1. RIGID
PAVEMENTS
R AV I K U M A R G A R R E

2. RIGID PAVEMENT
• The pavements which possess flexural
strength, are called as rigid pavements.
• The rigid pavements are generally made of
Portland cement concrete and some times
called as ‘CC Pavements’.
• The cement concrete used for rigid
pavements is called as ‘Pavement Quality
Concrete (PQC)’.
• The CC pavement slabs made of PQC are
generally expected to sustain up to 45kg/𝑐𝑚2
of flexural stresses.
• The rigid or CC pavements are designed and
constructed for a design life of 30 years.

3. WHERE RIGID PAVEMENT NEEDED?
• Rigid pavements are usually provided
under the circumstances:
 Very heavy rainfall
 Poor soil conditions
 Poor drainage
 Extreme climatic conditions
 Combination of some of these
conditions which may lead to
development of cracks in
pavements.

4. STRUCTURE OF RIGID PAVEMENT

5. COMPONENTS OF RIGID PAVEMENTS
• The components of rigid
pavement from bottom to
top consists of
Soil subgrade
Granular sub-base
course
Base course
CC/PQC pavement slab

6. SUBGRADE SOIL
• The subgrade soil of rigid pavements
consists of natural or selected soil from
identified locations fulfilling specified
requirements.
• Should contain require density and other
engineering properties.
• Subgrade ultimately supports all layers of
rigid pavement and traffic loads.
• The compressive stresses transmitting to
subgrade are very low.
• No need to consider allowable vertical
strains.

7. SUBGRADE
• The strength of soil subgrade is generally
evaluated by adopting plate load test.
• Relatively using a large diameter plate.
• The load supporting capacity of the
subgrade is assessed in terms of modulus
of subgrade reaction, K.
• Modulus of subgrade reaction, K may be
defined as the pressure sustained per unit
deformation of subgrade at specified
deformation or penetration, using specified
plate size (75cm).
• But for highway pavements, plate of 30cm
is used

8. GRANULAR SUB & DRAINAGE LAYER
• The granular sub-base course (GSB) serve as
drainage layer.
• To prevent early failures due to excessive
moisture in the subgrade soil.
• Crushed stone aggregates are preferred in
the granular sub-base course, contains high
permeability.
• Coarse graded aggregates with low % of
fines (<5.0% finer than 0.075mm size) will
serve as a good drainage layer.

9. DRAINAGE LAYER
An effective drainage layer under the
CC pavement has the following
benefits:
 Increase in service life and
improved performance of the CC
pavements
 Prevention of early failures of the
rigid pavement due to pumping
and blowing
 Protection of the subgrade
against frost action in frost
susceptible areas.

10. BASE COURSE
• The granular base course is generally
provided under the CC pavement slab.
• Base course provide in low volume roads
and in roads with moderate traffic.
• Roads carrying heavy to very heavy traffic
loads, high quality base course material
required.
• DLC: Lean cement concrete or dry lean
concrete.
• The DLC layer provides a uniform support,
high K value and
• An excellent working platform for laying
PQC.

11. PQC PAVEMENT SLAB
• M-40 cement concrete mix with a minimum
flexural strength of 45 kg/𝑐𝑚2 is to be used.
• The CC pavement slab should withstand the
flexural stresses caused by
1) Heavy traffic loads
2) Wrapping effects due to temperature
• High quality CC mix with high flexural
strength is used for the construction of the
PQC slab.
• Using steel reinforcement is not to bear
flexural/ tensile stresses developed.

12. RIGID PAVEMENT
 Subgrade
 Sub-base
 Base
 Separation layer
 PQC pavement
 Joints in CC pavements
A separation layer consisting of a
suitable type of membrane is laid over the DLC
base course before laying PQC slab in order to
prevent bonding between two.

13. COMPONENTS OF RIGID PAVEMENT

14. JOINTS IN RIGID PAVEMENT
• Joints are important components in
CC pavements and they have
important functions to perform.
• Main purpose of joints is to relieve
part of the stresses developed due to
the temperature variations in the
slabs.
• The joints in CC pavements are:
a) Longitudinal joints
b) Transverse joints

15. LONGITUDINAL JOINTS
• In pavements of width of 4.5m, there is a
need to provide a longitudinal joint.
• The need of these longitudinal joints is to
prevent the shrinkage cracks, happening
during the initial period of curing.
• However, as the lane of width is generally
3.5m to 3.75m, longitudinal joints provided
between each traffic lane.
Note:
Shrinkage cracks develop in slabs whose
width or length is more than 4.5 to 5m.

16. LONGITUDINAL JOINTS
• Tie bars are provided along the
longitudinal joints, in order to
prevent opening up of the
longitudinal joints in due course.
• These tie bars of specified diameter
and length are embedded at the
specified spacing, at the mid depth
of the pavement slab.

17. FUNCTIONS OF LONGITUDINAL JOINTS
• The longitudinal joints function as:
a) Contraction joints and prevent
development of additional
shrinkage cracks in the longitudinal
directions
b) Warping joints and relieve part of
warping stresses
c) Lane markings in highways with
two or more lanes

18. TRANSVERSE JOINTS
• The transverse joints are
subdivided into three
categories, based on their
purpose:
a) Contraction joints
b) Expansion joints
c) Construction joints

19. CONTRACTION JOINTS
• Contraction joints are formed by cutting
grooves across the pavement slab at regular
intervals.
• Width of grooves – not less than 3mm
• Depth of grooves – 25 to 30% of pavement
thickness
• Spacing of two contraction joints – 4 to 5m.
• The shrinkage cracks formed below the each
groove at the weekend section, during the
initial period of curing.
• Any how, shrinkage cracks formed at regular
intervals, to prevent those cracks, contraction
joints were provided.

20. CONTRACTION JOINTS
• Any how, shrinkage cracks developed
along these predetermined sections
only.
• In order to prevent widening of these
fine shrinkage cracks, steel
reinforcement may be provided across
the contraction joints.
• If no reinforcement provided across
the contraction joints, such a
pavement is – ‘pain jointed concrete
pavement’.
• Closely spaced contraction joints help
to relieve part of the warping stresses
developed.

21. EXPANSION JOINTS
• CC pavement slabs, during the summer
get expanded & during winter gets
contracted.
• To accommodate these variations in
length, expansion joints are provided in
transverse pavement at long intervals.
• The expansion joints are formed as
through joints across the full depth of the
slab with about 20mm gap between the
two slabs.
• The expansion joints provided after a
number of contraction joints

22. EXPANSION JOINTS
• The CC pavement slab is separated
across the expansion joint,
therefore there is no load transfer
across the expansion joint.
• Week cross section of the CC
pavement.
• In order to strengthen these
sections and to provide load
transfer across the expansion joint,
suitable dowel bars are designed
and installed during construction.

23. CONSTRUCTION JOINTS
• Construction joints formed due to gaps between the
continuous construction works.
• During the construction of CC pavements when the
concreting work is stopped at the end of the day,
the concrete paving is suspended, a construction
joint is formed.
• Construction joints formed across the pavement,
about full depth.
• It is necessary to provide dowel bars across these
joints for load transfer.
• It is better to make a construction joint as expansion
joint or contraction joint, if possible.

24. COMPONENTS OF RIGID PAVEMENT

25. FACTORS AFFECTING OF RIGID
PAVEMENT
• The factors which affect the design and performance of rigid pavement or CC
pavements are listed below:
a) Wheel load
b) Temperature variations at the location of the road
c) Types of joints and their spacing
d) Sub-grade and other supporting layers

26. FACTORS AFFECTING DESIGN
• The two major factors primarily to be
considered for the design of rigid
pavement are:
a) Heavy traffic loads
b) Temperature variation between
top and bottom of the CC
pavement slab
• The other factors which affect the
design and performance of rigid
pavements are,
a) Temperature stresses due to
expansion and contraction of
rigid pavement during summer
and winter
b) Volumetric changes in subgrade
due to changes in moisture and
temperature
c) Loss of subgrade support due to
some reasons at some locations

27. WHEEL LOAD
• The performance of rigid pavement and
its service life depends on the actual
magnitude of the heaviest wheel loads
of vehicles and their number of
repetitions during the design life.
• The wheel loads of highest magnitude
cause, flexural stresses in rigid pavement.
• The important factors associated with
wheel loads are:
a) Magnitude of load/ contact
pressure of loaded area
b) Location of the loading on the CC
pavement slab
c) Repetitions of loads of different
magnitudes during the design life

28. MAGNITUDE OF LOAD
• The magnitude of wheel load directly
affects the stresses in CC pavement.
• Higher the magnitude of wheel load will
cause higher stress in pavement.
• The wheel load expressed in terms of
the following:
a) Total load, P (Kg)
b) Contact pressure, p (Kg/𝑐𝑚2)
c) Contact area, A (𝑐𝑚2
) = 𝜋𝑎2
𝑝
where, a = radius of
equivalent circular area of contact
• Assume that the wheel loads acts on
circular contact area.

29. LOCATION OF LOAD APPLICATION ON SLAB
• The load stresses on slab are vary depending upon the location on which the
wheel load acts.
• Following three locations are considered in the analysis and design of CC
pavements:
a) Interior load, ‘i’ applied at a location away from the edges of the slab
b) Corner load, ‘c’ applied at the corner region of the slab
c) Edge load, ‘e’ applied at the edge region of the slab
• The magnitude of stress due to a given wheel load applied at the corner region
is the highest in comparison to the stresses due to the same load applied at the
edge or interior region of a CC pavement.
• The load stress applied at the interior region of a CC pavement, away from the
edges is found to be the lowest in comparison to the stresses due to same load
applied at the edge and corner regions of the pavement.

30. REPETITIONS OF LOADS
• The repeated application of light loads do not cause any structural deterioration to
roads. Therefore it is essential to measure the loads of higher magnitude which could
cause significant stress levels in the rigid pavement.
• For design of rigid pavement, it is essential to
a) Estimate the actual magnitude of heavier groups of axle or wheel loads
b) Determine the flexural stresses developed due to these heavy loads
c) Estimate the number of repetitions of each load group to use the road during
the design life
• Repeated application of high magnitudes of stresses are, to cause failures due to
fatigue in CC pavement structures.
• The plain CC specimens or slabs can withstand against number of repetitions of load
to cause stresses, if the magnitude of applied stress is less than 44% of its flexural
strength.

31. STRESS RATIO
• The ratio of flexural stresses due to
a load applied on a CC pavement
to its flexural strength is called the
‘stress ratio’.
• From the fatigue studies on CC
pavements, number of repetitions
up to fatigue failure, have been
determined by using various values
stress ratio between 0.45 to 0.90.
• While designing a CC pavement, if
stress ratio is less than 0.44, there
is no possibility of fatigue failure.

32. STRESS RATIO
IMPORTANCE OF DESIGN LOAD
• The repeated application of any
loads of magnitude less than design
load would cause, lower stress
ratios.
• Hence, there will be no structural
deterioration of the pavement due
to these loads.
• The design wheel load should be
carefully decided taking into
account wheel load distribution
studies and the expected no. of
repetition of loads of different
magnitudes during the design life of
• The movement of even a small
number excessively over loaded
vehicles with higher magnitude of
loads than the design load, can
develop tensile cracks at some
locations of the CC slab.
• It is suggested that, axle load
studies should be conducted on
heavy vehicles in order to arrive at
the design axle load.
• It is necessary to estimate the
possible movement of over loaded
vehicles with loads exceeding the

33. AXLE LOAD DISTRIBUTION STUDIES
• Axle load or wheel load distribution studies are carried out on the
selected heavy vehicles, that actually moving on the existing roads.
• It is also desirable to note the wheel base or spacing between the axles
of the heavy commercial vehicles (HCV).
• The objectives of the study are
a) To arrive at the design load
b) To assess the effect of repeated application of stresses due to
loads that are heavier than the selected design load which cause
stress ratios exceeding 0.44 and the number of repetitions of
such heavier loads expected during the design life.
• These data are necessary at the design stage for the fatigue analysis.

34. DETERMINATION OF DESIGN LOAD
• First of all complete the measurement of axle/ wheel loads on the
selected samples of heavy vehicles (with single, tandem and multiple
axles) at the identified locations.
• Axle load distribution table is prepared, by groping the loads at
convenient load intervals or ranges.
• The average of each load group is taken as the magnitude of the
applied load and the expected no. of repetitions of the vehicles of each
range during the design life is estimated.
• The total number of axle loads of each interval noted during project
preparation studies are noted as the initial traffic.

35. CONTD.,
• Considering the different vehicle classes, their growth rate, construction
period and design life of the CC pavement, the total number of
repetition of loads of each group load during design life of the CC
pavement are estimated.
• Based on the above data, the cumulative frequency distribution table or
diagram (representing load values and the total number of repetitions
during design life) is prepared.
• From this table or diagram, 98th percentile load (which will be exceeded
by only by 2.0%) may be taken as the ‘Design load’.
• It is also desirable to consider a ‘load safety factor’ of about 1.2 to
account for the possibility of further over loading of the heavy vehicles.

36. DAILY VARIATION IN TEMPERATURE
• The daily variation in atmospheric
temperature causes difference in
temperature between the top and
bottom of the CC pavement slab. This
results in warping of slab and
development of flexural stresses.

37. TEMPERATURE DURING DAY
• The temperature difference between
the top and bottom of the CC
pavement results in differential
expansion the slab causing it to warp
or bend.
• The temperature difference during day
is given by:
𝑡0C = (𝑡1 − 𝑡2)0C
where,
𝑡1= maximum temperature at top of the
pavement during day
𝑡2 = the temperature at the bottom of
the pavement during night

38. TEMPERATURE DURING NIGHT
• At late night top of the slab becomes
colder resulting in warping of the slab.
• The temperature difference during day
is given by:
𝑡0
C = (𝑡1 − 𝑡2)0
C
where,
𝑡1= minimum temperature at top of the
pavement during night
𝑡2 = the corresponding temperature at
the bottom of the pavement during
night

39. NO WARPING CONDITION
• During the two short durations
with in 24 hours, the
temperatures at top and bottom
of the slabs are equal, no
warping will takes place.
• This stage of the CC pavement
is called as ‘no warping
condition’ of the pavement.

40. STRESSES IN RIGID PAVEMENT
• Different types of stresses developed in CC pavements. The major types of stresses in
CC pavements consists of:
a) Wheel load stresses caused by heavy wheel loads
b) Warping stresses caused by temperature differential between the top and
bottom of the pavement.
• It is possible to determine the stresses developed due to wheel loads, warping and
contraction of CC slab and it not possible estimate the magnitude of stresses as result
of volumetric changes in subgrade.

41. WHEEL LOAD STRESSES
• Westergaard gave theoretical formulae to determine the stresses caused due
to wheel load applying on the rigid pavements.
• For this he carried out the following assumptions on rigid pavements:
a) Cement concrete slab is homogeneous
b) It is thin plastic plate
c) The subgrade reaction being vertical and proportional to the deflection
• Westergaard’s equations for stresses due to wheel load applied at the three
critical locations of interior, edge and corner as given below:

42. CONTD.,
• Load stress, Si due to interior loading,
Si =
0.316 P
h2 4log10(l
b) + 1.069
• Load stress, Se due to edge loading,
Se =
0.572 P
h2 4log10(l
b) + 0.359
• Load stress, Sc due to corner loading,
Sc =
3𝑃
ℎ2 1 −
𝑎 2
𝑙
0.6
Here,
h = slab thickness, cm
P = Wheel load, kg
a = radius of wheel load distribution, cm
l = radius of relative stiffness, cm
b = radius of resisting section

43. CONTD.,
• Maximum stress produced by a wheel at corner does not exist around the load, but it
occurs at some distance X along the diagonal. This distance X from the corner is given
by the relation
X = 2.58 𝑎𝑙
Here,
X = distance from apex of slab corner to section of maximum stress along the
corner bisector or diagonal, cm
a = radius of wheel load distribution, cm
l = radius of relative stiffness, cm

44. CONTD.,
Radius of relative stiffness:
• Westergaard defined, ‘radius of relative stiffness’, l which is expressed by the equation,
l =
𝐸ℎ3
12𝐾 1−µ2
1/4
Here,
l = radius of relative stiffness, cm
h = slab thickness, cm
E = modulus of elasticity of cement concrete, kg/cm2
µ = Poisson’s ratio for concrete = 0.15
K = modulus of subgrade reaction, kg/cm3

45. CONTD.,
Equivalent radius of resisting section:
• According to Westergaard, the equivalent radius of resisting section is approximated,
in terms of radius of load distribution and slab thickness,
b = 1.6a2 + h2 −0.675h
Here,
b = equivalent radius of resisting section, cm when ‘a’ is less than 1.724h
a = radius of wheel load distribution, cm
h = slab thickness, cm
When ‘a’ is greater than 1.724h, b = a

46. TEMPERATURE STRESSES
• Two types of stresses are produced due to temperature variations in
concrete pavements:
a) Warping stresses due to temperature differential between the
top and bottom of the pavement as a result of daily variation in
temperature at the location and
b) Frictional stresses due to over all increase or decrease in
temperature of the pavement slab as a result of seasonal variation
in temperature at the location

47. WARPING STRESSES
• Warping stress at interior, 𝑆𝑡(𝑖) is given by,
𝑺𝒕(𝒊) =
𝑬𝒆𝒕
𝟐
𝑪 𝒙+µ𝑪 𝒚
𝟏−µ 𝟐
• Warping stresses at the edge, 𝑆𝑡(𝑒) is given by,
𝑺𝒕(𝒆) =
𝑪 𝒙 𝑬𝒆𝒕
𝟐
or
𝑪 𝒚 𝑬𝒆𝒕
𝟐
(whichever is higher)
• Warping stresses at corner, 𝑆𝑡(𝑐) is given by,
𝑺𝒕(𝒄) =
𝑬𝒆𝒕
𝟑(𝟏−µ)
𝒂
𝒍

48. CONTD.,
Here,
E = modulus of elasticity of concrete
e = thermal coefficient of concrete per degree centigradeType equation here.
t = temperature differential between the top and bottom of the slab
µ = Poisson’s ratio of cement concrete
𝐶 𝑥 = coefficient in direction X which depends on the ratio,
𝐿 𝑥
𝑙
𝐶 𝑦 = coefficient in direction Y which depends on the ratio,
𝐿 𝑦
𝑙

49. FRICTIONAL STRESSES
𝑆𝑓 = 𝑊𝐿 𝑐 𝑓 / 2 × 104
Here,
𝑠𝑓 = stress developed due to inter-face friction in cement concrete pavement per
unit area, kg/cm2
W = unit weight of concrete (about 2400 kg/cm3)
f = coefficient of friction at the interface (maximum value is about 1.5)
Lc = spacing between the contraction joint = slab length, m
B = slab width

50. DESIGN OF RIGID PAVEMENT
• The design wheel load is first decided on relevant axle load studies and analysis.
• Based on the locality where the pavement is to be constructed, the temperature
differentials for pavement thicknesses are estimated.
• The supporting layers of the rigid pavement such as subgrade, sub-base layer and
base course layers are decided and the subgrade modulus is either determined or
estimated.
• The spacing between the longitudinal joints, Lc to provided, during the initial period of
curing.
• A trial thickness of pavement is first assumed, the load and warping stress values at
pavement edge are determined using the appropriate stress equations. If total value of
stress exceed the permissible limit, the trial is repeated assuming a higher pavement
thickness.
• The factor of safety of the trial thickness of the pavement is worked out by taking the
ratio of flexural strength to flexural stresses.

51. CONTD.,
• Design life should be estimated.
• If the stress ratios exceeding 0.44 due to the higher loading are noted
and then fatigue analysis is carried out based on the number of
repetitions during the design life.
• If the assumed thickness is failed, the next trail is made after suitably
revising the thickness.
• The total of the edge load stress due to the heaviest load and the edge
warping stress on summer mid day is calculated, if the total thickness is
less than flexural strength of CC (45 kg/cm2), the design is accepted;
otherwise the thickness is further revised until the highest possible total
stress value does not exceed the flexural strength.