The pavement structure tested consisted of bituminous concrete pavement, bitumen gravel base layer, crushed lateritic gravel foundation layer and lateritic gravel form layer on a PF3 support platform. Figure 1 shows the structure under test. The characteristics of these layers are shown in Table 1 .

The modules of the BB surface layer and the GB3 base layer are temperature-dependent. The road surface temperature reading was made using an infrared thermometer. The subdivision of the climate into two periods results from the temperature measurements from January 01 to December 31, 2022. Figure 2(a) presents the ambient, maximum, average, and minimum daily temperature, while Figure 2(b) shows pavement surface temperatures in 2022.

The traffic data and axle weighing are those obtained at the Nagréongo weighing station. Table 2 and Table 3 show the different types of multi-axle heavy goods vehicles most common on the road network of the WAEMU community. The loads defined as part of this work are those authorized by the current WAEMU standard regulations [14] [15] .

This analysis of pavement behavior considers a multilayer structure with elastic, linear, homogeneous and isotropic behavior with static loading. [16] [17] [18] . The pavement sizing considers an average coefficient of aggressiveness equal to 1. The pavement design process ends with a mechanical evaluation, which consists of verifying the following mathematical inequalities (calculated value ≤ allowable value) [19] [20] [21] . The approach refers to the principles of the French method of pavement sizing based on a multilayer asymmetric Burmist model used in the ALIZE L C P C software [16] [22] [23] [24] . This analysis of pavement behavior considers a multilayer structure with elastic, linear, homogeneous and isotropic behavior with static loading [16] [17] [18] . The pavement sizing takes an average aggressiveness coefficient equal to 1. The process of the design ends with a mechanical evaluation consists of verifying the satisfaction of the following mathematical inequalities (calculated value ≤ allowable value) [19] [20] [21] .

For bituminous materials ε_t ≤ ε_tadm (1)

For a bituminous seam stressed in bending extension, the permissible deformation is calculated through equation (2).

${\epsilon }_{tadm}={\epsilon }_6\times \sqrt{\left(\frac{E\left(10Hz;10°c\right)}{E\left(10Hz;30°c\right)}\right)}\times {\left(\frac{NE}{{10}^6}\right)}^b\times k_r\times k_c\times k_s$(2)

_t: where is Tensile deformation at the bottom of the bituminous layer

ε_tadm: Permissible tensile deformation at the bottom of the bituminous layer

₆: Deformation at 1 million loading cycles

E(f,T (˚C)): Modulus of stiffness of asphalt layers at a temperature

NE: Number of axles equivalent to heavy goods vehicle traffic

K_r: Risk coefficient of variation in thicknesses and dispersion of fatigue tests

K_C: Calibration coefficient

K_S: coefficient that depends on the type of support platform

For untreated materials and subsoil

${\epsilon }_z\le {\epsilon }_{zadm}$(3)

For a layer of untreated material and for the soil, the permissible load is the vertical surface deformation of the layer, calculated according to equation (4)

${\epsilon }_{zadm}=A\times {\left(NE\right)}^B$(4)

ε_Z: Horizontal deformation at the top of untreated layers or the platform

ε_Zadm: Permissible horizontal deformation at the top of the untreated layers or the platform

A: Permanent deformation

B: Slope of the Material Fatigue Law

These admissible deformation parameters are performance data of the pavement materials [16] [25] . These parameters are influenced by the type of traffic on the roadway during its lifetime [11] . The cumulative traffic was evaluated through equations 5, 6 and 7 [26] [27] . During the traffic assessment, only heavy goods vehicle traffic, expressed as the cumulative number of heavy goods vehicles expected during the lifetime of the roadway, is considered [17] . The configuration of heavy goods vehicles, which present the most aggressive elements in the traffic in Burkina Faso, has evolved rapidly, and the appearance of the multi-axle vehicle has led to the consideration of the impact on the roads of non-standard configurations following the UEMOA regulation 14 [28] .

$N_{PL}=365\times TMJA\times C$ (5)

$$ $C=\frac{{\left(1+\tau \right)}^n-1}{\tau }$(6)

$NE=N_{PL}\times CAM$(7)

NE: Number of heavy goods vehicles calculated for service life

TMJA: Annual average daily traffic

n: Road life

τ: Traffic growth rate

CAM: Average coefficient of aggressiveness

The different aggressiveness is calculated using the following equations:

-The aggressiveness of an axle is given by equation 8;

$A_i=k\times {\left(\frac{P_i}{P_0}\right)}^{\alpha }$(8)

-The aggressiveness of a heavy vehicle is calculated using equation (9);

$A_{PL}={\displaystyle \underset{i}{\sum }k\times {\left(\frac{P_i}{P_0}\right)}^{\alpha }}$(9)

-The aggressiveness of heavy goods vehicle traffic is determined by the equation (10).

$CAM=\frac{1}{N_{PL}}\left[{\displaystyle \underset{i}{\sum }{\displaystyle \underset{j=1}{\overset{3}{\sum }}{K}_j{n}_{ij}\times {\left(\frac{P_i}{P_0}\right)}^{\alpha }}}\right]$(10)

K_j: constant dependent on axle geometry and pavement structure

α: constant dependent on the structural nature of the pavement

P_i: Axle load i

P_O: Load of the reference axle which is 13T

Since the materials that make up the pavement are considered isotropic, they are then governed by the heat equation (11) [29] [30] .

The values of parameters for equations 8, 9 & 10 are those defined in the NF-P-98-086 standard [21] . These are conventional design values generally taken for sizing. In this work, only the heavy vehicle weight (HVW) or the total authorized rolling weight (TARW) according to WAEMU Regulation 14 [14] [15] , in addition to the tolerance granted in October 2022 by the Ministers of Transport of the Community [15] is considered for each type of heavy good vehicles.

The mechanical behavior of asphalt concrete is largely temperature-dependent, expanding with increasing temperature and contracting with decreasing temperature. The temperature profile within the bituminous layer, as an essential parameter for this work, is determined using prediction models [31] [32] .

To accurately predict pavement behavior, temperature prediction models [33] [32] [34] are required. These must predict the temperature at any pavement depth based on the ambient and surface temperature and the material properties [35] [36] [37] . As isotropic materials for the pavement, the governing heat equation (11) [29] [30] is given by:

$\frac{{\partial }^{2}T\left(x,t\right)}{\partial x^2}=\frac{1}{\alpha }\times \frac{\partial T\left(x,t\right)}{\partial t}$(11)

where T is the temperature, x defined the pavement Depth, t corresponding to the time and α referring to diffusivity of the material.

The pavement layer temperature was evaluated while measuring first the pavement surface temperature. An analytical approach drawn from the work of SHAO et al. 1999 [38] and SOLAIMANIAN et al. [39] has led to the development of a simple computational method requiring less raw data. This method includes the latitude effect, the location and the solar radiation. Mainly based on the equilibrium, the calculations are defined as follows [10] [38] [40] .

$q_a+q_{\stackrel{\to }{s}}-q_c-q_k-q_r=0$(12)

with

Energy from diffuse and atmospheric radiation [41] follows:

$q_a={\epsilon }_a\times \sigma \times T_a{}^4$(13)

The energy absorbed by a horizontal pavement [10] :

$qs=R_o\times {\alpha }_1\times {\tau }_a{}^{1/\cos z}\times \cos z$(14)

The energy transmitted (or received) to the massif by convection surrounding the air [42] :

$q_c=h_c\cdot \left(T_s-T_a\right)$(15)

The energy transmitted (or received) to the ambient air by conduction under the paving surface: $q_k=-k\cdot \left(T_x-T_{{}^s}\right)/x$ (16)

The energy emitted by asphalt by radiation [33] :

$q_r=\epsilon \cdot \sigma \cdot T_s{}^4$(17)

Either, $\begin{array}{c}{R}_0\times {\alpha }_1\times {\tau }_a{}^{1/\cos z}\times \cos z+{\epsilon }_a\times \sigma \times T_a{}^4-h_c\times \left(T_s-T_a\right)\\ –\left(k/x\right)\times \left(T_s-T_x\right)-\epsilon \times \sigma \times T_s{}^4=0\end{array}$ (18)

R₀: Solar constant

α₁: surface absorptivity

τ_a: airmass transmittance coefficient

z: angle of the Zenith (solar latitude-angle of declination)

ε_a: coefficient of atmospheric radiation

σ: Stefan-Boltzman constant

T_a: air temperature

T_s: Pavement surface temperature

T_x: temperature at depth X of the pavement

ε: emissivity factor of the pavement surface

h_c: surface area coefficient for heat transfer

k: Thermal conductivity factor

x: Pavement depth

The balance of energy exchanges is illustrated in Figure 3 .

After determining the temperature gradient inside the different layers of the pavement, the rates of permanent deformation were obtained using equations (19) [43] .

${\epsilon }_p=\frac{{\sigma }_v-{\sigma }_h}{2.E\left(V,T\right)}\times {\left[\frac{1}{450.V}\right]}^{\frac{1}{4}}\times N^{\frac{1}{4}}$(19)

ε_p: Plastic deformation

N: Number of applied load

σ_v: Main vertical constraints

σ_h: Main horizontal constraints

E(T,V): Modulus of stiffness of asphalt layers dependent on temperature and speed

V: Vehicle speed

And the rutted depths of the bituminous layer are evaluated through the equation (21) [43]

$u={\displaystyle \underset{i}{\sum }{h}_{i.}{\epsilon }_{pi}}$(20)

μ: Rut depth

h_i: Layer thicknessi

ε_pi: Permanent deformation of the i-layer

Figure 4 shows the evolution of permanent deformations on the asphalt concrete layer by month and for a cumulative 20 years. From Figures 4(a) , Figure 4 (c) and Figure 4(e) , it is clear that the permanent deformations are higher during March, April, May and June and smaller during January, February, July, August, September and December. A rebound of these deformations was observed during October. In Figure 4(a) and Figure 4(b) , the deformation rates of multi-axle heavy trucks indicate that the P25, P26 and P35 trucks generate higher deformation rates than other types of trucks. Figure 4(c) and 4d show the deformation rates of twin-axle semi-trailers. For these types of heavy trucks, the difference in deformation rates is insignificant. In Figure 4(e) and Figure 4(f) ,

which represent the deformation rates of heavy goods vehicles such as semi-trailers with isolated rear axles, the value recorded for the T12S5 with single axles is higher than those of the other types of heavy goods vehicles shown in these figures. Our finding is consistent with the work of BASSEM et al. (2006) [44] , which showed that single axles cause more damage to the pavement than twin axles. All the figures here show that the T12S5 semi-trailers with single axles contribute more to permanent deformation, followed by the P25, P26 and P35 type trucks and all semi-trailers with twin axles. P11, P12, P13, P22, P23 and P24 truck types contribute less to deformations. These results complete our previous work (KOBORI et al. (2023)) [45] , which indicates that heavy goods vehicles were the most aggressive cause of permanent deformation.

Figure 5 shows the permanent deformations of the gravel bitumen’s seam under the stresses of the various heavy goods vehicles over the course of a year ( Figure 5(a) , Figure 5(c) and Figure 5(e) .) and over 20 years ( Figure 5(b) , Figure 5(d) . and Figure 5(f) ). In general, it appears that the same heavy goods identified as being the most contributors to the rate of permanent deformation at the level of the bituminous concrete layer also turn out to be the most severe in the asphalt gravel layer. These permanent deformations in the gravel bitumen layer ( Figure 5 ) are less significant than in the asphalt concrete layer ( Figure 4 ) because gravel bitumen is stiffer than asphalt concrete.

On the other hand, in terms of seasonal variation, the gravel bitumen layer experiences more variation in permanent deformation than the asphalt concrete layer. The difference in these deformations between the warm and cold periods is more pronounced in the case of gravel bitumen than in bituminous concrete since bitumen is more sensitive to temperature variation than asphalt concrete [6] [40] [46] .

Figure 6 shows the effect of temperature over a year on the appearance of ruts and the accumulation of these ruts 20 years on the bituminous concrete layer, under the stress of heavy trucks with multi-axles. By referring to Figure 6(a) , Figure 6(c) and Figure 6(e) , the rutting depth appears higher during the warm period, consistent with existing results in the literature [44] [47] [48] . It is twice as large during the hot period as the cold one, under stress from all types of heavy goods vehicles.

The cumulative rutting depth is greater than 5 mm for single-wheel semi-trailers and P25, P26 and P35-type trucks. For dual-wheel semi-trailers, it is of 4 mm order and less than 3.5 mm for P11, P12, P13, P22, P23 and P24 type trucks.

Figure 7 shows the rutting depths generated on the gravel bitumen for a year ( Figure 7(a) , Figure 7(c) and Figure 7(e) ) and the cumulative rutting for 20 years ( Figure 7(b) , Figure 7(d) and Figure 7(f) ) under multi-axle loads. A comparison with the results in Figure 6 shows that the rutting depth is two times higher for the asphalt concrete level than that of asphalt gravel by the stress levels and temperature in the gravel bitumen, which are lower than those of asphalt concrete. We also observe that gravel bitumen gives sharp peaks of ruts during the hot period due to the very high sensitivity of this material to temperature. These results confirm the work of R.F DOLIN et al. (2021) [49] , which showed that temperature plays a role in the ruts formation in flexible pavements.

Figure 8 illustrates the durability of a bituminous seam under multi-axle loads as a function of three types of loading. Loading in compliance with WAEMU Regulation 14 [14] [15] ; then a loading following the recommendations of the Ministers of Transport of the WAEMU Community Area with the tolerance of 15% overload and to an alternating loading during a year which consists of a loading in compliance with Regulation 14 during the so-called hot season and a loading following the recommendations for the cold period. The results of the simulation show that alternating loading can double the durability of the bituminous layer under the stresses of heavy goods vehicles such as P25, P26 and P35. This lifetime of the bituminous layer is tripled for the full application of WAEMU Regulation 14 ( Figure 8(a) ) [14] [15] . The same finding was observed in Figure 8(b) . Figure 8(c) shows the durability of the bituminous layer under loads of heavy semi-trailers with insulated wheels as a function of load. Consequently, the road life is tripled for alternating loading and quadrupled for loading following the entire application of the WAEMU standard for a year. However, it is pointed out that the work was based on the French method of sizing pavements. This is a method that does not include cracks in pavements. If the analysis of the results showed that the flexible pavement is vulnerable in high temperatures. Because during this period, rutting formation and deformation

rates are higher. Several studies have also shown that periods of low temperature are also harmful to the road. These studies have shown that this so-called cold period is favourable to the formation of cracks on flexible pavements. [50] [51]

Figure 9 shows the evolution of the durability of granular materials as a function of multi-axle heavy truck loading. From this figure, the durability of these materials increases by 1.5 times for seasonal alternating loading and more than three times the loading according to WAEMU Regulation 14 [14] for heavy trucks of P25, P26 and P35 types ( Figure 9(a) ). There has also been a significant change in the durability of materials for alternating loading under the load of multi-axle semi-trailers with twin wheels ( Figure 9(b) ). Figure 9(c) shows that the durability of granular materials is multiplied by two for seasonal alternating loading and more than three times for loading complying with WAEMU standards under the stresses of semi-trailers with insulated wheels. Although the properties are insensitive to temperature variations, the durability of granular materials increases

with the alternation of loading due to the variation in the stress levels resulting from the decrease in the stiffness of the bituminous layer. These results are acceptable because the period from July to October is considered cold and wet in Burkina Faso. However, studies have shown that the strength of granular materials decreases with humidity. This period can then be detrimental to granular materials [47] .