Evaluating the Influence of Aggregate Size on Permeability of Porous Pavements Using Finite Volume Simulation

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1 Technical Paper ISSN Int. J. Pavement Re. Technol. 6(5):50-56 Chinee Society of Pavement Engineering Evaluating the Influence of Aggregate Size on Permeability of Porou Pavement Uing Finite Volume Simulation Lei Zhang 1, Ghim Ping Ong 1+, and Tien Fang Fwa 1 Abtract: Porou pavement i widely ued to enhance wet weather kid reitance on highway through it uperior drainage capacity. Poroity within the porou pavement tructure typically erve a the control variable during the deign and contruction phae, while permeability i the functional parameter indicating drainage performance during the operation phae. One potential implication of uing poroity during deign and contruction and permeability during operation i that porou pavement layer pore tructure reulting from different aggregate ize can reult in different permeability value depite having identical poroity value. Recognizing thi iue, thi paper firt preent a theoretical analyi on the drainage capacity of porou pavement. Outflow tet on typical porou pavement with variou aggregate ize are then imulated uing the finite volume method and imulation reult are validated againt experimental meaurement. It i concluded from our tudy that aggregate ize ha a ignificant influence on the permeability of porou pavement and hould be included during pavement deign, contruction and operation. DOI: /ijprt.org.tw/013.6(5).50 Key word: Aggregate ize; Finite volume model; Permeability; Porou pavement. Introduction 1 Wet-weather road afety i a major concern of road uer and pavement engineer. Hydroplaning and inufficiency of kid reitance are two of the mot dangerou ituation a vehicle may encounter when rain water i accumulated on pavement urface. Specially deigned with higher air void content, porou pavement i identified a an excellent engineering countermeaure to the reduction of kid reitance on wet pavement. The Aociation of Japan Highway reported an 80% reduction in accident on wet pavement when porou urface were ued [1]. The enhancement of wet pavement kid reitance brought forth by porou pavement i highly dependent on the drainage capacity within the porou layer. For a porou pavement with better drainage propertie, water can be effectively dipelled from tire-pavement contact area and reulting in greater tire-pavement contact and hence better friction. Drainage in the porou pavement layer i achieved through an interconnected pore network which erve a drainage channel to relieve hydrodynamic preure developed underneath the tire when a vehicle travel on a wet pavement urface. Two indicator are commonly ued in practice to evaluate the drainage capacity of a porou pavement layer. Poroity i a meaure on the amount of void within the layer, and permeability i a meaure on the ability of the porou layer to allow water to pa through it. Poroity i often accepted a a convenient volumetric parameter in aphalt or concrete mixture deign, becaue it can be efficiently meaured and controlled. Although drainage capacity i directly related to the fraction of connected air void within pavement material, it i inadequate to predict porou pavement 1 Department of Civil and Environmental Engineering, National Univerity of Singapore. + Correponding Author: ceeongr@nu.edu.g Note: Submitted January 15, 013; Revied May 3, 013; Accepted May 4, 013. permeability uing poroity a the ole parameter [-4]. One reaon i that aggregate hape and ize can ignificantly affect the ize of pore and the tortuoity of capillarie, all of which are influential in porou pavement drainage performance. To date, tudie on porou pavement permeability are mainly experimental in nature and there are few reearch tudie exploring the influence of aggregate ize on pavement permeability numerically. Thi paper therefore approache thi problem from a theoretical-numerical perpective. After a brief overview of aociated literature on meaurement and modelling of porou pavement permeability, the flow condition within a porou layer under pecific preure condition i analyed theoretically. A numerical model i then developed uing the finite volume method to imulate the outflow meter experiment. Simulation on porou pavement layer with imilar poroity value but different aggregate ize are next performed and the influence of aggregate ize on pavement permeability i analyzed numerically. Literature Review Contant-head and falling-head outflow meter are typically adopted to meaure pavement permeability both in field and in laboratory. Thee tet method were firt tandardized in geotechnical engineering [5] and i then widely accepted in pavement engineering [6]. Jone and Jone [7] developed a contant-head device to meaure permeability of compacted aggregate. Permeability of porou medium wa found to be dependent on the hydraulic gradient in a contant-head tet. Tan et al. [8, 9] developed a falling-head apparatu to meaure the permeability of porou aphalt. The permeability obtained from thi permeameter wa found to be in cloe agreement with that from a contant head tet. It wa alo found from their tudie that void content alone i inadequate to decribe the drainage property of porou aphalt. Neithalath et al. [10] conducted falling-head permeability meaurement on perviou concrete, and found that permeabilitie 50 International Journal of Pavement Reearch and Technology Vol.6 No.5 Sep. 013

2 differed by more than 100% for concrete pecimen with imilar poroitie. From the numerou pat experimental tudie [-4, 10-14], it wa concluded that while in general permeability i related to poroity, repreenting permeability a a function of poroity alone i inadequate and can be mileading. Pore ize ditribution, tortuoity of capillarie and pore connectivity have ignificant influence on the drainage propertie of porou pavement. Beide pat experimental tudie which aimed at developing a relationhip between permeability and pore tructure parameter, previou reearch tudie alo attempted to model flow within porou pavement numerically. Jackon and Ragan [15] decribed the hydraulic behaviour of porou pavement parking lot with the aumption of Darcy' flow and provided numerical olution to the Bouineq equation. Adler et al. [16] olved the Stoke equation of a Newtonian fluid in fictitiou porou media by a finite difference cheme. Finite element method i adopted by Chuai [] to tudy the flow propertie through porou lab. Bordier and Zimmer [17] developed an analytical olution of Bouineq equation with Izbah' law by a emi-analytical approach, which wa ued in water table prediction. Ranieri [18] developed a model to imulate the runoff on porou pavement, conidering road geometry, rainfall intenity and pavement permeability. Solution to the analytical hydraulic equation governing flow in porou pavement were preented by Charbeneau and Barrett [19] where teady tate Darcy flow and Dupuit-Forchheimer aumption were applied. Beide formulating the macrocopic flow condition within porou media, the microtructure of the pore network wa alo modelled. The effect of pore ize ditribution on aturated permeability wa tudied by Wie [0] uing a conceptual cubic network model with cylindrical capillary tube. Liang et al. [1] characterized geometric parameter of porou medium baed on morphological keletonization. The keleton wa derived by a fully parallel thinning algorithm and topological analyi. A three-dimenional pore network model wa developed by Acharya et al. [] where the location and ize of pore throat were determined by power function of Beti' influence line. Fractal theory wa adopted by Yu et al. [3] to model the permeability of fractal porou medium and derive the pore ize probability. Kuang et al. [4] generated the microtructure parameter from X-ray tomography and examined hydraulic conductivity of permeable pavement with a erie of pore-tructure model. X-ray tomography technique wa alo adopted by Maad et al. [5] and Gruber et al. [6] to rebuild the microtructure of porou aphalt, and imulate the flow field. Zhang et al. [7] propoed an iterative proce baed on a grid pore tructure to model the outflow tet, and predict the drainage capacity of porou pavement. Random-equential adorption approach wa ued by Umiliaco and Benedetto [14] to generate pore tructure from randomly extracted pherical particle, and Lattice-Boltzmann method wa ued to olve the unteady flow within thee pore. From the exiting literature, it i clear that the influence of aggregate ize on permeability of porou pavement ha drawn great interet among to pavement reearcher. Due to the difficultie in deign and control of pore-network tructure in practice, experiment cannot fully reveal the mechanim, nor anwer the quetion quantitatively. Numerical model of flow within Fig. 1. Porou Specimen in Cylindrical Coordinate. microtructure of porou media have the potential to cover thi gap, however few publication on thi particular topic are available to date. Therefore, thi paper analyze the influence of aggregate ize of a porou pavement on it permeability numerically, uing a imple tructural pore-network model which i proved capable in the drainage capacity imulation of porou pavement. Methodology The theorie and method ued in the numerical imulation i preented in thi ection. Permeability of a porou pecimen i firt derived under the aumption of both Darcy and non-darcy flow. The equivalence between contant-head tet and falling-head tet i alo demontrated. Thi theory i next applied in the finite volume model imulating the contant-head outflow tet on porou pavement. Computational fluid dynamic theorie conidered in the numerical model are briefly decribed. Air void within porou pavement are repreented by a implified pore network and aggregate ize i modeled uing variation in pore ize and pacing. The outflow reult obtained from imulation model are then validated againt experimental meaurement. Permeability Computation The concept of permeability and hydraulic conductivity are ometime miued without ditinction. Permeability i a meaure of the ability of a porou material to allow fluid to pa through it, while hydraulic conductivity i a property of material that decribe the eae with which water can move through pore pace. The relationhip between permeability ( ) and hydraulic conductivity (k) i k (1) g where μ = fluid dynamic vicoity, ρ = fluid denity, and g = acceleration due to gravity. Hydraulic conductivity i alo named a permeability coefficient. In practice, it i more convenient to meaure hydraulic conductivity through a contant-head or falling-head tet and then convert the reult to permeability through Eq. (1). Vol.6 No.5 Sep. 013 International Journal of Pavement Reearch and Technology 51

3 Three-dimenional hydraulic conductivity for Darcy flow can be derived from the teady-tate continuity equation [8]. For an iotropic porou pecimen located in cylindrical coordinate (Fig. 1), the continuity equation i 1 r h h r 0 r r z () x h with the boundary condition: r,z h t 0 r R ;z 0 (3) hr,z 0 r R ;0 z h r,z z h r,z z 0 0 (4) c b c If both R c and b c are infinite, the olution i given a hr,z h in 1 It i related to dicharge through R R r R ;z 0 (5) c 0 r R ;z (6) c b c r R z r R z R h r,0 Q k r dr 4kh R (8) 0 z Therefore, the iotropic hydraulic conductivity k can then be computed a Q k. (9) 4h R F where F i a hape factor addreing the effect of finite pecimen dimenion. To take account of the nonlinear effect in non-darcy flow, a heuritic correlation can be made and the following relationhip i propoed []: m v ki (10) where k i the peudo hydraulic conductivity, and m i the flow condition index (value in range of 0.5 to 1). An m value of 1 indicate a fully laminar flow while an m value of 0.5 repreent a fully turbulent flow. Apply the natural logarithmic ln v lnk mlni (11) For a falling-head tet, the variation of hydraulic head with time can be approximated with a cubic function [8]: 3 0 a1t at a3t h a. (1) The mean velocity can computed by differentiating Eq. (1) with repect to time: (7) (a) Geometry of porou pavement layer Fig.. Pore Network Structure of Porou Pavement Model. dh v a1 at a3t (13) dt Noting that i = h / l (l = thickne of porou pecimen), value of v and i can then be derived from tet data at different time t. Uing Eq. (11), permeability k can be obtained through regreion. For a contant-head tet, flow rate Q can be meaured at different hydraulic gradient i and the mean velocity v i eaily derived from flow rate Q and cro-ection area A. Model Geometry A grid pore-network model ha been developed by the author in their previou work [7]. Thi model i proved to be computationally efficient for permeability modelling application. Connected air void within porou pavement are implified a traight channel in all the longitudinal, tranvere and vertical direction (Fig. ), with a cubic pore element patially repeated in the three direction. Two variable are needed to pecify thi tructure, namely the edge length of each drainage channel a denoted by x, and the ditance between centre of two ucceive parallel channel a denoted by y. The ize of a ingle drainage channel i an indicator of the repreentative pore ize in the porou pavement layer, and the pacing of ucceive channel i related to the nominal aggregate ize in the porou mixture with ingle-ize aggregate. The ize of pore and aggregate in actual pavement can be characterized by tereological or mathematical morphology baed method [10, 8]. An iterative proce wa developed to calibrate the model. Detail of thi proce can be found in the author' previou work [7]. A nominal poroity 0 can be obtained from the mix deign, and a minimum x value i et to prevent the model to be numerically overize. The convergence criterion i a ufficiently mall reidual between numerical and experimental reult, typically 5%. CFD Conideration Water flow in porou pavement layer i cloe to turbulence rather than laminar. Therefore, k- turbulence model i ued to account for the turbulence effect. It relate Reynold tree to mean velocity gradient and turbulent vicoity by gradient diffuion hypothei. The continuity and momentum equation are defined a: y (b) Cubic pore element 5 International Journal of Pavement Reearch and Technology Vol.6 No.5 Sep. 013

4 Fig. 3. Illutrated Device and Model of Contant-head Permeability Tet. t U 0 U T U U p ' U eff U S t M (14) (15) where S M = um of body force, p = modified preure = P k eff U 3 3, and eff = effective vicoity = t. The turbulence vicoity t i calculated by: k t C (16) where k = turbulence kinetic energy, ε = turbulence eddy diipation, and C = contant. The value of k and ε come directly from the differential tranport equation: t k t Uk k P P k kb k t U C 1P P k b C t k (17) (18) where C 1, C, k and are contant, P kb and P b repreent buoyancy turbulence, and P k i the turbulence production due to vicou force. Model Validation The propoed model ha been validated againt pat experimental data. The one illutrated here i the contant-head experiment conducted by Charbeneau et al. [9]. The ketche of the tet apparatu and model etup are hown in Fig. 3. Simulation condition are pecified baed on actual experimental condition. Fig. 4 compare the outflow reult obtained from imulation model with that from experiment, and a good agreement can be oberved. Hydraulic Head (cm) Fig. 4. Comparion between Numerical and Experimental Reult of Charbeneau et al. Tet [9]. Reult and Dicuion Although porou pavement i commonly deigned with ingle-ize aggregate, it i not realitic for an actual mixture to be made up by aggregate with identical ize and hape. Moreover, pore ize and capillarie are never uniformly ditributed within the mixture. X-ray tomography i widely ued in experimental tudie to identify the pore network tructure within a porou mixture pecimen [4-6], however thi method need pecial technique and it i very difficult to artificially control the pore ize in experiment. Therefore, a implified repreentation of porou urface layer tructure i adopted in thi paper (Fig. 5) to tranform the actual pore tructure to a grid network a hown in Fig.. It i derived that, for a pecific poroity value 0, the ratio between pore ize x and aggregate ize y i a contant. If et x/y = c, the relationhip i V 3 pore 3x y x 0 c 3 c (19) 3 V y total Meaured Flow Rate (ml/) Simulation reult Porou mixture with three poroity level (15%, 0% and 5%) and four aggregate ize (8mm, 1mm, 16mm and 0mm) are Vol.6 No.5 Sep. 013 International Journal of Pavement Reearch and Technology 53

5 Aggregate ize Pore ize Equivalent quare pore Ma Flow Rate (kg/) Hydraulic Head (mm) Aggregate ize: 0mm 16mm 1mm 8mm Equivalent phere aggregate Fig. 5. Simplified Repreentation of Porou Layer Structure. Fig. 6. Simulation Reult of Contant-head Outflow Tet on Porou Pavement with 0% Poroity. Table 1. Geometry Parameter in Simulated Cae. Poroity [%] c = x/y Aggregate Size [mm] Pore Size [mm] Fig. 7. Influence of Poroity and Aggregate Size on Permeability Value. examined in thi cae tudy. The geometry parameter correponding to each cae are lited in Table 1. All the imulation are conducted on 100 mm thick porou layer and the diameter of outflow meter i 150 mm. The influence of outflow meter dimenion (60 mm, 90 mm, 10 mm and 150 mm) on the imulation reult i alo examined on a pecimen with 0% poroity and 1 mm aggregate ize. Simulation of contant-head outflow tet are conducted under five hydraulic head (00 mm, 300 mm, 400 mm, 500 mm and 600 mm) for each mixture type. The ma flow rate i monitored a the direct output of the model. Fig. 6 illutrate the imulation reult of 0% poroity mixture and imilar curve are obtained for mixture with poroitie of 15% and 5%. The permeability value are next derived from the direct model output. Specific velocity i eaily derived from flow rate, and hydraulic gradient i taken a the ratio between hydraulic head and pecimen thickne. Eq. (11) i then ued in liner regreion to calculate hydraulic conductivity, and permeability i derived by Eq. (1). The calculation reult of all the mixture type are hown in Fig. 7. A expected, the permeability of porou pavement increae with the increae of poroity. It i more important to ee from Fig. 7 that aggregate ize ha a ignificant influence on permeability of porou pavement depite having the ame poroity value. A larger aggregate Fig. 8. Influence of Outflow Meter Diameter on Simulated Permeability Value. ize tend to produce a higher permeability value. Thi may be a reult of having a lower orifice perimeter and higher hydraulic radiu. Thi obervation mean that when deign pavement mix and during contruction, deigner hould account for the potential effect of aggregate ize on poroity and permeability. It wa alo found from the imulation that the peed of the water being dicharged into the porou pavement layer i related to the outflow meter diameter and the relative poition the outflow meter i allocated (Fig. 8). It wa found from the analye that the larger the outflow diameter i, the maller variance it provide during the 54 International Journal of Pavement Reearch and Technology Vol.6 No.5 Sep. 013

6 tet. Therefore, a larger outflow diameter (and hence a larger outflow area) and a higher number of meaurement point extracted during the outflow tet can greatly enhance the reliability of outflow tet on porou pavement. Quantitative analye on thi problem could be conducted in the future work. Concluion and Recommendation The complicated pore tructure of porou pavement i implified by a grid network model, the drainage capacity of which i numerically equivalent to that of actual porou pavement. With proper calibration and validation, thi model i ued to analyze the influence of aggregate ize on porou pavement permeability. Three poroity level and four aggregate ize are examined numerically through the imulation of contant-head outflow tet. It i concluded from the imulation reult that aggregate ize ha a ignificant influence on permeability, depite the ame poroity being maintained. Pore formed by larger aggregate have higher hydraulic radiu. They are eaier for water to pa through, thu have a higher permeability. It i inadequate to conider poroity a the ole functional parameter repreenting the drainage capacity in the deign and contruction procee of porou pavement. It i neceary to control the aggregate ize and directly meaure permeability in laboratory and in field to undertand the drainage performance of a particular compacted porou mixture. In the other condition being equal, larger-ize aggregate are recommended in porou mixture deign to provide better drainage performance for the completed pavement. The influence of aggregate ize on permeability may alo affect the kid reitance performance of porou pavement with identical poroity. Such effect could be invetigated in the future with a imilar approach a preented in thi work. Reference 1. Aociation of Japan Highway (1996). Guide for Porou Aphalt Pavement. Maruzen Corporation, Tokyo, Japan.. Chuai, C.T. (1998). 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7 aniotropy of aphalt concrete baed on microtructure imulation of fluid flow, Computational Material Science, 40, pp Gruber, I., Zinovik, I., Holzer, L., Flich, A., and Poulikako, L.D. (01). A computational tudy of the effect of tructural aniotropy of porou aphalt on hydraulic conductivity, Contruction and Building Material, 36, pp Zhang, L., Ong, G.P., and Fwa, T.F. (01). Three dimenional modeling of porou pavement permeability uing a implified pore network tructure, Proceeding of the 7th International Conference on Maintenance and Rehabilitation of Pavement and Technological Control, Auckland, New Zealand. 8. Sumanaooriya, MS. And Neithalath, N. (009). Stereology and morphology baed pore tructure decriptor of enhance poroity (perviou) concrete, Material Journal, 106, pp Charbeneau, R.J., Klenzendorf, L.B., and Barrett, M.E. (011). Methodology for determining laboratory and in itu hydraulic conductivity of aphalt permeable friction coure, Journal of Hydraulic Engineering, 137, pp International Journal of Pavement Reearch and Technology Vol.6 No.5 Sep. 013