BALITBANG-03-C000135-89040102200254847-Analysis of Flexible Pav Reinforced With Geogrids

8/13/2019 BALITBANG-03-C000135-89040102200254847-Analysis of Flexible Pav Reinforced With Geogrids

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O R I G I N A L P A P E R

Analysis of Flexible Pavements Reinforced with Geogrids

Hema Siriwardane Raj Gondle Bora Kutuk

Received: 17 January 2008 / Accepted: 12 September 2008 / Published online: 23 October 2008

Springer Science+Business Media B.V. 2008

Abstract Effectiveness of glass fiber grids as a

reinforcement of the asphalt layer in a flexible pave-

ment system was investigated. The study involved both

laboratory experimental work and computer analysis

of pavement sections. Twenty flexible pavement

sections (with and without glass fiber grids) were

constructed and tested in the laboratory as a part of the

experimental study. The laboratory-scale pavement

sections were instrumented with pressure cells, dis-

placement gages, and strain gages. Test sections were

subjected to 1,000,000 load applications at a frequencyof 1.2 Hz. Static loading tests were conducted at

intervals of 100,000 load applications. In thirteen

experiments, glass fiber grids were used as reinforce-

ment in the asphalt layer. Several computer analyses of

flexible pavement sections were performed by using

the finite element method (FEM). The laboratory data

were compared with results obtained from the com-

puter analyses. Results from this study show that glass

fiber grids can be used to improve the performance of

flexible pavement systems. It was also observed that

the inclusion of glass fiber grid in the asphalt layerprovided resistance to crack propagation. Overall, the

flexible pavement sections reinforced with glass fiber

grids showed better performance under laboratory test

conditions.

Keywords Flexible pavements Glass grid Finite element method Reinforcement

Nomenclature

t Thickness of asphalt layer

rc Radius of contact surface

P Total load on the tire

pc Tire inflation pressure

D Diameter of contact area

[K] Global stiffness matrix

{r} Global displacement vector{R} Global load vector

U Strain energy densityX; Y Body forces in x- and y-directionsTx; Ty Surface tractions inx- and y-directions

S Portion of the body on which the surface

traction is applied

u, v Nodal displacements in x- and y-directions

e Strain vector

r Stress vector

r0 Initial stress vector

Pi Load acting at node i[C] Constitutive matrix

{Q} Element load vector

{q} Element displacement vector

1 Introduction

Flexible pavements have been frequently used to

construct highways and roads in the United States,

H. Siriwardane (&) R. Gondle B. KutukDepartment of Civil & Environmental Engineering,

West Virginia University, Morgantown, WV 26506, USA

e-mail: [email protected]

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Geotech Geol Eng (2010) 28:287297

DOI 10.1007/s10706-008-9241-0


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and many existing pavements have been treated with

bituminous or asphalt materials (Asphalt Institute

1989). Due to excessive traffic loads, many existing

pavements have already reached the end of their

service life. As a result, surface treatment methods

and the use of new pavement reinforcement materials

have been explored to improve the performance andservice life of flexible pavements. Asphalt overlays

have been used to improve the performance of

deteriorating pavements in the past. The application

of geosynthetic materials in highway repair work has

become popular in recent years due to their high

strength, durability, and ability to relieve stresses by

reinforcing the pavements (Barksdale 1991; Koerner

1994; Kwon et al. 2005). Several research studies on

the use of geosynthetic or steel reinforcements for

improving pavement performance have been reported

in the literature (Baek and Al-Qadi 2006; Clevelandet al. 2003; Kwon et al. 2005; Perkins and Cuelho

2007; Shuler and Hermelink2004).

In the past, various types of geosynthetic materials

like geotextiles and geogrids have been used to

improve the pavement performance, which provided

some reinforcing benefits. Previous studies (Lytton

1989; Barksdale 1991; Cleveland et al. 2003; Kwon

et al.2005) have shown that geotextiles provided less

resistance against lateral movements than that pro-

vided by glass fiber grids. The stiffness of the fabric

material reinforcing the hot mix asphalt (HMA) layerneeds to be greater than that of the surrounding HMA

(Lytton1989; Barksdale1991). High tensile strength

and elastic stiffness of glass fiber grids have made them

an attractive choice for reinforcing pavement systems.

There is limited published information available on

glass fiber grid reinforcement inside the hot mix

asphalt in a pavement system (Button and Lytton

1987). Designing a flexible pavement reinforced with

glass fiber grid and evaluating the effectiveness of

reinforced pavement performance is a complex prob-

lem requiring considerable research and study. Thispaper presents the results of an investigation on the

effectiveness of glass fiber grids as a reinforcement of

the HMA layer in a flexible pavement system.

The major objective of this research was to

determine the influence of glass fiber grids as

reinforcement within the asphalt layer on the perfor-

mance of a pavement section. Influence of the glass

grid reinforcement in 76 and 152 mm thick asphalt

sections was investigated in the laboratory. Three

different types of glass grids were considered. The

study involved both laboratory experimental work

and computer analyses of pavement sections.

2 Experimental Work

As a part of the experimental work, twenty flexible

pavement sections, with and without glass fiber grids

were constructed and tested in the laboratory. The

pavement sections were built in a rectangular container

with dimensions of 1.2 m 9 1.8 m 9 0.8 m. The cross-

section of a typical pavement section is shown in Fig. 1.

The laboratory pavement sections were instrumented

with pressure cells, dial gages and strain gages.

Pavements must be designed adequately to carry

traffic loads over the lifetime of the system. Usually,

the design thicknesses are based on the estimatednumber of load applications over the life-span. In this

study, test sections were subjected to 1,000,000 load

applications at a frequency of 1.2 Hz to simulate

traffic with a single axle load of 80 kN. A circular

loading plate was used to apply the wheel load on the

laboratory pavement sections. The following equa-

tions were used to determine the dimensions of the

loading plate to simulate the effects of a wheel load

(Yoder and Witczak1975):

rcffiffiffiffiffiffiffiP

pcp

s 1

D 2rc 2

wherercis the radius of contact surface, P is the total

load on the tire, pcis the tire inflation pressure and D

Loading Plate

Dial gage

Geogrid

Asphalt

Layer

Gravel

Subgrade

Pressure

Cell

Fig. 1 Cross-section of a pavement reinforced with glass fiber

grid

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is the diameter of contact surface. In this study, the

thickness of the loading plate was 25 mm and the

diameter of the loading plate was 305 mm.

Laboratory test section consisted of hot mix

asphalt (HMA), granular base, subgrade soil and a

glass fiber grid as shown in Fig.1. A geotextile was

used between the gravel base and the subgrade soil inall of the experiments. In this study, a layer of hot

mix asphalt was used as the base layer as shown in

Fig.1. The maximum size of the aggregate in the mix

was 25 mm and the fines-to-asphalt ratio for asphalt

base was 1.0.

Unit weight of the granular material was found to

be 17.7 kN/m3. The soil subgrade chosen for this

study was classified as A-4, according to AASHTO

soil classification system. The soil had a Liquid Limit

(LL) of 22.75 and a Plasticity Index (PI) of 8.57. A

laboratory CBR (California Bearing Ratio) value wasdetermined as 8% for the soil subgrade. The soil was

compacted to an average unit weight of 20.6 kN/m3.

Glass grids used in this study were considered to

have good bonding characteristics with the asphalt

due to their adhesive properties. Reinforcement using

glass grids in the pavement section is expected to

perform better than other polymeric fibers because of

its excellent bonding properties with asphalt and also

due to low creep properties. Three different types of

glass fiber grids (A, B and C) were used in the study.

Glass grid A represents the lightest grid while glassfiber grid C represents the heaviest glass fiber grid.

Glass grid B has a weight between those of glass grid

A and glass grid C.

Loading experiments were conducted with and

without reinforcement in the asphalt layer. In order to

evaluate the influence of asphalt thickness on the

pavement performance, two different thicknesses

were considered. Asphalt thickness of 76 mm was

considered to be the thin asphalt section and the

asphalt thickness of 152 mm was considered to be the

thick asphalt section in this study. Thin asphaltsections were compacted in two layers of 38 mm in

thickness, while the thick asphalt sections were

compacted in two layers of 76 mm in thickness. A

crack was also simulated by introducing a void in the

HMA layer having a thickness of 76 mm as shown in

the Fig.2. Twenty flexible pavement sections (with

and without glass fiber grids) were constructed and

tested in the laboratory as a part of the experimental

study. The laboratory-scale pavement sections were

instrumented with pressure cells, displacement gages,

and strain gages. Test sections were subjected to

1,000,000 load applications at a frequency of 1.2 Hz.

Static loading tests were conducted at intervals of

100,000 load applications. In thirteen experiments,

the glass fiber grids were used in the asphalt layer.

More details on the experimental program can be

found elsewhere (Kutuk1998).

3 Experimental Results

Vertical subgrade stresses and surface displacements

measured under different experimental conditions are

presented below to show the influence of asphalt

layer thickness and the glass reinforcement on

pavement performance under laboratory conditions.

Figure3shows the influence of different glass grids

on vertical subgrade stress in a test section with a

Wheel Load

Loading Plate152 mm

Dial Gauge

HMAt

Glass Grid

Gravel216 mm

Geosynthetic

Pressure Cell

Subgrade

152 mm

(a)without simulated crack

(b)with simulated crack

rid

etic

152 mm

216 m

t

Loading Plate

Dial Gauge15

ted Crack

Wheel Load

2 mmSimula

HMA

Glass G

Gravelm

Geosynth

Pressure Cell

Subgrade

Fig. 2 Experimental outline for pavement section (a) without

simulated crack and (b) with simulated crack

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152 mm thick HMA layer. As can be seen from this

figure, the measured stresses fluctuate within a

narrow range. These results indicated that the influ-

ence of different glass fiber reinforcement on vertical

subgrade stress was not significant when the thick-

ness of asphalt layer was 152 mm. Figure 4 showsthe variation of vertical subgrade stress in a rein-

forced pavement section for different glass grids in a

doubly reinforced test section. In one case, heavier

glass grid was used as the reinforcement in the HMA

layer. Based on these results, it appears that the

vertical stress in the subgrade is lower in the

pavement section with stronger glass grid for the

second half of the loading history.

Influence of asphalt thickness on the vertical

subgrade stress is shown in Fig. 5. As shown in this

figure, the vertical subgrade stress at cell # 1 for the

thicker non-reinforced asphalt section (t= 152 mm)is lower than that corresponding to the thinner non-

reinforced asphalt section (t= 76 mm). Figure5also

shows that inclusion of reinforcement within the

thinner asphalt section (t= 76 mm) results in a

slightly lower vertical stress for most part of the

loading. The glass grid reinforcement appears to

spread the circular load over a larger area in the lower

layers of the pavement section causing a slightly

lower vertical subgrade stress.

Within the experimental parameters considered in

this study, the vertical subgrade stress appears to bemore influenced by the thickness of asphalt layer than

the inclusion of reinforcement in the asphalt layer.

The thicker asphalt layer leads to lower vertical

subgrade stress. Reinforcement in the asphalt layer

also causes a slight but insignificant reduction in the

vertical subgrade stress.

Figure6a shows the vertical subgrade stress for a

thinner reinforced test section (t= 76 mm) with and

without a simulated crack. The vertical subgrade

stress does not seem to be significantly influenced by

the inclusion of a simulated crack. Even though aslight increase in the vertical stress was observed up

to 450,000 loading cycles as shown in Fig.6a, the

vertical stress was similar for both cases (with and

without the simulated crack) for the rest of the

loading history.

HMA

Gravel Base

Pressure Cell # 1 Pressure Cell # 2

Loading Plate

0

10

20

30

40

50

60

0.E+00 2.E+05 4.E+05 6.E+05 8.E+05 1.E+06

Number of Load Cycles

VerticalStress(kN/m2)

Experiment # 3 (Grid - A)

Experiment # 2 (Grid - B)

Experiment # 7 (Grid - C)

Pressure Cell # 1

Fig. 3 Influence of different glass grids on vertical subgrade

stress

0

10

20

30

40

50

60

70

0.E+00 2.E+05 4.E+05 6.E+05 8.E+05 1.E+06



Experiment # 8 (Grid C in HMA; Grid C between

Gravel Base and HMA)

Experiment # 9 (Grid A in HMA; Grid C between

Gravel Base and HMA)

Fig. 4 Variation of vertical subgrade stress for different glass

grids in a doubly reinforced section

0

10

20

30

40

50

60

0.E+00 2.E+05 4.E+05 6.E+05 8.E+05 1.E+06



Experiment # 12

(Without Reinforcement; t = 76 mm)

Average Values of Experiments # 11 and # 17

(With Reinforcement; t =76 mm)

Experiment # 4

(Without Reinforcement; t = 152 mm)

Fig. 5 Influence of asphalt thickness and reinforcement on

vertical subgrade stress

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Figure6b shows a comparison of vertical subgrade

stress for a non-reinforced thick asphalt section

(Experiment # 4; t= 152 mm) with a reinforced

thin asphalt section (Experiments # 14 and # 15;

t= 76 mm) that included a simulated crack. Results

from Fig.6b show that the vertical subgrade stress atcell # 1 for a non-reinforced thick asphalt section

(t= 152 mm) was almost steady throughout the

loading history. The Experiment # 15 is a duplicate

of Experiment # 14 that corresponds to a thinner

reinforced asphalt section (t= 76 mm) with a sim-

ulated crack. The average of the stress for

Experiments # 14 and # 15 is shown in Fig.6b.

The average vertical stress corresponding to the thin

reinforced section (t= 76 mm) with a simulated

crack was higher than that corresponding to the non-

reinforced thick asphalt section (t= 152 mm).

Based on the results shown in Fig. 6b, at 1,000,000

load cycles approximately 15% reduction in vertical

stress for non-reinforced thick asphalt section (Exper-

iment # 4) was possible in comparison to the average

vertical stress of the reinforced thin asphalt sections(Experiments # 14 and # 15) with a simulated crack.

However, it is noteworthy that the non-reinforced

thick asphalt section (t= 152 mm) exhibited higher

displacements as discussed in a subsequent section.

Moreover, there were visual signs of severe rutting

which may indicate failure in the non-reinforced

thick asphalt section (t= 152 mm). In other words,

the thin reinforced sections (with or without a

simulated crack) show higher vertical stress levels

at cell # 1, but the displacements are higher in the

non-reinforced thick pavement section as shown laterin this paper.

Figure7 shows the cumulative displacements for

reinforced and non-reinforced thick asphalt sections

where the thickness of the HMA layer was 152 mm.

The cumulative displacements decreased with the

inclusion of reinforcement within the asphalt layer.

An improvement of approximately 40% was

observed when the HMA layer was reinforced with

glass grid A. For thicker pavement sections, dis-

placements with lighter glass grids result in slightly

larger surface deformations in comparison to testsections with heavier glass grids.

For the larger thickness (t= 152 mm), doubly

reinforced pavement sections improved the pavement

performance in comparison to a singly reinforced

pavement section as shown in Fig. 8. In general, glass

0

10

20

30

40

50

60

0.E+00 2.E+05 4.E+05 6.E+05 8.E+05 1.E+06


Vertica

lStress(kN/m2)


(With Reinforcement; t = 76 mm; No Crack)


(With Reinforcement; t = 76 mm; Simulated Crack)

(a)Influence of crack on vertical subgrade stress inreinforced test sections

0

10

20

30

40

50

60

70

0.E+00 2.E+05 4.E+05 6.E+05 8.E+05 1.E+06


VerticalStress(

kN/m2)

(b)Comparison of a non-reinforced thick asphaltsection and a reinforced thin asphalt section with a

simulated crack

Experiment # 14 (Grid A; Simulated Crack; t = 76 mm)

Experiment # 15 (Grid A; Simulated Crack; t = 76 mm)

Average Values of Experiments # 14 and 15

Experiment # 4 (Without Reinforcement; t = 152 mm)

Fig. 6 Vertical stresses in reinforced and non-reinforcedpavement sections. (a) Influence of crack on vertical subgrade

stress in reinforced test sections. (b) Comparison of a non-

reinforced thick asphalt section and a reinforced thin asphalt

section with a simulated crack

0

2

4

6

8

10

12

14

0.E+00 2.E+05 4.E+05 6.E+05 8.E+05 1.E+06


CumulativeDisplacem

ents(mm)

Without Reinforcement

With Reinforcement (Glass grid A in HMA)

With Reinforcement (Glass Grid B in HMA)

With Reinforcement (Glass Grid C in HMA)

Fig. 7 Cumulative Displacements for reinforced and non-

reinforced thick asphalt sections

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grid reinforcements reduced the cumulative displace-

ments in pavement sections tested in the laboratory.

This substantial decrease in the cumulative displace-ments illustrate that an improvement can be gained

by doubly reinforcing the pavement section by adding

glass fiber grid between the gravel base and the hot

mix asphalt in addition to the one inside the HMA.

Approximately 60% improvement was observed in

doubly reinforced test section in comparison to non-

reinforced test section in terms of cumulative

displacements.

Figure9 shows the comparison of cumulative

displacements for a non-reinforced thick asphalt

section and a reinforced thin asphalt section. Mea-sured displacements show that the reinforced thin

asphalt section performed better than the non-rein-

forced thick asphalt section.

Figure10 shows the variation in cumulative

displacements with number of load cycles for a

thick non-reinforced section and a thin reinforced

pavement section with a simulated crack. Eventhough the non-reinforced thicker asphalt layer

causes lower subgrade stress than that corresponding

to thinner reinforced asphalt layer (Fig.6b), the

measured displacements (Figs. 9 and 10) indicate

that the thinner reinforced asphalt section performs

slightly better than the non-reinforced thicker

asphalt section.

In a few experiments, failure (as indicated by large

displacements) was observed in non-reinforced pave-

ment sections with a simulated crack. Moreover,

there were visual signs of severe rutting which mayindicate failure. However, no failures were observed

in any of the reinforced test sections with or without a

simulated crack. Reinforcement in the HMA layer

helps in reducing the crack propagation leading to

failure.

Static loading tests were conducted at intervals of

100,000 load applications. For thicker pavement

sections, displacements with lighter glass grids result

in slightly larger surface deformations in comparison

to test sections with heavier glass grids. For the thin

pavement sections, surface deformations for thereinforced test sections were slightly higher than that

of the non-reinforced test sections. This small differ-

ence was insignificant and may be caused by the

difference in the compaction effort. Even though this

difference was insignificant, observations have shown

that under static loading, non-reinforced pavement

sections with a simulated crack resulted in slightly

larger surface deformations than that of a non-

reinforced pavement sections without any crack.

0

2

4

6

8

10

12

14

0.E+00 2.E+05 4.E+05 6.E+05 8.E+05 1.E+06


CumulativeDisplacements(mm)

Without Reinforcement

Singly Reinforced (Grid A in HMA)

Doubly Reinforced (Grid A in HMA; Grid C between Gravel Base and HMA)

Doubly Reinforced (Grid C in HMA; Grid C between Gravel Base and HMA)

Fig. 8 Influence of reinforcement on cumulative displace-

ments for a thick asphalt section

0

2

4

6

8

10

12

0.E+00 2.E+05 4.E+05 6.E+05 8.E+05 1.E+06


CumulativeDisplacem

ents(mm)

Without Reinforcement; t = 152 mm

With Reinforcement (Glass Grid A in HMA); t = 76 mm

Fig. 9 Influence of reinforcement on cumulative displace-

ments for a thin asphalt section

0

2

4

6

8

10

12

14

0.E+00 2.E+05 4.E+05 6.E+05 8.E+05 1.E+06


Cumulative

Displacements(mm)

Experiment # 4 (Without Reinforcement; t = 152 mm)

Experiment # 14 (Glass Grid A in HMA; Simulated Crack; t = 76 mm)

Experiment # 15 (Glass Grid A in HMA; Simulated Crack; t = 76 mm)


Fig. 10 Performance of a non-reinforced thick asphalt section

and a thin reinforced asphalt section with a simulated crack

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Also, it was observed experimentally that the

surface deformations for reinforced thin asphalt

pavement sections (t= 76 mm) were smaller than

the surface deformations for non-reinforced thick

asphalt pavement sections (t= 152 mm) (see Figs. 9

and 10). Even though there is a cost for the

reinforcement, a thin reinforced pavement sectionmay be more cost effective than a thick non-

reinforced section. This is especially the case when

it becomes necessary to stop crack propagation

through the asphalt layer.

4 Computer Analysis

A number of methods have been used in the past for

the load-deformation analysis of pavements (Huang

1993). These methods include analytical methodsand numerical methods such as KENLAYER (Hu-

ang 1993) and the finite element methods (FEM).

KENLAYER (Huang 1993) computer program did

not have a capability of including geosynthetic

material in the layered system. Details of the

methods of analysis can be found elsewhere in the

literature. In this study, several computer analyses

were performed to analyze non-reinforced and

reinforced flexible pavements by using the FEM.

Glass grid was considered as a linear elastic material

since it has very low creep characteristics. Theresults obtained from the computer analyses were

compared with laboratory experimental results.

These analyses were used in investigating the effect

of glass fiber grid inside the asphalt layer on

pavement response. Finite element method is a

powerful tool for solving complex problems like

reinforced flexible pavements. In the present

research work, a well-known commercially available

finite element package ABAQUS was chosen to

analyze non-reinforced and reinforced flexible pave-

ments (ABAQUS 2006). Two-dimensional andthree-dimensional linear elastic analyses were per-

formed on non-reinforced and reinforced pavement

sections. Mathematical details of the finite element

method can be found elsewhere (Cook et al. 2003)

and only a summary is included here due to space

limitations.

By using the energy principles, the general

expression for potential energy can be expressed as

follows (Cook et al. 2003):

pp

ZZZR

Uu; vdV

ZZZR

Xu YvdV

ZZZS1

Txu TyvdSX

Pixui Piyvi 3

where U(u,v) = strain energy density = (1/2)er, X

and Y are the body forces, Tx and Ty are surface

tractions or surface loading per unit area, Srepresents

the portion of the body on which the surface traction

is applied,u and v represent the nodal displacements,

erepresents strain, rrepresents stress, and Pidenotes

the load acting at node i.

Equilibrium equations derived by minimizing the

potential energy functional, pp can be expressed as:

Kfqg fQg 4

where

K Element stiffness matrix

ZZZV

fBgTCfBgdv;

[C] = Constitutive matrix (Desai and Siriwardane

1984)

fQg Element load vector

ZZZV

NTf Xgdv ZZZS

NTf TgdS

ZZZV

BTfrogdv fPg

and {q} = displacement vector.

The global governing equations can be obtained by

combining element stiffness as described elsewhere

(Cook et al.2003). The system of equations becomes

non-linear due to complex behavior at material

interfaces. In this study, the geosynthetic-asphalt

interface was modeled by using contact elements at

the interface. The mathematical treatment of thecontact elements is complicated and can be found

elsewhere. When one component comes in contact

with another component in the pavement system, an

interface between the two components is formed.

Shear and normal forces are generated between two

surfaces across their interface when they come in

contact. The nodal points in one contact surface

(master surface) are constrained in their move-

ments so that the master surface does not penetrate

Geotech Geol Eng (2010) 28:287297 293

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into the second surface. These constrains make the

system of equations highly non-linear. While nodal

inter-penetration is constrained, there can be relative

sliding at the interface according to pre-defined

frictional characteristics. The relationship between

the shear and normal stresses across the interface is

expressed in terms of friction developed between thetwo contacting surfaces. The coefficient of friction

primarily depends on the slip rate and contact

pressure between the contacting bodies. The contact-

ing bodies are free to slide over one another when no

shear forces are developed at the interface i.e., at

coefficient of friction equal to zero. In this study,

interfaces were assumed to have friction. The

frictional properties at the interface can be changed

to simulate actual conditions.

Results obtained from these finite element analy-

ses were compared to the results obtained fromlaboratory experimental work. Both three-dimen-

sional and axi-symmetric finite element analyses

were performed. Three dimensional finite element

analyses for the reinforced and non-reinforced pave-

ment sections were carried out using ABAQUS

(ABAQUS 2006). All the layers except the glass

grid were modeled by using three-dimensional

deformable solid homogeneous elements. Glass grid

was modeled by using membrane elements. Table 1

shows the material properties used in the finite

element analyses. Thickness of the asphalt layer wasassumed to be 76 mm. Thickness of the glass grid

was assumed to be 2.5 mm. Four-noded quadrilateral

membrane elements were used to mesh the glass grid.

Eight-noded linear brick elements were used to mesh

all the other layers in the test set-up. Figure 11shows

the finite element mesh used in the analysis of the

pavement section. Sides of the box and the bottom of

the box were constrained and a tire pressure of

551 kN/m2 was applied on the surface of the circular

loading plate. In some cases, frictional properties

were assigned at the interface between the loadingplate and the HMA layer.

Figure12shows the vertical stress distribution for

a thin reinforced pavement section (t= 76 mm).

Observations show that the inclusion of a reinforce-ment layer spreads the circular load (wheel load) over

a larger area in the lower layers of the pavement

section slightly reducing vertical stresses. However,

this reduction is insignificant for the material prop-

erties used in the analysis.

Figures13and14show the vertical deformations

in the pavements sections for non-reinforced and

reinforced thin pavement sections (t= 76 mm),

respectively. In this analysis, relative slip was not

allowed between the HMA and the reinforcement

layer. Finite element results do not show a significantinfluence of the reinforcement on vertical stresses and

displacements in thin asphalt sections. The computed

displacements under the loading show that the

reduction in vertical displacement due to reinforce-

ment was about 1%, which is insignificant. This

indicates that the stiffness of the pavement section

did not change significantly due to the reinforcement

used in the study. This could be due to the small

thickness of the reinforcement.

Table 1 Material properties used in the finite element analysis

Layer Elastic modulus, kN/m2 Poissons Ratio

HMA 1,860,300 0.35

Gravel 316,940 0.30

Subgrade 41,340 0.30

Glass grid 28,972,450 0.30

Fig. 11 Finite element mesh for laboratory pavement section

Fig. 12 Vertical stress distribution for reinforced pavement

sections

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The modeling method presented in this paper canbe used to study the influence of any type of

reinforcement such as geogrids and geotextiles that

are embedded in pavement sections. Moreover, the

influence of interface properties on the pavement

performance can be evaluated by using this model-

ing methodology with the use of contact/interface

elements employed in the present study.

In some cases, glass fiber grid was allowed to slip

within the asphalt layer. This was accomplished by

assigning proper properties for the interface between

the reinforcement grid and the HMA layer. Figure15shows the deformed shape of the glass fiber grid on

an exaggerated scale. The reinforcement grid under-

goes deformations that depend on the interface

properties at the grid-HMA interface. The interface

properties can have a significant influence on the

pavement performance. This study shows that such

complex behavior can be modeled by using contact

elements and the reinforcement layer can be modeled

with membrane elements.

Three-dimensional analysis with contact interfaces

(contact surfaces) can be quite complex and takes a

significant amount of computational effort because of

the interface nonlinearities. Therefore, a two-dimen-

sional analysis was performed to explore its accuracyin comparison to a fully three-dimensional analysis.

All the layers except the glass grid were modeled by

using two-dimensional deformable elements. Fig-

ure16represents the finite element mesh used for the

axi-symmetric case.

Figure17 shows the vertical stress distribution

obtained from various computer analyses. As can be

seen from this figure, the vertical stress distribution

obtained from all these methods seems to be similar.

Fig. 13 Vertical deformations in a non-reinforced thin pave-

ment section. (a) Top surface. (b) Gravel surface. (c) Subgrade

surface

Fig. 14 Vertical deformations in a reinforced thin pavement

section with no slip. (a) Top surface. (b) Geogrid surface.

(c) Gravel surface. (d) Subgrade surface

Geotech Geol Eng (2010) 28:287297 295

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Therefore, it can be stated that a two-dimensional

analysis can be used to compute stress distribution in

a reinforced pavement section subjected to a single

load with reasonably good accuracy.

Figure18 shows a comparison of experimentally

measured vertical stress with those obtained from theKENLAYER program (Huang1993), which is based

on the theory of elasticity. More details of this

analysis can be found elsewhere (Kutuk1998). While

keeping the material properties of glass grid and the

HMA unchanged, the material properties of the

gravel base and the subgrade were varied between a

lower bound and an upper bound values which are

shown in Table2. The comparison between the

measured stresses and the computed values can be

considered as reasonable.

5 Discussion and Conclusions

Because of the need to extend pavement service life,

use of pavement reinforcements has received

increased attention during the last few decades.

Experimental and computational studies were per-

formed to investigate the influence of synthetic

grids in the hot mix asphalt (HMA) layer on the

Fig. 15 Deformed shape of the glass fiber grid within the

asphalt layer. (a) Undeformed glass fiber grid. (b) Deformed

glass fiber grid with no slip

CL GLASS

GRIDCircular Loading Plate

0.000HMA0.076 m0.076

VerticalDepth(m)

GRAVEL

BASE

0.216 m

0.292

SUBGRADE0.254 m

0.546

0.304 0.6090.1520

Radial Distance (m)

Fig. 16 Finite element mesh for axi-symmetric case

0

0.1

0.2

0.3

0.4

0.5

0.6

0 100 200 300 400 500 600

Vertical Stress (kN/m2)

VerticalDepth(m)

AXISYMMETRIC

3D FEA

Fig. 17 Variation of vertical stress with depth

0

20

40

60

80

100

120

140

160

0 10 20 30 40 50 60 70 80

Applied Load (kN)


Measured Stress # 1 at 500000 cycles (Experiment # 3)

Measured Stress # 1 at 500000 cycles (Experiment # 5)

Predicted Stress # 1(Upper Bound)

Predicted Stress # 1 (Lower Bound)

Fig. 18 Comparison of measured and predicted vertical

stresses in a thick asphalt section with reinforcement

Table 2 Assumed lower and upper bound values of elastic

modulus

Material Lower bound value

(kN/m2)

Upper bound value

(kN/m2)

Gravel 223,236 413,400

Subgrade 20,670 82,680

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performance of pavements. Experiments were con-

ducted in a container in the laboratory. Numerical

modeling analyses were performed by using both

two-dimensional and three-dimensional finite ele-

ment models of the experimental setup.

The thicker asphalt layer leads to lower vertical

subgrade stress. Reinforcement in the asphalt layeralso causes a slight but insignificant reduction in the

vertical subgrade stress. Inclusion of a reinforcement

layer spreads the circular load over a larger area in

the lower layers of the pavement section slightly

reducing vertical stresses. Even though a non-rein-

forced thicker asphalt layer causes lower subgrade

stress than that corresponding to a thinner reinforced

asphalt layer, the measured displacements indicate

that the thinner reinforced asphalt section performs

better than the non-reinforced thicker asphalt section.

The computed vertical stresses from the finiteelement analysis compare reasonably well with the

measured values at selected locations. In the three-

dimensional finite element analysis, the reinforcing

material was modeled as a membrane. The interface

properties between the reinforcing material and the

HMA layer have an influence on the computed

displacements and the stress distribution in the

pavement section. More computational modeling

work needs to be performed to study the influence

of interface properties and the influence of material

degradation (damage) due to repeated loading on thepavement performance.

Acknowledgements The paper contains results from a

research project funded by the West Virginia Department of

transportation (WVDOT), Division of Highways through a

research contract to West Virginia University. The authors

acknowledge the support provided by WVDOT.

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