Generalized Interface Shear Strength Equation for Recycled Materials Reinforced with Geogrids

: In this research, large direct shear tests were conducted to evaluate the interface shear strength between reclaimed asphalt pavement (RAP) and kenaf geogrid (RAP–geogrid) and to also assess their viability as an environmentally friendly base course material. The inﬂuence of factors such as the gradation of RAP particles and aperture sizes of geogrid ( D ) on interface shear strength of the RAP–geogrid interface was evaluated under different normal stresses. A critical analysis was conducted on the present and previous test data on geogrids reinforced recycled materials. The D / F D , in which F D is the recycled materials’ particle content ﬁner than the aperture of geogrid, was proposed as a prime parameter governing the interface shear strength. A generalized equation was proposed for predicting the interface shear strength of the form: α = a ( D / F D ) + b , where α is the interface shear strength coefﬁcient, which is the ratio of the interface shear strength to the shear strength of recycled material, and a and b are constants. The constant values of a and b were found to be dependent upon types of recycled material, irrespective of types of geogrids. A stepwise procedure to determine variable a , which is required for analysis and design of geogrids reinforced recycled materials in roads with various gradations was also suggested. Author Contributions: Conceptualization, A.U., A.S., M.H. and S.H.; methodology, A.U., M.H., A.P. and S.H.; software, A.U., A.P. and M.H.; formal analysis, A.U., A.S. and M.H.; writing—review and editing, A.U., A.S., S.H., M.H., N.C.T. and A.A.; visualization, M.H., A.A. S.H.; super-vision,


Introduction
Roadways and highways are commonly categorized based on the traffic volumes and service life into two main categories-namely, permanent roads and temporary roads. Permanent roads are subjected to heavy traffic volumes of more than a million traffic loads during their service life. Temporary roads, on the other hand, are subject to lower traffic volumes of less than 10,000 load applications during their service life. Temporary roads include access roads, haul, detours, and construction platforms, which are used to construct permanent roads on weak soil layers [1].
Due to the scarcity of high-quality natural materials, marginal soils have been used for road construction with some form of mechanical or chemical treatment. Chemical stabilization such as with cement, natural rubber latex stabilization [2][3][4], and geopolymer stabilization [5][6][7] are often used to enhance the mechanical properties of marginal materials.
Geogrid applications have also been found to improve the mechanical properties and performance of marginal materials for base/subbase courses [8][9][10][11]. Research on geosynthetics in pavement reinforcement application has reported that the use of a geogrid within an unbound layer of a pavement structure can improve the stiffness of pavement layers, especially below and above the location of the geogrid [1,12,13]. Geogrids stabilize the aggregate layer by increasing aggregate interlocking, enhancing confinement, and reducing the lateral movement of the pavement structure, leading to deformation reduction.
The advantages of utilizing geogrids in road construction include a decrease in the thickness of the pavement structure layers and prolonging the durability of the road structure. Geosynthetics reinforcement in asphalt layers has also been reported to reduce rutting, pavement material fatigue, as well as thermal and reflective cracking. Geocomposite materials, such as geotextiles sandwiched within geogrids are also used as a separation layer to prevent the movement of small particles into open-graded base layers, resulting in improving the drainage systems and enhancing the road performance [14].
In temporary roads, geogrids are used within the weak foundation to support the initial construction work. The geogrid-reinforced aggregates are used as a working platform to mobilize the heavy machinery into the construction sites. For a particular subgrade stabilization application, geogrids are used to reinforce the soft subgrade and to decrease the excessive deformation of pavement structures due to the traffic loads [15][16][17][18]. For basal reinforcement applications, geogrids are installed under or within unbound layers of a flexible road to enhance the bearing capacity of the pavement against cyclic loads [19,20]. For pavement surface reinforcement, geogrids are used within the asphalt layer to decrease fatigue and rutting of the pavement surface using the marginal quantity aggregate [21,22].
Annually across the globe, the construction industry generates large quantities of construction and demolition (C&D) wastes, including recycled concrete aggregate (RCA), as well as recycled glass and brick. Similarly, reclaimed asphalt pavement (RAP) is generated when asphalt pavements are removed for reconstruction and/or resurfacing. Road authorities in many countries have been seeking to develop innovative methods of recycling and reusing recycled aggregates for partial or total replacement of natural aggregates in roadwork applications. The use of recycled aggregates including RAP [23][24][25], RCA [26][27][28], and recycled glass [29][30][31] as an alternative aggregate is widely accepted for road construction, especially as pavement base/subbase materials. Reusing recycled materials can decrease waste and energy consumption and therefore significantly contributes toward the sustainable road construction industry [32,33]. However, these materials sometimes require mechanical improvement to meet the local and international standards for both design and construction.
Several researchers have reported on the successful application of commercial synthetic geogrids reinforced natural materials in road construction. However, the applications of geogrid-reinforced recycled aggregates remain limited due to the lack of research studies, accepted design methodology, and construction guidelines. Pioneering research on the commercial geogrid-reinforced recycled aggregates was recently undertaken by several researchers [29,[34][35][36][37][38][39]. Suddeepong et al. (2021) [40] investigated the interface shear behavior of natural kenaf geotextiles and RCA to promote the use of natural geotextiles with recycled aggregates for sustainable development of road construction and environmentally sound technologies. The performance of geogrid-reinforced recycled aggregates relies on various factors such as geometric forms and stiffness of geogrid, location and depth of geogrid installation, and particle sizes of aggregates [34,35,40].
This research aims to further contribute to the increased utilization of recycled aggregates in the pavement structure and to also facilitate the analysis and design by developing a generalized predictive equation of interface shear strength between geogrid and recycled aggregates. A large direct shear test (LDST) was first conducted to determine the interface shear strength behavior of RAP reinforced with natural kenaf geogrid in this research. The influence of gradation of RAP and aperture size of geogrid on the interface shear responses of RAP-geogrid under different normal stresses was investigated. The results were then compared with the previous results to introduce a prime factor for developing a generalized predictive equation that can be used for rapid estimation of the interface shear strength of recycled aggregates reinforced with both commercial and natural geogrids.

Materials
Reclaimed asphalt pavement (RAP) samples were obtained from the Bureau of Highways, Nakhon Ratchasima, Thailand. A cold milling machine was used to remove the asphalt pavement for resurfacing in the cold in-place recycling process. The asphalt content in RAP aggregate is approximately 3-5% by weight. Figure 1 indicates the gradations of large-sized RAP and small-sized RAP samples. The large-sized RAP is on the lower boundary and the small-sized RAP is on the upper boundary, designated by the Department of Highways, Thailand (DOH, 2001) [41].
This research aims to further contribute to the increased utilization of recycled aggregates in the pavement structure and to also facilitate the analysis and design by developing a generalized predictive equation of interface shear strength between geogrid and recycled aggregates. A large direct shear test (LDST) was first conducted to determine the interface shear strength behavior of RAP reinforced with natural kenaf geogrid in this research. The influence of gradation of RAP and aperture size of geogrid on the interface shear responses of RAP-geogrid under different normal stresses was investigated. The results were then compared with the previous results to introduce a prime factor for developing a generalized predictive equation that can be used for rapid estimation of the interface shear strength of recycled aggregates reinforced with both commercial and natural geogrids.

Materials
Reclaimed asphalt pavement (RAP) samples were obtained from the Bureau of Highways, Nakhon Ratchasima, Thailand. A cold milling machine was used to remove the asphalt pavement for resurfacing in the cold in-place recycling process. The asphalt content in RAP aggregate is approximately 3-5% by weight. Figure 1 indicates the gradations of large-sized RAP and small-sized RAP samples. The large-sized RAP is on the lower boundary and the small-sized RAP is on the upper boundary, designated by the Department of Highways, Thailand (DOH, 2001) [41].  Table 1 summarizes the basic and engineering properties of the RAP samples. The large-sized RAP and small-sized RAP samples were classified as poorly graded gravel (GP) and well-graded gravel (GW), respectively, according to the Unified Soil Classification System. Although the average particle size of the large-sized RAP sample and smallsized RAP sample was different, the specific gravity, maximum dry density (MDD) at optimum water content, California bearing ratio, internal friction angles, and cohesion were almost the same.
The natural kenaf fibers were obtained from Tai Song Huad Co., Ltd., Sai Mai, Bangkok, Thailand, and were used to fabricate kenaf geogrid in this research. The handmade biaxial kenaf geogrid was a planar grid, which possesses the same strength in both orthodirections (longitudinal and transversal) ( Figure 2). The single rib tensile strength of kenaf geogrid was 43 MPa, which was obtained from the tensile test using a universal testing   Table 1 summarizes the basic and engineering properties of the RAP samples. The large-sized RAP and small-sized RAP samples were classified as poorly graded gravel (GP) and well-graded gravel (GW), respectively, according to the Unified Soil Classification System. Although the average particle size of the large-sized RAP sample and small-sized RAP sample was different, the specific gravity, maximum dry density (MDD) at optimum water content, California bearing ratio, internal friction angles, and cohesion were almost the same. The natural kenaf fibers were obtained from Tai Song Huad Co., Ltd., Sai Mai, Bangkok, Thailand, and were used to fabricate kenaf geogrid in this research. The handmade biaxial kenaf geogrid was a planar grid, which possesses the same strength in both ortho-directions (longitudinal and transversal) ( Figure 2). The single rib tensile strength of kenaf geogrid was 43 MPa, which was obtained from the tensile test using a universal testing machine with a capacity of 2.5 kN based on ASTM-D6637 (2015) [42]. Two different aperture sizes of kenaf geogrids: 7 × 7 mm and 21 × 21 mm with a 3 mm rib thickness were prepared. ture sizes of kenaf geogrids: 7 × 7 mm and 21 × 21 mm with a 3 mm rib thickness were prepared.

Experimental Program
The LDST was undertaken in accordance with ASTM-D5321 (2020) [43] to investigate the interface shear strength of RAP-geogrid samples ( reinforced ) and the shear strength of unreinforced RAP samples ( unreinforced ). The LDST shear box apparatus with a dimension of 305 × 305 mm 2 and 204 mm high was divided into two parts, whereby the stationary upper half provides a confined vertical load to the sample, while the lower half of the box allows the application of horizontal shearing stress. To conduct the shear test, hand compaction was first carried out on RAP samples at optimum water content in three layers in the shear box under the modified Proctor effort to attain the MDD. For the consolidation process, the lower shear box and half of the upper one were filled with de-aired water to saturate the compacted RAP samples under different normal stresses (σn = 50, 100, and 200 kPa) for 12 h. LDSTs were conducted at the same σn levels with a constant shear rate of 0.025 mm/min at a controlled temperature of 20 ± 1 °C. The tests were completed when the horizontal shear displacement (HSD) attained 40 mm. Three samples were carried out for each direct shear test, and the mean value was reported in this study. The results under the same testing condition were reproducible with a low mean standard deviation, SD (SD/ ̅ < 10%, where ̅ is the mean value). Table 2 illustrates the names of the prepared sample for LDST. Figure 3 illustrates the LDST apparatus and a photo of the tested kenaf geogrid.

Experimental Program
The LDST was undertaken in accordance with ASTM-D5321 (2020) [43] to investigate the interface shear strength of RAP-geogrid samples (τ reinforced ) and the shear strength of unreinforced RAP samples (τ unreinforced ). The LDST shear box apparatus with a dimension of 305 × 305 mm 2 and 204 mm high was divided into two parts, whereby the stationary upper half provides a confined vertical load to the sample, while the lower half of the box allows the application of horizontal shearing stress. To conduct the shear test, hand compaction was first carried out on RAP samples at optimum water content in three layers in the shear box under the modified Proctor effort to attain the MDD. For the consolidation process, the lower shear box and half of the upper one were filled with de-aired water to saturate the compacted RAP samples under different normal stresses (σ n = 50, 100, and 200 kPa) for 12 h. LDSTs were conducted at the same σ n levels with a constant shear rate of 0.025 mm/min at a controlled temperature of 20 ± 1 • C. The tests were completed when the horizontal shear displacement (HSD) attained 40 mm. Three samples were carried out for each direct shear test, and the mean value was reported in this study. The results under the same testing condition were reproducible with a low mean standard deviation, SD (SD/x < 10%, where x is the mean value). Table 2 illustrates the names of the prepared sample for LDST. Figure 3 illustrates the LDST apparatus and a photo of the tested kenaf geogrid.

Results and Discussion
The shear stresses and dilatation characteristics of unreinforced RAP obtained from the LDST were demonstrated in Figure 4. The shear stress behaviors of large-sized RAP and small-sized RAP were similar. The shear strength of unreinforced material ( unreinforced ) versus horizontal shear displacement (HSD) relationship exhibited strainhardening behavior, whereby the shear stress increased with horizontal displacement and then became almost constant after HSD = 20-mm. The maximum unreinforced increased with the increased σn.

Results and Discussion
The shear stresses and dilatation characteristics of unreinforced RAP obtained from the LDST were demonstrated in Figure 4. The shear stress behaviors of large-sized RAP and small-sized RAP were similar. The shear strength of unreinforced material (τ unreinforced ) versus horizontal shear displacement (HSD) relationship exhibited strain-hardening behavior, whereby the shear stress increased with horizontal displacement and then became almost constant after HSD = 20-mm. The maximum τ unreinforced increased with the increased σ n .
The vertical shear displacement (VSD) versus HSD relationship of both large-sized RAP and small-sized RAP exhibited dilative behavior, which behaved similar to dense recycled glass [44] and RCA [35], at high σ n of 100-200 kPa. The VSD of large-and small-sized RAP samples were similar when the HSD < 20 mm. However, the VSD of the small-sized RAP was higher than that of the large-sized RAP when the HSD was > 20 mm, especially at a high σ n = 200 kPa.
In accordance with the Mohr-Coulomb failure criterion, the friction angle (φ) and cohesion (c) at the peak for both large-sized RAP and small-sized RAP samples were determined and are illustrated in Figure 5. The φ and c of small-sized RAP samples (φ = 54.81 • and c = 56.99 kPa) and large-sized RAP samples (φ = 56.99 • and c = 53.68 kPa) were similar. The high shear strength properties of RAP samples demonstrate that the material is stiff to withstand the traffic load and can be used as a base/subbase material based on the Department of Highways (DOH) specification [41]. The results also indicated  The vertical shear displacement (VSD) versus HSD relationship of both large-sized RAP and small-sized RAP exhibited dilative behavior, which behaved similar to dense recycled glass [44] and RCA [35], at high σn of 100-200 kPa. The VSD of large-and smallsized RAP samples were similar when the HSD < 20 mm. However, the VSD of the smallsized RAP was higher than that of the large-sized RAP when the HSD was > 20 mm, especially at a high σn = 200 kPa.
In accordance with the Mohr-Coulomb failure criterion, the friction angle (∅) and cohesion (c) at the peak for both large-sized RAP and small-sized RAP samples were de- strate that the material is stiff to withstand the traffic load and can be used as a base/subbase material based on the Department of Highways (DOH) specification [41]. The results also indicated that the RAP samples with gradation within the boundary specified by DOH can be used as base/subbase materials. The reinforced behavior of large-sized RAP samples was similar to that of the small-sized ones. reinforced , stiffness, and its peak values were found to increase with the increase in σn from 50 to 200 kPa. The relationship between reinforced versus HSD of RAP-geogrid samples for both RAP gradations indicated strain-hardening behavior, similar to unreinforced RAP samples.  The τ reinforced behavior of large-sized RAP samples was similar to that of the small-sized ones. τ reinforced , stiffness, and its peak values were found to increase with the increase in σ n from 50 to 200 kPa. The relationship between τ reinforced versus HSD of RAP-geogrid samples for both RAP gradations indicated strain-hardening behavior, similar to unreinforced RAP samples. (D) on the reinforced behaviors of large-sized RAP-geogrid and small-sized RAP-geogrid. The reinforced behavior of large-sized RAP samples was similar to that of the small-sized ones. reinforced , stiffness, and its peak values were found to increase with the increase in σn from 50 to 200 kPa. The relationship between reinforced versus HSD of RAP-geogrid samples for both RAP gradations indicated strain-hardening behavior, similar to unreinforced RAP samples.  For the large-sized RAP samples (Figure 6), the peak reinforced of the samples at σn = 50 kPa was found at an HSD of approximately 20 to 25 mm. The peak reinforced of the samples at σn of 100-200 kPa was, however, found at a large HSD of approximately 30 to 40 mm. For the small-sized RAP samples, the peak reinforced of the samples was at an HSD of approximately 25 to 35 mm for all σn (Figure 7). The peak reinforced of kenaf geogridreinforced small-sized RAP samples was slightly lower than those of kenaf geogrid-reinforced large-sized RAP samples at the same σn. For the large-sized RAP samples (Figure 6), the peak τ reinforced of the samples at σ n = 50 kPa was found at an HSD of approximately 20 to 25 mm. The peak τ reinforced of the samples at σ n of 100-200 kPa was, however, found at a large HSD of approximately  (Figure 7). The peak τ reinforced of kenaf geogrid-reinforced small-sized RAP samples was slightly lower than those of kenaf geogrid-reinforced large-sized RAP samples at the same σ n .
The relationship between VSD and HSD of RAP-geogrid with large-and small-sized RAP samples is also shown in Figures 6 and 7, respectively. A contraction behavior is noticed at an early stage, followed by continuous dilative behavior at the final stage. The dilative vertical displacements of kenaf geogrid-reinforced both large-and small-sized RAP samples were higher than those of unreinforced RAP samples at the same σ n . This implies that the interaction between geogrid and RAP particles was improved. The influence of kenaf geogrid aperture size on VSD versus HSD relation was clearly apparent for the small-sized RAP samples. At a particular σ n , the VSD of kenaf geogrid-reinforced small-sized RAP samples with 7 × 7 mm geogrid was higher than that of samples with 21 × 21 mm geogrid at the same HSD. The τ reinforced value of RAP-geogrid samples was dependent upon both RAP aggregate interlocking and the contact surface area between RAP particles and geogrid. Figures 8 and 9 show the Mohr-Coulomb failure envelopes of RAP-geogrids with different aperture sizes of geogrid and different gradations of RAP samples, compared with the failure envelopes of unreinforced RAP samples. For the large-sized RAP sample (Figure 8), the friction angle of unreinforced RAP samples (φ = 56.99 • ) was slightly higher than the interface friction angles of kenaf geogrid-reinforced RAP samples with 21 × 21 mm geogrid (δ = 55.06 • ) and 7 × 7 mm (δ = 54.18 • ). In contrast, the adhesion values of kenaf geogrid-reinforced RAP samples with 21 × 21 mm geogrid (c a = 56.92 kPa), 7 × 7 mm geogrid (c a = 59.29 kPa) were higher than the cohesion of unreinforced RAP samples (c = 53.68 kPa). For small-sized RAP samples (Figure 9), the interface friction angles of kenaf geogrid-reinforced RAP samples were similar for both aperture sizes of 21 × 21 mm geogrid (δ = 51.26 • ) and 7 × 7 mm geogrid (δ = 50.34 • ). These values were lower than the friction angle of the unreinforced RAP samples (φ = 54.81 • ). The adhesion values of kenaf geogrid-reinforced RAP samples with 21 × 21 mm geogrid and 7 × 7 mm geogrid were 64.41 kPa and 53.12 kPa, respectively, while the cohesion value of the unreinforced RAP sample was 56.99 kPa. This reveals that the aperture size of geogrid and gradation of RAP particles had a significant influence on the τ reinforced value of kenaf geogrid-reinforced RAP samples. The interface shear strength (τ reinforced ) of RAP-geogrid samples was found to be lower than the τ unreinforced of unreinforced RAP samples, which are consistent with the previous findings [29,35,40,45]. For all sizes of RAP samples, the higher aperture size of kenaf geogrid resulted in the higher adhesion but insignificantly affected the interface friction angles. This reveals that the aperture size of geogrid and gradation of RAP particles had a significant influence on the reinforced value of kenaf geogrid-reinforced RAP samples. The interface shear strength ( reinforced ) of RAP-geogrid samples was found to be lower than the unreinforced of unreinforced RAP samples, which are consistent with the previous findings [29,35,40,45]. For all sizes of RAP samples, the higher aperture size of kenaf geogrid resulted in the higher adhesion but insignificantly affected the interface friction angles.  To facilitate the analysis and design for pavement geotechnics applications, particularly by the finite element method, it is useful to interpret the reinforced using the interface shear strength coefficient (α) in the following expression [46,47]: The correlation between α and σn of RAP-geogrid samples for large-and small-sized RAP samples is presented in Figure 10. Though the unreinforced value of unreinforced RAP directly influenced the unreinforced value of RAP-geogrid samples, it was found that the α was irrespective of σn. The aperture size of geogrid (D) and gradation of RAP samples were found to strongly affect the interlocking mechanism of geogrid reinforcement and aggregates. The RAP particle content finer than the geogrid aperture size (FD), which is related to the influence of gradation of RAP samples on the interface shear strength is investigated. In other words, FD is the percentage passing obtained from the grain size distribution of RAP that is smaller than the aperture size of geogrid (D = 7 × 7 mm and 21 × 21 mm). The relationship between α versus D and between α versus FD is depicted in Figures 11 and 12, respectively. To facilitate the analysis and design for pavement geotechnics applications, particularly by the finite element method, it is useful to interpret the τ reinforced using the interface shear strength coefficient (α) in the following expression [46,47]: The correlation between α and σ n of RAP-geogrid samples for large-and small-sized RAP samples is presented in Figure 10. Though the τ unreinforced value of unreinforced RAP directly influenced the τ unreinforced value of RAP-geogrid samples, it was found that the α was irrespective of σ n . The aperture size of geogrid (D) and gradation of RAP samples were found to strongly affect the interlocking mechanism of geogrid reinforcement and aggregates. The RAP particle content finer than the geogrid aperture size (F D ), which is related to the influence of gradation of RAP samples on the interface shear strength is investigated. In other words, F D is the percentage passing obtained from the grain size distribution of RAP that is smaller than the aperture size of geogrid (D = 7 × 7 mm and 21 × 21 mm). The relationship between α versus D and between α versus F D is depicted in Figures 11 and 12, respectively.
The effect of F D on the α values of RAP-geogrid samples with different D and gradations of RAP samples is depicted in Figure 12. The effect of F D on the α values was found to be similar to the effect of D on α values (Figure 11). For the small-sized RAP samples, the large aperture size (21 × 21 mm) of geogrid exhibited higher α values than the small aperture size (7 × 7 mm), while the α values were found to be practically the same for both aperture sizes (21 × 21 mm and 7 × 7 mm) of geogrid-reinforced RAP samples, although F D was varied from 0.28 to 0.6. However, for the same F D of 0.6, the large-sized RAP + 21 × 21 mm geogrid had higher α than the small-sized RAP + 7 × 7 mm geogrid. It seems that F D = 0.28 for large-sized RAP and F D = 0.8 for small-sized RAP yielded the same α value of 0.96. In other words, both F D and D control the α value. Sustainability 2021, 13, x FOR PEER REVIEW 11 of 17     The effect of FD on the α values of RAP-geogrid samples with different D and gradations of RAP samples is depicted in Figure 12. The effect of FD on the α values was found to be similar to the effect of D on α values ( Figure 11). For the small-sized RAP samples, the large aperture size (21 × 21 mm) of geogrid exhibited higher α values than the small aperture size (7 × 7 mm), while the α values were found to be practically the same for both aperture sizes (21 × 21 mm and 7 × 7 mm) of geogrid-reinforced RAP samples, although FD was varied from 0.28 to 0.6. However, for the same FD of 0.6, the large-sized RAP + 21 × 21 mm geogrid had higher α than the small-sized RAP + 7 × 7 mm geogrid. It seems that FD = 0.28 for large-sized RAP and FD = 0.8 for small-sized RAP yielded the same α value of 0.96. In other words, both FD and D control the α value.
The relationship between α and D for the small-sized RAP samples ( Figure 11) showed that the large aperture size (21 × 21 mm) of geogrid resulted in higher α values than the small aperture size (7 × 7 mm) of geogrid. In contrast, the α values of the largesized RAP samples were found to be essentially the same for both large and small aperture sizes of geogrid. In addition, the α values of the large-sized RAP and small-sized RAP samples were similar for the 21 × 21 mm aperture size of geogrid, while the α value of small-sized RAP samples was lower than that of large-sized RAP samples with 7 × 7 mm geogrid. This implies that the aperture size of geogrid influences the α values of kenaf geogrid-reinforced RAP samples and ideally, a very large D results in the same α for different RAP gradations.
Several researchers have investigated the effect of a ratio of D to average aggregate particle size (D50) on the reinforced value of geogrid-reinforced aggregates [8,48,49]. However, the use of D50 to interpret the influence of the reinforced behavior of geogrid-reinforced aggregate remains elusive. The proportion of aggregates indicated by D50 might have a large variation in large-and small-sized particles, which can significantly influence the gradation of the recycled materials. Consequently, excessively small or large particles of aggregates impact the effectiveness of the interlock mechanism or the reinforced value of geogrid-reinforced recycled materials [50]. Some researchers studied the effect of a ratio of D to a single-sized gradation on the reinforced behavior of geogrid-reinforced aggregates [51]. On the other hand, the use of a single-size particle or a poorly gradation of aggregate might not be suitable for pavement material in some road projects. Therefore, The relationship between α and D for the small-sized RAP samples ( Figure 11) showed that the large aperture size (21 × 21 mm) of geogrid resulted in higher α values than the small aperture size (7 × 7 mm) of geogrid. In contrast, the α values of the large-sized RAP samples were found to be essentially the same for both large and small aperture sizes of geogrid. In addition, the α values of the large-sized RAP and small-sized RAP samples were similar for the 21 × 21 mm aperture size of geogrid, while the α value of small-sized RAP samples was lower than that of large-sized RAP samples with 7 × 7 mm geogrid. This implies that the aperture size of geogrid influences the α values of kenaf geogrid-reinforced RAP samples and ideally, a very large D results in the same α for different RAP gradations.
Several researchers have investigated the effect of a ratio of D to average aggregate particle size (D 50 ) on the τ reinforced value of geogrid-reinforced aggregates [8,48,49]. However, the use of D 50 to interpret the influence of the τ reinforced behavior of geogrid-reinforced aggregate remains elusive. The proportion of aggregates indicated by D 50 might have a large variation in large-and small-sized particles, which can significantly influence the gradation of the recycled materials. Consequently, excessively small or large particles of aggregates impact the effectiveness of the interlock mechanism or the τ reinforced value of geogrid-reinforced recycled materials [50]. Some researchers studied the effect of a ratio of D to a single-sized gradation on the τ reinforced behavior of geogrid-reinforced aggregates [51]. On the other hand, the use of a single-size particle or a poorly gradation of aggregate might not be suitable for pavement material in some road projects. Therefore, the use of the correlation between α versus D/F D compliance for interpreting τ reinforced of geogrid-reinforced recycled materials is a sound principle in this study.
Using the D/F D as a prime parameter and integrating the contribution from D and F D , the correlation between α and D/F D is presented in Figure 13 and Equation (2) in the following expression: where D is expressed in mm, and F D is expressed in decimal with a high degree of coefficient, determined as 0.94.
where D is expressed in mm, and FD is expressed in decimal with a high degree of coefficient, determined as 0.94. Equation (2) is a useful practical tool for geotechnical and pavement engineers and the rational development of the equation can be extended to develop a generalized equation for different types of recycled materials and geogrids. Therefore, the separate set of data from the previous studies on the reinforced behavior of the commercial polymer and natural kenaf geogrid-reinforced recycled aggregates such as RAP and RCA were taken and reanalyzed. Figure 14 shows the relationship between α and D/FD of geogrid-reinforced RAP and RCA samples. The general form of the relationship can be expressed as the following equation: where a and b are constant. It is worthwhile mentioning that values of a and b are irrespective of geogrid types (natural kenaf or commercial polymer), while they were mainly dependent upon the recycled materials. From the regression analysis, the values of a = 0.0046 and b = 0.8336 were obtained for geogrid-reinforced RAP samples, while values of a = 0.0057 and b = 0.7185 were for geogrid-reinforced RCA samples. This implies that the geogrid-reinforced RAP has a higher α value than the geogrid-reinforced RCA at the same D/FD for both natural kenaf and commercial polymer type. This might be due to the difference in shear strength, stiffness, and impurity of the recycled materials. The shear strength and stiffness of unreinforced RCA were higher than that of the unreinforced RAP material [34,51,52]. In other words, the geogrid-reinforced RCA samples exhibited a better Equation (2) is a useful practical tool for geotechnical and pavement engineers and the rational development of the equation can be extended to develop a generalized equation for different types of recycled materials and geogrids. Therefore, the separate set of data from the previous studies on the τ reinforced behavior of the commercial polymer and natural kenaf geogrid-reinforced recycled aggregates such as RAP and RCA were taken and reanalyzed. Figure 14 shows the relationship between α and D/F D of geogrid-reinforced RAP and RCA samples. The general form of the relationship can be expressed as the following equation: where a and b are constant. It is worthwhile mentioning that values of a and b are irrespective of geogrid types (natural kenaf or commercial polymer), while they were mainly dependent upon the recycled materials. From the regression analysis, the values of a = 0.0046 and b = 0.8336 were obtained for geogrid-reinforced RAP samples, while values of a = 0.0057 and b = 0.7185 were for geogrid-reinforced RCA samples. This implies that the geogrid-reinforced RAP has a higher α value than the geogrid-reinforced RCA at the same D/F D for both natural kenaf and commercial polymer type. This might be due to the difference in shear strength, stiffness, and impurity of the recycled materials. The shear strength and stiffness of unreinforced RCA were higher than that of the unreinforced RAP material [34,51,52]. In other words, the geogrid-reinforced RCA samples exhibited a better interlocking mechanism than that geogrid-reinforced RAP samples. The α of RAP-geogrid is found to be more sensitive to the D/F D than that of RAP-geogrid sample.
Logically, there is no interaction between kenaf geogrid and RAP particles when τ reinforced and τ unreinforced are equal (α = 1.0). Based on equation (3), the geogrid-reinforced RAP and geogrid-reinforced RCA have no interaction when D = 36.2F D and D = 49.4F D , respectively. The proposed equation was developed based on sound principles and can therefore be used to predict the α of the recycled materials reinforced with various geogrids once the values of the constants a and b are known. In practice, a stepwise procedure to determine α values for the design of geogrids stabilized base/subbase with recycled aggregates is proposed as follows: (1) From a selected recycled aggregate, adjust its gradation to meet the requirement for base/subbase courses specified by local or international standards; (2) From the gradation, which might be varied along the constructing road, select at least two gradations to determine D/F D values for a selected geogrid; interlocking mechanism than that geogrid-reinforced RAP samples. The α of RAP-geogrid is found to be more sensitive to the D/FD than that of RAP-geogrid sample. Logically, there is no interaction between kenaf geogrid and RAP particles when reinforced and unreinforced are equal (α = 1.0). Based on equation (3), the geogrid-reinforced RAP and geogrid-reinforced RCA have no interaction when D = 36.2FD and D = 49.4FD, respectively. The proposed equation was developed based on sound principles and can therefore be used to predict the α of the recycled materials reinforced with various geogrids once the values of the constants a and b are known. In practice, a stepwise procedure to determine α values for the design of geogrids stabilized base/subbase with recycled aggregates is proposed as follows: (1) From a selected recycled aggregate, adjust its gradation to meet the requirement for base/subbase courses specified by local or international standards; (2) From the gradation, which might be varied along the constructing road, select at least two gradations to determine D/FD values for a selected geogrid; (3) Perform the direct shear test on the selected recycled aggregate at various normal stresses in the range of field working stress; (4) Perform the direct interface shear test on the recycled aggregate reinforced with geogrid at various normal stress and D/FD values; (5) From Equation (3), determine values of a and b. With these two values, the α values of the selected geogrid and recycled aggregate can be approximated.
This proposed general equation can be used to estimate the α for analysis and design of related geotechnical projects including pavement projects, mechanically stabilized earth (MSE) wall design, embankment reinforcement construction, and foundation design, which deal with various types of geogrid-reinforced recycled aggregates. Furthermore, to fully understand the behavior of natural geogrid-reinforced recycled aggregates, the relevant experimental program including dynamic flexural strength and fatigue tests are suggested for further research [53]. The outcome of this research will lead to the promotion of recycled aggregates as green aggregate for sustainable geotechnical and pavement applications. This proposed general equation can be used to estimate the α for analysis and design of related geotechnical projects including pavement projects, mechanically stabilized earth (MSE) wall design, embankment reinforcement construction, and foundation design, which deal with various types of geogrid-reinforced recycled aggregates. Furthermore, to fully understand the behavior of natural geogrid-reinforced recycled aggregates, the relevant experimental program including dynamic flexural strength and fatigue tests are suggested for further research [53]. The outcome of this research will lead to the promotion of recycled aggregates as green aggregate for sustainable geotechnical and pavement applications.

Conclusions
In this research, a large direct shear test (LDST) was conducted to investigate the interface shear strength (τ reinforced ) between reclaimed asphalt pavement (RAP) and kenaf geogrid (RAP-geogrid) as a sustainable base course material. The influence of gradation of RAP particles and aperture sizes of geogrid (D) on τ reinforced of RAP-geogrid was evaluated under different normal stresses. Based on the critical analysis of the present and previous test data on both natural and commercial geogrid-reinforced C&D materials including RAP and RCA, it is found that the τ reinforced value of geogrid-reinforced recycled materials was controlled by the D/F D , where F D is the recycled materials' particle content finer than the aperture of geogrid. The generalized equation for predicting τ reinforced is proposed in the form: α = a(D/F D ) + b, where α is interface shear strength coefficient, which is the ratio of τ reinforced to τ unreinforced of recycled material, and a and b are constant. The values of a and b were found to be dependent upon types of recycled material, irrespective of types of geogrids. This proposed generalized equation is useful to determine α, a required parameter for analysis and design of geotechnical and pavement work dealt with the geogrid-reinforced recycled aggregates. It is advantageous to the designer to select the various aperture sizes of geogrids and gradations of recycled aggregates for geotechnical and pavement projects.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.