C Rouzaud

Fabrice Gatuingt

G Hervé

N Moussallam

O Dorival

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

Influence of the aircraft crash induced local nonlinearities on the overall dynamic response of a RC

structure through a parametric study

Influence of the aircraft crash induced local nonlinearities on the overall dynamic response of a RC structure through a parametric study loads during their lifetime. Load durations of a few microseconds to milliseconds can be caused by explosions, airplane crashes, etc... When a structure is subjected to a brief mechanical shock, as it is the case when a projectile impacts a structure, several vibration regimes can be separated in terms of the appearance of the displacement field observed. Assuming that the structure is appropriately sized to withstand an aircraft impact, the determination of the shaking induced by the impact requires nonlinear dynamic studies on a significant time range after the shock. The response cannot be completely described using classical methods. The reason is that the finite element method associated with explicit integration time schemes would lead to prohibitive computation costs since the calculation must be carried out with a very refined mesh to represent all the transient dynamic response (ten linear elements per wavelength for good accuracy is usually assumed) that implies small time steps in the time integration scheme. As a consequence, the medium (between 10 and 100 wavelengths per substructure) and high (over 100 wavelengths per substructure) frequency ranges are often ignored in this type of simulation. One can also note that is impossible to simulate the response of a complete civil engineering structure with complex nonlinear behavior models [START_REF] Hervé | On numerical implementation of a coupled rate dependent damage-plasticity constitutive model for concrete in application to high-rate dynamics[END_REF][START_REF] Ragueneau | Anisotropic damage modelling of biaxial behaviour and rupture of concrete structures[END_REF][START_REF] Snozzi | A meso-mechanical model for concrete under dynamic tensile and compressive loading[END_REF][START_REF] Chambart | Intrinsic dissipation of a modular anisotropic damage model: application to concrete under impact[END_REF].

To solve the problem of shock induced vibrations in a reinforced concrete structure we developed a numerical strategy define in [START_REF] Rouzaud | A new way for the simulation of the impact on reinforced concrete structures[END_REF] that is presented in Figure 1. In this paper we will only focus on the first step of our strategy. The load is applied on a finite element model of the target structure and its response is calculated by a nonlinear Finite Element (F.E.) analysis. To simplify the problem we use a classical approach in which the aircraft is replaced by an equivalent force-time function. The loading diagram can be found using the Riera model [START_REF] Riera | A critical reappraisal of nuclear power plant safety against accidental aircraft impact[END_REF][START_REF] Bangash | Impact and explosion: analysis and design[END_REF]. We can note that [START_REF] Hervé | Optimizing the analysis of airplane crash induced spectra by means of generic airplane methodology[END_REF] shows the differences in terms of results in the frequency range simulated between a finite element aircraft model and its equivalent loading via the Riera method. The FE modeling of the aircraft generates a higher frequency content, mainly due to the folding effect of the aircraft fuselage. The Riera method is explained in details in [START_REF] Riera | A critical reappraisal of nuclear power plant safety against accidental aircraft impact[END_REF].

Finally we use the current force calculated to determine the force-time history. Figure 2 shows the corresponding force-time history with an initial velocity of 120 m/s for the aircraft and a mass of 120 tons. In this figure, the impact force as a function of time, where the peak force is equal to 100 M N and the time duration of the force waveform is 350 ms, is normalized. According to the open literature, the evaluation of the type of impact generated in an aircraft crash leads us to consider the global impact as a soft shock [START_REF] Sugano | Full-scale aircraft impact test for evaluation of impact force[END_REF]. Indeed if aircraft components produce individually different types of impact (elastic, inelastic, with rebound, hard, soft, ...), the global aspect could be classified as soft. The initial kinetic energy of the impacter can be decomposed after the impact into kinetic energy due to the possible rebound and energy dissipated during the impact. For a given kinetic energy, the energy dissipated during an impact is more important than the kinetic energy of rebound. The definition of soft shocks given in [START_REF] Eibl | Soft and hard impact[END_REF] and [START_REF] Ceb | Concrete Structures under Impact and Impulsive Loading, Synthesis Report[END_REF] is interesting because it is associated with a method of study of this type of impact (decoupling the calculation of force by the Riera formula and the calculation of the impacted structure). However it is a problem relative to the distinction from hard shocks. Indeed, comparing the movement of the target relative to the projectile is convenient because it induces a decoupling of the phenomena; it also corresponds to the intuitive definition of soft shock: a soft missile which hits a hard target. However this classification does not integrate well hard impacts when a rigid projectile going through a softer target or when the projectile impacts a flexible but tough target. There should be a criterion to distinguish not only soft and hard impacts on displacement or stiffness, but also on the threshold of fracture of materials; as suggests by [START_REF] Koechlin | Classification of soft and hard impacts -application to aircraft crash[END_REF]. Following this analysis, characterization of shock is "a priori" separated from the perforation. A soft shock, as well as a hard impact, can be both perforating or non-perforating ones. In the following we assume that the structure withstands the impact and as a consequence the perforating problem is eliminated.

The second step of our strategy, that was presented in a companion paper [START_REF] Rouzaud | A new way for the simulation of the impact on reinforced concrete structures[END_REF], is based on the application of the temporal attenuated signal obtained with the previous F.E. analysis at the boundary of the damaged area. This methodology will not be presented in thsi papaer.This damaged area corresponds in fact to an area around the impact surface where the damage is irreversible. In the case of a concrete slab, this area could be defined as a macro cracking zone. The response of the rest of the structure, which behavior remains linear, is computed with the Variational Theory of Complex Rays (VTCR) method in combination with a FFT/IFFT strategy. The VTCR is a wave-based computational approach dedicated to the resolution of forced vibration problems at a given frequency [START_REF] Ladevèze | The variational theory of complex rays for the calculation of medium-frequency vibrations[END_REF][START_REF] Ladevèze | Calculation of medium-frequency vibrations over a wide frequency range[END_REF].

In the strategy presented it is interesting to know more precisely the dimension of the nonlinear zone of the impact. Indeed restrict the geometry of finite element calculation to the damaged area is integrated in the strategy for calculating the induced vibrations (Figure 1) and also limits the significant numerical efforts required by this method. It is also important to surround the damaged area around the impact area because it is a zone of high energy dissipation and thus the determination of the vibrations induced in the structure is directly related to the transmission of energy through this area.

Based on the load function shown in Figure 2 we will investigate in this paper the influence of various parameters on the size of the nonlinear, or damaged, zone. These parameters are:

• the thickness of the target (h),

• the reinforcement ratio (longitudinal and shear rebars) (τ ),

• the compressive strength of the concrete (f ck ),

• the loading surface (S),

• the momentum imposed.

The average tensile strength of concrete f ctm is estimated in Eurocode 2 [START_REF]Eurocode 2 -Calcul des structures en béton[END_REF] by the following equations:

f ctm = 0.30f 2/3 ck iff ck ≤ 50M P a f ctm = 2.12ln(1 + f ck +8 10 ) iff ck > 50M P a (1)
The impact of each parameter on the results will be explored using the Taguchi methods as defined in [START_REF] Taguchi | Introduction to Quality Engineering[END_REF] and [START_REF] Souvay | Les plans d'expériences, Méthode Taguchi[END_REF]. A parametric analysis associated with a sensitivity analysis allows us to determine the size of the damaged area and the attenuation of the nonlinear area on the input signal.

The paper is structured as follows: Section 2 presents the modeling choices and a simple parametric analysis (one-at-a-time strategy [START_REF] De Rocquigny | Uncertainty in industrial practice: a guide to quantitative uncertainty management[END_REF]) to define the ranges to be considered for the variables and then sensitivity analysis allows to account for combined effects; Section 3 illustrates a definition of sensitivity analysis and its application through the Taguchi method; Section 4 defines the empirical formulas derived from the sensitivity analysis application; finally, conclusions and perspectives are drawn in Section 5.

Using the parametric analysis to define the problem

Different impacts can be characterized and classified according to [START_REF] Koechlin | Classification of soft and hard impacts -application to aircraft crash[END_REF]. Nevertheless, this classification does not allow the prediction of the nonlinear damaged area of the impacted structure. Furthermore, this classification does not take into account the various input parameters of the target. In order to evaluate the influence of input parameters on this problem and to identify and eliminate the sets of parameters leading the perforation breakout of the target, we performed the following parametric study.

Modeling choices

In this work LS_Dyna [START_REF]Ls-Dyna[END_REF] was used for the numerical simulations, with Lagrangian finite elements and explicit time integration. We decided to focus our study on a slab target with a square geometry of 40 m × 40 m. The boundary conditions are defined as totally blocked (displacements and rotations) on each edge. A loading history corresponding to Figure 2 is taken into account, this force is applied over a period of 1 s. For a low computational cost the slab was modeled with a total of 40,000 uniform shell elements. To perform these FE calculations the element size should depend on the wavelength. Here we used ten element per wavelength as rule of thumb [START_REF] Babuška | A generalized finite element method for solving the helmholtz equation in two dimensions with minimal pollution[END_REF]. We consider a maximum frequency of 100 Hz in relation with the input force-time history. The entire slab is modeled and the mesh is the same for all tests. We used an explicit analysis and so the time step is affected by element size and material sound speed. In very rough terms, time step is proportional to element size soundspeed . Material sound speed is proportional to

1 √ density .
The reinforced concrete has a complex behavior due to its heterogeneity, the complex behavior of the concrete and that of the concrete-reinforcement interface. The concrete is a nonlinear material with different behaviors in tension and compression, permanent strain with softening in compression and damage due to cracking in tension. Additionally in dynamics there is an increase of the elastic limit due to strain rate. To model the rupture of the material one can use the numerical technique of element erosion which is defined as the removal of finite elements according to a damage or stress state criterion. The steel reinforcement is also a nonlinear material (elastic-plastic), with a symmetric behavior in tension and compression. One should also consider a small dynamic effect due to the strain rate. Its failure will be considered when the total strain is large enough.

The material models used in the numerical simulations must represent as accurately as possible the behaviors described above. To do this with an acceptable computational cost, we used the nonlinear constitutive law of reinforced concrete Mat_Concrete_EC2 implemented in LS_Dyna [START_REF] Hallquist | LS-DYNA theory manual[END_REF]. LS-DYNA Mat_Concrete_EC2 model is for shell and Hughes-Liu beam elements only. It can represent reinforced concrete or plain concrete/plain reinforcement steel only. The position of the reinforcement steel cannot be explicitly defined within the concrete; hence the steel is evenly distributed, smeared, over the concrete cross section. The model includes concrete cracking in tension and crushing in compression, reinforcement yield, hardening and failure. Properties are thermally sensitive. Material data and equations governing the behavior (including thermal properties) are taken from [START_REF]Eurocode 2 -Calcul des structures en béton[END_REF]. Reinforcement is treated as separate sets of bars in the local element x and y axes. The concrete is assumed to crack in tension when the maximum in-plane principal stress (bending+membrane stress at an integration point) reaches tensile stress to cause cracking. Compressive behavior of the concrete initially follows the curve defined in Figure 3 as:

Stress = F cmax 3ε ε c1 (2 + ( ε εc1 ) 3 ) (2)
Figure 3: Mathematical model used in [START_REF]Eurocode 2 -Calcul des structures en béton[END_REF] to define the constitutive law of concrete.

where ε c1 is the strain corresponding to the ultimate compressive strength F cmax , and ε is the current equivalent uniaxial compressive strain. The initial elastic modulus is given by E = 3 2 Fcmax εc1 . After reaching F cmax , the stress decreases linearly with an increasing strain, reaching zero ε cu . The strains ε c1 and ε cu are by default taken from the Eurocode 2 or EC2 (abbreviations for BS EN 1992, Eurocode 2: Design of concrete structures) and are a function of temperature. At 20°C they take values of 0.0025 and 0.02 respectively. F cmax is also a function of temperature, given by the input compressive strength of concrete (which applies at 20°C) times a temperature-dependent softening factor taken from [START_REF]Eurocode 2 -Calcul des structures en béton[END_REF]. At 20°C the behavior is elastic-perfectly-plastic, up to the onset of failure, after which the stress reduces linearly with increasing strain until final failure.

Figure 4 defines the EC2 tension-compression behaviour obtained from uniaxial compression and uniaxial tension quasi-static tests in displacements via a constant nodal velocity.

6

Parametric analysis

As said earlier, the parametric analysis should allow us to determine the influence of the input parameters on the response of the structure. This study eliminates the values which lead to the perforation of the target. Indeed, according to open literature, an aircraft impact can be identified as a bending problem and not a punching one. Consequently we define four target parameters which could play an important role in the nonlinear response of the target. These parameters to be studied are the following:

• the loading surface of the aircraft impact,

• the characteristic strength of the concrete slab target,

• the reinforcement ratio,

• the thickness of the concrete slab.

In our approach and in the perspective to use it later in the Taguchi method, only one parameter changes from one simulation to the other.

We will in particular pay attention to the maximum deflection of the concrete slab, the radius of the damaged area which is numerically defined through the damage Mazars model [START_REF] Mazars | A description of micro-and macroscale damage of concrete structures[END_REF], and reactions to boundary conditions in our simulation results. This damage model is a model simple, considered robust, based on the damage mechanics [START_REF] Lemaitre | Mechanics of solid materials[END_REF], which allow describe the reduction in the rigidity of the material under the effect of the creation of microscopic cracks in the concrete. It lean on only one scalar intern variable D, describing the isotropic damage of way, but distinguishing despite everything the damage from tension and the damage from compression. Please note that we chose to compare the response of the concrete slab with the elastic one (undamaged target). This comparison is done on the first oscillation cycle of the curve obtained.

Influence of the loading surface

In these simulations and for each loading surface configuration, the slab thickness was 1.2m. and the concrete has a compressive strength of 40 MPa. For the reinforcement, 2 layers composed of 32mm steel reinforcing bars, 20cm spacing (noted as HA32@20 cm) in both directions were considered. Several loading surfaces are then studied: 4 m 2 , 8 m 2 , 12 m 2 , 15 m 2 , 18 m 2 , 21 m 2 , 37 m 2 and an average commercial aircraft surface (fuselage (φ = 3.76m ⇒ Surface = 11m 2 ) + wings (L = 29m)).

All surfaces over which the loading force (Figure 2) is applied have a circular form, except for the last one. For the average commercial aircraft we consider two areas: a disk for the fuselage and a rectangle for the wings. In this case, the loading history is a little bit different (see Figure 5). For the two smallest loading surfaces (4 m 2 and 8 m 2 ), we got an inversion of the Jacobian for some finite elements in the impact area leading to a simulation stop. Indeed, in both cases the elements undergo significant deformation that led to the perforation of the slab. The results of these two surfaces are then not considered in this study.

In Figure 6 the deflection of the slab decreases when the loading surface increases. The minimal deflection obtained (except for the aircraft) is 50 cm for S=37 m 2 .

In Figure 7 the loading surface does not have a significant impact on the size of the nonlinear area. However, there is anyway a small decrease of the slab damage zone at the end of the simulation increasing the loading surface. The damaged area for the "Fuselage + Wing" is more important than can be explained by the size of the wings, and thus the dimension of the loading area.

In Figure 8 one can note a correlation between the boundary reaction and the slab damage area. Indeed the damage of the concrete slab dissipates some of the energy applied, hence a decrease in the force applied at the boundary conditions. One can also note that increasing the load surface provides a lower dissipation of energy at the boundary conditions. This directly translates into higher reaction force.

At the end for the simulations, the average radius of the damaged area is around 11m and the dissipation of the applied load through the nonlinear area is about 35 %.

In conclusion the load surface should be larger than the fuselage surface in order to avoid the perforation phenomenon for these slab dimensions. Finally, the results obtained for a loading surface that is more representative of an aircraft show a combination of the results for the various tested surfaces. For example the deflection of the slab is similar to teh one obtained for a very large load area and inversely the radius of the damaged area is close to that obtained for a small surface.

Influence of the concrete compressive strength

As in the previous subsection, in the simulations presented the slab thickness is 1.2 m and we used two layers of HA32@20 cm in both directions for the reinforcement. The load history (see Figure 2) is applied on a circular surface of 12 m 2 . Several concrete compressive strength are now studied: 30 M P a, 40 M P a, 50 M P a and 60 M P a.

These values were chosen in order to represent ordinary and commonly used concretes. We can see the results in terms of deflection of the slab, boundary reaction force and radius of the damaged area in Figure 9, 10 and 11. As in the previous paragraph, we were not able to obtain results for all the configurations tested. For the smallest concrete strength (30 M P a) we got a perforation of the slab that is not wanted. Here we can note, quite logically, that increasing the concrete strength (and as a consequence the tensile strength) has an important effect. Nevertheless, the overall results seems to tend towards an asymptote from a resistance of 50 M P a. Indeed, beyond this resistance, one obtain an average deflection equal to 40 cm, a damaged radius around 8.5 m and a dissipation of the applied load through the nonlinear area about 22 %.

Influence of the reinforcement ratio

In the simulations presented the slab thickness is again 1.2 m and the concrete has a compressive strength of 40 M P a. The load history (see Figure 2) is also applied on a circular surface of 12 m 2 . Four configurations of the reinforcement are then studied:

• HA25@25 cm (i.e. 0.2 %/m of steel) in both directions,

• HA25@20 cm (i.e 0.25 %/m of steel) in both directions,

• HA32@20 cm (i.e. 0.4 %/m of steel) in both directions,

• HA40@20 cm (i.e 0.63 %/m of steel) in both directions. These four configurations were chosen because they are common in the civil engineering structures to which this study refers. The results obtained in terms of deflection of the slab, evolution of the damaged area and reaction force are shown in Figure 12, Figure 13 and Figure 14. The first two steel ratios are not relevant, because in both cases we get a perforation of the concrete slab. Only two configurations remain: HA32@20 cm and HA40@20 cm.

Figures 12, 13 and 14 show that we obtain an important difference in the results between these two configurations. We observe in Figure 12 that the de-flection is reduced by a half; in Figure 13 that the damaged radius is reduced by more than 3 m and in Figure 14 that the maximum of the reaction force is multiplied by two. These results are in good agreement with the results of subsection 2.2.2. This shows that for a bending problem, the parameters which affect the flexural strength of the slab have a significant influence on the responses. However in the particular case of the reinforcement ratio, constructive arrangements put limits in terms of possible configurations. It would be difficult to design a slab with a reinforcement ratio higher than HA40@20 cm.

Influence of the slab thicknesses

In this subsection the slab thickness is the parameter. In the slab we impose two layers of HA32@20 cm in both directions for the reinforcement with a concrete compressive strength of 40 M P a. The load history (see Figure 2) is also applied on a circular surface of 12 m 2 . Seven configurations of the thickness are then studied: 0.6 m, 0.9 m, 1. The first two thicknesses are not relevant, because in both cases we have a perforation of the concrete slab. These simulations are not considered hereinafter. In Figure 15 one can see that when increasing the thickness of the slab the maximum displacement will decrease. Moreover the slab will have a lower amplitude of vibrations and its residual displacement will approach zero. In this study, one can see that the results about the deflection and the nonlinear area decrease almost continuously. In Figure 16 one can observe that a thicker slab is less damaged and a reaction force approaching the elastic case (see Figure 17).

Here we can conclude that the thickness of the slab has a significant impact on the nonlinear area. In the cases studied, the results do not seem to converge towards a limit value.

Parametric analysis conclusion

As a conclusion to the parametric analysis, we can say that the minimum values leading to a perforation of the slab were determined. In this case, we did not pay particular attention to these configurations because the aircraft impact is treated -according to the state-of-the-art of the reinforced concrete structures we want to represent -as a flexural problem.

The results are in a good agreement with what could logically be expected if the dynamic load case is treated as a static problem. It is also difficult to identify a trend between the input parameters and the results and the interaction among parameters are impossible to perform in this way. The sensitivity analysis described in the next section is intended to fill this gap.

Using a sensitivity analysis by the Taguchi method

The aim of this section is to achieve a sensitivity study with a comparison between the effects of different parameters. It should allow us to identify which factors have an important effect on the maximum deflection of the concrete slab, on the radius of the damaged zone and on the reaction force at the supports.

Design of experiments concept

Sensitivity analysis or more precisely design of experiments, DOE, deals with planning, conducting, analyzing and interpreting controlled tests to evaluate the factors that control the value of a parameter or group of parameters. One also seek to acquire new knowledge by controlling one or more input parameters to obtain results validating a model with good economy (for example number of tests as low as possible). Indeed, this method is widely used in connection with the design of an industrial product. The problem of the designer is to find the "right" values of these parameters, i.e. the values for which the product will have the required behavior. So we need to identify the influence of parameters on the response of the product. The cost of a sensitivity study depends on the number and on the order of the different tests needed. Design of experiments is therefore to select and order tests to identify, at lower costs, the effects of parameters on the response of one product. This is a statistical method using simple mathematical concepts. Implementation of these methods involves four stages: 1) identify system parameters. These parameters correspond to physical quantities of the industrial product, which are allowed to change;

2) specify the values that you want to give them. On the actual product the parameters can evolve continuously (with an infinite number of possible values) or in a discrete manner;

3) define a sensitivity analysis, that is to say a series of tests to identify the model coefficients;

4) perform tests to identify the coefficients and conclude.

Design of experiments are defined in two categories: full and reduced plans:

• Full plans This first category of sensitivity analysis intends to provide the most complete information possible on systems. The full plans are to test all possible combinations, varying all factors at all levels exhaustively.

• Reduced plans

In practice, full plans can only be used for systems with very few factors, or when each test is very simple and short. For example, in the case of a test with five parameters of three levels, it requires a full plan of 3 5 = 243 tests... The objective of reduced plans is to select only few combinations of the varying parameters. They naturally reduce experimental or numerical costs but also reduce the available information on the system behavior. It is then necessary to ensure the relevance of the selection with the model to identify. Different techniques of reduced plans were defined [START_REF] Box | Statistics for experimenters[END_REF][START_REF] Taguchi | Introduction to Quality Engineering[END_REF]. Among the most widely used and robust, let us mention the following two methods: Box and Hunter method The Box and Hunter method [START_REF] Box | Statistics for experimenters[END_REF], could build reduced plans from full plans. It is intended only for models with two levels per parameter and is based on the following definition:

x i and x j are two parameters, each admitting two values, marked as +1 and -1. We define the level of interaction l ij between x i and x j , the result of the product of their respective value. The level of interaction between these two parameters is therefore expressed formally if, in a given test, the two parameters proceed "in the same sense" or not. Table 1 shows the Box and Hunter table with 3 factors as an example. Taguchi method Another well known technique of reduced plans is the Taguchi tables designed by the statistician Genichi Taguchi [START_REF] Taguchi | Introduction to Quality Engineering[END_REF] in order to minimize the effect of uncertainties and measurement errors. In practice a Taguchi table is a table associated with one or more linear graph [START_REF] Taguchi | Orthogonal arrays and linear graphs: tools for quality engineering[END_REF]. Table 2 shows the Taguchi table for seven parameters with two values (-1 and 1).

Test x 1 x 2 x 3 l 12 l 13 l 23 l 123 1 -1 -1 -1 +1 +1 +1 -1 2 +1 -1 -1 -1 -1 +1 +1 3 -1 +1 -1 -1 +1 -1 +1 4 +1 +1 -1 +1 -1 -1 -1 5 -1 -1 +1 +1 -1 -1 +1 6 +1 -1 +1 -1 +1 -1 -1 7 -1 +1 +1 -1 -1 +1 -1 8 +1 +1 +1 +1 +1 +1 +1
Test x 1 x 2 x 3 x 4 x 5 x 6 x 7 1 -1 -1 -1 -1 -1 -1 -1 2 -1 -1 -1 1 1 1 1 3 -1 1 1 -1 -1 1 1 4 1 -1 -1 -1 -1 1 1 5 1 -1 1 -1 1 -1 1 6 1 -1 1 1 -1 1 -1 7 1 1 -1 -1 1 1 -1 8 1 1 -1 1 -1 -1 1 Table 2: Taguchi table L8 (2 7 )
The sensitivity analysis, such as the methods mentioned it, directly gives the test sequence to achieve. Once those are completed, it remains to use the results to identify the model coefficients. To this aim we use statistical techniques based on an important property of experimental design: the orthogonality property. To identify the model coefficients, the idea is to use calculations of averages over sets of "balanced" results, i.e. orthogonal: this is the concept of effect. We thus define the (total) effect of a factor x i at a level A i as: the average of results for which x i = A i -the overall average.

It immediately follows from this definition that for each x i factor, the sum of its effects at different levels is zero. Similarly, let us define the effect of the interaction between x i and x j at the levels A i and A j as: the average of results for which x i = A i and x j = A j x i effect at level A i x j effect at level A j the overall average.

The result is that for all factors x i and x j , the sum of the effects of their interaction with different levels of one or the other of the two factors is zero.

In conclusion, the design of experiments provides a simple and effective way to reduce the cost and increase the robustness of experimental studies in the design and validation of an industrial product. It allows the use of any product knowledge which the designer can have a priori, provides a framework for rigorous modeling, and its implementation requires only basic mathematical knowledge. In our approach, the choice of the methodologies used for sensitivity analysis could be discussed, in particular with respect to other approaches available for global sensitivity analysis. Let us mention two other methods. The Sobol indices adapted for probabilistic framework that is not our case. The Morris method is a one-step-at-a-time method (OAT) which implies that in each run only one input parameter is given a new value. This is more numerically costly than reduced plans methods.

Application of the Taguchi method to our study

As seen in the previous section, we have chosen to model an impacted reinforced concrete slab with shell elements using the EC2_Concrete nonlinear behavior with LS_Dyna. The boundary conditions are defined as totally blocked (displacements and rotations) on each edges. The remaining parameters to vary are the following:

• loading surface: S = 12; 15; 18; 21; 37m 2 ,

• compressive strength : f ck = 40; 50; 60M P a,

• slab thickness: h = 1.2; 1.35; 1.5; 1.8; 2.1m,

• reinforcement ratio: τ = 12.56; 15.71%,

• coefficient time: c t = 0.5; 1,

• loading coefficient : c c = 0.5; 1.

In the values to be taken into account, we removed those involving a perforation of the slab to overcome this kind of problem. We also added two other variables: c t and c c , a time coefficient, which could change the time duration of the force waveform, and a load factor respectively. The load factor could modify the peak force. These two values are factors which will allow us to observe the effect on the results of changing the momentum applied to the impacted slab. Table 3 relates the two extremum values considered for each parameter. Using a reduced Taguchi sensitivity analysis with variables at two levels, allows us to reduce the number of tests to 8 instead of 2 6 = 64 which leads to significant time savings in the numerical simulation. Table 4 shows the values taken by the simulations parameters for each test. For the numerical simulations we considered three important and representative results: the maximum deflection of the concrete slab, the radius of the damaged area and the maximum reaction force. These results are given in Table 5. As the reaction force is highly dependent on the applied load and as this applied load is different for the 8 tests, we have chosen to evaluate the maximum reaction force obtained compared to the maximum one in the elastic case (i.e. a slab which does not suffer any damage). This ratio gives an idea of the dissipation due to the nonlinear response of the slab. Using the formula given in the previous section for the Taguchi tables, the effect at a level is defined by the average of all the results minus the overall average. From this, one can calculate the influence of each parameter on the three quantities of interest (deflection, damaged radius and reaction force). The results are reported in Table 6 The influence of each parameter on each quantities of interest can then be compared (see Figure 18,[START_REF] Riera | A critical reappraisal of nuclear power plant safety against accidental aircraft impact[END_REF][START_REF] Rouzaud | A new way for the simulation of the impact on reinforced concrete structures[END_REF]. This reduced sensitivity analysis gives the effect of each parameter on the quantities of interest. We can then conclude to a strong dependence of the overall results on the momentum of the load (c t and c c ). We can also see that the thickness of the slab has a very important effect on the deflection of the slab and on the radius of the damaged area. Indeed, the stiffness of the impacted structure is directly linked to the thickness of the slab. In the case of the restitution to the boundaries of the load applied, the strength of the concrete and also the thickness of the slab both have a significant effect.

Levels S(m 2 ) f ck (M P a) h(m) τ (%) c t c c -1 12
Tests S (m 2 ) f ck (MPa) h (m) τ % c t c c 1

Sensitivity analysis conclusions

While a simple parameter study allows us to see only the influence of each variable separately, the realization of this sensitivity analysis associated with the Taguchi method allows us to compare the influence of each parameter on the results of the concrete slab. With this study we therefore prioritized these variables according to their importance on the nonlinear area. We can then conclude that firstly the momentum applied, secondly the thickness of the slab (Figures 18,19) and thirdly the concrete strength (Figure 20) are the parameters which have the more influence.

However, the results obtained are highly dependent on the choice of the levels for each variable. For example increasing the difference between the two levels of a parameter could, at the same time, increase its effect on the response. So levels must be chosen in this scope. It is in this context that the previous parametric studies allow to estimate these values and make our analysis robust.

Determination of predictive empirical formulas

The aim of this section is to link all the results obtained in the previous sections. The determination of a formula would allow us to have a rough estimate of the different results (maximum deflection of the slab, damaged radius and reaction ratio) before introduction of a finite element calculation.

In our case, we will introduce one equation for each quantity of interest. We will use the following methodology:

• let A be the sought quantity: F , r damaged or R max. f orce/max. elas. f orce ,

• in the range of assigned variation we have six parameters: the thickness h of the slab, the loading surface S, the maximum strength of the concrete in compression f ck , the ratio of the slab reinforcement τ and the momentum coefficients c t and c c .

• we then search for a simplified and empirical law as the following form:

A(h, S, f ck , τ, c t , c c ) = Ā + c A 1 . ĥ + c A 2 . Ŝ + c A 3 . f ck + c A 4 .τ + c A 5 . ĉt + c A 6 . ĉc (3) where c A 1 , c A 2 , c A 3 , c A 4 , c A 5
and c A 6 are constants associated to the quantity A which have to be determined from calculations of sensitivity analysis. In fact these constants determine the effect of each parameter. Ā is the average of the results considered A on all trials deducted from the Taguchi table. p corresponds to the normalized value of the parameter p defined as follows:

p = (p -p) σ p ∈ [-1; 1] ⇒ plevel -1 = -1 plevel 1 = 1 (4)
with p the average of parameter p between these two levels chosen and σ p the standard deviation (σ p = -p level -1 + p = p level 1 -p).

For three sought quantities, the following formulas are obtained: +0.2 (τ -0.1413) (0.1571-0.1413) -7.5 (ct-0.75) (1-0.75) -5.9 (cc-0.75)

F (h, S, f ck , τ, c t , c c ) = F + c F 1 . (h-h) σ h + c F 2 . (S-S) σ S + c F 3 . (f ck -f ck ) σ f ck + c F 4 . (τ -τ ) στ + c F 5 . (ct-ct) σc t + c F 6 . (cc-cc) σc c = -196.4 + 160.2 (h-1.65) ( 2
(1-0.75) (7) These formulas provide a rapid way to estimate the desired parameter in optimal design without using a finite element calculation. Due to the nonlinearity of the results obtained by the simulation, an error limited here by the range of parameters chosen is induced by these equations. This is especially true and even more important when the applied momentum is away from the initial one. It is therefore recommended to keep c t and c c as equal to 1 in order to have a lower error. The error induced for the other parameters is quite limited due to the linear results in the chosen range of variations.

However, this formulation is robust and provides reliable results in the range of variation of the parameters used and so if the impact does not produce the perforation of the structure. To conclude, uncertainty and errors are quite limited in these ranges of parameters but one should deepen this approach and associated statistical errors in order to are them in a more general framework for aircraft impact study on NPP. Here it is important to highlight that this statistical approach was developed to limit the numerical costs.

Conclusions and perspectives

In this paper the impact of different geometries and slab boundary conditions were first studied by means of parametric analysis.

We presented a parametric analysis to observe the influence of the different values taken by each chosen parameter. This provided us with essential informations on the simulations -the limit between perforation and bending range for instance. The aim was to place ourselves in a case of shaking of structures that refers to a bending problem. In addition, the perforation case creates various problems outside the scope of continuum theory.

The last step presents the results obtained by performing a reduced sensitivity analysis. For this, we used the Taguchi method taht gave a table for limiting the number of simulations. We then obtained the influence between the different parameters studied. From there, we were able to establish an order of importance for each variable and to propose empirical formulas to estimate roughly the influence of each parameters.

To conclude, this sensitivity study allowed us to realize that it is difficult to identify a direct relationship between inputs and outputs in the case of the simulation of aircraft impact on a civil engineering structure, particularly in terms of nonlinear area and reaction at the boundary of this area. Also the results and formulas obtained are valid for aircraft impact load cases leading to flexural problems. It is thus useful in an optimal design. Outside this range, these formulas are not usable.

Figure 1 :

 1 Figure 1: Global calculation strategy.

Figure 2 :

 2 Figure 2: Force as a function of time (normalized).

Figure 4 :

 4 Figure 4: Stress / strain curves (tension-compression) of the EC2 law for concrete material.

Figure 5 :

 5 Figure 5: Loading history for an average commercial aircraft

Figures 6 ,

 6 Figures 6, 7 and 8 show the results obtained in terms of deflection of the slab, evolution of the damaged area and reaction force.

Figure 6 :

 6 Figure 6: Evolution of the deflection of the slab for different load surfaces

Figure 7 :

 7 Figure 7: Evolution of the radius, in mm, of the damaged area for different load surfaces

Figure 8 :

 8 Figure 8: Evolution of the reaction force for different load surfaces

Figure 9 :

 9 Figure 9: Evolution of the deflection of the slab for different concrete strengths

Figure 11 :

 11 Figure 11: Evolution of the reaction force for various concrete strengths

Figure 12 :Figure 13 :

 1213 Figure 12: Evolution of the deflection of the slab for different reinforcements ratios

Figure 14 :

 14 Figure 14: Evolution of the reaction force for different reinforcements ratios

  2 m, 1.35 m, 1.5 m, 1.8 m and 2.1 m. The results are show in Figures 15, 16 and 17.

Figure 15 :Figure 16 :Figure 17 :

 151617 Figure 15: Evolution of the deflection of the slab with the slab thickness

Figure 18 :

 18 Figure 18: Influence of parameters on the deflection, in mm, of the concrete slab

Figure 19 :

 19 Figure 19: Influence of parameters on the radius, in mm, of the damaged area of the concrete slab

Figure 20 :

 20 Figure 20: Influence of parameters on the maximum reaction, in M N , on boundary conditions of the slab concrete

rc r damaged 1 . (h-h) σ h + c r damaged 2 . 3 . (f ck -f ck ) σ f ck +c r damaged 4 .c r damaged 5 .+ c r damaged 6 .f orce 1 . (h-h) σ h + c R f orce 2 . 3 . (f ck -f ck ) σ f ck +c R f orce 4 . 6 .

 12345612346 .1-1.65) + 16.9 (S-24.5) (37-24.5) + 23.5 (f ck -50) (60-50) -7.2 (τ -0.1413) (0.1571-0.1413) -123.2 (ct-0.75) (1-0.75) -128.7 (cc-0.75) damaged (h, S,f ck , τ, c t , c c ) = rdamaged + (τ -τ ) στ + (ct-ct) σc t (cc-cc) σc c= 4565.4 -2639.9. (h-1.65) (2.1-1.65) + 12.4 (S-24.5) (37-24.5) -217.6 (f ck -50)(60-50)-379.2 (τ -0.1413) (0.1571-0.1413) + 1611.7 (ct-0.75) (1-0.75) + 2124.2 (cc-0.75)(1-0.75)(6)R f orce (h, S, f ck , τ, c t , c c ) = Rforce + c R (cc-cc) σc c = 123.1 + 3.8 (h-1.65) (2.1-1.65) -2.1 (S-24.5) (37-24.5) -5.3 (f ck -50) (60-50)

Table 1 :

 1 Box and Hunter table with 3 factors

Table 3 :

 3 The sensitivity analysis levels

Table 4 :

 4 Lists of tests for the sensitivity analysis

	Max. reaction

Table 5 :

 5 Numerical results for each test of the sensitivity analysis

  .

	Variables		h(m)			τ (%)
		Max	Damaged Max. reaction	Max	Damaged Max. reaction
	Levels	deflection	radius	/max. elas.	deflection	radius	/max. elas.
		(mm)	(mm)	reaction (%)	(mm)	(mm)	reaction (%)
	-1	-160.2	2639.9	-3.8	7.2	379.2	-0.2
	1	160.2	-2639.9	3.8	-7.2	-379.2	0.2
	Variables		c t			c c
		Max	Damaged Max. reaction	Max	Damaged Max. reaction
	Levels	deflection	radius	/max. elas.	deflection	radius	/max. elas.
		(mm)	(mm)	reaction (%)	(mm)	(mm)	reaction (%)
	-1	123.2	-1611.7	7.5	128.7	-2124.2	5.9
	1	-123.2	1611.7	-7.5	-128.7	2124.2	-5.9
	Variables		S(m 2 )			f ck (M P a)
		Max	Damaged Max. reaction	Max	Damaged Max. reaction
	Levels	deflection	radius	/max. elas.	deflection	radius	/max. elas.
		(mm)	(mm)	reaction (%)	(mm)	(mm)	reaction (%)
	-1	-16.9	-12.4	2.1	-23.5	217.6	5.3
	1	16.9	12.4	-2.1	23.5	-217.6	-5.3

Table 6 :

 6 Effect of each variable on the 3 quantities of interest


Jacques Leonardi

Feasibility Study of a Network of Consolidation Centres in Luxembourg

Keywords: Urban Consolidation Centre, Clean Vehicle, City Logistics Management Models, Feasibility Study, Ex-ante Impact Assessment

The concept of a multi-actor network of Urban Consolidation Centres (UCCs) was tested in Luxembourg. The authors of this paper developed a feasibility study together with the Luxembourg's Ministry of Transport. The methods used are encompassing data collection and data analysis, ex-ante scenario development and impact assessment of different options, interviews, workshops, and consultation with key operators in the public and private sectors. The market size appears to be sufficient. Clean technology is available and the willingness to use it is given. The management structure can rely upon constructive partnerships, a draft Charter for Urban Logistics and regulatory changes.

INTRODUCTION

Recently, many different configurations and logistics systems have emerged around the topic of freight consolidation, and several city logistics policies in Europe are considering the establishment and set-up of an Urban Consolidation Centre (UCC) together with the use of clean trucks and vans for central area deliveries (Triantafylou et al. 2014). This is done because a high potential for climate change impact reduction is estimated to be available in the freight transport system [START_REF] Mckinnon | CO 2 Emissions from Freight Transport in the UK. Report prepared for the Climate Change Working Group of the Commission for Integrated Transport[END_REF]. To reach this objective, it is required to find and provide suitable buildings and clean vehicles, then to set up the delivery service. Many different additional activities are also needed, such as regulation change, data collection and processing, and innovative city logistics management, such as stakeholder engagement and consultation methods. All these activities were developed during this feasibility study of an Urban Consolidation Centre in Luxembourg.

In Luxembourg, a relatively small country of about 550,000 inhabitants in Western Europe, in which there are no public city logistics policies in place so far, a new initiative was started by the Ministry of Sustainable Development and Infrastructure (MDDI) and the large logistics operator CFL Multimodal. The objective of this initiative is to coordinate the management of a city logistics policy focusing on a new Urban Consolidation Centre. Far from being limited to a pure theoretical exercise of writing down the different potential solutions available, business needs and transport requirements, success factors and rules to be followed by the operators, the study participants were engaged into a policy process aiming at the successful set-up of an Urban Consolidation Centre.

Therefore, from the very beginning, the feasibility study was embedded in a much larger activity framework, aiming at developing an innovative and result oriented urban freight policy in Luxembourg.

More precisely, the feasibility, governance model, business model and critical market size would have to be demonstrated, before the project of starting a new UCC could be considered viable.

Due to the very high number of failed projects of (often subsidized) consolidation centres in the past, notably in Europe [START_REF] Allen | The role of urban consolidation centres in sustainable freight transport[END_REF][START_REF] Ville | The limits of public policy intervention in urban logistics: Lessons from Vicenza (Italy)[END_REF], it was important to define clearly the risks and opportunities of such an initiative, and to test an approach that could become replicable in other contexts, especially in cities which have not implemented any city logistics strategy so far. Luxembourg cities are such newcomers from the point of view of urban logistics and thus this feasibility study is facing multiple challenges.

As a first very broad working definition, the Consolidation Centre was considered to be a classical logistics storage and transhipment depot, from which clean vehicles would start to deliver goods to the central areas of different cities in Southern Luxembourg. The exact number of logistics activities was not pre-defined but central functions of the new depot would be cross-docking and consolidation, while stockholding and replenishment, returns management, packaging or other B2B or B2C logistics services were not considered essential at this stage.

Besides this central area of cross-docking and consolidation action, several other policy domains required attention:

-Legislation change, -Street design, -Consultation with multiple stakeholders, -Consensus building, -Data collection and processing, -Scenario development and impact modeling.

All these elements were to be included into the study. The paper presents the main outcomes of these topics, which are all integrated and logically connected in the analysis of the feasibility study. In the following Section 2, we present the general approach chosen and the methods applied. In Section 3, we review different existing or past solutions and provide a benchmark. In Section 4, we identify key results of our modelling efforts for the Luxemburg situation. Section 5 provides concluding remarks.

METHODS, APPROACH AND ASSUMPTIONS

The modeling approach is qualitative for the business and policy-oriented part, and quantitative for the impact evaluation part of the feasibility analysis. The central element is an ex-ante evaluation using an adapted mix of scenario modelling, data collection and beforeafter approach.

It was not the purpose of this feasibility study to develop any new, innovative method but to prepare a tangible result; therefore a mix of existing, well-validated methods was selected, applied and replicated.

The methodological basis of approaches to urban freight evaluation is presented in multiple studies. For example [START_REF] Macharis | The multi-actor, multi-criteria analysis methodology (MAMCA) for the evaluation of transport projects: Theory and practice[END_REF] use Multi Actor, Multi Criteria Analysis, which is very inspirational for this study. For an overview, clear explanations and a review of different concepts and evaluation methods on consolidation, see [START_REF] Allen | The role of urban consolidation centres in sustainable freight transport[END_REF].

For the past 20 years, economics literature on consolidation centres has developed a way of doing studies which includes two basic elements, a theoretical one and a case study oriented one. While in the theoretical works all elements of definitions, methods and modelling imply a rather top-down approach, in the case studies, the bottom-up approach, learning by doing and learning from examples and tests prevail. Case studies are in high number, and the on going key projects in Europe have been a source of inspiration for this study. The publications of many dozens of case studies and lessons learnt can be found at the respective online documentation of BESTFACT, SMARTFUSION, STRAIGHTSOL, LAMILO, and SUGAR projects (see the reference Section below). One of the main challenges faced by these projects is to streamline a structured approach to case studies so that all the different initiatives can be compared to each other. Using a standard grid and a fixed structure of analysis (process, success factors, barriers, costs, impacts, etc.) provides this.

The most popular information for decision makers is to understand how a solution was applied successfully. Once this has been made clear through the information provided, the case study can be considered as 'ready for use'.

The main difficulty of all case studies is to demonstrate the economic feasibility and this is due to a lack of good costs data. Therefore one focus of this feasibility study was to collect cost data in as many relevant fields as possible and in the highest possible quality. Of course, there are very good reasons why good costs data are very difficult to obtain, for example confidentiality, too much effort involved, separated datasets, etc. [START_REF] Thompson | Evaluating City Logistics Schemes[END_REF]. These technical barriers to the collection of costs metrics could not be entirely removed but much time was employed to overcome this difficulty. Costs data were obtained through interviews with current operators of successful UCC schemes (see below).

The main methodology of the before-after assessment used in this feasibility study was developed in previous studies [START_REF] Leonardi | Before-after assessment of a logistics trial with clean urban freight vehicles: A case study in London[END_REF]. Of course there is a very substantial literature, on which the authors could heavily rely upon, on how to best evaluate the potential application of an innovative solution in the frame of a well-managed city logistics policy [START_REF] Taniguchi | City logistics: Mapping the future[END_REF]. To simplify the whole impact evaluation methodology to a maximum: The first step for the Luxembourg UCC feasibility study is an ex-ante impact assessment that consists in collecting key data on the before situation and the second step aims at developing plausible scenarios with key actors in order to quantify the future impacts on different elements.

To read more about the calculation methods and equation used here, please see [START_REF] Leonardi | Before-after assessment of a logistics trial with clean urban freight vehicles: A case study in London[END_REF]. The main difference with this reference work from the year 2012 is that there are no 'after' data collected. The 'after' situation was the product of assumptions and estimates developed with the main businesses operating in urban delivery in Luxembourg.

The relevant impacts are measured with key urban freight impact indicators defined as follow:

The number of parcels delivered daily: the volume, expressed in parcels or pallets, is a key urban logistics indicator. One pallet in these calculations corresponds to 50 parcels.

The distance driven per parcel: measured in km/parcel, the distance is a key indicator of the presence of delivery vehicles in urban traffic. Our assumption is that any reduction in the distance per parcel results in the same reduction in a similar percentage of external costs of traffic accidents, noise, emissions, congestion. This is the main measure of the beneficial impacts of a solution.

CO 2 emissions per parcel, measured in kg CO 2 e / parcels, is a key efficiency indicator for estimating the environmental impact of logistics solutions. Fuel is expressed in l/100km and then in litres per day. The result is divided by the number of packages per day to achieve litres per package. The DEFRA (2012) equivalent of 3.1kg CO 2 factor for one litre of diesel is applied to get the result in kg CO 2 e / parcel. The choice of electric vans and the purchase of electricity from regenerative sources allow to sharply reduce the total freight transport emissions measured with this indicator. Hybrid trucks lower emissions by about 20% compared with standard diesel trucks.

The number of staff: It is an employment indicator. Generally, UCCs allow a reorganization, an increase in the number of parcels per stop and therefore increased productivity and fewer staff. But here, the approach chosen is to maintain the same parcel / staff ratio before and after the creation of the UCC. This is a conservative assumption that would need to be checked during the monitoring of the tests.

The total cost per parcel: This is an economic benefit indicator, calculated in € / parcel delivered. This includes personnel costs, fuel, fixed vehicle and building costs and other variable costs. These data are first collected per km or per day, then in combination with parcels per day to obtain costs per parcel.

REVIEW OF SOLUTIONS: CASE STUDIES AND BENCHMARKING OF UCCs IN 2014

According to [START_REF] Triantafyllou | Urban Freight Consolidation Centers: Case Study in the UK Retail Sector[END_REF], two types of UCCs are mainly in use:

1) Large operators and logistics service providers develop privately their own regional depot in order to consolidate the flow to and from a large metropolitan area. 2) Cities or public authorities set up and manage multi-user logistics centres. While the first type of UCC is mainly owned and run by a single operator, the second type is used by multiple logistics providers and is the product of cooperation. For the feasibility study, the original focus was more on how to set up the second type of UCC. But, because of the established presence of the first type of UCC in Luxembourg, one of the hypotheses was to try to include all existing types of UCCs into a single broad concept that would encompass many different solutions and lead to a more consolidated urban freight delivery system overall. This type will be called in the following 'network of UCCs.' According to this objective, the first requirement is to analyse potential solutions in terms of their practicalities and adaptability to the Luxembourg situation. A review of solutions was included in the full report, and is summarised here.

From all aspects of Consolidation Centres, the most relevant criteria that were chosen for the review were those that are essential to understand how it has come to a market success and how not to replicate failures. Therefore, particular attention was directed to the successful configuration and preparation process, to the high impacts on costs and on CO2 reduction, and to the managerial and technological solutions leading to logistics efficiency gains such as a better load factor, or a lower distance per delivery.

Fundamental studies were performed on the demand side, in order to test the viability of different types of potential solutions. [START_REF] Marcucci | The potential demand for a urban freight consolidation centre[END_REF] found out in a stated preference survey in Italy that "UCC service cost, delivery time, annual cost of the access permits to the LTZ (Low Traffic Zone), and parking distance from the shop" are the key decision influencing factors for the future user. Other elements such as Track and Trace and Warehousing have much less or no influence.

A high number of publications were issued on the best possible management solution for the set-up of consolidation centres, and the current debate seems to focus more on the analysis of success stories, in order to better understand how to avoid past mistakes and risks (van Duin et al. 2012[START_REF] Ville | The limits of public policy intervention in urban logistics: Lessons from Vicenza (Italy)[END_REF], Gonzales-Feliu et al. 2014).

One of the most reccurent items in the literature is about the lessons learned from past failures. Many UCCs were established as a result of private initiatives, partly because their promoters anticipated increased access difficulties for transport companies due to a strengthening of regulations or an increase in congestion in dense urban areas. But, in Europe, it is the opposite effect that has been observed. Because municipal policies have been targeting (and achieving in many cases) a reduction in car traffic in central areas, they have paradoxically left more roadspace to commercial transport. "Anti truck" regulations were expected by the road transport industry and promoters of UCCs, but theses tough rules did not materialized, until the arrival of environmental zones by the late 2000s [START_REF] Dablanc | Impacts of environmental access restrictions on freight delivery activities, the example of Low Emission Zones in Europe[END_REF]. It is in this way that the manager of UCC Basel, opened in 1993 and closed eight years later, explained his lack of success: incentives to use the UCC gradually disappeared (as easing of congestion resulted from car traffic reduction in the city centre), while the price of using his depot did not diminish. [START_REF] Panero | Urban Distribution Centers -A Means to Reducing Freight Vehicle Miles Traveled[END_REF] indicate another side-effect of transport policies in Fukuoka in Japan that hampers the development of UCCs. A recent municipal policy to increase the supply of public parking space in the city centre has reduced the market advantage of UCCs, which was to provide parking for transport operators to deliver businesses and retail stores in the downtown area.

Learning from these lessons, the main strategy is to avoid the pitfalls or escaping the barriers. To this aim, new UCC models are developped, that are both more robust and better targeted. The local authorities incentivise, organise or set up UCC schemes, using a qualitative development strategy (advertising), targeted subsidies, or specific regulations giving priority to carriers using the UCC. This solution is at risk on a legal level, but as demonstrated by the case of Vicenza in Italy, the courts may ultimately give their blessing to the regulatory action of a municipality [START_REF] Ville | The limits of public policy intervention in urban logistics: Lessons from Vicenza (Italy)[END_REF].

Many projects have been completed through public-private partnerships, in which cases governments often financed at least parts of the initial investments, preparatory studies and evaluation studies. Sometimes the municipality, or an association of store owners in the case of Motomachi, near Tokyo, is up to finance partly the operation of the service. The UCC in La Rochelle is included in a public service concession, and its managers are receiving subsidies for each parcel delivered. Some examples show that a purely privately owned service can be profitable without subsidies, for example Binnenstadservice in the Netherlands, although the economic model is still fragile. The organization of a number of UCCs has become more professional (appearance of major players such as DHL or Transdev), and the legal framework used for setting up a delivery consolidation activity is getting more robust. A law from January 2014 in France actually mentions that a municipality can set up a UCC as a public service "if the private supply of urban delivery services is ill-adapted."1 In some cases, such as Lille in France, UCC operations are assigned to a new service provider that was previously external to the local distribution market, facilitating the acceptance of the new organization by the other carriers.

A recent trend in Europe is the emergence of parcels and freight networks and the increased concentration of the urban logistics industry. A very recent trend is the appearance of systematic approaches to urban delivery services. Until today, for innovative urban freight solutions, the most frequently used approach for one innovator was just to start bottom-up with a trial or a case study, then expand it in case of commercial and technical success; but this approach was using isolated experiments made in single cities. Instead, the new approach is more systematic and targets cross-city, sometimes cross-country networks. Examples are the following:

Large logistics groups like UPS, DHL or Fedex today commonly engage contractors for operations in the most central areas of many large cities, which are using electric or innovative vehicles (such as electrically assisted cargocycles). They use service providers that can provide this type of cleaner operation, which requires the use of logistics distribution centres nearby. These companies or their subcontractors are in search of land opportunities close to cities or within cities in order to develop these networks of logistics centres.

The Geodis Group announced the development of Distripolis, a network of urban consolidation centres. Distripolis aims at consolidating the urban distribution of three parcel express transport subsidiaries of Geodis within the same national urban distribution network, using clean delivery vehicles for the final segments of distribution. The network takes longer than expected to deploy, notably because, among others, a lack of available urban spaces to accommodate the urban cross-docking operations, and other land use problems. However, this example is worthy of attention as it systematizes a network approach.

Star's Service is a delivery company that has become dominant in France as the main home delivery partner of marketplaces and urban retail chains. It now operates more than 1200 delivery vehicles from logistics centres that are located near major urban centers to minimize the stem mileage and time, and maximize the reactivity and quality of service.

Across Europe, powerful e-commerce parcel delivery networks are now organized at a national or a European level (Kiala/UPS, Pickup services, ByBox, Packstations, etc.). The concept it to use local stores or automatic locker boxes at certain central points to offer consumers the possibility to pick-up a parcel at their convenience, while reducing the need for transport operators to reach the home of each single consumer. Their spatial deployment is now outstanding [START_REF] Morganti | Final deliveries for online shopping: The deployment of pickup point networks in urban and suburban areas[END_REF].

Innovative start-ups are gradually taken over by large groups: in France, Star's Service bought La Petite Reine (one of the first urban delivery operators using cargocycles in the early 2000s) in 2011, Kiala was acquired by UPS in 2012.

RESULTS

Market analysis

Our market analysis has focused on the current state of urban logistics activities in Luxembourg. The main result is that market potential for a UCC has been verified, due to an estimated total number of deliveries per day of about 20,000 in the cantons of the Ville de Luxembourg and Esch-sur-Alzette, the two main cities in the Southern part of the country.

The few business leaders that are currently running successfully profitable UCC schemes in Europe, and were willing to share their experience, stated in interviews that the minimum conditions for a profitable UCC business would be to deliver a volume of 1000 parcels per day, to sell the service at 2.5 Euro per drop, and to rely upon a very good client relationship. Logistics operators in Luxembourg were asked and stated that these volume, price and relationship targets seemed achievable.

According to the same business leaders currently running UCCs, electric vans and CNG trucks are available on the market at prices that are comparable with diesel options. Even if the purchase price is slightly higher, operating costs are lower and the total costs of ownership are similar for electric vans and natural gas powered trucks. For clean vehicles, there is also the question of the autonomy range for battery powered vans. The geographical catchment area of a potential UCC seem to be limited by the short range of clean vehicles. If only electric freight vans are considered, the delivery area would have to be within a 45-50 km radius of the Centre. This is corresponding to a round trip distance of about 120-160km per day. The boundaries of the two cantons of Luxembourg and Esch-sur-Alzette are well within these limits and therefore the autonomy range is not considered as a limitation for the choice of vehicle fuel technology. Consequently, there is also demonstrated market feasibility in terms of using clean vehicles.

The feasibility studies regarding actual facilities and logistics buildings showed that there are at least two running logistics facilities and depots located within Luxembourg city centre. There are also several municipality-owned parking facilities that could potentially accommodate a small cross-docking area. The two operators of these depots showed willingness to start using those locations for the UCC. The surface estimated to be needed for distributing 1000 parcels a day in a cross-docking activity is about 300-400 m 2 ; under the condition that no other logistics service activity would take place. This surface is available in at least two depots, and could be used in the short term for a kick-off of the consolidation system. Therefore, the market feasibility is also demonstrated in terms of available building space.

Network of UCCs, options and identification of scenarios

A consultation process with the industry, commerce and key stakeholders took place, and a governance model for the future consolidation centre was developed.

Our business case analysis suggests that different options for consolidation activities seem to be suitable for an initial start-up phase. Notably, an option with one single logistics depot and another option with a network of existing logistics hubs. In both cases, the operator of a UCC would be allowed to deliver to a restricted area in the city centre, provided they use clean vehicles. Especially the network option, if retained, would be a managerial, policy and governance innovation in city logistics. To our knowledge, there is currently no network of multiple urban consolidation centres in operation. The set-up of a network would have the advantage to preserve the business of every current logistics operator in Luxembourg, modifying only each operator's city centre deliveries. For an established operator, the only condition to fulfil to be considered a UCC , would be to use clean vehicles and deliver to the central area in a consolidated manner. In this scenario, access rules in the central area would become more restrictive, notably for diesel trucks. Under these new regulations, operators using diesel vehicles could not access the restricted zone, and would have to drop their shipments at the UCC instead. The UCC would then see its market volume increase, permitting further consolidation of its delivery activities.

The advantage of a network of UCCs, compared with a single UCC, is that it provides an impulse for many more logistics providers to operate with clean vehicles and in a more optimized manner.

The regulation changes are a crucial element of the feasibility of a successful UCC scheme. Access rules to specific areas, such as pedestrian zones, would need to be changed in favour of clean vehicles and specific time windows allowed for deliveries from the UCC.

To decide on the final configuration for the future UCC concept, it is important to identify the potential effects of different options, developing several scenarios, and quantifying their impacts on the indicators above.

To this aim, each scenario has been sketched and defined so that it has only one major difference option compared with other scenarios.

The basic requirement of an option is that it is not supposed to reproduce all the elements that will become effective in the final establishment of the UCC.

To illustrate the options available and the potential changes induced by a UCC introduction in Luxembourg, see Figure 1. • Scenario 2: one UCC + 10% market share increase through capture of international flows + clean vehicles

• Scenario 3: one UCC + Micro-depot + 10% international flows + clean vehicles • Scenario 4: Scenario 3 + Group of retailers from the same street • Scenario 5: Alliance of one large + many small businesses • Scenario 6: Alliance of two large companies: one specialist in logistics, the other in trade Many descriptions and assumptions are needed to calculate the impact of generic scenarios. UCC business solutions are based on qualitative and quantitative assumptions used in the scenarios. These assumptions are the following: BEFORE Scenario 0 (BAU): 1200 parcels per day are delivered to the centre of Luxembourg city and Esch-Alzette, including 400 (equivalent of 8 pallets) with 1 diesel truck (HGV) and 800 by 8 diesel vans (LGVs). 100 parcels are delivered daily per HGV or LGV.

AFTER Scenario 1: Using 8 electric vans and a clean hybrid truck. All vans are 100% electric, distributing 800 parcels / day, and the hybrid truck delivers the equivalent of 400 parcels or 8 pallets / day. No CO 2 emission occuring from electric vans, due to renewable sources of electricity. Clean truck is a hybrid electric 7.5t diesel with a capacity of 400 parcels or 8 pallets.

AFTER Scenario 2: Scenario 1 + 10% of total volume (120 parcels) is added from international routes. One electric van and one van delivery driver are added, distributing 10% more volume. The total volume delivered is 1320 parcels / day.

AFTER Scenario 3: one diesel truck of 40 tonnes carries 400 parcels to the microdepot at night or off-peak hours before continuing its round. After a transshipment at microdepot, the 400 parcels are delivered by four electrically assisted tricycles. Among the remaining volumes, 520 parcels are delivered by six electric vans and 8 pallets (equivalent of 400 parcels) are delivered by one hybrid truck. The micro-hub is large enough to handle the transfer of 400 parcels and provide parking for 4 tricycles or small electric vans, or 200 m 2 . This surface, according to the working hypothesis is in a public car park or at an existing depot and is made available to the operator without a charge. The organization of the tests will determine whether it is possible to arrange the delivery through an existing micro-depot without necessarily making an additional break in the supply chain or setting up a completely new logistics facility. At night, the micro-hub must provide parking for electric vehicles and thus be equipped with charging stations. No logistics activity or service is provided on the micro-hub. No staff is present except the drivers.

AFTER Scenario 4: + 10% (120) of the total parcels are added to the total volume of parcels of scenario 3, with the retailers' group in a single destination. This group could be a single street in the pedestrian area of Luxembourg city. The total volume delivered is equivalent to 1440 parcels / day. One more van and one delivery driver are added to carry the 10% additional volume.

AFTER Scenario 5: same conditions apply as in Scenario 3, but there are 20% of revenues and staff more through an alliance of a logistics company with several small logistics providers.

AFTER Scenario 6: Alliance of two large companies. Same conditions apply as Scenario 1, but with doubled initial volume (2400 parcels per day before) and no volume increase AFTER (2400 parcels per day after). Use of micro-hub and tricycles, as for scenario 3, for 400 parcels per day after. Other trips are made by electric vans from the suburban depot.

Before and After: one driver per vehicle. The truck driver who delivers the microdepot does not end their round trip after delivering there, but continues the journey to other destinations. Half a working day is allocated for that driver to calculate labour costs in the options that include the micro-depot.

Before and After: 100 parcels per day per vehicle for the van or the tricycle, 400 parcels equivalent of 8 pallets per day for the truck.

The additional quantitative assumptions are:

Impacts of scenarios

The impacts of scenarios 1 to 5 are presented in Figure 2. The impacts for scenario 6 are presented in Figure 3. Scenario 1 has two effects: a strong reduction in emissions and a much smaller reduction in costs due to the low price of electricity. Because all other logistics indicators remain stable in the assumptions, including staff and distance, the main business indicators remain the same, and only the fuel consumption and vehicle fuel costs are going down. Fuel cost represents a small percentage of the overall costs and its reduction is too small to cause a substantial overall decrease in costs per parcel.

Scenario 2 shows an increase by 10% in the volume of packages. Keeping a ratio of 100 packages/ vehicle leads to the findings that the key indicators also remain fairly stable, except for emissions that going strongly down. A better result would be obtained if we assume that a driver could deliver 10% more parcels due to the close proximity of the client's destinations. In that case the consolidation of the vehicles would be higher, which would lower further the distance per parcel and the costs per parcel.

Scenario 3 introduces two simultaneous changes: the use of a micro-depot or mini-hub in the city centre and the use of power-assisted tricycles for the final delivery. To supply the micro-depot, a diesel truck delivers 400 packages early in the morning or during a night shift, coming from the UCC, before continuing its tour. This route generates more emissions than the equivalent of four electric vans, but lowers the distance per van between the UCC and the city centre. The final distribution with four tricycles has the same ratio of parcel delivered / staff than the parcels delivered by truck. The decline in the total distance leads to a reduction of fixed costs and variable costs, as these costs are also calculated on a km basis. Thus, the effect on logistics total distance of four cycle delivery trips results in lower costs per package.

This applies in the event that the micro-depot does not create additional real estate costs, or any costs that would have to arise in case an additional breaking point is introduced for the load in the supply chain (see description of the scenario 3 above).

For scenarios 4 and 5, volume growth increases the number of drivers and the number of parcels, and this effect could potentially result in reduced profitability; but the calculation shows that is not the case, with an index of the total cost per package that remains in all scenarios lower than the costs of BAU. The beneficial effect of a micro-depot on total mileage remains constant in absolute value in scenarios 4 and 5. This explains the good profitability of these two solutions. As the number of packages that pass through the micro-depot does not increase above 400 in all these scenarios, the relative share of micro-depot use decreases. Thus the total distance per package and therefore costs per package do not diminish further. In all scenarios, the main effect for a total distance reduction is the replacement of four vans by one truck on the trips between the UCC and the micro-depot. It would be fairly possible to increase the capacity of the micro-depot and start using electric vans from there but this has not been taken into consideration at this very early stage. Of course it would be possible to assume that more load would be transiting through the micro-depot without additional breaking point in the supply chain, for example through re-arrangement of existing operations and reallocation of space use in city centre depots. In that case the impacts on distance and on costs reduction would be even more beneficial.

For Scenario 6 (cooperation of two large companies), the reduction of key indicators is substantial because the estimated consolidation is strong. The total distance is reduced by about 10% per package, because the distance driven by a tricycle from the minihub is significantly lower than the distance of a round trip in a van from the UCC. Thus, distance, costs and emissions are going down significantly in this scenario. This conservative scenario is assuming that the final distribution through a micro-hub is remaining for volumetric amount identical to scenario 3 (400 packages) delivered with four tricycles. If the number of packages that pass through the micro depot doubles, and if the number of tricycles doubles, the reduction in distance travelled per parcel would reach 20% instead of 10%.

It is therefore advisable to think big and consider an alliance between two large companies, because this option has a higher operational impact potential for a network of UCCs in Luxembourg.

CONCLUSION

The feasibility study was completed at the end of January 2015 with an overall positive outcome, as the market, technology, building and business conditions seem favourable for the creation of a UCC network.

The expected planning of the consolidation centre has already started and business consultations are taking place.

The policy changes are becoming more specific and therefore the targets of establishing a clearer and more rationale basis for the planning, preparation and set-up of a UCC, or of a network of UCCs, have been reached.

Knowledge about the urban logistics sector in Luxembourg has improved and the data made available through observation surveys have demonstrated that the day to day practice is very similar to other cities in Europe.

Therefore it seems reasonable to expect that the technologies, concepts and business solutions applied elsewhere for UCCs could potentially be transferred to many different logistics and retail businesses in Luxembourg.

The development of each current logistics business established in Luxembourg and providing deliveries to city centres will probably evolve in short terms towards a more sustainable urban freight system. If the solutions presented in this study are fully applied by a high number of operators, this system will be based on a network of UCC serving the central area with consolidated and clean vehicles. The expected overall impacts are lower costs for businesses and reduced negative externalities for local communities.

The feasibility study itself was certainly not a methodological innovation, in so far as it did not invent any additional equation of impact assessment. But the review of existing solutions and the dialogue with different actors were leading to the development of an innovative practical solution, the network of UCCs. This solution could be further facilitated through a mix of practical tests, participative stakeholder involvement and consultation, market research and impact assessment, data collection and evaluation, and regulatory changes.

In all these fields, activities have already started to be implemented beyond the duration of the project, and consequently, the feasibility study can be seen as a validated research and managerial tool facilitating public policy action and business decisions in city logistics.

The next steps will if the solution of a Network of UCCs can be successfully tested in small experimentations and later implemented at a larger scale.

Figure 1 :

 1 Figure 1: Logistics scheme of the Luxembourg delivery area with and without a UCC

Figure 2 :

 2 Figure 2: Impacts on key indicators of UCC scenarios 1 to 5

Figure 3 :

 3 Figure 3: Impacts of an alliance of two large companies in scenario 6

  • Distance from UCC to city center is 15 km • Distance from UCC to micro-depot is 15 km • Distance / day within the city center, for trucks or vans or tricycles is 20 km

	• Number of parcels per day delivered per truck, van or tricycle driver is 100
	• Large 40 tonne truck fuel use in urban conditions is 40 l / 100km
	• Diesel van fuel use is 22l / 100km
	• Clean hybrid truck fuel use is 28l / 100km
	• Emission factor is 3.1 kg CO 2 / l diesel
	• Cost of personnel per working day is €135
	• Number of staff per vehicle is 1.25
	• Diesel price is 1,2 € / l
	• Fixed costs except personnel and fuel are €3,5 / km
	• Electricity prices are € 0.20 / kWh
	• Electricity consumption for an electric van is 10 kWh / day
	• Electricity consumption for a tricycle is 6 kWh / day

Translated from article L1231-1 of the current French Transport Code.

Acknowledgment and context of research

This research was funded by the Ministry of Sustainable Development and Infrastructure (MDDI) of Luxembourg and CFL Multimodal. The authors would like to thank all businesses that have provided excellent data and all participants involved.