An assessment of the geometry effect of geosynthetics for base course reinforcements

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1 International Journal of Tranportation Science and Technology vol. 1 no page An aement of the geometry effect of geoynthetic for bae coure reinforcement Xiaoming Yang, Ph.D. School of Civil and nvironmental ngineering, Oklahoma State Univerity, 207 ngineering South, Stillwater, OK 74078, USA ABSTRACT Geoynthetic-reinforced bae coure i potentially a cot-effective olution for flexible pavement contruction. With the recent advance in the mechanitic-empirical pavement deign in the United State, there i a need to develop the next generation deign method for geoynthetic-reinforced bae in flexible pavement. To develop uch a deign method require an improved undertanding about the mechanitic behavior, epecially the in-plane elatic behavior, of geoynthetic. In thi paper, the geometry effect of geoynthetic wa dicued. The author firt reviewed recent experimental and numerical tudie. Analytical equation baed on cellular material mechanic were preented for determining the in-plane elatic propertie of geoynthetic. The analytical equation were ued to evaluate a few geoynthetic with typical geometrie. The reult howed that, with the ame polymeric material and typical product geometrie, the geocell ha a better confinement effect than geogrid, and the triaxial geogrid with a triangular aperture ha a better confinement effect than the biaxial geogrid with a rectangular aperture. It wa alo demontrated that the traditional uniaxial tenile modulu may be a poor indicator of the effectivene of geoynthetic for bae coure reinforcement. 1. INTRODUCTION Low- to medium-volume road compoe a majority of the public roadway ytem. Mot of low- or medium-volume road were contructed with thinly paved flexible pavement (i.e., le than 10-cm thick aphalt concrete on top of unbound bae and ubgrade layer). Due to the relatively thin aphalt concrete layer ued, unbound bae aggregate are ubjected to a larger vertical tre under the traffic load. The induced vertical tre will force the unbound bae particle to move laterally aide from the wheel path. A the number of vehicle pae increae, the unbound bae layer will develop an unrecoverable (or permanent) vertical deformation, which will reult in Thi i an open acce article under the CC BY-NC-ND licene (

2 248 An aement of the geometry effect of geoynthetic for bae coure reinforcement rutting a well a other type of ditree to the road urface. In order to minimize the lateral movement of the unbound bae material, a thick unbound bae layer ha to be deigned with high-quality aggregate material. However, the local reource of highquality aggregate i not alway available to highway adminitrative agencie. A an alternative, geoynthetic may be ued to reinforce the aggregate bae and reduce the total thickne required for the unbound aggregate layer of the pavement. Geoynthetic i a general term ued to decribe a wide variety of polymeric product ued in civil engineering tructure. For bae coure reinforcement, two mot commonly ued geoynthetic product are geogrid and geocell (Figure 1). In term of geometry, both of the two product have a regular, periodic, cellular tructure. The major difference between the two product i that geocell ha a three-dimenional tructure with a typical height of 10 to 15 cm, wherea geogrid i a planar geoynthetic product with a typical thickne of everal millimeter. The mechanim of the two geoynthetic product in the bae coure reinforcement are alo lightly different, a illutrated in Figure 2. Geogrid retrain the lateral movement of the granular material through the interlocking between aggregate particle and geogrid aperture. To achieve a atifying interlocking, the grain ize ditribution of the aggregate hould be properly elected. On the other hand, geocell provide direct lateral confinement to the in-fill unbound material, which allow a wider variety of granular material to be ued in the bae coure contruction. Proper application of the geoynthetic bae reinforcement technique relie on rational deign method. Ideally, the deign method for geoynthetic-reinforced bae (a) (b) Figure 1. Typical geoynthetic product ued for bae coure reinforcement: (a) geogrid, (b) geocell Aphalt Concrete Aphalt Concrete Figure 2. Subgrade Subgrade The mechanim of geoynthetic bae reinforcement

3 International Journal of Tranportation Science and Technology vol. 1 no hould be compatible with the pavement deign and be applicable to a wide range of geoynthetic product from different manufacturer. In the pat, empirical deign method have been developed for geogrid-reinforced bae [1-3]. However, with the recent advance in mechanitic-empirical pavement deign in the United State, there i a need to develop the next generation deign method for geoynthetic-reinforced bae in flexible pavement. To achieve thi goal, an improved undertanding about the mechanitic behavior of the geoynthetic i required. It ha been generally accepted that the in-plane tenile tiffne i the mot influential property of the geoynthetic on the performance of the reinforced bae, becaue it determine the magnitude of lateral confining tre applied to the unbound aggregate under the ame lateral diplacement. For a cellular tructure, the apparent tenile tiffne (referred a tenile tiffne hereafter) of the tructure depend on the elatic modulu of the material and the geometry of the tructure. Obviouly, the tenile tiffne of geoynthetic increae with the modulu of the polymeric material. However, the fundamental effect of the geometry of the geoynthetic product ha not been well undertood. In thi paper, typical geometrie of geogrid and geocell product were firt introduced. Recent tudie on the effect of geoynthetic geometry were reviewed. Analytical equation for determining the in-plane elatic propertie of cellular material were preented. The equation were then ued to analyze everal geoynthetic with typical geometrie. Finally, the analytical reult were dicued. 2. TH GOMTRY OF TYPICAL GOSYNTHTIC PRODUCTS The mot common geogrid product for bae coure reinforcement i the biaxial geogrid (a hown in Figure 3a). Thi type of geogrid conit of rib in two orthogonal direction. The aperture of the biaxial geogrid are rectangular-haped. Recently a new geogrid product, alo called the triaxial geogrid, ha been developed. The triaxial geogrid conit of rib in three direction that are 60 degree from each other (Figure 3b). Correpondingly, the aperture of the triaxial geogrid are equilateral triangularhaped. Geocell product on the market are alo available in different geometrie. However, the mot commonly ued geocell product for the bae coure reinforcement ha a hexagonal-haped tructure, a hown in Figure 3c. 3. RVIW OF RCNT STUDIS ON TH GOMTRY FFCT OF GOSYNTHTICS Several reearcher have compared the performance of the biaxial geogrid-reinforced aggregate with that of the triaxial geogrid-reinforced aggregate in the laboratory. Abu- Farakh and hi colleague conducted both cyclic load triaxial compreion tet and cyclic plate load tet [4][5]. Cyclic load triaxial compreion tet were performed on cylinder ample of aggregate reinforced by a piece of geogrid at the mid-depth of the ample. Five different geogrid product were ued, three biaxial and two triaxial. Under the ame number of cyclic load repetition, the ample reinforced by triaxial geogrid developed lightly le permanent deformation than thoe reinforced by biaxial geogrid [4]. Large-cale cyclic plate load tet were performed on laboratory-prepared flexible pavement ection with 2-in. aphalt concrete, 12-in. aggregate bae coure, and a oft

4 250 An aement of the geometry effect of geoynthetic for bae coure reinforcement (a) biaxial geogrid (b) triaxial geogrid (c) geocell Figure 3. Geometry of typical geoynthetic ilty clay ubgrade. Two biaxial and two triaxial geogrid were ued to reinforce the aggregate bae. The permanent deformation on top of the aphalt concrete wa monitored and compared. The reult howed that the two triaxial geogrid performed lightly better than the two biaxial geogrid in reducing the permanent deformation of the pavement [5]. David et al. conducted a field accelerated load tet on everal unpaved aggregate road ection reinforced by different type of geoynthetic: a biaxial geogrid, a triaxial geogrid, and a woven geotextile [6]. After the road ection were contructed, traffic load wa applied by a heavy vehicle. The wheel-path rutting of the road ection wa monitored and compared. It wa found that the triaxial geogrid-reinforced ection developed the lowet rutting. Although the above experimental tudie howed encouraging reult about the triaxial geogrid, the concluion drawn from thee tudie were clouded by the fact that the biaxial and the triaxial geogrid were typically made from different polymer material. In other word, the geometry effect wa complicated by the difference in material propertie. With the difficulty in direct evaluating the geometry effect through experiment, other reearcher invetigated the problem through numerical analyi. Dong et al. created numerical model to imulate the elato-platic behavior of biaxial and triaxial geogrid under uniaxial tenile tre in different direction [7]. The numerical reult indicated that biaxial geogrid have a relatively high uniaxial tenile

5 International Journal of Tranportation Science and Technology vol. 1 no tiffne at machine and cro-machine direction (i.e., direction parallel to the orthogonal rib, ee Figure 3a), wherea the uniaxial tenile tiffne in other direction wa nearly zero. On the other hand, the tiffne of triaxial geogrid wa more uniform in all direction. Thee obervation matched the laboratory tet reult very well. Dong et al. tudy emphaized the hortcoming of the current practice of uing uniaxial tenion tet to characterize the mechanitic property of geoynthetic. In fact, geoynthetic in flexible pavement, epecially directly under the wheel load, are ubjected to multi-directional tenion. Therefore, ome reearcher propoed uing pecial bi-axial tenion device to tet the tenile tiffne of geoynthetic [8]. 4. ANALYTICAL QUATIONS FOR TH IN-PLAN TNSIL STIFFNSS OF GOSYNTHTICS 4.1 Cellular Material Mechanic Obviouly, both the uniaxial tenion and the biaxial tenion are pecial cae of a general in-plane tre condition. From aniotropic elatic theory, if the tiffne matrix of a geoynthetic product i determined, the behavior of the geoynthetic under any in-plane tre condition can be predicted. A mentioned previouly, both geogrid and geocell have a regular, periodic, cellular tructure. In fact, the in-plane elatic behavior of thee product can be predicted uing the theory of cellular material mechanic. Cellular tructure have been extenively tudied by aeropace engineering reearcher for many year. In thi paper, only the analytical equation for determining the elatic propertie of rectangular, triangular, and hexagonal haped tructure are preented. Thee three tructure correpond to the biaxial geogrid, the triaxial geogrid, and the geocell product. Figure 4 preent the unit tructure of the three type of geoynthetic. Note that the unit tructure for geocell wa characterized a a regular hexagon for implicity. Actually, the behavior of any arbitrary hexagonal-haped tructure can alo be predicted uing lightly more complicated equation. In thi paper, ubcript 1 and 2 were ued to define the two orthogonal axe in the plane of the geoynthetic. Meanwhile, the Young modulu and the Poion ratio of the geoynthetic material are denoted by and v. Biaxial geogrid ha two axi of ymmetry (Figure 4a), thu it i an orthotropic material. The in-plane elatic behavior of an orthotropic material can be characterized by five elatic contant (i.e., 1, 2, v 12, v 21, and G 12 ), of which four elatic contant are independent. quation (1) to (3) can be ued to calculate the elatic contant of the biaxial geogrid [9]: l 1 l 2 l t l t 2 t 1 (a) biaxial geogrid t (b) triaxial geogrid (c) geocell Figure 4. Geometry parameter

6 252 An aement of the geometry effect of geoynthetic for bae coure reinforcement v t = = v l v t = = v l (1) (2) G 3 3 tt2 = 3 3 ll ( lt + lt ) For orthotropic material, the Young modulu in any direction θ can be calculated uing quation (4). 1 2 (3) v = co θ + θ θ G in co + in 4 θ θ (4) where θ i the angle between the arbitrary direction to direction-1. It ha been demontrated that the cellular material with a unit tructure of regular triangle and regular hexagon are both iotropic material [10]. The in-plane elatic behavior of an iotropic material can be characterized by two elatic contant (i.e.,, and v). The equation for determining thee contant are a follow: For a triaxial geogrid: = 115. t l (5) v = 1 3 (6) For a geocell with a regular hexagonal tructure: t = 23. l v = 1 3 (7) (8) It i intereting to note that, according the continuum mechanic theory, the upper bound value of the Poion ratio i 0.5. However, for cellular material, the Poion ratio can exceed thi limit. 4.2 Verification of the analytical equation In thi tudy, the numerical reult publihed in Dong et al. [7] paper were ued to verify the analytical equation (quation (1) to (6)) for biaxial and triaxial geogrid. Material and geometry parameter ued in the verification were obtained from the

7 International Journal of Tranportation Science and Technology vol. 1 no original paper [7]. The calculated tenile tiffne (modulu divided by thickne) from the analytical equation and the numerical reult publihed by Dong et al. are compared in Figure 5. It i hown that the analytical reult obtained in thi paper matched the numerical reult from the original publication very well. Both the numerical and the analytical reult howed that triaxial geogrid ha a more uniform ditribution of tenile tiffne along different direction, wherea biaxial geogrid only ha coniderable tenile tiffne along the rib direction. Table 1. Parameter of the geoynthetic ued in the verification analyi Geoynthetic Propertie Value Biaxial geogrid (BX) l 1 (mm) 35 l 2 (mm) 25 t 1 (mm) 3 t 2 (mm) 3 Thickne (mm) 1.27 (GPa) 2.63 v Triaxial geogrid (TX) l (mm) 39 t (mm) 1.95 Thickne (mm) 1.95 (GPa) 2.63 v Figure 5. Verification of the analytical equation (tenile tiffne of the geogrid M, unit = kn/m)

8 254 An aement of the geometry effect of geoynthetic for bae coure reinforcement 4.3 Calculated biaxial tenion tet reult In thi ection, the analytical equation introduced previouly are ued to calculate the tenile train of a biaxial geogrid, a triaxial geogrid, and a geocell under the biaxial tenion tet condition. The load condition of a biaxial tenion tet i hown in Figure 6. In thi tet, the geoynthetic ample i ubjected to the ame magnitude of tenile tre in two orthogonal direction (often coincide with the machine direction and the cromachine direction of the geoynthetic). In reality, the biaxial tenion tet require pecial tet device. There are ome practical iue with thi thee device, for example, the cale effect and ample bending due to undeired out-of-plane tre. σ Geoynthetic ample σ Figure 6. Biaxial tenion tet condition (σ = the tenile tre applied) The ame et of material parameter were ued for all the three type of geoynthetic ( = 2.63 GPa, v = 0.333). For demontration purpoe, typical geometry parameter were ued in thi part of analyi (Table 2). The uniaxial tenile tiffne and the Poion ratio of each geoynthetic wa firt determined (Table 3). Then quation (9) and (10) were ued to calculate the tenile train of the ample along the two principle axe. The tenile tre ued in the analyi wa σ = 10 kn/m. The analytical reult are lited in Table 3. Table 2. Geometry parameter of the geoynthetic Geoynthetic Propertie Value Biaxial geogrid l 1 (mm) 35 l 2 (mm) 25 t 1 (mm) 3 t 2 (mm) 3 Thickne (mm) 1.27 Triaxial geogrid l (mm) 39 t (mm) 1.95 Thickne (mm) 1.95 Geocell l (mm) 40 t (mm) 1.95 Height (mm) 100

9 International Journal of Tranportation Science and Technology vol. 1 no v ε1 = ε v = σ σ (9) (10) It i hown in Table 3 that biaxial geogrid ha the highet uniaxial tenile tiffne, yet it developed the highet tenile train under biaxial tenion tet. On the contrary, geocell ha the lowet uniaxial tenile tiffne, but it developed much lower tenile train than the two geogrid. Thi reult, although urpriing at the firt glance, can be explained by the difference in the Poion ratio. Note that biaxial geogrid ha the lowet Poion ratio, which mean tenion in one direction will provide little benefit to the tenile tiffne in the tranvere direction. Triaxial geogrid ha a higher Poion ratio of 0.333, thu tenion in one direction will increae the tenile tiffne of the triaxial geogrid in the tranvere direction. Regular hexagon geocell, on the other hand, ha the larget Poion ratio of 1. Thi type of tructure become much tiffer when ubjected to biaxial tenion. It may be argued that the height of the geocell wa much higher than the thickne of the two geogrid, and it developed lower tenile train becaue the tenile force i ditributed to a much thicker layer. However, imagine that the tenile tre of the geogrid i tranferred to the adjacent 10-cm thick aggregate layer through particle interlocking. The reult in Table 3 implie that under the ame lateral train, geocell can mobilize much higher confining preure than the two geogrid to the ame thickne of aggregate layer. The above reult alo demontrated that the traditional uniaxial tenile tiffne may be a poor indicator of the effectivene of a geoynethetic product in bae coure reinforcement. Future tudie are needed to develop a better performance indicator of geoynthetic under multi-axial load condition. Table 3. Calculated biaxial tenion tet reult Geoynthetic Uniaxial tenile tiffne Tenile train Biaxial geogrid M 1 (kn/m) 400 ε 1 (%) 2.36 M 2 (kn/m) 286 ε 2 (%) 2.44 v v Triaxial geogrid M (kn/m) 294 ε 1 (%) 2.28 v ε 2 (%) 2.28 Geocell M (kn/m) 69.9 ε 1 (%) 0.14 v 1 ε 2 (%) 0.14

10 256 An aement of the geometry effect of geoynthetic for bae coure reinforcement 5. CONCLUSIONS Thi paper dicued the geometry effect of the geoynthetic on the bae coure reinforcement in flexible pavement. The following concluion can be drawn from thi tudy: Cellular material mechanic theory provide an analytical tool to undertand the geometry effect on the mechanitic behavior of geoynthetic. The in-plane elatic propertie calculated by the analytical equation compared well with the previou numerical modeling reult. Triaxial geogrid with a triangular aperture hape ha a higher in-plane Poion ratio than the biaxial geogrid with a rectangular aperture hape. The higher Poion ratio will bring benefit to the tenile tiffne when the geogrid i ubjected to multi-axial tenion, which i probably one of the reaon that triaxial geogrid performed better in bae coure reinforcement than biaxial geogrid in the previou experimental tudie. Geocell with a regular hexagon tructure provide a higher Poion ratio than both triaxial and biaxial geogrid. The regular hexagon tructure, although with a low uniaxial tenile modulu, become much tiffer when ubjected to biaxial tenion. Therefore, under the ame lateral train, geocell can mobilize much higher confining preure than geogrid to the ame thickne of aggregate layer. The traditional uniaxial tenile tiffne may be a poor indicator of the effectivene of a geoynthetic product in bae coure reinforcement. Future tudie are needed to develop an alternative performance indicator of geoynthetic under multi-axial load condition. RFRNCS [1] Webter, S. L. (1992). Geogrid Reinforced Bae Coure for Flexible Pavement for Light Aircraft, Tet Section Contruction, Behavior Under Traffic, Laboratory Tet, and Deign Criteria. Technical Report GL-93-6, Geotechnical Laboratory, US Army Corp of ngineer Waterway xperimentation Station, Vickburg, MS. [2] Giroud, J.P. and Han, J. (2004). Deign method for geogrid-reinforced unpaved road, Part I theoretical development. ASC Journal of Geotechnical and Geoenvironmental ngineering, 130(8), [3] Giroud, J.P. and Han, J. (2004). Deign method for geogrid-reinforced unpaved road, Part II calibration and verification. ASC Journal of Geotechnical and Geoenvironmental ngineering, 130(8), [4] Abu-Farakh, M., Souci, G., Voyiadji, G. Z., and Chen, Q. (2012). valuation of factor affecting the performance of geogrid-reinforced granular bae material uing repeated load triaxial tet. ASC Journal of Material in Civil ngineering, 21(1), [5] Abu-Farakh, M. and Chen, Q. (2011). valuation of geogrid bae reinforcement in flexible pavement uing cyclic plate load teting. International Journal of Pavement ngineering, 12(3),

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