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
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
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
2
Three–Dimensional Finite Element Analysis
of Doweled Joints for Airport Pavements
Jiwon Kim, Ph.D., Research Scientist
Pavement Research Group, Korea Highway Corporation
293-1, Keumto-Dong, Soojung-Gu, Sungnam-Si
Kyunggi-Do, R. O. Korea, 461-703
and
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., 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
Kim and Hjelmstad TRB 2003
3
Three–Dimensional Finite Element Analysis
of Doweled Joints for Airport Pavements
Jiwon Kim, Ph.D., Research Scientist
Pavement Research Group, Korea Highway Corporation
293-1, Keumto-Dong, Soojung-Gu, Sungnam-Si
Kyunggi-Do, R. O. Korea, 461-703
and
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., 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).
Kim and Hjelmstad TRB 2003
4
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
Kim and Hjelmstad TRB 2003
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
Kim and Hjelmstad TRB 2003
6
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
Kim and Hjelmstad TRB 2003
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.
Kim and Hjelmstad TRB 2003
8
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
Kim and Hjelmstad TRB 2003
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
Kim and Hjelmstad TRB 2003
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
Kim and Hjelmstad TRB 2003
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
Kim and Hjelmstad TRB 2003
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
Kim and Hjelmstad TRB 2003
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.
Kim and Hjelmstad TRB 2003
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.
Kim and Hjelmstad TRB 2003
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
---2.2Coordinate (cm)
(a) Shear Force Distribution of Dowel at Joint
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
---2.2Coordinate (cm)
Ratio(%)
21.926.2
32.8
3043
56
23.519.6
29.4
TransferredLoad (kN)
Thickness ofslab (cm)
Normalized Stress
Loaded Adjacent
1.40
0.72
1.35
0.81
1.00 1.00
(a) Shear Force Distribution of Dowel at Joint
(c) Transferred Wheel Load and Normalized Stress
FIGURE 4 Results of Single Wheel Load Case under Slab Thickness Change
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
)
(1 cm = 0.394 inch and 1 kN = 0.225 kips)
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)
(a) Shear Force Distribution of Dowel at Joint
(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
TransferredLoad (kN)
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
(1 cm = 0.394 inch and 1 kN = 0.225 kips)
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
---4.4Coordinate (cm)
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
TransferredLoad (kN)
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
FIGURE 6 Results of Single Wheel Load Case under Slab Thickness Change
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
)
(1 cm = 0.394 inch and 1 kN = 0.225 kips)
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
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