Hello students welcome to lesson 16 of module
IV. Module IV is on pavement design. This
lesson is about designing concrete pavements
as per PCA and AASHTO design procedures. In
the previous lesson that is lesson 4.15 we
have discussed about designing concrete pavements
as per Indian Road Congress guidelines that
is IRC: 58 - 2002 version. We will see the
similarities and differences between these
two procedures that I am going to discuss
in this lesson and the Indian Road Congress
design procedure also.
So the specific objectives of this lesson
would be after completing this lesson the
student is expected to understand the basis
for the PCA and AASHTO methods for design
of concrete pavements. PCA is the Portland
Cement Association and AASHTO is the American
Association of State Highway and Transport
Officials as we have learnt in the earlier
lessons. Therefore the student would be in
a position to understand the basis for the
PCA and the AASHTO methods for the design
of concrete pavements. They would be familiar
with the concepts adopted for these two different
agencies for design of concrete pavements.
The students would be able to select appropriate
traffic and material inputs for design as
per these two different procedures and they
would be also be in a position to carry out
designs of concrete pavements as per PCA and
AASHTO criteria.
So the two design methods that we are discussing
today in this lesson are those adopted by
Portland Cement Association PCA method and
the American Association of State Highway
and Transport Officials AASHTO.
We will first start with Portland Cement Association
method PCA method. The first set of guidelines
as per PCA was published in 1984. The performance
criteria and design criteria and the design
methodology that was published in 1984 was
based mainly on the performance data collected
at the AASHO road test. In fact as i indicated
AASHO test had various types of pavements,
flexible pavements, and different types of
concrete pavements. So the performance of
different types of concrete pavements were
observed during the AASHO road test, that
data and those pavements were analyzed with
subsequently led to different types of performance
criteria for different types of pavements.
We have already seen AASHTO guidelines for
design of flexible pavements. We will also
discuss about AASHTO guidelines for design
of concrete pavements in this lesson and with
the same data form the basis for most of the
other design procedures such as Portland Cement
Association also. the main failures considered
in the PCA design procedure are fatigue cracking
of concrete and erosion of foundation, these
are the two main failures.
If you recollect in the previous lesson on
design of concrete pavements as per IRC procedure
there also we made a mention of erosion failure
but IRC does not make any specific design
provisions for carrying out erosion analysis.
But one provision that was made to handle
erosion in IRC concrete pavement design was
provision of concrete rather paved shoulders
of 1.5 m width. But there is no specific analysis
included in the IRC procedure for erosion
analysis. So PCA considers two types of failures
fatigue cracking and erosion of foundations.
Fatigue failure is the one in which the pavements
fail by fatigue of concrete. Erosion failure
is the one in which the pavements fail by
pumping. We have discussed about pumping in
the previous lesson. Erosion of foundation
leading to formation of gaps below the slab
and joint faulting that is joint being at
different levels.
For fatigue analysis the critical stress is
because if the load is placed in different
regions of the slab the tensile stresses that
will be developed will be different so the
critical condition of load position has to
be selected. The critical stress condition
is considered to be edge stresses and the
midway between the transverse joints. If you
consider these two transverse joints 
and if this is the longitudinal edge which
is the free edge and next to this we have
a shoulder so we are concerned about the edges
that are developed along the sides when the
wheel load is placed close to the edge with
the tire imprints being tangential to the
longitudinal edge and it is away from these
two transverse joints, that's what we mean
by midway. So this is the position of the
load that we are concerned about, the edge
stresses midway between the transverse joints
in the edge region away from the joints. There
are two cases that we consider with and without
concrete shoulders. This is what PCA considers,
there are two cases. There will be concrete
shoulders tied to the main slab or without
tied concrete shoulders.
Cumulative fatigue damage concept is used
in PCA. Stresses due to warping and curling
are not considered for fatigue analysis. these
stresses are not added to the wheel load stress
while carrying out fatigue damage analysis
because both of them happen throughout the
year throughout the life period both the combination
being additive is not possible, sometimes
it is additive and sometimes it is subtractive.
So the warping and curling stresses are not
considered and they are not added to the wheel
load stresses for carrying out fatigue analysis.
The combined stresses due to warping which
occurs because of variation moisture within
the slab and curling which occurs because
of the variation in temperature within the
slab are usually subtractive from load stresses
most of 
the time.
The fatigue damage is computed using this
expression where Dr is the cumulative damage
caused to the slab given as sum of ni divided
by Ni where i varies from 1 to m. Here m is
the number of load groups. suppose if you
have the axle load data and then you have
to group the axle load data into m groups,
group 1 being say 0 to 4 tons, group 2 could
be 4 to 8 tons whichever way you classify
it we have eight groups of load groups then
Ni is the predicted number of repetitions
for ith load group.
What is the number of load repetitions of
the ith group?
Say 0 to 4 tons expected to be applied on
the pavement during its service life period.
This is has to be available to us from traffic
projections. So small ni is the number of
load repetitions of group i. Capital Ni is
the allowable number of repetitions for ith
load group. That means if you apply only the
ith load group loads say 0 to 4 ton loads
only then how many repetitions of this load
group the slab can handle before it fails?
That is capital Ni. So once you get this ratio
for different load groups you can sum up all
those relative damages and accumulated damage
ratio should be smaller than hundred percent
for the slab to be safe.
This is the fatigue relationship considered
for concrete. In terms of the stress ratio
these relationships explain how many repetitions
the slab can handle or the concrete material
can handle before it fails in fatigue damage.
As you have seen in the case of IRC guidelines
in fact these are similar guidelines. For
different stress ratio conditions different
relationships are given correlating the number
of repetitions the concrete can handle for
a given stress ratio before it fails in fatigue
damage. As you can see in this slide for different
stress ratio values given by sigma by Sc where
sigma is the tensile stress in concrete because
of the load under consideration where Sc is
the tensile strength of concrete we have represented
this as stress ratio SR. So, if the stress
ratio is greater than or equal to 0.55 the
number of repetitions to fatigue failure Nf
is given as the function of stress ratio sigma
by Sc by this equation.
For stress ratio range of 0.45 to 0.55 number
of repetitions to failure of the slope group
are again given as a function of stress ratio.
For N less than 0.45 it is assumed that the
concrete is capable of handling infinite number
of repetitions.
For carrying out fatigue analysis that means
for calculating the wheel load stresses the
wheels placed close to the edge produce maximum
stresses. Even if the loads are slightly placed
away from the edge the reduction in stress
is significant. So it is important to understand
what percentage of wheel loads are going to
be placed close to the pavement edge. All
those loads that are placed even slightly
away from the pavement edge it is seen that
the reduction in stress is significant and
it is not going to significantly be contributing
towards fatigue damage. So we are concerned
about those wheel loads which are placed very
close to the pavement edge.
Portland Cement Association PCA analysis indicates
that considering only 6% of total traffic
traveling in one direction and assuming that
all these trucks have their outer wheels placed
in the edge region produces the same cumulative
fatigue damage produced by all the trucks
positioned at different locations from 
the edge.
But again what we are trying to indicate is
if this is the pavement, for example at a
given point of time if this is how the vehicles
are placed if we put these wheels exactly
in the same position if this is the realistic
practical position of vehicles then depending
on the traffic intensity depending on the
facility that is available all the wheels
are not going to travel along the same path,
they are not going to follow any particular
path but they are going to be distributed
across the carriage way breadth.
One vehicle may travel all along this path,
another vehicle will travel along this path
and another may take a slightly different
path so the wheel load positions are going
to be distributed across this width. So, if
you put these wheel loads exactly in the same
position and calculate stresses in the edge
region and on the other hand if you put only
six percentage of all these vehicular traffic
exactly in the edge region position as shown
here then in both cases the edge stresses
that are going to be computed will almost
be similar. So that is what PCA has worked
out.
Hence to repeat this again PCA analysis indicates
that considering only six percentage of traffic
and assuming that all these trucks have their
outer wheels placed in the edge region produces
the same cumulative fatigue damage produced
by all the trucks positioned at different
locations from the edge. So what is being
emphasized here is that we need to consider
only certain portion of all the truck traffic
and then assume that these vehicles are traveling
with their outer wheels placed tangential
to the outer edge and then analyze the slab
only for those wheels.
If the total traffic is considered, for example,
if you trying to consider the total traffic,
assume all the hundred percent repetitions
you are considering then it can still be done
but the edge stress computed will have to
be reduced by a factor of 0.894 that will
be corresponding to the actual total cumulative
damage that you can obtain.
Coming to erosion analysis that is considered
in PCA analysis pavement problems such as
pumping, faulting and erosion of foundation
etc are more due to the deflection than due
to stresses in the slab. Deflection is the
consideration that we have to be concerned
about. If there are more deflections there
is going to be more amount of pumping, more
amount of erosion and more faulting problems
also are likely to be there if the slab deflects
more.
Most critical location for deflection obviously
is the corner because of its discontinuity
in two directions that is when the load is
placed in the corner region. Erosion is influenced
by the type of joint. obviously if there is
low transfer across the joint the deflection
is going to be lesser erosion is going to
be lesser so we have to consider what is the
type of joint that is there, what is the type
of low transfer mechanism whether it is through
granular interlocking or if there is a provision
of dual bars placed across the joints so we
have to take all these things into account
before computing what is the deflection and
accordingly what is going to be the erosion
damage caused to the foundation.
So, for carrying out erosion analysis the
critical loading positions will be the corner
location as we just discussed. So the load
has to be placed in a corner region. this
is one free edge there is shoulder on this
side, there is another free edge this may
not be exactly free but there is another slab
that is on the other side and there is a joint
here so this is where some amount of discontinuity
is there in both the directions so we have
to place these wheel loads as close to the
corner as possible and that is when we are
going to be having maximum deflection in the
corner region that is the critical condition.
Again we will have to assess what percentage
of total traffic will have their wheel load
positions in the corner region, whether it
is hundred percent or part of that.
This is the erosion criteria that PCA adopts
to estimate how many repetitions the pavement
can sustain before unacceptable levels of
erosion takes place before the slab or the
foundation fails because of erosion failure.
This is given as log N = 14.524 -- 6.77 into
C1 P -- 9 to the power 0.103. In this case
C1 is an adjustment factor. To account for
different types of sub-bases that are used
C1 will be one for untreated granular sub-base
and C1 will be 0.9 for stabilized sub-base.
The other parameter that we use here P is
the rate of work computed as 268.7 into P
square by h into k to the power of 0.73. This
is the function of the pressure on the foundation
under the slab corner, h is the thickness
of the slab and k is the modulus of subgrade
reaction. So the rate of work is a function
of all the pavement parameters, thickness
of slab and modulus of subgrade reaction and
the deflection of the slab at the corner which
can be used to obtain the pressure as p = kw
where' w' is the deflection in the corner
region because of load applied in the corner,
'k' is the modulus of subgrade reaction because
of the assumption that we made about the spring
foundation the reactive pressure is proportional
to the deflection proportional to constant
as we know is the modulus of subgrade reaction.
So, if you can calculate the deflection in
the corner region due to a load that is placed
in the corner then using this expression we
can find out 'p' slab thickness has to be
known and 'k' also is an input parameter so
you can calculate the rate of work. So substituting
this in the above equation we can find out
given the load how many repetitions the slab
can sustain before it fails because of erosion
failure.
Percentage erosion damage, again here we are
going to have different magnitudes of loads
and different magnitudes of load would produce
different amount of deflection so the erosion
damage caused by different axle load groups
will be different so we have to sum up all
the damage caused because of all the groups
of axle loads so this is how we do the summation.
So the total erosion damage is again a summation
of a multiplication factor C2 small ni divided
by capital Ni
C2 takes values of 0.06 or 0.94 depending
upon what type of a shoulder is provided,
whether it is without concrete shoulder or
with a concrete shoulder which is tied to
the main slab, accordingly C2 will take values
of either 0.06 or 0.94. The percentage erosion
should be less than 100%.
Again small ni as discussed in the previous
slide or as discussed in the case of fatigue
damage analysis is the number of repetitions
of group i and capital Ni is the number of
repetitions the slab can sustained as per
the criteria given in the previous slide for
a given load because we can calculate the
corresponding deflection for that load and
for that deflection for a given pavement system
how many repetitions it can sustain can be
obtained from the erosion criteria as given
in the previous slide. So the total percentage
erosion should be less than 100%.
The design inputs that are to be obtained
for carrying out design as per PCA analysis
are; about the concrete we need to have the
flexural strength of concrete represented
in terms of modulus of rupture expressed as
MR, we have to have information regarding
the subgrade strength in terms of the modulus
of subgrade reaction, we also have to have
information in terms of the loading, magnitudes
of axle loads and also the frequency of axles
of commercial vehicles, we are interested
in only commercial vehicles. Normally design
period is considered to be 20 years.
The flexural strength of concrete influences
the fatigue behavior of concrete.
Modulus of rupture determined at 28 days under
third point loading; how this has to be obtained
is also specified, the specimens have to be
prepared, third point loading has to be conducted
and the modulus of rupture obtained from the
test at a 28 day period has to be used for
design.
Subgrade strength has to be obtained by conducting
a plate load test. This is what is recommended
by Indian Roads Congress also. The load per
unit loaded area per unit deflection is the
modulus of subgrade reaction as we already
know.
PCA also suggests that k value can be estimated
from California Bearing ratio value of the
subgrade or its R-value. It also recommends
that normal summer or fall k values should
be used. Seasonal variation of k is not normally
considered.
These are the typical modulus of subgrade
reaction values for different types of subgrade
soils.
For example, for plastic clay one can expect
the k value expressed in terms of pounds per
cubic inch in the range of 50 to 100 whereas
for gravels it can be more than 300, for cement
or asphalt treated bases it can be more than
400, sands and clayey gravels 200 to 300,
silt and silty clays 100 to 200. This is just
an approximate idea of what could be the modulus
value of k, the modulus of subgrade reaction
value of different types of soils.
We may provide sub-base to avoid mud-pumping.
Sub-base can be untreated granular base or
cement treated especially for heavy duty highways
high volume roads
So normally we provide granular sub-base untreated,
untreated either with cement or asphalt or
bitumen so that is what is known as granular
sub-base or we can also have cement treated
base. If you recollect IRC: 58 recommends
use of dry lean concrete as sub-base. Especially
IRC: 58 is meant for high volume roads like
national highways and other heavy traffic
roads. So dry lean concrete is what is recommended
there. So PCA also recommends that you can
either use an untreated granular surface or
cement treated base. And wherever the sub-base
is used obviously the k value has to be increased
suitably.
This is how we can increase the modulus of
subgrade reaction of a given subgrade if sub-base
of different thicknesses are used. This table
here gives us guidelines about how to obtain
the corresponding increased effect to combined
modulus of subgrade reaction for the two layers
subgrade and the granular sub-base this is
for untreated sub-base. If you provide a 6
inch untreated sub-base over the subgrade
having 100 pci modulus of subgrade reaction
the combined effect to modulus of subgrade
reaction can be taken to be 140 pci pounds
per cubic inch. Similarly, if we place a 12
inch granular sub-base over a subgrade having
a k value of 300 pci the effective k value
can be taken as 430.
Similarly if cement-treated sub-base is used
on subgrade this is how you select the combined
effective subgrade modulus of reaction. So
for different thicknesses for different subgrade
k values the effect to k values are given
here.
Other design parameters relating to traffic
are; we have to select a design period or
the traffic analysis period, this has to be
selected on the basis of economic analysis
of pavement costs and services. Other traffic
parameters are selecting number of heavy axle
loads expected during the pavement life. These
are to be derived from commercial traffic
as percentage of average daily traffic average
daily traffic, average daily truck traffic
in both the directions and also we have to
have information regarding axle loads spectrum.
The traffic projections are to be made in
the following manner:
Design ADT will be a projection factor multiplied
by the present average daily traffic.
Projection factors normally range from 1.2
to 1.8 for annual growth rates of 2 to 6%.
PCA also recommends usage of load safety factors
LSF as you have done in the case of IRC: 58
also.
For different types of facilities different
load safety factors are given. as you can
see here for high traffic volume roads load
safety factor of 1.2, for moderate volumes
of truck traffic load safety factor of 1.1,
for roads, residential streets, other streets
where small volumes of truck traffic is there
a load safety factor of 1 can be used. These
are similar to the values that are adapted
in the case of IRC: 58.
The other inputs that are required for design
are what type of joints are provided, what
is the type of shoulder that is there; concrete
shoulder, unpaved, tight concrete shoulder
etc, so different PCA gives design provisions
for different types of shoulders.
Concrete flexural strength at 28th day has
to be obtained and the k-value of subgrade
or the combined modulus of subgrade reaction
of subgrade and any granular treated or untreated
base has to be available. We have to select
a load safety factor depending on the type
of facility, we have to have information on
the axle load distribution, and we also have
to have projection about the expected number
of repetitions of different axle load groups
during the design period.
The design method follows the following steps:
For both fatigue analysis and erosion analysis
separate tables are available and separate
charts are available. Although if the program
is available one can do the analysis independently
but for somebody who is doing the analysis
on the basis of tables and charts a series
of charts and tables are available in the
PCA guidelines to easily work out what is
the fatigue damage and also what is the erosion
damage.
Separate tables are used to evaluate fatigue
and erosion damage.
Equivalent stress tables are available which
give us for a given thickness of slab say
4 to 14 inches thick and for a given k-value
of foundation either only the subgrade or
the combined effective k value of subgrade
and the base we can find two values in the
table. For example, for 4 inches and for a
k-value of 50 825 and 679 are the values that
are available whereas 829 is the equivalent
stress for single axle and 679 is an equivalent
stress parameter for a tandem axle. So the
number on the left that is 825 in this case
is for single axle and the number on the right
that is 679 in this case is for a tandem axle.
This table is for a case where no concrete
shoulder is used but a similar table is available
for pavement with concrete shoulder.
These stress analysis tables were developed
using a finite element program JSLAB for the
following data:
• Modulus value of concrete was considered
to be 4 into 10 to power of 6 psi
• Poisson ratio is taken as 0.15
• For dowel bar that were considered the
dowel bar dia was taken as 0.5 inches
• The dowel spacing was 12 inches
• Modulus of dowel support was taken as
2 into 10 to power of 6 pci
• Spring constants were used to model the
aggregate interlocking and similarly spring
constants were also used to model the joint
between the shoulder and
• The main slab through this tied concrete
shoulder so these are the spring constants
that are used 5000 psi and 25000 psi.
The equivalent stresses shown in the tables
are edge stresses multiplied by 0.894. This
is to account for the portion of loads placed
close to the edge. So it's assumed we are
considering only those loads which are going
to be placed close to the edge so to account
for that the stresses are already multiplied
by a factor of 0.894.
Edge design is considered to be critical and
the stresses that are computed are for edge
design.
The single axle considered is 18 kip and tandem
axle considered is 36 kip in this analysis.
These stresses are corresponding to 18 kip
single axle and 36 kip tandem axle.
The fatigue analysis proceeds like this; we
assume a trial thickness and determine equivalent
stress for single axle that is 18 kip axle
and tandem axle that is 36 kip axle. We determine
these from the tables for a given slab thickness
for a given k-value and for either single
axle or tandem axle as you have seen in the
previous slide we have equivalent stress values
available for both single and tandem axle
so we can select those values from those tables.
Next we compute stress ratio factor as the
ratio for equivalent stress to the design
MR. For the given concrete grade that you
have selected we know the modulus of rupture
value that is the flexural strength of concrete.
Once we know that we have already selected
the equivalent stress value from the table
so equivalent stress divided by modulus of
rupture gives us the stress ratio. Obviously
we will have one stress ratio value for single
axle because we have a different equivalent
stress value selected from the table for a
single axle.
Similarly we will have another value of stress
ratio for tandem axle because there is another
equivalent stress value that is obtained from
the table.
For modulus of rupture we use 28 days strength.
We estimate allowable repetitions Nf from
the following chart which will be shown in
the next slide. For allowable repetitions
falling outside the range of the chart it
is assumed that the allowable repetitions
are considered to be infinite.
This is the chart that we are going to use
to find out for a given axle load whether
single or tandem how many repetitions the
slab can sustain. So once you select a single
axle say 20 kip and as we have already worked
out what is the stress ratio of a factor for
single axle for the given pavement system
connect these two points extend it to meet
this line then this is the value which gives
us the allowable repetitions if this is the
load that is going to be applied repeatedly.
Similarly, for other single axles we can find
out what is the number of repetitions the
pavement can sustain so the same thing can
be done for tandem axle also. Therefore for
both single axle and tandem axle if you know
the axle load groups and their magnitudes
we can find out the corresponding allowable
number of repetitions using this chart.
Similar analysis can be done for erosion also.
We have tables available in PCA design procedure
for finding out erosion factors. Again these
are functions of slab thickness and the k-value
of the foundation. Here also we have different
erosion factors for single axle and then tandem
axle. You can see that the tandem axle factors
are larger than the values given for single
axle whereas in the case of stresses the stress
factors are more for single axle when compared
to the tandem axles. Here also we have tables
available for different types of shoulders.
Therefore like we have done in the case of
fatigue analysis we can carry out erosion
analysis also for a single axle load if you
know the magnitude so this will be connected
to the erosion factor that is selected from
the table connecting these two extending this
to meet the other line we will get the number
of repetitions the pavement can sustain before
it fails in erosion damage. So we can select
other magnitudes of single axle also connect
this to this, find out how many repetitions
it can sustain and a similar analysis can
be done for random axles also.
So if you have axle load spectrum available
different load groups for single axle the
number of repetitions of single axle that
are going to be expected these charts will
give us for fatigue analysis how many repetitions
of this load group are going to be permissible
if it's a single axle and similarly how many
repetitions of this particular load is going
to be acceptable if it is a tandem axle. We
know what repetitions are expected, we know
what repetitions are permitted so from this
we can calculate the cumulative damage.
Now let us take a design example.
The input data that we were considering is
this is a 4-lane interstate pavement with
doweled joints with no concrete shoulders
so we are not providing any concrete shoulders
here. We are providing a 6 inch thick untreated
sub-base on a subgrade having k of 100 pci,
modulus of rupture of concrete that is flexible
strength of concrete is 600 psi and the expected
load repetitions are given in the following
tables:
For single axle for different load groups
this is the frequency. For example, for the
load group having a midpoint value of axle
load of 30 tons there are going to be about
6000 repetitions. Similarly for a load group
having a midpoint of 16 tons we are going
to have about 450,000 repetitions. Similarly
axle load spectrum for tandem axles is also
given in the slide.
Starting with a trial thickness of about 10
inches for the 6 inches untreated sub-base
that we have provided let us assume we are
going to provide dowel joints there is no
concrete shoulder so the combined k-value
is selected from the charts that are available
from PCA as 140 pci, MR is given as 650 and
this being an important road we will select
a load safety factor of 1.2, the design period
let us consider to be 20 years.
For a slab thickness of 10 inches and combined
k-value of 140 pci equivalent stress this
being a case without shoulders for single
axle is 189 so the stress ratio is 189 divided
by 650 which is the flexural strength of the
concrete that is 0.291. Similarly, for tandem
axle the stress ratio is 0.272, the erosion
factors for the given case it is 2.53 for
single axle and 2.73 for tandem axle.
This table here shows both the fatigue and
erosion analysis due to single axle loads.
The axle load group is given here this is
multiplied by load safety factor 1.2. This
is the frequency that is expected as given
in the previous tables. So using the charts
that I have shown earlier these are the expected
or allowable repetitions for this load group.
For 30 it is 70000, for 28 it is 160,000 but
for smaller loads it is infinite. Similarly
it is for erosion analysis also so this is
the total fatigue life consumed by this load
group, 7.5% is the life consumed by 28 ton
load group and the smaller loads do not consume
any load.
Similarly you have 3%, 1% you can find out
what is the total fatigue life consumed by
the entire single axle load that are going
to be expected. Similarly for erosion analysis
these are the allowable repetitions obtained
from charts. This is the damage that is caused
by 30 ton axle load groups, 0.2 percentage
is the damage caused by 28 ton axle load groups
similarly this is the total damage caused
by all the single axle load groups; 20.07
and 2.525%.
Let us do a similar analysis for tandem axle
load groups also. Total fatigue damage that
is caused, none of the tandem axle load groups
are causing any fatigue damage but they are
causing more erosion damage as expected.
So the total fatigue damage caused by single
axle load groups and tandem axle load groups
is 20.07 + 0 that is a total of 20.07 which
is of course well below 100% and the total
erosion damage is 2.53 + 22.73 = 25.26 which
also is well below 100%. So obviously the
thickness that was selected is quite safe.
However, it is desirable that more trials
be made to reduce the slab thickness because
the slab is over safe in this case.
We will next deal with the American Association
of State Highway and Transport Officials design
method of designing concrete pavements.
We are referring to the guide for design of
pavement structures 1993 as discussed in the
case of design of flexible pavements using
AASHTO design procedure. This design procedure
is also based extensively on the findings
from AASHO road test which were conducted
in the 1950s. There was an interim guide published
in 1972, there is a revised guide in 1981
and there was another one in 1993. There is
a draft revision of 2002 version being discussed
at present.
But the salient features and the design features
that we are going to discuss in this lesson
will be those which are there in the 1993
version of AASHTO guidelines. There are number
of salient features that are incorporated
in these guidelines like reliability concept,
traffic consideration in terms of 18 kip standard
axle repetitions, to convert a given axle
load into 18 kip standard axle load repetitions
use of the equivalent axle load factors, then
measuring performance in terms of present
serviceability index and so on. We have discussed
earlier that present serviceability index
at a particular time is obtained from measurements
of roughness and distress which will be in
terms of cracking and patching.
So the AASHO road test equation for present
serviceability index for concrete pavements
is given as present serviceability index is
equal to 5.41 -- 1.71 log 1 + SV -- 0.09 multiplied
by C + P under root. We discussed about slope
variance in the lesson on design of flexible
pavements as per AASHTO procedure.
Slope variance gives us an indication of how
the longitudinal slope varies when it is measured
over a small base length of 9 inches. C is
the cracked area expressed in terms of square
feet per thousand square feet of paved area,
P is the patched area again expressed in terms
of square feet of patched area in terms of
thousand square feet of paved area.
The one thing that is different in this equation
compared to the one that we have used for
flexible pavements is that in flexible pavements
we have also used the parameter rutting. Obviously
these being concrete pavements we would not
consider rutting of concrete pavements.
This is the performance equation which is
the heart of design of concrete pavements
using AASHTO procedure. As you can see here
the number of repetitions which is expressed
in terms of standard axle load repetitions
is expressed as a function of all the pavement
parameters and the reliability parameters.
Let us have a look at this equation. we will
have the explanation of what all these expressions
or parameters stand for; log W18 = ZR into
So and we have another expression in terms
of D which is the thickness of the slab and
another expression in terms of delta PSI loss
in serviceability and another expression in
terms of D thickness of slab, another expression
in terms of terminal serviceability index,
expressions in terms of Sc which is the parameter
of concrete, Cd drainage coefficient which
reflects the drainage conditions thickness
of slab, J is the parameter representing the
joint efficiency low transfer mechanism, D
thickness of slab, E modulus value of concrete
and k modulus of subgrade reaction.
So as you can see W18 is the function of thickness
of slab concrete modulus value, modulus of
subgrade reaction, concrete flexural strength,
drainage coefficient, low transfer efficiency,
reliability parameter and loss in serviceability
and of course terminal serviceability value
that we consider for designing a given pavement.
AASHTO performance equation:
• W18 is the number of 18 kip single axle
load repetitions to time t
• ZR is standard normal deviate which corresponds
to the level of reliability that we select
• So is the combined standard error of traffic
prediction and performance prediction
• D is the slab thickness expressed in inches
• delta psi is the drop in present serviceability
index starting from the time of construction
• Pt is the serviceability at time t
• Sc is the modulus of rupture of concrete
flexural strength of concrete
• Cd is the drainage coefficient which reflects
the drainage conditions that would be prevailing
• J is the load transfer coefficient
• Ec is the modulus of elasticity of concrete
and
• k is the modulus of subgrade reaction
expressed in terms of pci
The modulus of subgrade reaction k has to
be determined by conducting a plate load test.
It can also be estimated from the resilient
modulus value of a subgrade material if the
resilient modulus value is available. It can
be obtained as k = Mr by 19.4 where k is in
pci and Mr is in psi.
For combined foundations with sub-base placed
over subgrade AASHTO gives us charts using
which we can estimate the effective of equivalent
modulus of subgrade reaction for the combined
foundation. That can be done as a function
of k value of subgrade and thickness of the
sub-base and also the material quality of
the sub-base.
Elastic modulus value of concrete can be estimated
from its compressive strength using this expression.
These are the guidelines for selecting load
transfer coefficient J for different types
of shoulder and different types of asphalt
shoulder, tied PCC shoulder, different types
of presence or absence of load transfer device,
especially we were referring to presence or
absence of dowel bars whether they are present
or not present and also the type of slab such
as plain cement concrete, jointed reinforce
concrete, continuously reinforced concrete
pavement the corresponding load transfer coefficients
can be selected.
This is how we select the drainage coefficient.
This is similar to the drainage coefficient
that we have used in the case of flexible
pavement design as per AASHTO. This can be
selected as a function of percentage of timing
for which the foundation is going to be under
saturated condition in a year and also we
can find out how fast the water can be removed,
what are the drainage arrangements that can
be made depending on the rating that we can
give to the drainage facility that is available.
So accordingly you can select different values
of Cd depending on the conditions that we
have in a given situation.
Reliability: Obviously for different types
of facilities we go for different levels of
reliability. The overall standard deviation
which accounts for variability in materials,
variability in construction, variability in
prediction models can be selected as 0.34
if traffic projection errors are not considered
and 0.39 if traffic projections errors are
considered.
This is a nomograph that is available for
estimating the slab thickness. One can of
course solve the performance equation that
is given for any given inputs. One can find
out the thickness of the slab for a given
number of W18 by substituting all the other
parameters. But of course that has to be done
in an iterative fashion because D appears
at more than one place in that equation so
we have to select a trial thickness, compute
the W18 value substituting all the other input
parameters, check whether the W18 value compares
with the projected W18 value if not we will
change the thickness value and then redo the
calculations again. But using this nomograph
we can obtain it directly.
We will start with 
the effective modulus of subgrade reaction
k this is the combined k-value then these
different lines give you R for different modulus
of concrete value then from this we go up
to this select the concrete modulus value
raise this vertical line and this point will
be connected to a point which corresponds
to the concrete flexural strength so connect
these two points extend this to a line known
as transfer line or transition line TL, after
this we select a point on this line which
corresponds to the load transfer coefficient
J which we have already selected. So connecting
these two we extend it to another transfer
line TL and then you select another point
corresponding to drainage coefficient connect
these two points and extend it to meet a match
line, this is a match line because there is
another nomograph which will be matching with
this.
Hence starting from this match line we select
a loss in serviceability value delta psi connect
these two points let it meet this chart here
then we start with the selected reliability
value let us say 95% and then we also select
the standard deviation value So connect these
two points and then extend it, this meets
the transfer line here and from this point
we select the point which corresponds to W18
and then connect these points let it meet
here, so extend these two lines like this
and wherever these two lines meet that is
the thickness of the slab. In this case it
is coming out to be approximately around 9
inches. One can solve the equation or one
can also use this nomograph to easily find
out the thickness of the slab.
Here is the design example. You have to design
a concrete slab for the following inputs:
K effective is 100 pci, Ec is 5 into 10 to
the power 6 psi, Sc is 650 psi J is 3.2 for
the given conditions, Cd is 1.0, Pt is 2.5,
delta PSI is 2.0, reliability selected is
95%, So is 0.32, W18 for which we have to
design is 10 millions 10 into 10 to the power
of 6. Solving the performance equation by
trial and error the slab thickness worked
out to be 10.5 inches. The thickness can also
be obtained using nomographs.
Let us take a few questions from this lesson.
1) What are the main differences in terms
of failure or performance models considered
in PCA and AASHTO Designs?
2) Which are the critical regions for a half
slab to be considered for fatigue and erosion
damage analysis?
3) Do PCA and AASHTO consider thermal that
is curling stresses in the design of jointed
concrete slabs?
Let us consider the answer to the questions
we have asked in lesson 4.15 which was on
design of concrete pavements as per Indian
Roads Congress guidelines IRC: 58 -- 2002.
1) How to estimate the modulus of subgrade
reaction of a concrete pavement? This is with
reference to IRC: 58. We know that the modulus
of subgrade reaction of concrete pavement
has to be determined by connecting a plate
load test in a particular season which corresponds
to the worst season of the year using the
750 mm dia plate. But if this cannot be done
this value of modulus of subgrade reaction
of foundation can be obtained if we know the
CBR value of the subgrade.
So IRC: 58 gives us guidelines to select the
k-value of modulus of subgrade reaction from
its CBR value. On the other hand if you also
have a sub-base placed over subgrade the combined
k-value also can be estimated if you know
the k-value of the subgrade and also if you
know the thickness of the sub-base that is
going to be placed. So IRC: 58 also gives
us guidelines as how to select an appropriate
equivalent combined k-value for both the layers
together.
2) Why is the separation membrane provided
between the slab and the sub-base?
If you have understood the procedures that
were discussed for PCA and IRC: 58 design
procedure many concepts are similar. But PCA
does not recommend use of plastic sheet between
the sub-base and the slab which would make
it to be a smooth interface. It may not be
perfectly smooth but it will not be roughly
bounded. But IRC recommends that for the higher
pavements that we have a plastic sheet has
to be placed between the sub-base and the
slab. The reasons for this are the concern
for lot of shrinkage failures and cracks that
are occurring in concrete slabs because of
volumetric contraction and shrinkage. To prevent
that if you provide a smooth interface between
slab and the foundation the restrain that
is offered to the slab for its contraction
will be significantly reduced. So when the
slab is free to contract the stresses that
are going to be generated will be significantly
less so the possibility of cracking because
of contraction or shrinkage is going to be
reduced significantly.
3) What is the critical position of load considered
for design of concrete pavement as per IRC:
58?
Concrete pavement considers the edge position,
the wheel load has to be placed in the edge
region, this is considered to be the critical
position for wheel loads.
4) What is the need for using load safety
factor?
Because we know in the analysis we multiply
the load by a load safety factor of 1.2, 1.1
or 1.0 depending on the importance of the
facility. If you are using a load safety factor
of 1.2 then we are trying to build in more
safety into the consideration, we are also
trying to take care of those unexpectedly
high loads that may come because we are trying
to consider only the 98th percentile speed
98 percentile wheel load, thank you
