply the same values for average daily traffic in the two directions.

Table 3 has been compiled from measured traffic by estimating an average daily traffic, which in both directions equals around 7,000 vehicles, while the road project hypothesis adopted in 1998 called for 8,800 vehicles/day, for an overestimation of approx. 20 %. Moreover, the proportion of heavy vehicles (>3.5 tons) is slightly higher, with 26 % vs. 23 % in the initial hypothesis.

Since this initial assumption on vehicle evolution was not consistent with measurements, we decided to consider a stable traffic in terms of evolution in the number of vehicles over 10 years. As regards traffic composition, we tracked the scenario of evolution in the French fleet, as defined by the French Ministry of Environment, Energy and Maritime Affairs [START_REF] Meem | Chiffres du transport -édition 2017[END_REF]. With these two assumptions, the total traffic volume for each vehicle class can be estimated over a 10-year period. Table 4 presents both the averaged measured traffic values and estimated traffic values. It is clear that this ten-year traffic volume estimation is rough and cannot be considered as an accurate traffic model. Nevertheless, the objective of our case study is to demonstrate the feasibility and interest of the given optimization method. Hence, this traffic model can be modified without having any consequence on the methodology. In road infrastructure projects, a very thorough traffic estimation is performed, and these data would be considered in the Sloop method.

Vehicle simulation

Traffic is divided into vehicle classes, and dynamic models are introduced to represent the vehicle behavior in each class. In France, diesel engines are installed in roughly 70 % of all passengers cars, but nearly 100 % in trucks and vans. Since the traffic composition on the test section remains quite similar to the overall French composition, it was decided to adopt the same assumption on the division of engine types. Moreover, the "diesel personal car" class has been split into three categories, modeled by a given vehicle type (small, medium and high), as available in VEHLIB. The data used to calibrate these models were derived from vehicles that had been tested and characterized with an Ifsttar chassis dynamometer, while the heavy vehicle characteristics entered into the models were provided by CEREMA Lyon. The number of vehicles in each class was then determined by means of the data obtained from CEREMA Lyon during the traffic measurement campaign. Table 5 lists the technical characteristics of the various vehicles used for this assessment, i.e.:

• number of vehicles passing in one day in one direction over the studied part of the road;

• mass of each type of vehicle (including load and passengers);

• product of the drag coefficient and the front surface area, denoted S.C x ;

• tire rolling resistance coefficients, in assuming a constant part (C rr0 ) and a part proportional to vehicle speed (C rr1 ).

Optimized profiles

The initial profile is the current one denoted Ps actual (x); it is divided into six subsections (n = 6) and its length equals 4.75 km (see "Longitudinal profile optimization section" in Figure 9). The number of degrees of freedom is therefore 18, according to the formulation of the simplified optimization problem (see Equation 18), i.e.:

• 5 abscissas defining the intersection point between two consecutive straight lines;

• 6 slopes, one per section;

• 7 radii for the circle linking the section, since the two radii of the two extremities are also degrees of freedom.

A nonlinear constraint is applied to respect the final altitude (Ps f ) and in order to connect the optimized section with the existing road. Several technical constraints, based on guidelines and state-of-the-art, have been added to produce a consistent profile. The number of subsections is fixed, but the length and longitudinal slope of each subsection are free to be adjusted by the optimization algorithm. The simplified optimization problem (eq. 18) is solved using the Sequential Quadratic Programming (SQP) algorithm available in the "fmincon" Matlab Software function; it starts with the initial profile defined by Ps actual (x).

Figure 9 exhibits the optimized profiles, the reference longitudinal profile and the natural terrain. The reference profile is that of the existing road (Ps actual (x)). The reference profile is smoother than the natural soil profile. The large natural soil variations in altitude have indeed been lowered to build the road. The flat profile is unrealistic profile that it links the beginning and end points with a straight line. It provides the maximum potential gain during the operation phase.

Results of the optimization process indicate a 6 % savings of the global primary energy (Table 6) compared to the existing profile. A 9 % savings on GWP is also obtained. According to the criteria of primary energy and GWP impact, the optimized profiles are smoother and lower than the reference profile. The solution to the GWP optimization is the lowest profile. The reasons for these differences are detailed in the following section. Optimized profiles are however not completely different from the initial profile so that the assumptions of a local optimization described in section 2 are fulfilled (in particular, the maintenance phase is the same for the initial profile and the optimized profile).

Discussion

Analysis of optimized solutions

For starters, the energy savings and GWP gains are significant between the optimized longitudinal profiles and the reference profile. According to Table 6, these gains are equivalent to the energy consumption and GWP impact of the construction phase alone. An energy savings of 31 TJ (resp. 4129 teqCO 2 for GWP) is achieved during both the operation (24 TJ) and construction (7 TJ) phases. In comparison, the primary energy consumption for the construction phase alone equals 35 TJ (resp. 5950 teqCO 2 for GWP), with respect to the reference profile, and this figure decreases to 28 TJ (resp. 3422 teqCO 2 for GWP) in the optimized profile. This finding means that by taking into account the future use of the road over 10 years, the cost of the construction phase in GWP or energy can be nearly offset by optimizing road slopes.

Secondly, an optimization procedure that takes both construction and operating costs into account is mandatory. The solution optimizing just the operating cost is obviously a flat profile between the beginning and end of the studied section (see Figure 9). According to Table 6, the ). This profile also shows that compared to the reference profile, the gain during the operations phase can be evaluated at 26 TJ. Moreover, the energy-optimized profile is close to the minimum attainable profile (i.e. 472.6 TJ vs. 470.9 TJ). Thirdly, the gain in GWP is greater than in primary energy (9 % vs. 6 %). In targeting energy optimization, the gain is mainly generated by the operation phase (24 TJ vs. 7 TJ for construction). On the other hand, when optimizing with GWP as the objective, the gain is mainly due to the construction phase (2,528 teqCO 2 vs. 1,501 teqCO 2 for the operation phase). Moreover, the energy-optimized profile differs slightly from the GWP-optimized profile (see Figure 9). These two facts are explained by the quicklime soil treatment, which is costly in terms of both energy and GWP. It has a higher relative GWP cost than a relative energy cost: in Table2, the parameter is 2200 kgeqCO 2 /m3 for GWP, which is roughly 2,000 times the cost for the Spread, while the parameter is 9,000 MJ/m3 for Energy, i.e. less than 1,000 times the cost for the Spread. The algorithm seeks to minimize this treatment by minimizing the embankment. For this reason, optimized profiles are lower in altitude than the reference profile and GWP-optimized profiles are lowest in altitude (see Figure 9). This Sloop behavior is due to local conditions at the worksite. If the soil does not require any treatment, the optimized solutions will differ.

As a consequence, generation of the optimized profile according to GWP would create too many cuts; this profile cannot be built directly. One solution consists of adding a constraint to the optimization problem in order to exclude this type of unbalanced solution. However, in this practical case, the optimized profile according to energy is also significantly better than the reference profile in terms of GWP, showing a gain of 8 % (see Table6). Hence, we did not attempt to improve the optimization problem but rather selected this profile as an alternative to the actual one for the GWP criterion as well. Subsequent analyses will focus on this optimized energy-based profile.

The optimized profile according to energy is well balanced in terms of fill and cut and moreover is compliant with the constraints of an actual construction project (see Figure 9).

We have remarked that the construction gains are derived from minimizing soil treatment, but what are the actual sources of gains during the operations phase? The answers are displayed in Table 7, which presents, for each vehicle class, the primary energy, fuel consumption and corresponding GWP calculated on a 10-year basis for both the reference profile and the profile optimized according to energy. The last row of this table lists the global values of energy consumption or GWP for all vehicles. The global gains of 6 % Energy and 8 % GWP are mainly due to articulated vehicles and trucks. This finding is explained by the fact that the optimized profile tends to limit the longitudinal slope (up and down) and then the energy dissipated during the braking phases.

Applicability of Sloop to other projects

This methodology offers new perspectives to stakeholders by raising awareness about the environmental impact of the operations phase due to the longitudinal profile. This methodology however cannot bring significant improvements to a constrained area like the mountains or a zone without slopes like flat plains.

We have proven the applicability of this methodology to a real case study but on a relatively small section (the optimized length is 4.75 km). For large projects, the number of degrees of freedom increases and the optimization is more complex the longer the computation time.

Hypotheses and limits of Sloop

Sloop results depend on traffic assumptions, i.e. number and type of vehicles. In our case study, we have limited the traffic evolution to 10 years. Moreover, since we are focusing on an actual road, we were able to carry out real traffic measurements and obtained accurate readings. It is very difficult to guess the nature of the traffic after 10 years, in particular with the development of electric vehicles. The prediction of the number of vehicles that will be traveling on the road depends on various exogenous factors like economic growth, fuel cost, regulations and, more generally, transportation policy (taxes, new infrastructure, etc.). From this perspective, the methodology remains valuable in testing various traffic evolution scenarios.

In general, Sloop yields results without an indication of uncertainty. Two major sources of uncertainty are:

• the assumptions adopted on traffic and its evolution: further investigation is needed to test the optimization algorithm with more complex traffic assumptions;

• characteristics of the natural soil: if the initial material has to be treated, then the cost in terms of GWP is higher. This specific problem can be addressed by carrying out geotechnical measurements or by computing the effect of this unknown factor on the uncertainty of the optimized solution.

Beyond this initial work effort, a complete sensitivity study will be carried out in the near future in order to assess uncertainty.

The optimization with just one criterion oversimplifies the problem and can lead to unrealistic solutions. One perspective calls for carrying out a multi-criteria optimization in order to propose a set of efficient solutions (a Pareto front) to stakeholders. The decision to choose among these solutions is left up to the stakeholders. These algorithms serve to remove inefficient solutions. Decision-makers can then focus on relevant solutions.

The initial number of sections is fixed by the initial longitudinal profile. This parameter could be another degree of freedom for the optimization program. It is difficult however to take this parameter into account in the optimization program, whose number of degrees of freedom remains quite high.

Conclusion

This paper presented a methodology for optimizing the longitudinal road profile from a Life Cycle Assessment perspective. Two environmental indicators, namely primary energy consumption and GWP, have been considered in the analysis. The objective here is to minimize either energy or GHG emissions during both the construction and operations phases. This optimization protocol is based on models describing these two phases.

The model of the construction phase is based on:

• standard geometric models for natural soil and the road project; a comparison of the two models provides the basis of the earthmoving analysis; the earthmoving task is assessed using actual measurements of earthworks equipment fuel consumption;

• soil treatment.

The model of the operation phase is based on:

• dynamic models for the different types of vehicles; from dynamic models, the engine models provide fuel consumption and emissions;

• a 10-year traffic estimate; this estimate is calculated from actual traffic measurements.

These dynamic models have been validated during previous research work. They were selected in considering their accuracy, reliability and capability of assessing the effect of longitudinal profile on energy consumption and GWP.

This methodology was then applied to a real case study. With our assumptions of traffic evolution over 10 years, the optimized profile features a 6 % decrease in the primary energy consumption and a 8 % drop in the GWP impact. These results are indeed significant and can be explained by mechanical considerations. For example, the optimized solution mitigates the braking of trucks during a downhill descent.

These valuable results provide a new perspective for decision-makers by raising awareness about the environmental impacts of the operations phase due to the longitudinal profile. point, h f is calculated as h i but at the end of the segment (at the metric point x f ). w ph i , is the width on top of the formation level at the beginning of the segment, and, w ph f , is the same at the end. w pb i is the width of the basis of the formation level at the beginning of the segment line. It is computed from h i and the slope s bi of the bank, w pb f is computed at the end of the segment. The differences are symbolized by ∆: ∆h = h f -h i , ∆w ph = w ph f -w ph i , ∆w pb = w pb f -w pb i . The discretization step, d, is chosen by the surveyor. Equation A.1 remains unchanged in the case of an excavation, with V simply becoming the earth volume to be extracted.

For the sake of clarity, we have only presented the computation of the volume corresponding to the simplest embankment cross section in Figure 4. The volume computations were performed for all types of cross-sections, as described in Figure 5 by conducting the same method.

Figure 1 .

 1 Figure 1. Framework of the infrastructure design optimization process based on a life cycle assessment

Figure 4 .

 4 Figure 4. Elementary earthmoving Volume, X is the longitudinal direction, Y is the transverse direction

Figure 5 .

 5 Figure 5. Cross-sections of the embankment and trench road

Figure 6 .

 6 Figure 6. Fuel consumption computation

Figure 7 .

 7 Figure 7. Specific fuel consumption maps of a diesel engine

Figure 8 .

 8 Figure 8. Longitudinal profile (in red) modeled as a sequence of straight lines linked by circular arcs

  the longitudinal slope of the straight line k, x k , h k are the abscissa and altitude of the point of the intersection of straight line k and straight line k + 1. b k-1 and a k are internal variables output from the computation of the circle linking this straight line k to the next straight line.

Figure 9 .

 9 Figure 9. Optimized profiles vs. the initial (reference) profile

Table 1 .

 1 Values of the emission factors

Table 2 .

 2 Values of the parameters used to assess the construction phase

	Tasks	Energy label Value (MJ/m 3 ) GWP label Value (kgeqCO 2 /m3)
	Extract	e extrac	9.6 gwp extrac	0.753
	For 1km of transportation e trans	15.4 gwp trans	1.235
	Spread	e spread	11.6 gwp spread	0.913
	Quicklime	e lime	9000 gwp lime	2196

Table 3 .

 3 Measured traffic for the different vehicle categories (t: metric ton)

	Vehicle class	Traffic (per day/per direction)	Distribution Actual average speed (km/h)
	Car	2 419	70 %	113
	Van (< 3.5 t)	130	4 %	103
	mini-truck	102	3 %	95
	Truck and articulated vehicle	802	23 %	88
	Total	3 453	100 %

cycle inventory databases. In addition, the values of energy consumption and GWP for each task, as extracted from the tool ECORCE M

(Jullien et al. 2015b

) during earthmoving are considered in this assessment (see Table

Table 4 .

 4 Evolution in the traffic assumption for the different vehicle categories (Proj means Projected, veh for vehicle)

	Vehicle class	Traffic 2016	Fuel and veh subclass	Projected Proj. Average distribution distribution
				for 2016	2016 to 2025
	Car	2419	gasoline diesel	793 1626	797 1618
	Small van < 3.5 t	130	diesel	130	134
	mini-truck	102	diesel	102	102
	Truck and articulated veh.	802	Diesel truck < 32 t Diesel articulated < 44 t	447 355	406 396
	Total	3453		3453	3453

Table 5 .

 5 Vehicle data (t: metric ton)

	classes	vehicles per day Mass S.C x	C rr0	C rr1
			(t) (m 2 ) (1 × 10 -3 ) (m -1 s × 10 -6 )
	articulated vehicle (40t)	198	40	5.2	4.824	39.5
	articulated vehicle (25t)	198	25	5.2	4.824	39.5
	truck (19t)	406	19 3.27	4.824	39.5
	gasoline Car	799 1.48 0.73	11.84	5.25
	small class diesel Car	540 1.12 0.68	11.84	5.25
	medium class diesel Car	540 1.23 0.97	11.84	5.25
	high class diesel Car	540 1.51 0.82	11.84	5.25
	mini-truck	102 3.69 3.18	11.84	5.25
	Van	130 2.53 1.98	11.84	5.25

Table 6 .

 6 Overall results (TJ: Tera Joules, teqCO 2 : metric ton equivalent CO 2 )

		Reference Opt. profile Gain Opt. profile Gain	Flat
		profile	energy in %	GWP in % profile
	Primary energy use (TJ)	497	472.6	5	477.5	4 470.9
	Primary energy construction (TJ)	34.9	28.1	19	32.1	8	267
	Global primary energy (TJ)	531.9	500.7	6	509.6	4	738
	GWP use (teqCO 2 )	38174	36291	5	36673	4 36165
	GWP construction (teqCO 2 )	5950	4382	26	3422	42 52443
	Global GWP (teqCO 2 )	44124	40673	8	40095	9 88611
	construction costs of this simple solution explode: 267 TJ and 52,4433 teqCO 2 , in comparison with
	35 TJ and 5,950 for the reference profile. Its total costs (738 TJ and 88,6113 teqCO 2 ) significantly
	outweigh the total cost of our optimized solution (500 TJ and 40,0953 teqCO 2

Table 7 .

 7 Comparison by class of vehicle (TJ: Tera Joules, teqCO 2 : metric ton equivalent CO 2 )

			Reference			Optimized
	Vehicle	Energy	GWP	fuel	Energy	GWP	fuel
		(TJ) (teqCO 2 ) (l×10 6 )	(TJ)	(teqCO 2 ) (l×10 6 )
	Articulated vehicle (40t)	102.7	7899	2.64	92.2	7089	2.37
	Articulated vehicle (25t)	78.2	6014	2.01	75.2	5786	1.94
	Truck	117.18	9010	3.02	106.7	8207	2.75
	Gasoline car	63.9	4871	1.83	63.8	4858	1.82
	small class diesel car	13.6	1050	0.35	13.5	1037	0.35
	medium class diesel car	41.8	3215	1.07	41.8	3214	1.07
	high class diesel car	37.8	2905	0.97	37.9	2915	0.97
	mini-truck	19.1	1468	0.49	18.9	1454	0.48
	small Van	22.6	1739	0.58	22.4	1727	0.58
	Global	497.0	38174	12.99	472.6	36291	12.3

Appendix A. Elementary volume computation

In this Appendix, the elementary volume corresponding to Figure 4 is computed. The mathematical computation of the elementary volume V, is performed by integrating of a trapezoid from the beginning of the segment, with an initial index i, to the end, denoted by a final index f . This integration step yields the following result:

1) The height, h i , is the difference in altitude between the natural terrain and the road project at the beginning of the segment. h i = Ps(x i ) -Pn(x i ) where x i is the position of the initial segment

Appendix B. Notation

The following symbols have been used in this paper: d = step of discretization of the longitudinal profile (m); e cnu = the energy consumption by cubic meter spread on a final deposit (J/m 3 ); e f = the energy consumption by cubic meter for fill (J/m 3 ); e lime = energy consumption of one cubic meter of quicklime (J/m 3 ); e t = the energy consumption by cubic meter for cutting in order to build trench road (J/m 3 ); e extrac = the energy consumption by cubic meter in order to extract material (J/m 3 ); e trans = energy cons. for transport. of one cubic meter of mat. on 1 kilometer (J/m 3 /km); e spread = energy consumption in order to spread one cubic meter of materials (J/m 3 ); gwp cnu = GWP by cubic meter for cutting not used and spread on a final deposit (kgeqCO 2 /m 3 ); gwp f = GWP by cubic meter for fill (kgeqCO 2 /m 3 ); gwp t = GWP by cubic meter for cutting in order to build trench road (kgeqCO 2 /m 3 ); gwp extrac = GWP by cubic meter in order to extract material (kgeqCO 2 /m 3 ); gwp trans = GWP for transport. of one cubic meter of mat. on 1 kilometer (kgeqCO 2 /m 3 /km); gwp spread = GWP in order to spread one cubic meter of materials (kgeqCO 2 /m 3 ); gwp lime = GWP of one cubic meter of quicklime (kgeqCO 2 /m 3 ); h = the difference of altitude between the natural terrain and the road project (m); m = mass of the vehicle (kg) n = number of straight lines; r limeC = rate of quicklime of the treated materials stored in final deposit (%); r limeF = rate of quicklime of the treated materials for fill (%); s b = transversal slope of the embankment (%); v = speed of the vehicle (m/s); w ph = the width of top of the formation level (m); w pb = the width of the basis of the formation level (m);

x = longitudinal abscissa (m); C rr0 = constant part of the tire rolling resistance; C rr1 = part of the tire rolling resistance proportional to speed (s.m -1 ); C x = Drag coefficient; Dist D = average distance between cut and final deposit (km); Dist FC = average distance between cut and fill (km); E = primary energy consumption of the project (J); E c = primary energy consumption of the construction phase (J); E f = primary energy consumption of fill (J); E AddMat = energy consumption due to additional materials (J); F t = traction force (N); F r = running resistance (N); FC = Fuel Consumption; GWP = GWP of the project (kgeqCO 2 ); GWP c = GWP of the construction phase (kgeqCO 2 ); GWP f = GWP of fill (kgeqCO 2 ); GWP AddMat = GWP due to additional materials (kgeqCO 2 );

GWP o = GWP of the operation phase ; J = Cost of the project (cost is either primary energy consumption or GWP ); J c = Cost of the construction phase of the project; J o = Cost of the operation phase of the project; Pn = profile of the natural soil (m) (function of the altitude according to the abscissa) ; Ps = longitudinal profile of the project (m); Ps actual = longitudinal profile of the actual project (already built) (m); R = Radius of circular arc (m); S = front surface of a vehicle (m 2 ); V = Earthmoving Elementary Volume (m 3 ); V c = Cut Volume (m 3 ); V e = fill Volume (m 3 ); α = longitudinal slope (%); α r = longitudinal slope in radians ; ρ = air density (kg/m 3 ); τ d2Energy = Emission factor diesel to energy (MJ/l); τ FC2GWP = Emission factor fuel consumption to GWP (kgeqCO 2 /l); τ g2Energy = Emission factor gasoline to energy (MJ/l); τ d2GWP = Emission factor diesel to GWP (kgeqCO 2 /l); τ g2GWP = Emission factor gasoline to GWP (kgeqCO 2 /l);

Appendix C. Funding statement

This research did not receive any specific grant from funding agencies in the public, commercial, or nonprofit sector. The study was conducted with funding from the authors' respective institutes (Ifsttar and Cerema, France).

Appendix D. Data Availability Statements

Construction and Traffic data have been included in this paper. Vehicle consumption data are generated from the software, VEHLIB, which is not open source; nonetheless, the main parameters of the simulation carried out with this software have been displayed herein. All Data generated are available from the corresponding author upon request.


domain: chim phys spi spi.mat

text:
Pierre Gibot
email: pierre.gibot@isl.eu

François Quesnay

Christelle Nicollet

Lydia Laffont

Fabien Schnell

Julien Mory

Denis Spitzer

Detonation synthesis of ZrO2 by means of an ammonium nitrate-based explosive emulsion

Keywords: Ammonium Nitrate, Detonation, Zirconium (IV) oxide, Energetic emulsion, Ceramics Detonation, Zirconium (IV) oxide, Energetic emulsion, Ammonium nitrate, Ceramics

A zirconium (IV) oxide powder was successfully synthesized from the detonation of an explosive emulsion previously mixed with zirconium sulfate tetrahydrate salt (Zr(SO4)2•4H2O) as a ceramic precursor. After detonation of the energetic mixture in a detonation tank, the as-synthesized ceramic material was purified and characterized by X-ray diffraction, transmission and scanning electron microscopy techniques, nitrogen physisorption and dynamic light scattering. The ceramic powder is made of crystalline nanosized particles exhibiting a homogeneous sphere-like morphology. An attempt to explain the oxide ceramic synthetic mechanism is discussed. The detonation synthetic route implementing high temperatures and high pressures in a short time may be seen as an encouraging method for large-scale production of nanopowder.

Introduction

Ceramics are of great interest for of scientific research worldwide. Ceramic materials can be of different chemical natures such as oxides (Al2O3, TiO2, ZrO2, MnFe2O4 (ferrite), CaTiO3 (perovkite), LiMn2O4 (spinel)…) or non-oxides with carbides (SiC, TiC, B4C…), nitrides (Si3N4, AlN, BN, W2N…) and borides (TiB2, ZrB2…) [START_REF] Riedel | Ceramics Science and Technology -vol. 2 Materials and properties[END_REF]. This diversity in chemical composition explains the numerous and diverse properties exhibited by these materials and consequently the permanent interest in them. For example, ceramics claim high hardness and strength, elevated melting and boiling points, low electrical and thermal conductivities, a chemical inertia and even good optical and magnetic characteristics [START_REF] Riedel | Ceramics Science and Technology -vol. 2 Materials and properties[END_REF].

Ceramics are therefore a solution of first choice for a plethora of applications in various domains, including catalysis, electronics, magnetism, pyrotechnics, automotive, energy and the environment, aerospace and medical equipment [2].

The physico-chemical properties of ceramics, and from a larger point of view the materials, strongly depend of the synthetic experimental conditions, and authors have suggested and implemented numerous routes or processes to design tailored ceramics (size, morphology, particle-size distribution, aggregation rate, purity…). The synthetic methods include solid thermal decomposition, solid-solid and solid-gas reactions, precipitation, the sol-gel process, the hydrothermal approach, pyrolysis spray, vapour phase synthesis [START_REF] Haussonne | Céramiques et verres -Principes et techniques d'élaboration. Traité des matériaux[END_REF], flame synthesis [START_REF] Pratsinis | Flame aerosol synthesis of ceramic powders[END_REF], self-propagating high-temperature synthesis [START_REF] Levashov | Self-propagating high-temperature synthesis of advanced materials and coatings[END_REF], and combustion and detonation routes [START_REF] Kiminami | Combustion synthesis of nanopowders ceramic powders[END_REF][START_REF] Cudzilo | Detonative synthesis of inorganic compounds[END_REF]. Regarding this last approach, as per the literature, it can be described as either an instantaneous release of energy at very high temperatures (> 1000 °C) and pressures (> GPa) over an extremely short time or a chemical decomposition reaction with shock wave generation [START_REF]Groupe de travail de pyrotechnie spatiale (GTPS), Dictionnaire de pyrotechnie[END_REF]. From an experimental point of view, these physico-chemical properties seem to be extremely favourable for synthesizing (nano)powders, metastable phases and potentially novel structures. The additional rapid quenching operation at the end of the detonation reaction allows minimization of the growth phenomena. This concept was first used to synthesize nanosized diamond particles from the detonation of a mixture of two organic energetic molecules such as 2,4,6trinitrotoluene (TNT) and 1,3,5-trinitro-1,3,5-triazine (RDX) [START_REF] Titov | 9th Symposium on Detonation[END_REF]. This result succeeded due to temperatures and pressures as high as 2000-3000 °C and 20-30 GPa, respectively, corresponding to the diamond stability zone in the carbon phase diagram. This first success encouraged researchers to try producing other inorganic materials and a large majority of oxide materials [START_REF] Cudzilo | Detonative synthesis of inorganic compounds[END_REF]. For example, diverse oxides were thus synthesized as solid solutions of nanosized cerium oxide-gadolinium oxide (Gd2O3-CeO2) [START_REF] Vasylkiv | Nano-blast of nano-size CeO2-Gd2O3 powders[END_REF], manganese ferrite (MnFe2O4) [START_REF] Wang | Nano-MnFe2O4 powder synthesis by detonation of emulsion explosive[END_REF], lithium manganese oxide (LiMn2O4) [START_REF] Xie | Growth and morphology of nanometer LiMn2O4 powder[END_REF], strontium aluminate (Sr2Al2O4) [START_REF] Li | Preparation of Sr2Al2O4:Eu 2+ , Dy 3+ nanometer phosphors by detonation method[END_REF], titanium oxide (TiO2) [START_REF] Qu | Detonation synthesis of nanosized titanium oxide powders[END_REF], zinc oxide [START_REF] Xie | Detonation synthesis of zinc oxide nanometer powders[END_REF] zirconium oxide (ZrO2) [START_REF] Bukaemskii | Nanosize powder of zirconia. Explosive method of production and properties[END_REF] or even cerium oxide (CeO2) [START_REF] Zh | Study on the application of emulsion explosives in synthesizing nanostructured ceria[END_REF]. This approach was patented by Innovnano, a manufacturer marketing yttria-stabilized zirconia nanopowder [START_REF] Silva | Nanometric-sized ceramic materials, process for their synthesis and uses thereof[END_REF][START_REF] Santos | Process for nanomaterial synthesis from the preparation and detonation of an emulsion, products and emulsions thereof[END_REF][20]. All of these investigations describe the precise control of the morphology, stoichiometry and particle size of the synthesized products depending on the explosive used. Recently, detonation synthesis was successfully used for producing high value carbide ceramics such as silicon carbide nanoparticles (SiC) from a [TNT/RDX-polycarbosilane] composite [START_REF] Langenderfer | Detonation synthesis of silicon carbide nanoparticles[END_REF].

Herein, a successful synthesis of zirconium (IV) oxide ceramic particles by means of the detonation of a totally mechanically insensitive zirconium-doped ammonium nitrate-based explosive emulsion is reported. An explosive emulsion, such as Emulstar 3000, and zirconium sulfate hydrate were used as the explosive and ceramic precursor, respectively. In contrast to the literature, where the impactsensitive RDX secondary explosive is used as the energy source in a non-negligible number of investigations [START_REF] Vasylkiv | Nano-blast of nano-size CeO2-Gd2O3 powders[END_REF][START_REF] Xie | Growth and morphology of nanometer LiMn2O4 powder[END_REF][START_REF] Li | Preparation of Sr2Al2O4:Eu 2+ , Dy 3+ nanometer phosphors by detonation method[END_REF][START_REF] Qu | Detonation synthesis of nanosized titanium oxide powders[END_REF][START_REF] Bukaemskii | Nanosize powder of zirconia. Explosive method of production and properties[END_REF], which may contribute to creating a hazardous environment for the operator [START_REF]Explosives, impact sensitivity tests[END_REF][START_REF]Explosives, friction sensitivity tests[END_REF], the Emulstar 3000 explosive emulsion is likely insensitive. More, while zirconium carbonate was used as the Zr-source in [START_REF] Santos | Process for nanomaterial synthesis from the preparation and detonation of an emulsion, products and emulsions thereof[END_REF], and the Zr-sulfate salt was preferred here due to its high watersolubility, which may lead to a more homogeneous mixture with an explosive emulsion (water/oil mixture). After detonation, the product in the soot was characterized using the usual laboratory techniques.

Experimental section

Zirconium sulfate tetrahydrate (Zr(SO4)2 . 4H2O, 99%) was purchased from Alfa Aesar (Ward Hill, MA, USA). The Emulstar 3000 explosive emulsion was obtained from Titanobel (Pontailler, France).

According to the data provided by the manufacturer, the explosive emulsion is composed of ammonium nitrate (NH4NO3, 70 wt. %), sodium nitrate (NaNO3, 20 wt. %) and a mixture of water, oil and surfactant (10 wt. %). Some characteristics of the explosive emulsion are given in Table 1. The booster was homeprepared from graphitic carbon and a wax/1,3,5-trinitro-1,3,5-triazinane secondary explosive (RDX, C3N3H6(NO2)3, Eurenco, Massy, France) mixture. The components were mixed according to a mass ratio of 0.5:5:94.5%. An SA4000 electric initiator from Davey Bickford (Héry, France) was used to ignite the detonation reaction.

Density (g/cm

Preparation of the explosive emulsion/ceramic salt mixtures

Typically, the zirconium-based explosive mixture was prepared as follows: Zr(SO4)2 . 4H2O was added to the commercial explosive emulsion in a 10:90 weight ratio and mixed with a Turbula® mixer (model T2A, W.A. Bachofen) at 23 rpm for 20 min. The mixture (~250 g) was placed in a polypropylene tube (Ø = 43 mm, L = 150 mm, Supporting Information 1) according to a loading density of 1.15 g/cm 3 . The charge was placed in a plastic bag containing distilled water and hung in the centre of a steel detonation tank. The water medium was used to achieve a high quenching rate of the detonation products. A booster (55 g, Ø = 28.4 mm, L = 57.5 mm) and an electric initiator (SA4000, Davey Bickford) were used to complete the energetic train. After the detonation, the soot coated on the inner wall of the tank was collected, filtered to remove plastic and copper fragments and calcinated (800 °C, 2 hours) to remove the carbon phase that may originate from the combustion of the polypropylene tube.

Characterization techniques

Characterizations of the explosive emulsion/ceramic salt mixture

Before the preparation of large quantities of the explosive emulsion/ceramic salt mixture dedicated to the detonation experiments, small batches (5 g) were prepared and subjected to diverse security tests (shock, friction and thermal stresses) to validate their safe preparation and handling for the operator.

The impact sensitivity threshold, expressed in joules (J), was determined by means of a fall-hammer apparatus. The principle is based on the dropping of weights (1 or 5 kg) from an adjustable height on the sample (40 mm 3 ) embedded between two metallic cylinders. The friction sensitivity test was performed on a Julius Peter BAM device (Suceska 1992). The friction sensitivity, given in newton (N), is measured by scraping the powder (10 mm 3 ) between a ceramic stick and a ceramic plate. The force of the stick is determined by the position of weights suspended from the lever bearing the stick. The mechanical sensitivity values (shock and friction) correspond to the value of six consecutive "no-go", i.e., without any reaction (colour change, combustion reaction, clapping sound…). Regarding the thermal sensitivity of the explosive mixture, differential scanning calorimetric analysis (AQ 20, TA Instrument, New Castle, DE, USA) was implemented. A 1-2 mg sample of mixture was placed in a sealed gold crucible and heated from 25-400 °C following a heating rate of 4 °C/min under nitrogen flow (100 mL/min.). The analysis software was used to precisely determine the decomposition temperature, termed the onset temperature (Tonset).

Characterization of the detonation products

The X-ray powder diffraction pattern of the detonation product was recorded on a D8Advance Coulter, Brea, CA, USA). Prior to the measurement, the material was outgassed at 423 K for 10 hours under a helium flow. The specific surface area was determined according to the Brunauer-Emmet-Teller (BET) method in the 0.05-0.20 relative pressure domain. The particle-size distributions of the different powders were established by the dynamic light scattering method using a Zetasizer nanoZS apparatus (Malvern Instrument, Worcestershire, United Kingdom). For that, a dispersion of the sample in ethanol solvent (0.1 g/L) was prepared.

Results and Discussion

Characterization of the Emulstar 3000/ceramic precursor explosive emulsion

The sensitivity thresholds of the impact and friction tests tied to the onset temperature of decomposition of the zirconium-based energetic formulation are gathered in Table 2. For comparison, the values of the pure Emulstar 3000 explosive emulsion and standards required for ranking an energetic material as insensitive are also given [START_REF]Explosives, impact sensitivity tests[END_REF][START_REF]Explosives, friction sensitivity tests[END_REF]. As can be seen, both explosive emulsions (raw and mixed with a Zrbased salt) show total insensitivities to mechanical and thermal tests since their threshold values are higher than those mentioned by the standards (> 40 J, > 360 N and > 100 °C for the impact, friction and thermal tests, respectively). It should be noted that for the impact test, the value > 49 J is the highest value that can be determined from our fall-hammer apparatus. Then, by comparison with the Emulstar 3000 counterpart, the as-prepared Emulstar3000/Zr(SO4)2•4H2O mixture shows a slight sensitization to thermal heating with an onset temperature of 184.5 °C (vs. 207.8 °C), which may come from accelerated ammonium nitrate decomposition (main component of the explosive emulsion) upon contact with the metal ion (zirconium); however, this does not prevent the preparation of the mixture and detonation experiments [START_REF]NATO Standardization agreement, Explosives, thermal analysis using differential thermal analysis (DTA), differential scanning calorimetry (DSC), heat flow calorimetry (HFC), and thermogravimetric analysis (TGA)[END_REF]. Finally, compared to the literature, the sensitivity thresholds of the as-formulated Emulstar3000/Zr(SO4)2•4H2O explosive emulsion, in particular the mechanical ones, are higher than those of the 1,3,5-trinitro-1,3,5-triazinane organic explosive (RDX, C3N3H6(NO2)3) used by A. A.

Sensitivity test

Bukaemskii for the synthesis of zirconia nanoparticles [START_REF] Zh | Study on the application of emulsion explosives in synthesizing nanostructured ceria[END_REF]. In fact, the literature related threshold values are 7.5 J and 120 N for the RDX substance regarding the impact and friction tests, respectively [START_REF]Explosives, impact sensitivity tests[END_REF][START_REF]Explosives, friction sensitivity tests[END_REF].

Definitely, the explosive used in this work ensures total safety for the operator.

Characterization of the detonation product

Figure 1 shows the X-ray diffraction pattern of the product obtained after the detonation of the Emulstar 3000/Zr(SO4)2•4H2O explosive charge and the purification steps. The most intense diffraction peaks were attributed to a tetragonal structure with the P42/nmc space group describing the zirconium (IV) oxide structure (ZrO2, JCPDS card No. 72-7115). Miller planes were mentionned on the diffractogram.

Other low intensity diffraction peaks observed on all the diffraction domains were assigned to a polymorph of the zirconia phase, namely, the monoclinic phase (P21/c space group, JCPDS card No. 37-1484). For clarity's sake, the corresponding Miller planes were not mentioned on the diffractogram. The volume fraction of the monoclinic phase (Vm) in the ZrO2 zirconia powder was determined by using the following formula (1) [START_REF] Schmidt | Quantitative analysis of polymorphic mixes of zirconia by X-ray diffraction[END_REF]:

𝑉 𝑚 = 1.311.𝑋 𝑚 1+0.311.𝑋 𝑚 (1)
where Xm corresponds to the integrated intensity ratio defined by formula (2): (2)

𝑋 𝑚 =
with I(hkl) referring to the X-ray intensities of the diffraction peaks of the monoclinic and tetragonal phases identified by the subscripts m and t, respectively. The (-111) and ( 111) diffraction peaks characteristic of the monoclinic polymorph were located on both sides of the (101) most intense peak of the tetragonal structure (2 theta # 30°). A volume fraction of ~28% monoclinic phase was then calculated. The crystallite size or coherence length (D) of the ZrO2 zirconia powder was determined from Scherrer's equation shown below (3):

Dhkl = k• / (•cosθhkl) ( 3
)
where k is a dimensionless constant,  is the X-ray wavelength of the radiation ( = 1.54056 Å for copper radiation),  is the corrected peak width at half-maximum intensity and θ is the diffraction peak position. Taking into account the most intense diffraction peak (101)t, the coherence length was estimated to be equal to 20.3 nm. Figure 2 shows TEM and HRTEM micrographs of the as-detonated zirconia powder. The zirconia powder can be described as being made of spherical particles, in which the particle-size distribution seems to be narrow and centred at approximately 20 nm, as depicted in Figure 2A. The selected area electron diffraction pattern (SAED) exhibits diffraction rings with d spacings that could be attributed to the (101), ( 110) and (112) Miller planes, well-fitting to the P42/nmc space group corresponding to the ZrO2 tetragonal phase. The HRTEM images (Figures 2B andC) show diffraction planes on numerous particles, thus confirming the high degree of crystallinity of the ZrO2 powder synthesized by the detonation process. Moreover, the Fast Fourier transform done on HRTEM image of one nanoparticle (black square on Figure 2C) permits to identify the (101) plane characteristic of tetragonal ZrO2. Figure 3 shows representative SEM views of the as-detonated zirconium (IV) oxide powder. The low magnification pictures (Figure 3A) present a powder made of agglomerated particles with the size of the primary particles strictly below the sub-micrometre range (< 100 nm). The magnified SEM image, as shown in Figure 3B, reveals a quasi-spherical morphology for the particles constituting the sample since the shape-factor seems to be very close to one. From the highest magnification view of the powder (Figure 3C), the primary particle size can be estimated to be near 20-25 nm with a narrow particle size distribution. From a nitrogen physisorption measurement, the specific surface area of the as-detonated zirconium (IV) oxide powder was determined to be equal to 53 m 2 /g. This result is slightly higher than the one obtained by [START_REF] Santos | Process for nanomaterial synthesis from the preparation and detonation of an emulsion, products and emulsions thereof[END_REF] (i.e., 35 m 2 /g). Assuming that the powder is made of monodispersed spherical and dense particles; the following formula (4) can be used to calculate the average diameter (Ø) of the particles:

Ø = 6 / SBET (4)
where  is the density of the material (5890 kg/m 3 ) and SBET is the specific surface area of the considered material. An average diameter of 19 nm was thus determined for the ZrO2 particles. A way to evaluate the agglomeration state of the investigated powder is formula (5) described below and suggested by J. M. Haussonne et al. [START_REF] Haussonne | Céramiques et verres -Principes et techniques d'élaboration. Traité des matériaux[END_REF]:

FAG = dV50/dBET ( 5
)
where FAG is the agglomeration factor, dV50 is the medium diameter in volume and dBET is the average diameter deduced from the specific surface area of the considered powder. In the present case, a value of 7.5 was calculated for the zirconia powder, implying the dispersability of the as-detonated particles in liquid medium. To achieve a better possible dispersion, the experimental procedure will have to be improved.

A possible mechanism occurring during the detonation reaction of the mixture considered in the present work leading to the ZrO2 zirconia nanopowder synthesis can be suggested from the chemistry of explosives [START_REF] Akhavan | The chemistry of explosives[END_REF]. The composition of the ammonium nitrate-explosive is known to be 90 wt. % (70 wt.

% ammonium nitrate (NH4NO3) and 20 wt. % sodium nitrate (NaNO3)), with the rest consisting of water, oil and surfactant of an unknown chemical nature. To simplify the system, only the two nitrate salts will be taken into consideration as explosive sources, and the Zr-reactant will be regarded as an inert molecule.

The chemical reaction occurring when energetic molecules undergo an explosion can be described taking into account the amount of oxygen available during the reaction and provided by the reactants.

These data are referenced as the oxygen balance (OB) [START_REF] Akhavan | The chemistry of explosives[END_REF]. Due to the OB value being positive, nil or negative, the molecule then contains an excess, sufficient or a default in the concentration of oxygen compared to that needed for complete oxidation. In the last case, toxic gases such carbon (CO) and nitrogen (NO) monoxides can be released. In the present work, the OB for ammonium nitrate and sodium nitrate are positive and are 19.99% and 45%, respectively, leading to the following decomposition chemical equations:

NH4NO3(s)  N2(g) + 2H2O(g) + 1/2O2(g) (6)
2NaNO3(s)  N2(g) + Na2O(s) + 5/2O2(g)

Now, considering an intimate mixture of both, the OB value (OBAN/SN) was calculated from equation ( 8):

OBAN/SN = OBAN.CAN + (1-CAN).OBSN [START_REF]Groupe de travail de pyrotechnie spatiale (GTPS), Dictionnaire de pyrotechnie[END_REF] with OB and C being the oxygen balance and weight percent of each ingredient, respectively. Subscripts AN and SN are used for the ammonium and sodium nitrate compounds, respectively. The OBAN/SN is 25.3%. The decomposition reaction can be thus rewritten, taking into the hypothesis 1 g of energetic composition (77.77 and 22.22 wt. % of NH4NO3 and NaNO3, respectively) as follows:

0.0096NH4NO3(s) + 0.0026NaNO3(s)  0.109N2(g) + 0.0192H2O(g) + 0.00805O2(g) + 0.0013Na2O(s)

Regarding the zirconium-ceramic salt, an inert molecule from a pyrotechnics point of view, the decomposition reaction can be defined as follows:

Zr(SO4)2•4H2O(s)  ZrO2(s) + 4SO2(g) + 3O2(g) + 4H2O(g) [START_REF] Vasylkiv | Nano-blast of nano-size CeO2-Gd2O3 powders[END_REF] Now considering the three ingredients NH4NO3, NaNO3 and Zr(SO4)2•4H2O and their respective weight amounts within the final explosive mixture (explosive emulsion/Zr-salt: 90/10 wt. %), namely, 70, 20 and 10 wt. %, respectively, the global detonation reaction of 1 g of mixture can be summarized by equation [START_REF] Wang | Nano-MnFe2O4 powder synthesis by detonation of emulsion explosive[END_REF]:

0.00874NH4NO3(s) + 0.00235NaNO3(s) + 0.00028Zr(SO4)2•4H2O(s)  0.00991N2(g) + 0.01860H2O(g) + 0.00758O2(g) + 0.00117Na2O(s) + 0.00028ZrO2(s) + 0.00056SO2(g) [START_REF] Wang | Nano-MnFe2O4 powder synthesis by detonation of emulsion explosive[END_REF] As the explosive charge is placed in a bag containing demineralized water, the Na2O sodium oxide solid phase is converted into sodium hydroxide (NaOH) liquid phase during detonation. The zirconia solid material is the only solid phase formed during the detonation of the charge.

Conclusion

A zirconium (IV) oxide powder was successfully synthesized via a detonation process implementing an insensitive ammonium-based explosive emulsion and a zirconium sulfate salt as the detonating substance and ceramic precursor, respectively. With an explosive substance/ceramic precursor weight ratio of 90/10, a nanosized ZrO2 powder was obtained. The resulting powder was composed of agglomerated spherical particles with an average diameter of 20 nm. Generally, the synthetic method executed here presents a simple, efficient and tuneable route, which is exploitable for producing ultrafine oxide ceramic particles.

  diffractometer using Cu-Kradiation (= 1.54056 Å) equipped with a Lynxeye detector and operating at 40 kV and 40 mA ((Bruker, Billerica, MA, USA). The diffractogram was recorded from 20 to 80° with a 2 step size of 0.02°. The microstructure of the sample was observed by scanning electron microscopy (SEM) on a DSM 982 Gemini (Zeiss) with a 10 kV current. The transmission electron microscopy (TEM) and high-resolution (HRTEM) images were collected by means of a JEM 2100F (JEOL, Tokyo, Japan) microscope operated at 200 kV. The diffraction patterns of the investigated material were recorded using the selected area electron diffraction mode with a 150 nm aperture or by Fourier transform of the HRTEM images. The specific surface area (aS) of the powder was determined by a nitrogen physisorption measurement carried out on a SA 3100 surface area analyser (Beckman

Figure 1 :

 1 Figure 1: XRD pattern of the zirconium (IV) oxide sample (ZrO2) synthesized by means of a zirconiumdoped ammonium nitrate-based explosive emulsion detonation. The symbols t and  are attributed to the tetragonal and monoclinic structures, respectively.

Figure 2 :

 2 Figure 2: TEM images of the ZrO2 powder synthesized by means of a zirconium-doped ammonium nitrate-based explosive emulsion detonation. a) Bright field TEM image combined with the SAED pattern using a aperture of 150 nm b) and c) HRTEM images showing the high cristallinity of the nanograins specially on c) with the FFT of the HRTEM image corresponding to the (101) planes of ZrO2 tetragonal.

Figure 3 :

 3 Figure 3: SEM images in secondary electron mode of the ZrO2 powder synthesized by means of a zirconium-doped ammonium nitrate-based explosive emulsion detonation a) global view b) and c) same view with higher magnification.

Figure 4 :

 4 Figure 4: Granulometric distributions of the ZrO2 powders synthesized by means of a zirconium-doped ammonium nitrate-based explosive emulsion detonation.

Detonation pressure (GPa)* 8 Detonation velocity (m/s.) 5000

	3 )	1.2-1.3
	Produced gas volume (L/g)*	0.9
	Oxygen balance (g/100g)*	-0.3
	Energy (cal/g)*	907

Table 1 : Characteristics of the Emulstar 3000 explosive emulsion. (* manufacturer's calculated parameters)

 1

Table 2 : Sensitivity thresholds of the Emulstar 3000 (*manufacturer's data) and the Emulstar 3000/ceramic precursor mixture (90/10 weight %). The standards for an energetic material to be ranked as insensitive were added for comparison.

 2

Acknowledgements

The authors gratefully acknowledge the French National Centre for Scientific Research (CNRS), French German Research Institute of Saint-Louis (ISL, Saint-Louis, France) and University of Strasbourg (UNISTRA, Strasbourg, France) for funding. The authors express their acknowledgements to E.

Fousson (ISL, Saint-Louis) for his assistance in the detonation experiments.