The material studied is crushed 0/31.5 aggregate from Inkissi sandstone in Kombe located south of Brazzaville on the banks of the Congo River ( Figure 2 ). Its bulk density, specific weight and Los Angeles coefficient were determined in the Civil Engineering Laboratory of the Higher Polytechnic National School (ENSP) at Marien Ngouabi University.

OriginPro2019b software is designed to generate interactive 2D and 3D graphs and analyze data. Data analysis in Origin includes statistics, signal processing, curve fitting and peak analysis. Origin’s curve fitting is performed by a non-linear least squares fitter based on the Levenberg-Marquardt algorithm. Various scientific studies on geotechnics and the study of construction materials have been successfully carried out using OriginPro2019b [17] .

Procedure for developing the segregation mechanism

Five 05 samples of 0/31.5 mm aggregate (PD, DL, SCS, SCB, Q) taken using specific sampling methods were subjected to a series of physical and mechanical tests. Four standardized samples were taken in accordance with the standard (EN 932-1) [18] and one sample was taken directly from the bulk sample, as is done on construction sites and in laboratories. The particle size analysis of dry material samples subjected to vibration made it possible to quantify segregation. Modified Proctor test and CBR test were used to assess the mechanical effects induced by segregation under vibration of the material. For each sample, checks based on the tests (compactness, granular spindles, fineness modulus, bearing capacity) were carried out to verify the degree of segregation in the material.

Modeling segregation control equations

Modeling of segregation control equations is performed using the ANOVA calculation model (OriginPro2019b), which generates various multiple linear regression equations to model optimal particle size distribution curves. ANOVA model analysis is an analysis of variance, which is a set of statistical models used to verify whether the means of the groups come from the same population. Using this model (ANOVA) provides more smoothing points for the curve, allowing for a more accurate assessment of the fit, due to the large number of particles of different sizes in granular materials [19] .

For a given sample ( $Y_i,X_{i1},\cdots ,X_{ip}$) $i\in \left\{1,n\right\}$, it is necessary to explain as precisely as possible the values taken by $Y_i$, known as the endogenous variable, based on a series of explanatory variables $X_{i1},\cdots ,X_{ip}$. The theoretical model, formulated in terms of random variables, is generated in the following form (1):

$Y=a_0+a_1{X}_{i1}+a_2{X}_{i2}+\cdots +a_p{X}_{ip}+{\epsilon }_i,i=1,\cdots ,n$(1)

where ${\epsilon }_i$ is the model error that expresses or summarizes the information missing from the linear explanation of the values of $Y_i$ based on $X_{i1},\cdots ,X_{ip}$ (specification problem, variables not taken into account…). The coefficients $a_0,a_1,\cdots ,a_p$ are the parameters to be estimated.

Figures 3-7 illustrate some of the experimental steps involved in analyzing material samples in the laboratory. Figure 3 shows the tested 0/31.5 aggregate sample and the schematic cone composition of the separated aggregates.

Figure 3 shows the stockpile formed beforehand ( Figure 3(a) ) and the segregation resulting from the unloading of material from a fixed conveyor ( Figure 3(b) ). This is suitable for sampling based on the actual state of segregation. It explains the causes of segregation during material handling. The core at the top of the pile forms a cone made up of fine particles, while the material spilling out on either side of the core consists of medium-sized particles resting on the coarse particles forming triangles at the base [7] [20] [21] . Figure 4 shows the process of material preparation by manual and standardized sampling.

Parameters of tested materials

The particle size distribution, characterized by grain diameter, shape and coefficients of uniformity and curvature, allows the nature of the material to be defined in accordance with standards NF P 94-056 and EN 933-2 [22] [23] . Five samples (PD, DL, SCS, SCB, Q) were analyzed on 22 sieves with diameters ranging from Dmax (31.5 mm) to d (0.08 mm). The particle size distribution curve is obtained from sieve analysis values ( Figure 5 ). Sieve analysis expresses the quantity of material that passes through a set of sieves and is determined by the following formula:

$\%\text{P}=100\%-\%\text{R}$(2)

$\%\text{R}=\frac{\text{MR}}{\text{MT}}\ast 100$(3)

P: passing; R: refusal; MR: cumulative rejection mass; MT: total dry mass.

The uniformity (Cu) and curvature (Cc) coefficients help to analyze the particle size distribution curve obtained on the basis of the sieve diameter ratios, where Dx is the grain size corresponding to x % by weight of sieved material:

$\text{Cu}=\frac{\text{D}60}{\text{D}10}$(4)

$\text{Cc}=\frac{{\left(\text{D}30\right)}^2}{\text{D}10\times \text{D}60}$(5)

The apparent density determines, in accordance with standard NF EN 1097-3 [24] , the density of the material before compaction or manufacture. It corresponds to the ratio between the mass of the dry aggregate and the volume it occupies without compaction in a metal mould, including the volume of intergranular voids ( Figure 6 ).

The bulk density or apparent density ρ_b (T/m³) is calculated using the following formula:

${\rho }_b=\frac{\text{m}2-\text{m}1}{V}$(6)

where: V is the volume of the container (l);

M1: mass of the mould and sample (kg)

M2: mass of the empty mould (kg)

Intergranular porosity γ corresponds to the percentage of intergranular voids in the container; it is calculated using the following equation:

$\gamma =\frac{{\rho }_p-{\rho }_b}{{\rho }_p}$(7)

where ρ_p is the actual density in T/m³, determined in accordance with standard EN 1097-6 [25] .

The modified Proctor was measured on samples of material compacted in a standardized mould at a conventional energy level in accordance with standard NF P94-093 [26] . The material tested is characterised by the maximum dry Proctor density (γdmax) corresponding to an optimum water content (W_OPM).

The CBR (California Bearing Ratio) test measures the bearing capacity of the material or soil that has undergone prior compaction energy in accordance with the standard (NF P94-078, NF EN 13286-47) [27] [28] . The bearing capacity of the material is characterized by the CBR index calculated during the punching of the test specimen after 4 days of immersion ( Figure 7 ). The index sought is conventionally defined as the greater of the two ratios calculated as follows:

$\text{CBR}1=\frac{100\ast F_{2.5\text{mm}}}{13.35}$; $\text{CBR}2=\frac{100\ast F_{5\text{mm}}}{19.93}$ (8)

where F is the force exerted by the piston to drive it into the test piece (kN).

Analysis of the effect of segregation on the particle size distribution of crushed aggregate

Figure 8 shows the particle size distribution curves obtained from the five samples.

In Figure 8 , the PD, DL, SCS and Q curves approach the upper range, while the DL and SCB curves are entirely within the granular reference ranges (CEBTP, 84; EN 13285) [29] [30] . This range incorporates a relationship between the particle size distribution and the mechanical strength of the material (Los Angeles coefficient, LA ≤ 45; Micro-Deval coefficient, MDE ≤ 35), which takes into account the effects of compaction on the bearing capacity. Key upper and lower limit percentages are, for example, sieve (min; max): 0.5 mm (5; 85%); 2 mm (16; 47%)…16 mm (55; 85%). The SCB curve also approaches the lower limit of the range.

The particle size analyses by quartering of the materials show the greatest deviation from the reference ranges (Q curve). The deviation zone of the particle size curves is in the same interval between the sieve openings of 0.5 and 4 mm. The extremes are those of the quartering between coarse sand and gravel (0.5 mm and 4 mm). For PD, SCS and DL, the deviation from the reference range only occurs between the 0.5 mm and 2 mm sieves, which correspond to the coarse sand zone ( Table 1 ). The SCB curve shows that the material lacks coarse sand and does not come out of the pin; it generates granular segregation relative to the overall appearance of all the curves and does not represent the general nature of the sample. The 0/31.5 aggregate studied, despite its high gravel content, consists entirely of coarse sand with a fineness modulus (Mf) between 5% and 45%. Among all the curves obtained, the material is characterized by a spread or varied grain size (Cu > 2), but poorly calibrated (Cc < 1 and Cc > 3). Consequently, this material is prone to segregation phenomena.

In terms of sampling methodology, the curves show that the PD (16.64%) and Q (16.07%) models favor the collection of fine elements during sampling. These results are similar to those obtained when sampling at the top of the cone stock (15%), which is an anomaly for the overall representation of the sample.

The SCB curve at the base of the conical stock contains fewer fine elements (8.25%) than the others; it is rich in gravel and pebbles (44.81% and 27.64% respectively), and therefore has a high proportion of coarse elements. The DL curve contains the median values for fines, i.e. 13.79%. All the curves obtained model the possibility of granular segregation linked to the handling of the material. The SCB curve strongly represents the phenomenon of segregation in a granular mass compared to the initial sample. Table 1 lists the values of the Cu, Cc and Mf coefficients and the proportions of minerals constituting the material on a 5 mm sieve.

The bulk density of the 0/31.5 aggregate

The average apparent density of each sample tested varies between 1.790 and 1.920 g/cm³. The lowest densities were obtained from the sample taken by quartering Q (1.790 g/cm³), while the highest values were obtained from direct sampling PD (1.920 g/cm³) and at the top of the conical stockpile SCS (1.915 g/cm³). The density values obtained are higher than the average density obtained for Kombe sandstone, which is approximately 1.400 g/cm³ for coarse elements [31] . This can be explained by the presence of crushed sand in the 0/31.5 aggregate. The apparent density values and intergranular porosity calculated using a specific weight γ of 2.630 g/cm³ are shown in Table 2 .

ρb-bulk density; ρp-specific weight; γ-intergranular porosity.

Effect of segregation on the compaction of crushed aggregate 0/31.5

Figure 9 shows the modified Proctor curves for the samples tested.

Figure 9 shows that, depending on the shape, maximum moisture content and position, the PD curve shifts to the left relative to the others, with the material behaving like silty clay, with a maximum dry density γdmax (2.20 g/cm³) and an optimum water content W_OPM (5.17%); The same applies to the SCS curve, whose maximum dry density γdmax (2.18 g/cm³) corresponds to an optimum water content W_OPM (6.96%). The compaction behavior of the SCB, DL and Q curves is similar to that of gravelly sand, with maximum dry densities γdmax and optimum water contents WOPM of (2.24 g/cm³; 5.29%), (2.17 g/cm³; 6.31%) and (2.17 g/cm³; 6.76%). Based on this analysis, the dispersion of the PD curve indicates significant segregation of the mixture. However, the curves for the SCS, DL and Q samples, which have a rich composition in fine elements, show that these parts of the material require approximately 1.2% more water content for good compaction compared to the PD and SCB samples. The variability of these values for the same aggregate highlights the difficulty of obtaining similar granular compositions for each sample taken using different procedures. Table 3 provides information on the modified Proctor values obtained and their correction.

r(%)-rejects content on a 20 mm sieve.

Figure 10 models the influence of the percentage of fines (0.02 - 0.2 mm) on the dry density of the aggregate. Although the densities are within the same range (2.10 - 2.25 g/cm³), it can nevertheless be seen that the presence of fine particles reduces the dry density by approximately 3.04%, if we consider the extremes for the SCB model (DD = 2.24 g/cm³; fine sand = 27.57%) and the Q model (DD = 2.17 g/cm³; fine sand = 51.94%). This clearly shows the effect of granular segregation on the compaction of materials, which means that the presence of a small or large granular fraction alters the compactness of road material layers. The curve forms a parabola with an extremum between the SCS and Q models, for which the maximum dry density would be 2.21 g/cm³ and the percentage of fine sand 49.6%. DL (DD = 2.20 g/cm³ and fine sand 48.5%) is the model that comes closest to the maximum density extremum, which shows that it is indeed the model that minimizes granular segregation.

Effect of granular segregation on CBR bearing capacity

Figure 11 shows the penetration effort curves from the CBR test, and Figure 12 shows the influence of the modified Proctor optimal dry density (OPM) on the bearing capacity of the material.

The average CBR and compactness values for the five samples are shown in Table 4 .

C (%)-average compactness; γ_CBR-density of CBR.

The CBR values obtained in this study are significantly higher than those obtained in the work of Hydzik-Wiśniewska et al. (2018) on 0/31.5 crushed aggregates, for which the values vary between 22.4 and 40.3%. This may be related to the geological nature of the terrain, as the geology of a soil varies from one point to another. Based on the sampling method, the PD model has the lowest CBR values (69.5% and 73.5%). This model leads to significant segregation in terms of the implementation method. It is clear that the data (results) for this model are scattered, lack logic and do not follow the overall average representing the original sample. The Q model, which has a high percentage of fines (51.94%), also shows low CBR values (87% and 90.6%), as the sample behaves like gravelly sand. The SCB model has higher CBR values (137% and 158.5%). This is due to the high proportion of coarse particles (44.81%) in the sample. The SCS model taken from the top of the conical stockpile, rich in fines (47.46%), has low CBR values (99% and 103%) compared to the DL model, which continues to show median values (117.2% and 129.75%) in all tests performed. The DL model therefore offers the best control of segregation in 0/31.5 granular materials.

Analysis of CBR test specimens for segregation

The water absorption test values for the CBR samples are recorded in Table 5 . The absorption rates of the CBR samples show that the PD and Q samples with the lowest CBR values are those with the highest absorption rates (PD = 2.29% and Q = 1.27%). This is because the friction of sizes in a granular mixture is mainly affected by inter-particle forces, which decrease with water saturation and increased water pressure in the voids, resulting in a decrease in the bearing capacity of the material due to compaction effect [32] . However, there appears to be an inconsistency in the SCB test tube, which has a high imbibition rate but CBR values ranging from 137% to 158.5%. This inconsistency can be explained by intergranular porosity ( Table 2 ). Without taking into account the PD model, which causes segregation in each of the samples, we can see that the imbibition rate follows that of intergranular porosity. The Q and SCB models, rich in fine and coarse elements respectively, behave as described in Figure 8 as a limiting case of a perfect bimodal distribution. As a result, some models have voids that cannot be completely filled, creating high porosity in the stacking. The SCS model, which has lower imbibition values, is certainly the one where the grain arrangement is balanced in terms of compactness, i.e. the grains fill each other perfectly. Except that it does not represent the original granular spindle. It behaves like gravelly sand (fines = 47.46%). This is justified by low CBR values (99% and 103%) compared to the DL and SCB models. The DL model seems to best control segregation in the material. Table 5 summarizes the imbibition analysis of the test specimens. The DL model appears to best control segregation in the material. Table 5 summarizes the analysis of the imbibition of the test specimens.

maV—mass before immersion; mAp—mass after immersion; me—test specimen mass; mc—compacted material mass; mWi—water-soaked mass; i—average soak rate; γ—intergranular porosity.

Segregation model simulation

Of the five sampling models studied, only the DL curve clearly models a granular material without significant segregation. Therefore, the modeling of the percentage of passers based on granular fractions is used to simulate a predictive model of segregation rates. Figure 13 shows the correlation between the percentage of passers and the granular fraction of the five models.

The SCB curve deviates completely from the others, and the Q curve deviates slightly between the granular fractions of 0 to 10 mm, confirming the assumptions of material segregation in these samples. Based on the ANOVA modeling of the PD, DL and SCS curves in OriginPro, we can see that these curves are well correlated and simulated, although the coefficient of determination (R²) for all models is equal to 0.99. Figure 14 shows an illustration of the DL model simulation.

The overall segregation control equation obtained by ANOVA simulation and the associated index values are recorded in Table 6 .

Y_i-Percentage of passers, RSS-Residual Sum of Squares, I-Intercept, X-corresponding sieve diameter.

The residual sum of squares (RSS), also known as the sum of squares of estimated errors (SSE), is the sum of the squares of the residuals. It measures the deviation between the data and an estimation model, such as a linear regression. A low RSS indicates a good fit between the model and the data, which is a criterion of optimality for the selection of mathematical models. Given that the segregation of the PD model in each of the samples was justified by the variability of the data, its lower CBR values (69.5% and 73.5%) with a high imbibition rate (PD = 2.29%) and its high RSS (64.22%), it can be excluded as a model for controlling granular segregation. The DL model, which gives the best mechanical properties and the lowest RSS (63.32%) of the five models, best controls the granular segregation of 0/31.5 crushed aggregates, particularly in comparison with the SCS model from the same group, which has a higher RSS (98.00%). This is justified by the fact that the PD and SCS models deviate from the reference limits only between the 0.5 mm and 2 mm sieves, which correspond to the coarse sand zone, compared to the DL model ( Figure 8 ). Based on these analyses, the equation derived from the DL can be used to correct particle size distribution curves with high segregation and to define the optimal intervals for representing a sample with no or low segregation