Keith D. Hjelmstad, Elastic Pavement Analysis Using Infinite Element, In Transportation Research...

Three–Dimensional Finite Element Analysis

of Doweled Joints for Airport Pavements

By

Jiwon Kim, Ph.D.

Research Scietist

Pavement Research Group, Highway Research Institute

Korea Highway Corporation

293-1, Keumto-Dong, Soojung-Gu, Sungnam-Si

Kyunggi-Do, R. O. Korea, 461-703

Tel: (822) 2230-4659

Fax: (822) 2230-4185

[email protected]

Keith D. Hjelmstad, Ph.D.

Professor and Associate Head

Department of Civil and Environmental Engineering

University of Illinois at Urbana-Champaign

205 N. Mathews Ave. #1114

Urbana, IL 61801Tel: (217) 244-8738

Fax: (217) 265-8040

[email protected]

7468 word counts for text and figures

Submitted for the Presentation at the 2003 Annual Meeting of

Transportation Research Board Washington, D. C. and

for Publication in Transportation Research Record

Kim and Hjelmstad TRB 2003

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Jiwon Kim, Ph.D., Research Scientist

Pavement Research Group, Korea Highway Corporation



and

Keith D. Hjelmstad, Ph.D., Professor and Associate Head


University of Illinois at Urbana–Champaign

205 N. Mathews Ave., Urbana, IL, 61801

Abstract

This paper investigates various aspects of the structural behavior of doweled joints, including load

transfer, in rigid airport pavement systems using nonlinear three–dimensional finite element methods.

The finite element models include two concrete slab segments with dowels connecting them. The

concrete slab and supporting layers are simulated by continuum solid elements to enhance the

accuracy of the simulation. Solid elements can capture the severe deformation gradients in the

concrete slab in the vicinity of wheel loads, allow the modeling of non linear behavior in the

supporting layers and the modeling of frictional contact interfaces between the concrete slab and

supporting layers. These features have not been considered in classical approaches. The structural

behavior of the doweled joint is investigated for various design and loading conditions, including: (1)

tire pressure, (2) dowel spacing, (3) slab thickness, (4) dowel looseness and (5) multiple wheel loads.

The amount of load transfer can be obtained directly from the shear force in the Timoshenko beam

elements that simulate dowel. According to the finite element results, 15 to 30% of the applied wheel

load is transferred to the adjacent slab segment by the dowels. This number varies in accord with

design and loading conditions. In addition, 95% of the transferred shear force is carried only by the

nine or eleven dowels which are closest to the applied load.

Key words

3–D finite element analysis, doweled joint, airport pavement, load transfer, dowel looseness


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Jiwon Kim, Ph.D., Research Scientist

Pavement Research Group, Korea Highway Corporation



and

Keith D. Hjelmstad, Ph.D., Professor and Associate Head


University of Illinois at Urbana–Champaign

205 N. Mathews Ave., Urbana, IL, 61801

1. INTRODUCTION

A rigid airport pavement system is composed of numerous discrete concrete slabs, longitudinal and

transverse joints, and dowels. Longitudinal joints are provided for construction convenience and

transverse joints are provided to control cracks caused by thermal deformation and drying shrinkage of

the concrete slab. Despite those benefits, the joint often reduces the load carrying capacity of the

concrete slab near the edge and results in pavement damage under repeated wheel loads [1, 2]. Field

experience has demonstrated that dowel load transfer systems are among the most effective means of

increasing the load carrying capacity of rigid pavements. A dowel connects concrete slabs and

transfers wheel load across the joint primarily through shear force. For rigid airport pavements, the

importance of doweled joints is much greater than for ordinary highway pavements because the

applied load level of airport pavements is much higher than that of ordinary ones and the

consequences of inter–slab faulting is much greater.

The doweled joint has been employed in rigid pavements since the early twentieth century. A

great deal of research has been devoted to assessing the amount of load transfer across a doweled joint.

An intact joint is known to transfer more wheel load to adjacent concrete slabs than a damaged joint.

Unfortunately, there is no way to directly measure the shear force in a dowel with available sensor

technology. Various indirect measures have been developed to estimate the load transfer over doweled

joint. Among them, the displacement–based load transfer efficiency (LTEδ) has been widely used. The

LTEδ is defined as the ratio of displacement of the unloaded slab to that of the loaded slab at a joint.

Although LTEδ can easily be measured in the field with a Falling Weight Deflectometer, it does not

correlate well with actual load transfer across a joint. Rather, it gives an implication of the magnitude

of damage at the joint due to the pumping and funnelling (dowel looseness).


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This paper reports on an analytical investigation of load transfer across doweled joints under

various loading and design conditions using 3–D FE(Finite Element) models. The parameters

investigated include (1) load level, (2) dowel spacing, (3) concrete slab thickness, (4) multiple wheel

loads and (5) dowel looseness. For parametric analysis, FE models were constructed with two concrete

slab segments composed of solid elements with Timoshenko beam elements to simulate the dowels.

This approach enhances the accuracy of FE solution with solid elements simulating the

concrete slab and supporting layers. Solid element can capture severe deformation gradients in the

concrete slab under multiple wheel loads, which is impossible with classical approaches using

Kirchhoff plate elements [3]. Further, solid elements used in supporting layers count on heterogeneous

material properties of each layer. Hence, this approach can provide more accurate displacement field,

which affects on the stress response of the concrete slab, than the classical approaches with Winkler

foundation [3]. We modeled the frictional contact interface between the concrete slab and supporting

layers [3]. In addition, the FE mesh density can be easily varied with regard to the stress gradient to

improve mesh efficiency. Above all, this approach can directly evaluate the amount of load transfer

across doweled joint by computing the shear force in the beam elements. Therefore, one can observe

dowel shear force distributions for each case and determine the number of engaged dowels as well.

2. SIMULATION OF DOWELED JOINTS

Four primary approaches to modeling doweled joints have been reported in the literature: (1)

Timoshenko beam elements (often called bar elements) directly connected to plate elements [4], (2)

elastic spring elements directly connected to plate elements [5], (3) Timoshenko beam elements

indirectly connected to plate elements through elastic springs [6], and (4) 3–D continuum solid

elements with contact interfaces [7]. Approaches (1), (2), and (3) have been widely used in the

pavement community with various classical 2–D FE analysis programs (plates on elastic or Winkler

foundation). Approach (4) has recently been introduced to the pavement community.

Approach (1) was the first attempt to simulate the behavior of doweled joints. The main

purpose of the dowel is to transfer the wheel load to the adjacent slab through shear force. Due to the

importance of shear deformation, Timoshenko beam elements are used to simulate the behavior of the

dowels. In this approach, a beam element directly connects Kirchhoff plate elements belonging to two

adjacent concrete slabs (i.e., the embedded portion of the dowel does not influence the response). The

exposed part of the dowel has a length to depth ratio less than 1.0, because the dowel diameter is often

larger than the joint width. Using Timoshenko beam elements may be a suitable approach to simulate

the behavior of an intact doweled joint, but this approach should not be used to simulate a damaged

doweled joint. Damage of dowel–jointed pavements often involves the dowel casing through the

phenomenon called dowel looseness or funnelling. In this circumstance, the concrete slab no longer

provides strong support for the embedded portion of the dowel. Such a casing failure begins at the


5

joint and gradually propagates inside the concrete slab. As a result, the dowels are often free to deform

until they touch undamaged surrounding concrete.

In approach (2), the dowels are simulated by elastic spring elements directly connected to

plate elements over the joint. Therefore, the dowel cannot resist bending. The amount of transferred

shear force is determined by

where V is the dowel shear force, K is the spring constant and D is the relative displacement between

loaded and adjacent concrete slabs.

Approach (3) uses Timoshenko beam elements to simulate the dowels, but they are indirectly

connected to plate elements by elastic springs. Approach (2) and (3) can simulate dowel looseness

through the elastic deformation of spring elements. However, the behavior of the doweled joint is

dominated more by the artificial spring constant than it is by the mechanical properties of the dowel

and concrete slab. The contact force acting between the beam (dowel) and plate elements (slab) is

determined by the artificial elastic spring constant. Further, these approaches always require

calibration of the artificial spring constants with FWD test measurements. Often, calibrated spring

constants show a wide range of variation, from 21 to 10000kPa (from 3 to 1500ksi) [8]. Hence, the

simulation of dowel looseness is not well bounded by physical observation.

Approach (4) is suitable for simulation of both intact and damaged dowel joints because it

uses continuum solid elements for both the dowel and concrete slab. It simulates their interaction

through frictional contact. The detailed stress and strain distribution within a dowel and the interaction

between the dowel and the concrete slab can be observed from this approach. Further, pavement

damage can be simulated by using plastic constitutive models for the concrete in the vicinity of the

dowel or by specifying the funnel geometry at the outset. Despite these advantages, the problem size

becomes too large to be solved on today’s computational platforms. The dimensions of the dowels are

much smaller than those of the concrete slab. Hence, a much finer mesh is necessary to simulate the

dowel and concrete casing, while a coarser mesh is adequate to model the far–field behavior of the

concrete slab and other parts of pavements. An adequately refined mesh leads to a huge problem size,

especially if the model is composed of multiple concrete slabs. The large problem size either prohibits

or limits our ability to perform parametric analysis.

The objective of this paper is to understand the behavior of dowel–jointed rigid airport

pavement systems with both intact and loosed joint with dowel load transfer. Timoshenko beam

elements [9, 10] were selected to simulate dowels. They were directly connected to continuum solid

elements, which simulate the concrete slabs, for intact joint. The same approach was used in 2–D plain

strain analysis for rigid highway pavement in the MN–ROAD project [11]. The entire length of the

dowel is simulated by seven beam elements so that the rotation field can be adequately resolved.

∆= KV


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Therefore, the load transfer action does not include artificial springs. The dowel shear force is directly

transferred to concrete slab.

The gap contact algorithm was employed for loosed joint simulation. The gap contact allows a

physical gap between concrete slab (solid elements) and dowel (beam elements). In order to simplify

the simulation, the looseness is represented by the size of a gap and is only assumed to be present on

the adjacent concrete slab - not the loaded one. This approach requires two separate models for intact

and loosed joints but it demands much smaller problem size than approach (4) because a refined 3–D

solid mesh is not required to simulate the dowels.

3. CONSTRUCTION OF FINITE ELEMENT MODEL

FE models were constructed based on the Denver International Airport (DIA) pavement design

properties, detailed in Table 1. Two concrete slab segments sit on top of supporting layers, as

illustrated in Figure 1(a), and two frictional contact interfaces are present between slab segments and

supporting layers to allow discontinuous deformation. Eight node continuum solid elements were used

to model the concrete slabs and supporting layers. A refined mesh zone was located at the center of the

joint, where wheel loads are applied, and a course mesh was used in the outer domain, as shown in

Figure 1(b). A radially–graded mesh was used to make a smooth transition between the refined and

course mesh zones [3, 12]. The presence of bedrock was assumed at 762cm (300inch) depth in the

subgrade layer, and infinite elements were used to simulate the horizontally unbounded domain [13].

One plane of symmetry was assumed to reduce the problem size.

The Boeing 777-200 wheel load was used as the model airplane load, detailed in Table 2. For

the single wheel load analyses, single wheel load data of the Boeing 777-200 was used. For

comparison purposes, tandem and dual–tandem gears for multiple wheel load analysis were created

from combinations of two and four Boeing 777-200 single wheel loads using the same spacing. An

elliptical tire print was assumed with uniform tire pressure and it was discretized by the equivalent

nodal force algorithm developed by Kim and Hjelmstad [3, 12].

Figure 1(c) illustrates the FE model for the joint used in this research. The thickness of the

concrete slab was simulated by six solid elements, and Timoshenko beam elements were attached at

the middle. A full depth joint gap was assumed to model the worst case for the load transfer. Load

transfer contributions from aggregate interlock was assumed to be zero. Therefore, wheel load was

transferred only through the dowels. In a real pavement, the gap usually opens up due to the dry

shrinkage and temperature variation. Therefore, the load transfer contributions from aggregate

interlocking could be attenuated [1].

A total of 23 dowels are included in the model with symmetry. The nominal dowel spacing

was 30.5cm (12inch) in the DIA design and this spacing was maintained for 19 inner dowels (see

Figure 1(b)). Spacing for outer dowels was changed to 35.5cm (14inch) to accommodate easy mesh


7

construction. The contribution of outer dowels to the global pavement behavior was expected to be

negligible because they are far from the applied wheel load. The numerical verification of this

assumption will be discussed in the following section. From experimental results in the literature, one

can also find that most of the load transfer is achieved by a few dowels near the applied load [14, 15].

A linear elastic constitutive model was used for the concrete slab because the stress under the

wheel load was expected to be far less than the strength of concrete. A linear elastic constitutive model

was also used for the subgrade layer even though they are composed of granular material. Again, the

computed stress was very small and always in compression. The Mohr-Coulomb elasto–plastic

constitutive model was used for the cement–treated base layer, and a 1365kPa (198psi) cohesion limit

was used to define the yield condition, which is approximately equivalent to a 1650kPa (240psi)

tensile strength [3]. In addition, a frictional contact interface exists between the concrete slab and the

cement–treated base layer in order to simulate uplift and sliding. It allows discontinuous deformation

through the depth and attenuates unrealistic tensile stress developed by layered elastic analysis [3].

The FE parametric analysis was performed with commercial FE software ABAQUS [16].

4. BEHAVIOR OF DOWELED JOINT UNDER SINGLE WHEEL LOAD

The behavior of the doweled joint was evaluated in terms of load level, dowel spacing and slab

thickness. In order to simulate different load levels, three different magnitudes of wheel load pressure

(740, 1480, and 2970kPa / 108, 215, and 430psi) were applied to the FE model. They were determined

to be half, full, and twice the Boeing 777 wheel load pressure computed from the gross weight. For

dowel spacing variation, two FE models were created with 30 and 61cm (12 and 24inch) spacing. Four

FE models were constructed according to four different concrete slab thicknesses, 30, 43, 56, and

69cm (12, 17, 22, and 27inch). Numerical modeling results are presented in various formats, including

dowel shear force distribution, load transfer ratio, and normalized bending stress.

4.1 Behavior of Doweled Joint under Load Level Variation

Figure 2(a) demonstrates the dowel shear force distribution. Each marker shows the amount of shear

force transmitted by a dowel. The origin of the abscissa is the symmetry line. From this plot, one can

observe that nine engaged dowels (noting symmetry) carry more than 99% of the transferred shear

force across the joint. The contribution from other dowels, including the two end ones, is virtually zero

no matter what load levels are applied. Hence, the 35.6cm (14inch) spacing used for two end dowels

has virtually no effect on the global behavior. A dowel is considered “engaged” if the shear force

carried by that dowel is larger than 1% of the total shear force transferred across the doweled joint.

The number of engaged dowels appears to be independent of the magnitude of the applied wheel load

pressure. The upper right box in Figure 2(a) shows the shear force distribution for non–engaged

dowels at a magnified scale.


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Figure 2(b) shows the relative displacement between loaded and adjacent slab segments along

the joint. The largest positive relative displacement is observed at the origin (symmetry line), where

the wheel load is applied, and a small negative relative displacement is observed at the corner. The

relative displacement distribution is almost identical to the dowel shear force distribution along the

joint shown in Figure 2(a). In addition, the negative relative displacement at the corner corresponds

with the negative shear force at last dowel. Approximately 330cm (130inch) from center or near the

second outer dowel, the sign of the relative displacement changes from positive to negative. This

means less displacement is observed on the loaded slab than on the adjacent slab after this point,

because the loaded slab always has a larger curvature than the adjacent slab. Further, maximum

displacement always occurs beneath the wheel load as does the maximum relative displacement along

the joint. In addition, the negative dowel force vanishes if the last dowel is taken out.

Figure 2(c) shows the ratio of load transfer (the amount of transferred load by the dowels

divided by the amount of applied wheel load). This ratio increased with the increase of applied tire

pressure, while the size and location of pressure load remained identical for all three cases. That means

more wheel load can be transferred to the adjacent concrete slab if wheel load pressure increases. This

phenomenon is also evident in the dowel shear force distribution. The inner seven dowels of the

2970kPa case carried almost five times more shear force than those of the 740kPa case. However, the

total amount of applied load was only four times more. Only 3.5% of the shear was carried by the

outer sixteen dowels for the 2970kPa case, while 6.2% of the shear was carried by them for the

740kPa case. The high wheel load increases the load transfer ratio. Meanwhile, it also increases the

demand on a few inner dowels beneath the wheel load, which may cause more damage to the joints

and eventually lead to pavement failure.

4.2 Behavior of Doweled Joint under Dowel Spacing Variation

Two different dowel spacings, 30 and 61cm, were evaluated under a single wheel load with 2.54cm

diameter dowels. Two 61cm spacing models were made by eliminating even or odd numbered dowels

from the 30cm spacing model, which is the nominal DIA pavement design. The location of dowels is

written in Figure 3(b). The center of the wheel load was on top of the dowel at the symmetry line for

the ODD case, while it is located between two dowels for the EVEN case. Figure 3(a) shows the

dowel shear force distribution. Figure 3(b) represents the contribution of each dowel to the total

amount of transferred load. Figure 3(c) shows the ratio of load transfer and normalized maximum

tensile bending stress.

Figure 3(a) shows two lines of dowel shear force distribution, the upper line for both 61cm

spacing cases and the lower line for 30cm spacing. Each dowel in the 61cm spacing cases carries more

shear force than the 30cm spacing case due to the wider spacing. Nevertheless, the total amount of

transferred shear for the 30cm spacing case was about 4% larger than for the 61cm spacing cases. The


9

total amount of transferred load does not change much in terms of relative location between wheel

load and dowel, if the spacing remains the same.

Figure 3(b) shows that only five or six dowels were engaged for both 61cm spacing cases,

while nine were engaged for the 30cm spacing case. This result suggests that the size of the region

containing engaged dowels does not change with dowel spacing; only the distribution of shear forces

varies. This issue will be discussed further in Section 4.3. The last column shows the summation of the

contribution for internal dowels (until dowel No. 8). For the 30cm and 61cm EVEN spacing cases, the

summation value exceeds 100% because the negative shear forces (up to 0.5%) from the outer dowels

are not included.

The last column of the table in Figure 3(c) shows normalized maximum tensile bending stress

of loaded and adjacent concrete slabs. Those of the 30cm and 61cm ODD spacing cases were almost

identical to each other, but that of 61cm EVEN spacing case was quite different. The difference

suggests that the stress response of the concrete slab is more sensitive to the relative location between

applied wheel load and dowels than the dowel spacing. The wheel load was located between two

dowels in the 61cm EVEN case and created more deformation on the loaded concrete slab segment.

As a consequence, this extra deformation caused more bending stress in the loaded slab segment. In

contrast, less deformation was observed on the adjacent slab and correspondingly less stress was

generated in the adjacent slab. Friberg anticipated such behavior in his paper, and our numerical

results support his observation [14].

4.3 Behavior of Doweled Joint under Slab Thickness Change

Four different FE models were constructed with four different thicknesses of concrete slab (30, 43, 56

and 69cm) to evaluate the behavior of the doweled joint under slab thickness change. The nominal

DIA design is 43cm. Figure 4(a) illustrates the dowel shear force distribution. Figure 4(b) shows the

contribution of each dowel to the total amount of load transfer. Figure 4(c) shows the amount of load

transfer and the normalized maximum tensile bending stresses.

Figure 4(a) shows that the amount of load transfer increases, as the slab thickness increases.

Further, the number of engaged dowels increases with slab thickness. Figure 4(b) shows that thirteen

dowels contributed to load transfer for the 69cm thickness case, while only seven dowels do so for the

30cm case. The ratio of load transfer also increases with slab thickness as shown in the fourth column

of Figure 4(c).

The thicker concrete slab is stiffer and, therefore, develops less curvature along the loaded

side of the joint. The deformed shape explains why more dowels are engaged in the load transfer for

thicker concrete slab models. From Figure 4(b), the contribution of the three internal dowels (location

0 and ±30cm) is decreased with the increase of slab thickness, while that of the outer dowels is

increased. The last column shows the sum of the contribution from internal dowels. Except for the


10

30cm thickness case, the summation values exceed 100% because the negative shear force

contributions (up to 1.7% for the 69cm case) from the outer dowels are not included.

The last column of the table in Figure 4(c) shows the normalized maximum tensile bending

stresses of loaded and adjacent concrete slab segments with respect to those from the 43cm thickness

case. As a consequence of the stiffness increase for a thick concrete slab, a much reduced tensile

bending stress was observed for the 56 and 69cm cases. In fact, a thick concrete slab provides two

significant benefits: higher load transfer and lower maximum tensile stress of concrete slabs.

5. BEHAVIOR OF DOWELED JOINT UNDER MULTIPLE WHEEL LOADS

Four different landing gear configurations (single, tandem, dual–tandem, and tri–tandem gears) were

applied to the FE model to investigate the behavior of doweled joints under multiple wheel loads.

Various numerical results are presented in Figure 5, including the dowel shear force distribution, the

deformed shape of the concrete slab, and the maximum stress and displacement. In addition, the

difference in behavior between doweled joints and plain (undoweled) joints was demonstrated in

Figures 5(e) and 5(f).

Figure 5(a) shows the dowel shear force distribution. The tandem wheel load case results

shows that the thirteen dowels closest to the wheel load carried most of the transmitted shear force.

For the dual– and tri–tandem load cases, the two or four internal wheels were located 165cm (65inch)

away from the joint. As a consequence, the magnitude of the dowel shear force increased, even though

the number of engaged dowels is the same as the tandem wheel load case. In addition, a large negative

shear force was observed at the outer–most dowel at the corner for the dual– and tri–tandem cases.

Their magnitudes were 5% to 10% of the largest shear force beneath the wheel loads because the

presence of multiple wheel loads caused a large curvature, as illustrated in Figure 5(c). Further, the

point of sign change of the relative displacement moved closer to the corner when more wheel loads

were applied.

Figure 5(b) shows the ratio of load transfer with respect to the landing gear configuration. The

amount of transferred load increased while the ratio of load transfer decreased as more wheel loads

were applied. For the dual– and tri–tandem cases, applied load from the two or four internal wheels

was supported more by the supporting layers than by the adjacent concrete slab because the load was

applied away from the joint. Nevertheless, they still remained in the denominator for evaluating the

load transfer ratio. Therefore, one can observe almost a doubling of the transferred wheel load from

the single to the tandem gear case but smaller increases for other cases.

Figures 5(c) and 5(d) show the wheel load associated deformed shape of the concrete slab

along the joint line and symmetry line, respectively. The vertical scale is exaggerated to emphasize the

deformed shape. It is interesting to observe the deformed shape caused by the tri–tandem wheel load

case. The maximum displacement occurred beneath the internal wheel load, while those of the other


11

cases always occur at the edge. That means one large deformation basin develops under the tri–tandem

wheel loads, as if the wheel loads were applied at the interior of the concrete slab. In fact, dowels

provided partial continuity to the discrete concrete slab segments by transferring shear forces. On the

contrary, two separate deformation basins were observed under the dual– and tri–tandem wheel load

from the undoweled pavement analysis [17]. From Figure 5(c), the magnitude of displacement

increased relatively little from the dual–tandem to the tri–tandem cases compared to others because the

internal wheel loads are, again, carried more by the supporting layers than by dowels. In addition,

uplift was observed on the opposite side of the adjacent slab, and the magnitude was proportional to

the amount of transferred load. This uplift would be restrained by gravity loading, if an additional slab

were to exist next to the adjacent slab and if they were connected with dowels.

Figures 5(e) and 5(f) show the maximum stress and displacement results from the FE models

with and without dowels along the joint, respectively. All values have been normalized by those from

the single wheel load case. Maximum stress and displacement data for the single wheel load case are

listed at Figure 5(g). From the observation of pavement models with and without dowels, one can see

that the dowel reduces the magnitude of maximum compressive and tensile bending stress by

approximately 13% and 16%, respectively, for every wheel load case. Further, maximum

displacements were reduced by 7% in dowel–jointed pavement results. From the wheel load

interaction analysis of the single slab segment model, a surface tensile bending stress zone existed

between two edge wheels and the two or four internal wheels for dual– and tri–tandem gear cases [17].

Such a zone exists because two edge wheel loads dominate the behavior of the entire structural

system. On the contrary, the surface tensile bending stress zone vanishes in a dowel–jointed rigid

pavement because its dominance is reduced by the dowel load transfer system. Nevertheless, global

stress and displacement contours are quite similar for both models with and without dowels, as one

can see similarity in normalized maximum stress and displacement and their locations for the two

models.

6. BEHAVIOR OF DOWELED JOINT WITH DOWEL LOOSENESS

The dowel looseness simulation discussed in this paper is based on the preliminary research result.

Hence, this modeling approach requires couple of assumpsions restricting the behavior of doweled

joint. As shown in Figure 6(a), the gap is assumed to be present only in the adjacent concrete slab for

downward direction(uni-directional contact). This assumption is determined from test runs to finalize

FE model construction. The bi-directional and two slab contact were also tested but those cases

demonstrated poor convergence characteristics. The size of a gap is varied from 0.000254mm

(0.00001inch) to the point that no contact occurred between adjacent concrete slab and dowel. The

size of the gap for no-contact is 1.1mm (0.043inch) for tri-tandem wheel load and 0.28mm (0.011inch)

for single wheel load. They are different because the tri-tandem wheel load case initiates more


12

deformation on loaded concrete slab than the single wheel load case. Pumping and other joint damages

were not included in this analysis.

The variation of gap size makes significant changes on the behavior of load transfer. Wider

gap reduces the amount of transferred load over the joint. Figure 6(b) and 6(c) show the result of

dowel looseness study for single wheel load case. The amount of load transfer reduced from 22% to

0%, while the gap between concrete slab and dowel reduced from 0.00254mm to 0.254mm. The

number of engaged dowels are reduced from five(same as intact joint) to zero. In the meantime,

maximum bending stress also varies. Due to the reduced load transfer, wider gap increases the

maximum bending stress in loaded concrete slab up to 16%, while it decreases the maximum bending

stress in adjacent slab. From the observation on joint, traditional LTEδ varied from 95%(intact joint) to

60%(0.28mm).

Figure 6(d) demonstrates dowel shear force through the joint for tri-tandem wheel load case.

For small gap between concrete and dowel(up to 0.25mm), the third dowel from the center, which is

located under the wheel load, makes the largest load transfer contribution. This phenomena change

after gap size 0.5mm because the maximum relative displacement between loaded and adjacent slabs

occurs on the center of joint. Figure 6(f) shows the maximum relative displacement, which makes the

largest load transfer contribution, occurs beneath wheel load for gap size 0.25mm case. On contrary, it

occurs at center line for gap size 0.76mm case. At the corner of concrete slab, it is found that the

displacement of loaded slab is always smaller than the adjacent slab. Once again, it is because the

curvature of loaded slab is greater than adjacent slab. Figure 6(e) shows the amount of transferred load

and normalized maximum tensile bending stress. Transferred load reduces with the increase of gap

size between slab and dowel. After the gap size of 0.76mm, the amount of transfer load is negligible.

From the observation of maximum tensile bending stress in Figure 6(e), one can infer the maximum

bending stress of concrete slab can be magnified up to 18% due to the damaged joint.

7. COMPARISON WITH EXISTING OBSERVATIONS

Dowels have been used in rigid pavement systems for a long time and, as a result, a great deal of

research has been done on the behavior of doweled joints. Friberg [14] found that the maximum

positive moment of the concrete slab for the edge loading case occurs right beneath the wheel load and

that maximum negative moment occurred at a point 1.8l from the point of loading, where l is the

radius of relative stiffness defined by Westergaard.

He observed that the magnitude of bending moment showed only minor changes after this 1.8l

distance. Friberg further stated that “effective dowel shear decreases inversely as the distance of the

( )25.0

2

3

112

−=

kv

Ehl


13

dowel from the point of loading, to zero at a distance of 1.8l. No dowels beyond that point influence

the moment at the load point.” This observation implies that most of load transfer should occur within

1.8l of the loading.

Figure 7(a) illustrates the schematic deformed shape of a concrete slab along the joint under

single edge wheel load. According to the previous FE results, the relative displacement between

loaded and adjacent slabs determines the magnitude of dowel shear force. Further, the magnitude

decreases as the distance from the wheel load increases. From numerical results in Section 4, the

extent of engaged dowels varied only with the slab thickness. Tire pressure and dowel spacing did not

change the extent of engaged dowels. Spacing did change the number of engaged dowels, but they still

stayed within the same distance, if the thickness of the concrete slab was constant. Seven, nine, eleven

and thirteen engaged dowels were identified from the thicknesses 30, 43, 56, and 69cm, respectively.

From Figure 7(b), one can find that the location of the last effective dowel demonstrated a good match

with Friberg’s 1.8l distance observation. Here, the radius of relative stiffness was computed based on

the subgrade reaction modulus measured by plate loading test simulation with axisymmetric FE model

[3]. The last row of this table shows the amount of load transfer by the engaged dowels, and they were

very close to 100%. Hence, one can conclude that numerical results support Friberg’s observation.

8. CONCLUSIONS

This paper has investigated the load transfer and structural behavior of doweled joints with respect to

the variation of load level, dowel spacing, slab thickness, dowel looseness and landing gear

configuration. Timoshenko beam elements were used to simulate dowels. The ratio of load transfer

was predicted from 18% to 30% with respect to above parameters. In contrast, the number of engaged

dowels depended only the slab thickness. For the 43cm slab thickness, nine engaged dowels achieved

almost 99% of the entire load transfer. This behavior was independent of the variation in load level

and dowel spacing.

From the multiple wheel load analysis, the load transfer ratio decreased with an increase in

applied wheel load. The two or four internal wheel loads (from dual– and tri–tandem landing gear) are

applied away from the joint and, therefore, make a small contribution to load transfer. From the

comparison between models with and without dowels, the dowel load transfer action reduces

maximum tensile bending stress up to 20%. Further, the dominance of the edge wheels, identified

from single slab analysis, was attenuated by the dowel load transfer mechanism. Hence, dowels indeed

contribute to better durability of rigid airport pavement systems. Dowel looseness magnifies maximum

bending stress up to 18% for the worst case. Through the FE analysis, small looseness gap between

concrete slab and dowel makes a significant change in the behavior of concrete pavement.


14

9. REFERENCES

1. Huang, Y. H., Pavement analysis and design, Prentice Hall, Eaglewood Cliffs, New Jersey, 1993, pp. 186-187.

2. Tayabji, S. D. and B. E. Colley, Improved pavement joint, Transportation Research Record 930, TRB, National Research Council, Washington, D. C., 1983, pp. 69-78.

3. Kim, J., Three–dimensional finite element analysis of multi-layered system: Comprehensive nonlinear analysis of rigid airport pavement systems, Ph.D. Thesis, Department of Civil Engineering, University of Illinois at Urbana-Champaign, 2000.

4. Tabatabaie–Raissi, A. M., Structural analysis of concrete pavement joints, Ph.D. Thesis, Department of Civil and Environmental Engineering, University of Illinois at Urbana–Champaign, Illinois, 1978.

5. Huang, Y. H., A Computer package for structural analysis of concrete pavements, Proceedings, Third International Conferenceon Concrete Pavement Design and Rehabilitation, Purdue University, West Lafayette, Indiana, 1985, pp. 295-307.

6. Guo, H., J. A. Sherwood, and M. B. Snyder, Component dowel–bar model for load–transfer systems in pcc pavements, Journal of Transportation Engineering, ASCE, Vol. 121(3), 1995, pp. 289-298.

7. Shoukry, S. N, 3D finite element modeling for pavement analysis and design, Proceedings. The First National Symposium on 3D Finite Element Modeling for Pavement Analysis and Design, Charleston, West Virginia, 1998, pp. 1-92.

8. Ioannides, A. M. and G. T. Korovesis, Analysis and design of doweled slab–on–grade pavement systems, Journal of Transportation Engineering, ASCE, Vol. 118, 1992, pp. 745-768.

9. Bathe, K.–J., Finite element procedures, 2nd ed., Prentice–Hall, Inc., New Jersey, 1996, pp. 234-251.

10. Cook, R. D., D. S. Malkus, and M. E. Plesha, Concepts and applications of finite element analysis, 3rd ed., John Wiley & Sons, New York, 1989, pp. 278-280.

11. Zhang, Z., H. K. Stolarski, and D. E. Newcomb, Development and simulation software for modelling pavement response at Mn/ROAD, Minnesota Department of Transportation, Minnesota, 1994.

12. Hjelmstad, K. D., J. Kim, and Q. H. Zuo, Finite element procedures for three–dimensional pavement analysis, Proceedings, Aircraft/Pavement Technology, ASCE, Seattle, Washington, 1997b, pp. 125-137.

13. Hjelmstad, K. D., Q. H. Zuo, and J. Kim, Elastic pavement analysis using infinite elements, Transportation Research Record 1568, TRB, National Research Council, Washington D.C., 1997a, pp. 72-76.

14. Friberg, B. F., Design of Dowels in Transverse Joints of Concrete Pavements, Transactions, ASCE, Vol. 105, 1940, pp. 1076-1095.


15

15. Foxworthy, P. T., Concepts for the development of a nondestructive testing and evaluation system for rigid airfield pavements, Ph.D. Thesis, Department of Civil Engineering, University of Illinois at Urbana–Champaign, Illinois, 1985.

16. ABAQUS Theory Manual and Users Manual, Hibbitt, Karlsson & Sorensen, Inc., Pawtucket, Rhode Island, 1994.

17. Kim, J., K. D. Hjelmstad, and Q. H. Zuo, Three–dimensional finite element study of wheel load interaction. Proceedings, Aircraft/Pavement Technology, ASCE, Seattle, Washington, 1997, pp.138-150.

1

List of Tables and Figures

TABLE 1 Material Properties of Example Pavement Section: Denver Interna-tional Airport

TABLE 2 Boeing 777--200A Loading Data

FIGURE 1 Problem Definition and Finite Element Mesh

FIGURE 2 Results of Single Wheel Load Case under Load Level Variation

FIGURE 3 Results of Single Wheel Load Case under Dowel Spacing Variation

FIGURE 4 Results of Single Wheel Load Case under Slab Thickness Change

FIGURE 5 Results of Multiple Wheel Load Cases

FIGURE 6 Results of Dowel Looseness Analysis

FIGURE 7 Verification of Numerical Results

2

Layer Thickness(cm)

Poisson’sRatio

Elastic Modulus(MPa)

43 27,600 0.15

20 13,800 0.20

30 345 0.35

760 55 0.45

1. Concrete slab

3. Subbase

4. Soil subgrade

2. Cement-Treated Base

TABLE 1 Material Properties of Example Pavement Section:Denver International Airport

TABLE 2 Boeing 777--200A Loading Data

Total Load (kg) 287,800

Tire pressure (kPa) 1,480

Tire Contact Width (cm)

55.4Tire Contact Length (cm)

34.7

Wheel Load (kg) 22,800

Longitudinal Spacing (cm)

Transverse Spacing (cm)

145

140

175 cm

345

cm

3

(b) Finite Element Mesh for Concrete Slab and Dowels

(a) Problem Definition

(c) Numerical Model for Joint

Plane ofSymmetry

Applied Wheel Load

Concrete Slab

SupportingLayers

Dowels

30.5

@9

=27

4.5

Plane of Symmetry

35.5

@3

=10

6.5

TimoshenkoBeamelements

4

0.7

3810

40.0

---4.0Coordinate (cm)

She

arFo

rce

(kN

)

(a) Shear Force Distribution of Dowel at Joint

AppliedLoad

TransferredLoad

112

224

(Unit : kPa and kN)(1 kPa = 0.145 psi and 1 kN = 0.225 kips)

11.7

26.2

56.6

TirePressure

---0.5

0.0

740

1480

2970

56

23.5

21.0

25.3

(c) Applied and Transferred Wheel Load

FIGURE 2 Results of Single Wheel Load Case under Load Level Variation

0 381Coordinate (cm)

.075

---.025

0.0

Diff

eren

ce(m

m)

(b) Relative Displacement betweenLoaded and Adjacent Slab

2970 kPa Case

Wheel Load

Ratio (%)

5

3810

24.5



Ratio(%)

21.9

26.2

21.7

30

61---O

61---E

23.5

19.4

19.6

TransferredLoad (kN)

Spacing(cm)

Normalized Stress

Loaded Adjacent

1.09

1.01

0.93

1.00

1.00 1.00

(c) Transferred Wheel Load and Normalized Stress

FIGURE 3 Results of Single Wheel Load Case under Dowel Spacing Variation

%of

She

ar

Location (cm)

30 cm

61---O cm

61---E cm

0 30 61 91 122 152 183 213

53.5 20.1 2.8 0.3

30.9 20.4 8.9 3.3 1.2 0.5 0.3 0.1

41.0 8.4 1.0 ---0.1

(b) Contribution of Each Dowel to Total Wheel Load Transfer

Total

99.9

100.3

100.6

Dowel Number 1 2 3 4 5 6 7 8

30 cm Spacing61 cm Spacing ODD61 cm Spacing EVEN

AppliedLoad (kN)

112

112

112

She

arFo

rce

(kN

)

(1 cm = 0.394 inch and 1 kN = 0.225 kips)

Wheel Load

6

3810

20.0


Ratio(%)

21.926.2

32.8

3043

56

23.519.6

29.4


Thickness ofslab (cm)

Normalized Stress

Loaded Adjacent

1.40

0.72

1.35

0.81

1.00 1.00


(c) Transferred Wheel Load and Normalized Stress


33.869 30.2 0.55 0.63

%of

Dow

elS

hear

Location (cm)

30 cm

43 cm

56 cm

69 cm

38.2 21.6 6.8 1.6 0.3 0.1 0.1 0.1

30.9 20.4 8.9 3.3 1.2 0.5 0.3 0.1

28.6 19.3 9.1 4.0 1.8 1.0 0.6 0.2

25.0 18.2 9.6 4.8 2.4 1.5 1.1 0.4

Total

99.4

100.3

100.6

101.0

Dowel Number 1 2 3 4 5 6 7 8

30 cm Slab Thickness43 cm Slab Thickness56 cm Slab Thickness

69 cm Slab Thickness

0 30 61 91 122 152 183 213

AppliedLoad (kN)

112112

112

112

She

arFo

rce

(kN

)


Wheel Load

(b) Contribution of Each Dowel to Total Wheel Load Transfer

7

0 381

0.0

0.25

---2.54

3810

22.2

---4.4

---2.54---762 762

SingleTandemDual-TandemTri-Tandem

Symmetry Line

AdjacentSlab

LoadedSlab

0

Coordinate (cm)

Coordinate (cm)

Coordinate (cm)

Dis

plac

emen

t(m

m)


(c) Deformed Shape along Joint

(d) Deformed Shape along Symmetry Line

FIGURE 5 Results of Multiple Wheel Load Cases (cont’d)

Single

Tandem

Dual-Tan.

Tri-Tan.

AppliedLoad

Trans.Load

Ratio(%)

112

224

447

671

26

49

76

91

23.5

21.8

17.0

13.5

WheelLoad

(b) Transferred Wheel Load

Joint Line

She

arFo

rce

(kN

)

(Unit : kN, 1 kN = 0.225 kips)

Dis

pl.(

mm

)

TandemWheel Load

Single Wheel Load

8

TandemWheel

SingleWheel

Dual-TandemWheel

Tri-TandemWheel

Location ofMaximum

Bending Stress

1.401.461.863.46

1.271.301.662.89

1.010.991.281.81

1.001.001.001.00

[�c]max

[�t]max

[� t]max

[� w]max

25882151

.2052

.0716

(Units: kPa and cm)(1 kPa = 0.145 psi, 1 cm = 0.394 inch)

(g) Single Wheel Load Results

(f) Normalized Maximum Stress and Displacement Results without Dowels

22681800

.2002

.0665

W/O Dowels

10891096

.1986

.0650

Loaded Adjacent

Values are Normalized by Single Wheel Case

1.381.471.793.51

1.261.321.612.84

1.021.011.271.80

1.001.001.001.00

(e) Normalized Maximum Stress and Displacement Results with Dowels

1.651.641.793.41

1.471.471.612.87

1.111.121.271.82

1.001.001.001.00

[�c]max

[�t]max

[� t]max

[� w]max

1.001.001.001.00

FIGURE 5 Results of Multiple Wheel Load Cases

9

SingleWheel Load

Intact Joint

Ratio(%)

24.616.512.6

0.00250.0250.051

14.822.0

11.3


Normalized Stress

Loaded Adjacent

1.00

1.05

1.00

0.881.02 0.94

(b) Shear Force Distribution of Dowel at Joint for Single Wheel Load

(c) Transferred Wheel Load and Normalized Stress for Single Wheel Load

FIGURE 6 Results of Dowel Looseness Analysis (Cont’d)

4.20.127 3.8 1.11 0.71

AppliedLoad (kN)

112112112112


Gap btw. Slab andDowel (mm)

0.00.254 0.0 1.16 0.58112

0.0025 mm Gap0.025 mm Gap0.051 mm Gap0.127 mm Gap0.254 mm Gap

3810

22.2


She

arFo

rce

(kN

)

(a) Dowel Looseness Simulation Model for Joint

Uni---directional Gap Contact Node Setbetween Concrete Slab and Dowel

WheelLoads

Adjacent Slab Loaded Slab

Gap fromDowel

Looseness

10

3810

22.2

---4.4

Coordinate (cm)

Ratio(%)

85.770.243.4

0.00250.0250.25

10.512.8

6.6


Normalized Stress

Loaded Adjacent

1.00

1.05

1.00

0.901.00 0.99

(d) Shear Force Distribution of Dowel at Joint for Tri--tandem Wheel Load

(e) Transferred Wheel Load and Normalized Stress for Tri--tandem Wheel Load


12.60.76 1.9 1.16 0.65

0.0025 mm Gap0.025 mm Gap0.25 mm Gap0.76 mm Gap

AppliedLoad (kN)

671671671671

She

arFo

rce

(kN

)


Tri---tandemWheel Load

1.02 mm Gap

Intact Joint

Gap btw. Slab andDowel (mm)

9.71.02 1.4 1.18 0.49671

0 381

---0.76

---2.54

Coordinate (cm)

Dis

plac

emen

t(m

m)

0 381

---0.76

---2.54

Coordinate (cm)

Dis

plac

emen

t(m

m)

(f) Deformed shap of loaded and adjacent slabs along joint

Gap = 0.025 mm Gap = 0.76 mm

Loaded Slab

Adjacent Slab

11

Wheel Load

Loaded Slab

Adjacent Slab

(a) Deformed Shape along the Joint Line

Dowel Shear Force

1.8l

(M+)MAX

(M� )MAX

(b) Relationship between Number of engaged dowels and 1.8l

FIGURE 7 Verification of Numerical Results

(k = 3640 kPa/cm, E = 27.6 GPa, n = 0.15)

Slab Thickness (cm) 30 43 56 69

1.8l (cm) 118 153 185 216

No. of Engaged Dowels 4 5 6 7

Location of LastEffective Dowel (cm)

122 152 183 213

Ratio of Load Transferby Effective Dowels

98.2 98.5 99.0 100.2

Keith D. Hjelmstad, Elastic Pavement Analysis Using Infinite Element, In Transportation Research...

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