Avaliação numérica da influência da geogrelha no desempenho de pavimentos flexíveis

<jats:p>O objetivo deste trabalho é desenvolver uma metodologia de análise mecanicista em elementos finitos, no programa ABAQUS, para investigar a influência da geogrelha como elemento de reforço no desempenho de pavimentos flexíveis. Para isso, uma metodologia analítica foi adaptada para o cálculo do acréscimo de confinamento lateral proporcionado pelo reforço, também foi considerado o comportamento não linear dos materiais de base e subleito, por meio da introdução de uma sub-rotina escrita em linguagem Fortran, e adotou-se as devidas propriedades de interface entre geogrelha e material geotécnico. Os resultados de afundamento na trilha de roda modelados e experimentais foram comparados, mostrando que a metodologia adotada apresentou um ajuste satisfatório. Com isso, diferentes configurações de pavimento foram simuladas e avaliadas. Os resultados evidenciam que a inserção da geogrelha como elemento de reforço melhora a resposta do pavimento, principalmente por diminuir as tensões verticais na camada em que está inserida e consequentemente a deformação permanente, o que resulta no aumento da vida útil do pavimento.</jats:p>

section_content: Most Brazilian pavements are classi ied as lexible, and the main function of these lexible pavements is to allow traf ic load redistribution from the surface to the underlying layers. Therefore, when following a design, two types of rupture are taken into account: a) Fatigue -located in the layer with the largest resilient module and caused by alternate lexion of the layer during the traf ic load, b) Permanent deformation -resilient vertical displacement of each pavement layer, which can cause rutting damage on the pavement surface. Thus, the layers must have suf icient thickness and stiffness to limit their excessive vertical deformation (Yoder and Witczak, 1975). 

One of the most widespread ways of dimensioning pavements and which is constantly being studied are mechanistic empirical pavement design methods. These methods are based on stresses, strains and displacements of the pavement structure subjected to traf ic. Among different mechanistic methods of pavement response that can be used, the multilayer elastic theory (MLET) and the inite element method (FEM) are the most common. The ABAQUS inite element program has been used in the academic environment to study pavement stresses and strains, as it allows the modeling of nonlinear material behavior, forms of loading and interface elements (Santos et al., 2019). 

A subgrade is natural soil at a construction site, and according to Vertematti (2015) in some lexible pavement structures, an unbound granular layer is placed directly above a low support subgrade. This can lead to damage on the pavement, such as: rutting due to excess deformation of the pavement layers; or fatigue cracking, which may be associated with the migration of ines from the subgrade and the penetration of the granular base layer into the subgrade. In the presence of weak subgrade, laboratory studies have shown the bene it of using a geogrid as reinforcement (Kakuda et al., 2011 and Costa et al., 2017). These studies indicate a decrease in vertical displacements in the pavement structure and, consequently, a reduction in permanent deformation. 

In this context, according to Perkins and Ismeik (1997), the performance of geosynthetic reinforcement in lexible pavements is due to the lateral con inement mechanism, in which the interaction between the base granular material and the geosynthetic reinforcement allows the transfer of stress from the base to the geosynthetic. Therefore, the function of the geosynthetic is to avoid the horizontal displacement of the material, maintaining its con inement. 

According to Kwon et al. (2005), the design using geosynthetic reinforcement needs to be incorporated into mechanistic empirical analysis, as it is the most suitable alternative to evaluate the effectiveness and bene its of the presence of geosynthetics in the pavement structure. However, there is a dif iculty in quantifying the additional con ining stress applied from the geosynthetic in the unbound granular material. To account for the increase in con ining stress, in FEM analyses, studies such as those by Nazzal et al. (2010); Abu-Farsakh et al. (2014) and Tang et al. (2016) proposed an increase in the geosynthetic modulus, when compared with that obtained in the laboratory. Moreover, Kwon et al. (2005) empirically added a horizontal stress in the reinforced area. In addition, Perkins et al. (2009) presented a numerical model in two stages. The irst is a compaction model, which resulted in increases in horizontal stresses in the reinforced layer and the second stage considers the horizontal stresses from the compaction model and the traf ic load. On the other hand, Yang and Han (2013) and Gu et al. (2016) proposed an analytical model to calculate the additional con ining stress provided by the reinforcement based on the results of repeated triaxial compression tests. 

In Brazil, with the evolution of mechanistic design methods for lexible pavements and the introduction of the SisPav program proposed by Franco (2007), there is a need to incorporate geogrid reinforcement in these analyses. In this context, this article aims to adapt the methodology proposed by Yang and Han (2013) and Gu et al. (2016) regarding the mechanistic design of lexible pavements incorporating geosynthetic reinforcement, of the geogrid type, using the ABAQUS program. Furthermore, this paper aims to compare the results obtained by the proposed model with the results of the experimental model by Kakuda (2010). Finally, based on the proposed numerical model, the in luence of the geogrid stiffness, the location of the reinforcement and the interface parameters on the performance of the simulated pavements is evaluated.
section_name: INTRODUCTION

section_content: Finite element analyses were performed using the ABAQUS program to predict the pavement response (stresses and strains), and thus, estimate its long-term performance (total permanent deformation) with the permanent deformation model proposed by Guimarães (2009). 

Similar to the studies carried out by Nazzal et al. (2010 ), Abu-Farsakh et al. (2014) and Tang et al. (2016), an axisymmetric analysis was adopted whereby the pavement layers were modeled as a solid 8-node element and the geogrid as a 3-node membrane element, both with reduced integration. To minimize the edge effects, a width of 2. 4 m was considered as the model and 1. 4 m as the depth of the subgrade, which represent approximately 15 and 10 times the diameter of the wheel loading area, respectively. 

To optimize the simulation, the mesh density next to the wheel loading was increased and near the edges of the model it was decreased. The boundary conditions were adopted to prevent vertical and horizontal displacement at the bottom of the model and horizontal displacement at the sides. 

As exempli ied in Santos et al. (2019), the interface between layers in ABAQUS ( 2014 ) is deined through the contact among two nodes and two adjacent surfaces belonging to the inite element mesh. Furthermore, it is represented by the Coulomb Equation (Equation 1 ). p: contact pressure between the surfaces. In Equation 1, the friction coef icient μ can vary between 0 and 1, whereby the value of 0 allows the free displacement between the layers, thus 1 corresponds to the layers that are bonded. In this study, the non-bounded condition was adopted for the interface between layers, and for the reinforcement interfaces, the experimental values available in Marques (2018) were adopted. 

As the objective of this paper is to evaluate the permanent deformation of the layers below the asphaltic surface on a lexible pavement, a veri ication on fatigue has not been incorporated. Therefore, in the model veri ication stage, based on the adopted experimental reference results, there is no asphalt surface. However, afterwards, in the parametric analysis there is a presence of an asphalt surface, which was modeled using an elastic linear model.
section_name: NUMERICAL ANALYSIS IN FINITE ELEMENTS OF FLEXIBLE PAVEMENT REINFORCED WITH GEOGRID

section_content: Under the repeated application of traf ic loads, most of the pavement deformations are recoverable and considered elastic. Therefore, the Resilient Modulus (MR) is de ined for the materials elastic stiffness, i. e. the deviation stress σd divided by the recoverable strain (εr), MR = σd / εr. Repeated load triaxial tests are commonly used to evaluate the resilient modulus. 

According to Bernucci et al. (2006), it is known that paving materials are not elastic and that they depend on climatic conditions, as well as the stress history. As the stress states vary within a layer, the MR also changes according to the depth and horizontal distance. To represent the MR change with the stress state, the Uzan (1988) model shown in Equation 2 considers both the effect of the con ining and deviator stress. In ABAQUS, to properly characterize the resilient behavior of pavement materials, the nonlinear stress-dependent modulus from the Uzan (1988) model was programmed in a user-deined material (UMAT), which is a subroutine written in Fortran language to characterize the behavior of geotechnical materials. Therefore, the constitutive model in ABAQUS was written in the form of a matrix relating stress and strain. 

In this paper, the UMAT equation developed by Hjelmstad and Taciroglu (2000) was used to represent the nonlinear behavior of the materials. According to these authors, the program transmits the stresses, strains, and state variables at the beginning of each time increase together with the current stress increase. The subroutine, therefore, updates the values of stresses and strains and at the end of the time increment provides the material stiffness matrix. The analysis starts with an arbitrary stiffness matrix and the irst load increment, then the MR is calculated, and the convergence condition is veri ied (the error between the MR of the previous and current increment must be less than 1%). If convergence is not achieved, a reduction factor of 0. 3 is applied to the next increment. 

The Guimarães model ( 2009 ), synthesized in Equation 3, is used in this paper to calculate permanent deformation, using a nonlinear multiple regression, correlating the con ining stress, deviation stress, and loading cycles from a repeat cyclic triaxial test. Moreover, Guimaraẽs et al. (2018) showed that the classic permanent deformation models do not present a good correlation for tropical soils, such as Brazilian soils, and that the model proposed in Equation 3 presents better results. 

where Ɛp:

permanent strain; σ3:

con ining stress (kPa); σd: deviator stress (kPa);
section_name: Resilient and permanent deforma on models of base and subgrade materials

section_content: cycles of loading; and ψ1; ψ 2; ψ 3; ψ4: repeat load permanent deformation constitutive material parameters.
section_name: N:

section_content: Figure 1 presents a schematic model of a geogrid (gray) reinforced granular base layer subject to traf ic load. The granular material is in a stress and strain state, in which it accumulates strains in both axial and radial directions. The radial interaction stress by the granular material and the geogrid generates the tensile stress T, which develops a uniform radial stretch d on the geogrid. Then, the geogrid contact friction interlocks the granular material. According to Perkins and Ismeik (1997), the interlocking of granular material in contact with the geogrid is the lateral con inement main reinforcement mechanism. 

The interlocking of the granular layer induces in an in luence zone with additional con ining stress Δσ3, represented by the letter h in Figure 1. Previous studies, such as those by Perkins (2004) and Schuettpelz et al. (2009) showed that the in luence zone height of the reinforcement varies between 10 and 15 cm. As reported by Tang et al. (2013), the geogrid radial strain is a dif icult parameter and needs the construction of a fully laboratorial instrumented session to be acquired. Therefore, Yang and Han (2013) proposed the α parameter referring to the bonding between the granular material and geogrid. This parameter correlates the radial strain of the geogrid with the radial strain of the granular material α ε ε = g a r r, where α equal to 1 represents fully bonded and where α equal to 0 the geogrid has no interaction with the granular material. This bonding coef icient value is determined by construction conditions, geogrid opening and granular material diameter. 

The additional con ining stress Δσ3 is distributed in the in luence zone as shown in Figure 1 and can be obtained by dividing force T by the reinforcement in luence zone thickness h, as presented in Equation 5. It should be emphasized that force T developed in the reinforcement is the same throughout its extension and the con inement stress Δσ3 is constant within the in luence zone. 

( )

where h:

reinforcement in luence thickness (mm); α:

bonding coef icient;

Δσ3:

additional con ining stress (MPa); and

Ɛr a :

granular material radial strain. In Equation 5, the granular material radial strain Ɛr a can be divided into an elastic and a plastic portion. According to Yang and Han (2013), the dilatation angle ψ is obtained through cyclic triaxial tests and correlates the radial strain with the axial strain of a specimen. 

As the dilation angle is a parameter of rare laboratory acquisition and to simplify the use of the model, radial permanent deformation and axial permanent deformation were adopted equiva-

The granular material axial permanent deformation is obtained according to Equation 6, which uses the model proposed by Guimarães (2009). 

where Ɛ3,p a : radial permanent deformation; ψ: dilatation angle; and Ɛ1,p a : axial permanent deformation. Equation 7 presents the granular material radial deformation elastic portion, which was obtained through the generalized Hooke's Law. For this, the following simpli ications were adopted: 1) the granular material horizontal and vertical elasticity modulus are the same, 2) the Poisson's ratio is the same in all directions. 

( )

where Ɛ3,e a : elastic deformation of the granular material; Substituting Equations 6 and 7 into Equation 5, we have Equation 8.
section_name: Analy cal model to quan fy the addi onal confining stress

section_content: )

Equation 8, referring to the additional con ining stress Δσ3, is an algebraic expression which is the function of the properties form the granular material, the geogrid, and the layer stress state. As the stress state depends on the additional con ining stress, a MathCad iterative calculation routine was used to solve it. 

The additional con ining stress along the reinforcement in luence zone causes an increase in the resilience module within this zone. Then, a new resilience modulus value is calculated from Equation 9. 

The theoretical reinforcement in luence thickness δ adopted in this paper is 15 cm, however it is also dependent on the location of the reinforcement and the thickness of the layer in which it is inserted. Equation 10 takes these factors into account to determine the effective in luence thickness h'. 

where δ: theoretical reinforcement in luence thickness (15 cm);

h': effective reinforcement in luence thickness (cm);

H: thickness of the reinforced layer (cm); and l: distance between the geogrid layer and the bottom of the base course (cm). The lowchart (Figure 2 ) summarizes the steps and the equations to evaluate the reinforced pavement performance.
section_name: ( ) (

section_content: According to Tang et al. (2013) and Kakuda et al. (2011), the greatest bene it of geogrid reinforcement is the permanent deformation reduction. Therefore, the proposed model was veri ied by comparing it with the experimental results of Kakuda (2010). 

In a laboratory experiment conducted by Kakuda (2010) and, consequently, in the inite element model analysis in this paper, a traf ic load of 550 kPa was applied to a plate with 15 cm radius. The pavement structure consists of a 20 cm granular base and a 50 cm clay subgrade. Three pavement conditions were analyzed: 1) without reinforcement; 2) with base/subgrade interface reinforced and 3) the middle of the base layer reinforced, as shown in Figure 3.
section_name: MODEL VERIFICATION

section_name: Materials properties and pavement structure

section_content: Pavement response (σ,Ɛ) and permanent deformation prediction (Equations 3 e 11)
section_name: Input parameters

section_content: Calculation of the reinforcement effective influence thickness (Equation 10 ) and additional confining stress (Equation 8 )

Upgrade of the equivalent layer resilience module (Equation 9 ) Table 1 shows the materials properties from Kakuda (2010), which were utilized in this paper. To represent the nonlinear behavior of the base and subgrade material, the parameters in Equation 2 were used. Equation 3 represents the permanent deformation of both the base and subgrade. The geogrid was characterized by its stiffness (kN/m), Poisson's ratio and interface friction rate. Based on the lowchart in Figure 2, irst the structure is analyzed without the reinforcement, then from its stress and strain response, the reinforcement in luence thickness (h) and the new resilient modulus coef icients of the equivalent reinforced zone are obtained (k1, k2 and k3). Both parameters are illustrated in Figure 3 and quanti ied in Table 2. It is emphasized that to obtain the additional con ining stress (Equation 8 ), a α = 1 (fully bonded geogrid) value was adopted. Moreover, in the reinforced structure simulations, the interface among layers assumed the following values: 1) μ is equal to 0 (not bonded), between the base and subgrade; 2) μ is equal to the values in Table 1, between the base/subgrade contact with geogrid and 3) μ is equal to 1 (bonded), between the base and equivalent reinforced zone. 

From Equation 3, the stress state of a point provides its non-recoverable deformation as a function of the number of cycles. In this paper, the points adopted for the permanent deformation analysis are both on the loading line, located ¾ from the base thickness and 150 mm from the subgrade beginning. The total permanent deformation or rutting is the cumulative non-recoverable pavement deformation, considering all its layers, throughout its service life. This parameter is calculated by Equation 11, proposed by Barksdale (1972). 

where δp: rutting (mm);
section_name: Geogrid location and properties

section_content: permanent deformation of the ith layer; and H: thickness of the layer. The comparison of experimental results with numerical results showed a signi icant reduction in permanent deformation. In the experimental results without reinforcement, the rutting for 4. 10 5 cycles was 2. 0 mm, and in the reinforced cases, approximately 1. 0 mm, providing a 50% reduction. For numerical results with the same number of cycles, the permanent deformation without reinforcement was 1. 8 mm and 0. 9 mm with reinforcement, also providing a 50% reduction. This comparison shows that the results from the proposed numerical model are compatible with the experimental results, as presented in Figure 4. 

It can be seen in Figure 4, that the numerical model for all structures simulated showed a large increase in rutting at the beginning, and then gradually increasing rutting over the cycles. On the other hand, in the experimental analyses the same behavior is veri ied with the structure without reinforcement. However, with the geogrid reinforcement presence, this large increase in initial rutting was not observed. According to Chen et al. (2013), one of the reasons for this phenomenon is that the geogrid tends to delay the occurrence of constant plastic deformation. 

The numerical modelling with the reinforcement positioned at the base/subgrade interface (Figure 4-b ) showed lower values of rutting, when compared with other structures. This is because the base layer has low deformability and the subgrade is highly deformable. Therefore, for these simulated structures, the geogrid placed at the interface, with the function of protecting the subgrade, resulted in the best ef iciency. 

The pavement's response to permanent deformation is related to the layer's stress state, according to Equation 3. Figure 5 shows a graph with the stress reduction in the pavement layers, when comparing the conditions with and without reinforcement. 

As shown in Figure 5, the numerical modelling results indicate a 43% vertical stress reduction in the base, when the geogrid is placed in the middle of the base, and a 27% reduction at the interface with the subgrade. Therefore, the ef iciency of the reinforcement lies in the reduction of stresses in the base layer and, consequently, in permanent deformation. 

Just as the reinforcement placed in the middle of the base is more ef icient considering the reduction of vertical stress of this layer, the octahedral stress in the subgrade is lower when the geogrid is positioned at the interface.
section_name: Ɛp(i):

section_content: Two lexible pavement structures were simulated. The irst consists of an asphaltic layer, a granular base, subbase, and soil subgrade. The second has an asphaltic layer, granular base, and soil subgrade. A reinforcement element (geogrid) was inserted in two conditions: in the middle of the base or at the interface with the subgrade.
section_name: PARAMETRIC ANALYSIS OF PARAMETER SENSITIVITY

section_content: The traf ic load adopted in parametric analyses corresponds to a standard road axis with the following characteristics: axle load equal to 8. 2 ton-force; tire pressure of 0. 56 MPa; contact area radius of 10. 79 cm; and wheel spacing of 32. 4 cm. For the geometry of the load, the Huang (2004) principle was considered, which was idealized for inite elements, as shown in Figure 6. The materials properties adopted were according to MeDiNa program recommendations (Franco, 2019) and are presented in Table 3. As the aim of the paper is to evaluate geogrid reinforcement in luence regarding the permanent deformation developed in layers below the asphaltic layer, a traf ic load with an N value of 10 5 was considered, making it possible to adopt a 5 cm asphaltic layer, which is the smallest thickness allowed by paving design instruction DER/SP (2006). 

The choice of materials was in luenced by the need to model a pavement structure that could have a high permanent deformation, with a rutting damage value close to the adopted limit of 10 mm. According to Al-Qadi et al. (2012), geogrid reinforcement is justi ied for pavements with a subgrade CBR value below 7% and/or a thick granular base. Taking this indication into account, a granular base of simple graded gravel was adopted and, in the subgrade, a ine soil with high deformability. Therefore, the inclusion of geogrid and its in luence in reducing strains/vertical stress of the layers is justi ied. The numerical simulations were planned considering a factorial design based on three factors and with two levels, with independent variables: x1 -geogrid stiffness; x2 -geogrid position; and x3 -α bonding coef icient of interface. A control simulation (0,0,0) was also considered without geogrid reinforcement. Figure 7 summarizes the numerical simulations performed.
section_name: Material proper es and factorial design

section_content: In the factorial experiment, the rutting damage pavement performance was adopted as a dependent variable, and it was analyzed separately regarding the subgrade, base, and total (sub-grade+base). Therefore, the effect of the independent variables, previously described, on the structural response of the pavement was analyzed. 

To obtain the rutting damage of each layer, the point within the layer under analysis was considered, in which the stress state is the most critical. The point referring to the second pair of wheels and between the wheels was assumed, positioned at ¾ of the base/subbase layer thickness and 500 mm below the subgrade. 

Figure 8 shows the results of rutting in different simulated pavement structures, wherein: a) corresponds to pavement 1 and b) pavement 2. In both pavement structures, the geogrid reinforcement decreases the amount of rutting, when compared with the control condition (0; 0; 0). Regarding the total rutting, it can be seen from Figure 8 that the simulation with the factors (1; 1; 1) presented the best results for the two structures analyzed. The reduction in total rutting was 28. 54% and 23. 78% for structures 1 and 2, respectively. 

The subgrade rutting had a value of 5. 58 mm and 5. 87 mm for structures 1 and 2 (Figure 8 ), respectively. Both values are greater than 5. 0 mm, which is the recommended limiting from the MeDiNa program (Franco, 2019). For structure 1, all reinforced simulations showed subgrade rutting values lower than the limit, and the con iguration (1; -1; 1) had better ef iciency and presented a subgrade rutting value of 3. 54 mm, corresponding to a 36. 56% reduction. In structure 2, only the con igurations (-1; 1; -1) and (-1; 1; 1) did not present values lower than the recommended limit, and similar to structure 1, the con iguration with the best ef iciency was (1; -1 ; 1), presenting a reduction of 27. 43% and a subgrade rutting value of 4. 26 mm. 

The regression equations obtained from the pavement response are shown in Table 4. Moreover, a 95% signi icance level was considered. It is emphasized that all values obtained for the p-value are lower than 5% and all equations resulted in a high R 2 (above 95%), indicating the strong correlation of factors associated with independent variables. Table 4 and Figure 8 show that the geogrid position (factor x2) is the factor with the greatest in luence on rutting damage. Although both geogrid positions reduce the subgrade rutting, it can be observed that the geogrid position in the interface with the subgrade performs better. On the other hand, the geogrid positioned in the middle of the base/subbase has better ef iciency reducing the base/subbase rutting. 

Analyzing the reduction in base/subbase rutting with the presence of reinforcement in the middle of this layer, the sensitive analyses showed that the reinforcement in pavement 1 had a better ef iciency than pavement 2 (Figure 8 ). Thus, the greater thickness of the base layer+ subbase present in structure 1 resulted in the best ef iciency. 

In general, the geogrid stiffness (factor x1) sensitivity analysis assumes values of 300 kN/m or 400 kN/m (Figure 7 ), which shows that the 400 kN/m stiffness value implies a higher addition con ining stress (Equation 8 ) and resilient modulus from the reinforced equivalent layer (Equation 9 ), consequently, reducing the rutting damage. Considering the values in Table 4, it should be mentioned that in the pavement structures in which the reinforcement was placed in the middle of the base, factor x1 had less in luence when placed in the interface with the subgrade. 

Among the analyzed factors, the interface parameter (factor x3) had the least in luence on rutting damage results (Table 4 ). However, this result is not negligible, because as factor x1 and factor x3, it changes the additional con ining stress (Equation 8 ), the equivalent layer resilient modulus (Equation 9 ) and the rutting damage (Equation 11 ). Thus, according to Figure 8, a higher value of α results in a lower rutting value.
section_name: Effect of geogrid on permanent deforma on

section_content: This paper presented a inite element model to simulate a geogrid reinforced lexible pavement. To do this, an analytical methodology was adapted to calculate the addition con ining stress provided by the reinforcement, in which nonlinear behavior of the base and subgrade materials was considered, throughout a UMAT introduction. The geotechnical materials properties (geogrid and soils) and interface were adopted from results available in the literature. 

Initially, the rutting from experimental analysis results was used to calibrate the inite element numerical model proposed. A satisfactory it between them were observed, therefore the numerical procedure developed in this paper has the potential to be used for geogrid reinforced lexible pavement design. However, other calibrations with experimental laboratory and ield results must be performed to evaluate the numerical ef iciency for other con igurations. 

It is noteworthy that the numerical curve modeled for rutting versus the number of cycles did not present the same shape as the experimental one, as the numerical curve is more accentuated in initial rutting values and reaches a constant N value smaller than the experimental curve. 

In addition, a parametric study was carried out to verify the following parameter sensitivity: geogrid position, geogrid stiffness and geogrid/geotechnical material interface. From the results obtained, it can be concluded that the best position of the geogrid to reduce total rutting depends on which pavement layer has the greatest contribution to permanent deformation. Inserting the reinforcement into the middle of the base layer was ef icient to reduce permanent deformation in this layer. Moreover, the geogrid positioned at base/subgrade or subbase/subgrade interface showed a better performance in reducing permanent deformations in the subgrade layer. 

Among the factors evaluated in the regression analysis, it was observed that the increase in geogrid stiffness (parameter x1) had the greatest in luence on additional con ining stress and equivalent layer resilient modulus. Consequently, it resulted in less permanent deformation. 

It is noteworthy that, in the regression analyses, the α bonding coef icient (parameter x3) between geogrid and geotechnical material had the least total rutting in luence. However, it is a fundamental parameter which governs the interaction between materials, in other words, if it assumes a zero value there is no additional con ining stress. Therefore, it is recommended to implement a correlation between the α bonding coef icient and granular material average diameter, geogrid installation conditions and geogrid properties. 

Finally, it was concluded that the geogrid reinforcement element provides an improved pavement response, mainly by reducing the vertical stresses and, consequently, permanent deformation, which results in an increase in pavement service life.
section_name: CONCLUSION