Pavement Design Engineering: PCC Slab Stress Analysis & Dowel Design

This assignment delves into the analysis and design of Portland Cement Concrete (PCC) pavements. It begins by calculating the maximum tensile stress in a 12-inch un-reinforced PCC slab under a 10,000 lb load at different locations: the corner, edge, and interior. The analysis considers warping stresses due to temperature differentials and recommends pavement reinforcement based on combined stress levels. The assignment also addresses dowel design for load transfer, considering temperature differences, and discusses various types of rigid pavements, including Jointed Plain Concrete Pavements (JPCP), Jointed Reinforced Concrete Pavements, and Continuously Reinforced Concrete Pavements. Furthermore, it differentiates between tie bars and dowel bars and explains the function of joints in concrete pavements, such as expansion, contraction, hinge, and construction joints. Finally, the assignment applies AASHTO guidelines for JPCP design with and without dowels, considering factors like drainage, reliability, traffic, and subgrade strength, to determine appropriate slab thickness, joint spacing, and reinforcement requirements.

Pavement design engineering
Student University
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1. For a 10,000 lb load applied on dual wheels ( 100 psi tire pressure ) spaced at 16
inches, the maximum tensile stress in the slab when the load is located at:
According to Elliott & Thornton (2008). The loads on the concrete slab induce stress. The
quantity of the stress depends on the point of application of the load. Westergaard developed
equations used to compute the stresses and deflections generated by loads applying at the
corner, edge and interior of the slab as ideal situations. The loads applied at the corners
contribute to breakage of the corners while those at the edge and interior of the slab cause
transverse cracks.
a) The corner of the slab;
When the load is applied at the point where the slab forms an intersection with the pavement.
Since this situation is less likely to occur due to the large width of the pavement, no equation
is used to determine the tensile stress in the slab.
b) The edge of the slab: at this point, the load is applied on the edge far away from any
corners. The tensile stress when a load is applied on the edge depends on the time of
the day due to changes in temperature of the slab.
The equation used is:
∝= 0.572 p
h 2 ¿
Where p is the load, h is the loaded area, r is the radius of pressure.
Substituting values into the equation:
Tensile pressure = ( ( 0.572 × 10000 ) / 122 ) ( 4log10 ( 31.2 / 16 ) + 0.359 = 78.09 lb /
in2.
c) The interior of the slab: Westergaard formulated the equation to calculate the stress
of a slab when a load is subjected interiorly in a circular area of radius r.
∝= 0.316 p
h 2 ¿.069
Substituting the symbols for values,

Tensile stress = 0.316 ×10000
144 ¿.069 = 179.45lb / in2.
2. Cross-section of the slab showing the horizontal stress distribution on the vertical
plane for the case where the load is located at the edge of the slab.
3. Warping stresses at the edge and at the interior of the slab with a temperature
differential between top and bottom pf slab to be 3ºF per inch of thickness.
Warping stress are due to changes in moisture in the slab. These stresses are described by
steel and joint design of the concrete.
Interior warping stress = Eat
2 ¿)
Where e is modulus of elasticity, μ is the Poisson’s ratio, a is the coefficient of thermal
expansion are correction factors.
Substituting the values:
Interior warping stress = 5000000∗0.0000005∗36
2 ¿) = 241 psi
Edge warping stress = CEat
2

Substituting values:
Edge warping stress = 1.07∗0.0005∗5000000∗36
2 = 224psi
4. Combined warping and load stress at the edge of the slab
Combined stress = 224 psi + 78.01 = 302.01 psi
5. Combined stress at the interior
Combined stress = 241 + 179.45 = 420.45 psi
6. Recommendation for pavement reinforcement.
Yes, I would recommend the pavement be reinforced because the total warping and tensile
stresses are lower than expected for the concrete slab and therefore would not support the
load. The slab would develop transverse cracks.
7. If a temperature difference at 40ºF between the times the concrete was placed and the
lowest mean monthly temperature for this pavement, recommendations for dowels for
load transfer would be:
The efficiency of load transfer across joints in a concrete slab is influenced by the levels
of joint opening during temperature changes across different times. This computation to
determine joint opening was developed by Darter and Barenberg.
In the context of this slab, I would recommend dowel bars to provide flexural, shearing
and bearing resistance. The dowel bars must be of a larger diameter than the steel used
and lubricated on one end to allow expansion.
Change in Joint opening = CL ( at + e )
Where a is the thermal expansion coefficient of the material, l is the joint spacing, e is the
drying shrinkage coefficient and t is the temperature change.
Substituting values;
Change in Joint opening = 0.65 × 264 ( 0.000005 × 40 + 0.0005)
Change in Joint opening = 0.03482
Joint opening for undoweled joints = 0.05 ÷ 0.03482
Joint opening = 1.44m.
8. Types of pavements.

According to Solanki, Zaman, & Dean (2010). Portland cement is used to form concrete slabs
for rigid pavements. Steel rods may or may not be used to reinforce the concrete. The subbase
should be able to provide support to the load on the pavement, hence it can or may not be
bonded. The slab is a combination of water, coarse and fine aggregate and Portland cement.
Steel may be introduced in the slab to provide more tensile strength, bonding sections of the
slab and load transfer across joints. Pavements transfer traffic load over the subbase. They
have differences in design concerning depth, length, joint; positioning and spacing and type
or amount of reinforcement.
Three types of such rigid concrete pavements have been described in consideration of such
differences into:
Jointed plain concrete pavements, which are the most commonly used pavement design
because they are simple and cheap to design and construct. They do have reinforcement, but
dowels are used for load transfer across transverse joints while to bars are used to hold firmly
longitudinal joints.
Jointed reinforced pavements, although little reinforcement is used, are like JPCPs but with
longer slabs and are not doweled for load transfer but tie bars are used.
Continuously reinforced concrete pavements, have no joints but large lengths of slab.
Jointed plain concrete Jointed reinforced concrete Continuously reinforced
No reinforcement is used. Light reinforcement is used Heavily reinforced
Contraction joints are placed
every 12-20 ft.
Longer joint spacing,25-
40ft.
Have no contraction joints
Dowel or tie bars are used
for transverse or
longitudinal joints.
Temperature steel are used
to hold joints strongly
together.
There are no bars placed
since they do not have
joints.
9. Tie-bars and dowel bars
Apart from serving the primary function of reinforcement, steel bars are added into rigid
pavements to connect sections and transfer loads across joints. The steel reinforcement is
therefore divided categorically according to purpose. The steel reinforcements are therefore,
temperature steel, dowels and tie bars.

Tie bars Dowel bars
Are used to bond two sections of the
pavement together.
They are used as load transfer bars across
joints.
Are of smaller diameters Are of larger diameters
Have hooks or deformed to prevent
movement
One end is smooth and lubricated to allow
for expansion of the joint
Typical diameter is 0.75 inch Typical diameter is 1 to 1.5inches.
They are spaced at 3 ft. apart at large
centres.
Spaced at 1ft. centres across transverse
joints.
10. Joints in concrete pavements.
Joints which are used in rigid pavements. They are:
 Expansion joints, this are type of joints which are placed transversely along the course
of the slab, these joints allow for an increase in the size of the concrete material with
increases in temperature without buckling. The joints spaces are packed with material
that allows compression such as bituminous fabrics and a load transfer dowel is
placed.
 Contraction joints; this type of joints are used across the slab in order to reduce tensile
stresses which is caused by contraction of the material due to reductions in
temperature.
 Hinge joints; this type of joints are located along the centre line of the pavement.
Typical hinge joints are keyed, and the core function of this joint type is to reduce
cracking at the centre.
 Construction joints; this joint type form the transition between slabs constructed at
different times.
These joints are used to perform the following core functions;
I. They are used to limit the stress which is caused by temperature changes over the
course of the day when the concrete heats up and cools.
II. They are used to hold together sections and prevent movements when traffic loads are
applied on the pavements.
Pavement systems design.

According to Kim (2008). A rigid pavement is a block laid on the subbase. The mechanism of
action is an advanced function of the beam, the primary difference being the width of the
beam and slab. A concrete slab will be damaged when a load is applied over it. This
resistance to deformation depends on the slab thickness and Young modulus of the concrete
material. Charts have been developed by the American association of state Highway and
Transportation(AASHTO) to estimate values required to design a pavement from the known
factors of modulus of the concrete, estimated traffic load, characteristics of the base and
drainage coefficient of the underlying material. The AASHTO design includes a load safety
factor from the Highway Safety Manual that categorizes axle loads of the traffic for the
different types of highways. For this situation, a load safety value of 1.1 is assigned for this
highway design arterial with moderate track volumes.

1. JPCP with no dowels and with asphalt shoulders.
Rigid pavement design using the American association of state Highway and Transportation
under the highway safety manual. In the AASHTO procedure for design, the following are
items under consideration: drainage, reliability, traffic, slab width and subgrade strength.
Using AASHTO charts to determine the composite subgrade reaction, slab thickness, length
and spacing of joints, Huang (2014)..

Using the charts, by inputting values in the relevant segments, these values are used to
determine a value to the match line.
Using the values and the effective subbase modulus, to determine the pavement design that
will be adequate on a rural primary arterial for 30 years, the following design criteria was
established:
 P1 is 4.5
 P2 is3.0
 Subbase thickness is 9inches
 Subbase modulus of 100,000psi
 Subgrade modulus of 4,500,000psi and tensile strength of 500psi.
 Drainage coefficient is 1.0
 Reliability of 95% , ZR = 1.645
The standard deviation of 0.4
These values are used to determine the following design standard
Required thickness of the slab is 11 inches, rounded off.
The slab length is 13 ft.
Dowel bars spacing is 15 ft.
Tie bars are placed 3 ft. apart.
2. JPCP with dowels and tied PCC shoulders design.
A 15 ft. slab has been determined.
Mean concrete modulus of rupture = 725 lb./in2
modulus thickness= 9 inches
Modulus subbase = 100000 psi
Drainage coefficient, Cd = 1.0
Design ΔPSI loss= 4.5-3.0= 1.0
Reliability, R% = 95% (ZR = 1.645)
Overall standard deviation, So = 0.4
Cumulative modulus = (4.5 * 106)

These values are used to determine output parameters for jointed plain concrete pavement
from the charts correlating with the match line values.
The slab thickness is 12inches.
Diameter of each dowel is 3.81cm
Spacing between each dowel is 12 inches.
Tie bar spacing at 3 ft.
3. JRCP with 40-ft slab length
with tied PCC shoulders.
Using the AASHTO charts, a value line
with
determined levels was plotted. The
characteristics of the slab were computed
as:
Slab thickness, 12 inches.
Longitudinal reinforcement 3 ft.
Transverse reinforcements at 21 ft.
Diameter and dowel spaces, 60mm at 21ft.
Tie bars spacing a 3 ft.

References:
Elliott, R. P., & Thornton, S. I. (2008). Resilient modulus and AASHTO pavement design.
Transportation research record, (1196).
Kim, Y. R. (2008). Modeling of asphalt concrete.
Huang, Y. H. (2014). Pavement analysis and design.
Solanki, P., Zaman, M., & Dean, J. (2010). Resilient modulus of clay subgrades stabilized
with lime, class C fly ash, and cement kiln dust for pavement design. Transportation
Research Record: Journal of the Transportation Research Board, (2186), 101-110.
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