Types of Pavements, Layers present in the pavements, Stresses on the rigid pavements, wheel load, repetitions etc.. and Indian Standard Method of design of Rigid Pavements.

1. DESIGN OF RIGID
PAVEMENTS
PART- II

2. DESIGN OF SLAB THICKNESS
The Analysis of Stresses, the Design of SLAB THICKNESS and its protection
involves the following procedures.
a) Critical Stress Condition,
b) Calculation of Stresses
i. Edges Stresses,
ii. Stresses due to Temperature,
iii. Corner Stresses.
c) Design Charts,
d) Stress ratio and fatigue analysis,
e) Erosion consideration,
f) Hard Shoulder,
g) Composite Rigid Pavement,
h) Anchor Beam and Terminal Slab and
i) Recommended Design Procedure.

3. CRITICAL STRESS CONDITION
The Factors commonly considered for the design of Pavement
Thickness are.
a) Flexural Stresses due to TRAFFIC Loads,
b) Temperature differentials between top and
bottom of concrete slab.
c) The effect of moisture changes
The factors (a) and (b) additive and major,
The factor ( c) is opposite of Factor and very minor, hence
not considered in designing the Slab thickness.

4. CRITICAL STRESS CONDITION
The Concrete Pavement undergo a daily cyclic
change of temperature differential
During day TOP surface is hotter than BOTTOM
surface.
During night TOP surface is cooler than
BOTTOM surface.

5. Day time

6. WARPING STRESSES
• During day time the temperature of the top portion
of slab may be considerably greater than that of
bottom.
• The top portion of slab tends to expand more than
bottom portion.
• The resultant slab convex towards top as shown

7. • But the weight of slab resists the convex in concrete
slab resulting following section
WARPING STRESSES
• The fibers in top are in compression and those in
bottom are in tension.
• This condition is called “temperature wrapping
stresses” .
• This “temperature wrapping stresses” is very important
in design of cc pavement.

8. Night time

9. WARPING STRESSES
• DURING NIGHT

10. DESIGN OF SLAB THICKNESS
•The THREE different
regions recognized for
Pavement are
–1) SLAB INTERIOR
–2) SLAB EDGE
–3) SLAB CORNER

11. DESIGN OF SLAB THICKNESS
• Combination of critical Regions and Stresses
• i) Temperature stresses induced in pavement are
– A) Maximum @ Slab Interior
– B) Moderate @ Slab Edge and
– C) Negligible @ Slab Corner
ii) Load stresses induced in Pavement are
A) Negligible @ Slab Interior
B) Moderate @ Slab Edge and
C) Maximum @ Slab Corner

12. EDGE STRESSES
• Combination of critical Regions and Stresses
• i) Temperature stresses induced in pavement are
– A) Maximum @ Slab Interior
– B) Moderate @ Slab Edge and
– C) Negligible @ Slab Corner
ii) Load stresses induced in Pavement are
A) Negligible @ Slab Interior
B) Moderate @ Slab Edge and
C) Maximum @ Slab Corner

13. CALCULATION OFEDGE STRESSES
• The STRESS CHARTS
• Axles Loads for
Single Axle Loads of
6, 8, 10, 12, 14, 16, 18, 20, 22 and 24 T
Tandem Axles Loads of
12, 16, 20, 24, 28, 32, 36, 40, 42 and 44 T
• The SLAB THICKNESS for 14,16,18,20,22,24,26,28,30,32,34,36
cm.
• With k- values
6,8,10,15,30 kg/cum.cm
Are used to arrive the values of stresses for respective conditions.

14. STRESSES in RIGID PAVEMENTS – S.A.L. = 6.00 T

15. STRESSES in RIGID PAVEMENTS – S.A.L. = 8.00 T

16. STRESSES in RIGID PAVEMENTS – S.A.L. = 10.00 T

17. STRESSES in RIGID PAVEMENTS – S.A.L. = 12.00 T

18. STRESSES in RIGID PAVEMENTS – S.A.L. = 14.00 T

19. STRESSES in RIGID PAVEMENTS – S.A.L. = 16.00 T

20. STRESSES in RIGID PAVEMENTS – S.A.L. = 18.00 T

21. STRESSES in RIGID PAVEMENTS – S.A.L. = 20.00 T

22. STRESSES in RIGID PAVEMENTS – S.A.L. = 22.00 T

23. STRESSES in RIGID PAVEMENTS – S.A.L. = 24.00 T

24. STRESSES in RIGID PAVEMENTS – T.A.L. = 12.00 T

25. STRESSES in RIGID PAVEMENTS – T.A.L. = 16.00 T

26. STRESSES in RIGID PAVEMENTS – T.A.L. = 20.00 T

27. STRESSES in RIGID PAVEMENTS – T.A.L. = 24.00 T

28. STRESSES in RIGID PAVEMENTS – T.A.L. = 28.00 T

29. STRESSES in RIGID PAVEMENTS – T.A.L. = 32.00 T

30. STRESSES in RIGID PAVEMENTS – T.A.L. = 36.00 T

31. STRESSES in RIGID PAVEMENTS – T.A.L. = 40.00 T

32. STRESSES in RIGID PAVEMENTS – T.A.L. = 42.00 T

33. STRESSES in RIGID PAVEMENTS – T.A.L. = 44.00 T

34. Stresses due to Temperature
The Temperature stress at
the CRITICAL EDGE Region, Ste
2
*** CtE
ste


Ste= Edge Warping Stress
E= Elastic Modulus of Concrete ( kg/cm2)
t= ="Maximum temperature difference between top and bottom
of slab during day time
a= Coefficient of thermal expansion

35. Stresses due to Temperature
C= Bradbury’s coefficient of value of L/I and B/I
L= Slab length or spacing between adjacent contraction joints.
B= Slab width or spacing between longitudinal joints ,cm
I= Radius of relative stiffness, cm
u= Poisson’s ratio
H= Thickness of concrete slab , cm
k= Modulus of subgrade reaction, kg/cum.cm.

36. Stresses due to Temperature
Chart showing the Values of Brodbury’s Coefficient C

37. Stresses due to Temperature
Chart showing Edge Temperature stresses

38. CORNER STRESS DUE TO LOAD
Sc= Load stress in the corner region kg/ sqcm
P= Wheel Load, kg
a= Radius of equivalent contact area , cm
The Load stress in the corner region is obtained
from the following equation

39. Stress Ratio and Fatigues analysis
For a given slab thickness and other design parameters,
The Flexural stress at the EDGE due to the application of
Single or Tandem Axle Loads is obtained from the appropriate STRESS
CHART.
Stress Ratio
= Flexural Stress/ Flexural Strength of Concrete
From Stress Ratio, Fatigue Life (N)
= Allowable number of Repetitions (N) is obtained
Fatigue Damage
= Expected repetitions/ Allowable number of Repetitions
Fatigue damage for each different axle loads calculated.
CUMULATIVE FATIGUE DAMAGE
SHOULD BE LESS THAN OR EQUAL TO 1.000

40. DESIGN PRINCIPLE OF CC PAVEMENT
• STEP 1 ( DESIGN)
• The concrete slab thickness is DESIGNED to with stand
1) the stresses due to Warping and Wheel loads at EDGE REGION.
2) The Cumulative fatigue damage obtained and should be Less than or
equal to 1.00
• STEP 2 ( CHECK)
– The concrete slab is CHECKED to the stresses at CORNER REGION, if
the dowel bars are not provided at transverse joint and if there is no
possibility of load transfer by aggregate inter-lock

41. DESIGN PRINCIPLE OF CC PAVEMENT
• The above Principle of Design and Check
for worst conditions will seldom takes
place, hence the methodology is likely to
result in much higher life of the pavement
than considered.

42. CONCRETE
1) It is strong in Compression,
2) But it is weak in Tension,
3) Its volume increases with increase of
temperature and vise-versa,
4) It shrinks with decrease in moisture
content,
5) It expands with increase in moisture
content,
6) It cracks.

43. JOINTS AND JOINT SPACINGS
 Joints are installed in concrete pavements to control
stresses induced by volume changes in concrete.
 These Stresses may be produced in concrete slab
because of
 1) Its CONTRACTION due to uniform temperature drop or
decrease in moisture,
 2) Its EXPANSION due to uniform temperature increase,
 3) The effect of WRAPPING of pavement due to vertical
temperature or moisture differential in the slab.

44. CONTRACTION STRESSES
• When the “contraction” or “ movement” of
the slab is wholly or partially prevented
TENSILE stresses are developed.
• In a pavement, resistance to movement of
slab is caused by friction between bottom of
slab and the Sub-base.

45. EXPANSION STRESSES
• When the Long length of concrete slab
prevented from expansion the concrete slab
may “blow up” or buckle.
• In order to prevent blow ups, relief may be
provided by the installation transversal
expansion joints.

46. N.B. on EXPANSION STRESSES
The EXPANSION is prevented by friction between
slab and base.
The SHRIKAGE in concrete during hardening
compensates some of expansions.
The COMPRESSIVE strength of concrete is much
higher than the stresses created by preventing
this expansion.
Hence
The EXPANSION joints may either be provided at
greater interval or may be dispensed with.
.

47. JOINTS DESIGN
• The Stresses effecting the Rigid Pavements
are due to
1) Moisture changes,
2) Temperature changes and
3) Wheel loadings.
The stresses will be combined effect of some or
all of the above factors.

48. JOINTS DESIGN
• To control the stresses resulting from the
above,
• FOUR types of joints are commonly provided
for concrete pavements.
– 1) Transverse Contraction joints,
– 2) Transverse Expansion joints and
– 3) Transverse Construction joints,
– 4) Longitudinal joints.

49. 1)TRANVERSE CONTRACTION JOINTS
• These are “dummy” contraction joints.
• These joints control cracking of the slab,
• Also relieve he warping stresses in slab.
• These are weakened plain joints provided by creating
GROOVE of depth ¼ of Slab thickness.
• Dowel bars are provided in these joints if heavy vehicles
are expected on these roads

50. 1)TRANVERSE CONTRACTION JOINTS
• 3 METHODS OF PROVIDING THESE JOINTS
1. 1) By inserting 6x50 mm mastic pad or thermo coal while
concrete is green or
2. 2) by pressing with MS “T” Section at right time or
3. 3) by diamond cutting within 24 hours i.e., before inherent
contraction cracks are developed.

51. CONTRACTION JOINT
• These are dummy groove type.
• These are to be provided to guide (by creating weak
section) the inevitable cracks in rich mixed CC
wearing coat.

52. SPACING OF CONTRACTION JOINTS
SLAB THICKNESS
( cm )
Maximum
contraction joint
spacing (m)
Un reinforced
Slab
15 4.5
20 4.5
25 4.5
30 5.0
35 5.0

53. CRACKS & CONTRACTION JOINTS
C.C. ROAD WITH IMPROPER CONTRACTION JOINTS
C.C. ROAD WITH PROPER CONTRACTION JOINTS
C.C. ROAD WITHOUT CONTRACTION JOINTS

54. TYPICAL CONTRACTION JOINTS

55. 2)TRANVERSE EXPANSION JOINTS
These joints are full depth joints.
Width of these joints 19-25 mm.
Dowel bars are used in these joints if heavy
vehicles are expected on these roads.
If the contraction joints are provided as per
provisions made in, and the concrete does not
have unusual expansive qualities expansion
joints are spaced at a great interval ( 30-60m)

56. TYPICAL EXPANSION JOINTS

57. 3 )TRANSVERSE CONSTRUCTION JOINTS
These joints are placed at the end of days
work or when the work is suspended for
more than 30 minutes.
These joints are provided at the regular
location of contraction joints using Dowel
bars.

58. 4) LONGITUDINAL JOINTS
These joints run continuously along the
length of the Pavement.
These joints are provided when the width of
Pavement is more than 4.0 m.
These joints control the magnitude of
temperature warping stresses.
Tie bars are provided all along these joints to
arrest the movement of one slab w.r.t.
adjacent slabs.

59. DETAILS OF TIE BARS FOR LONGITUDINAL JOINT
OF TWO LANE RIGID PAVEMENTS
Slab
thickness
(cm)
Tie Bar Details
Diameter
(d) (m)
Max. Spacing (cm) Minimum Length (cm)
Plain bars Deformed
bars
Plain bars Deformed
bars
15 8 33 53 44 48
10 52 83 51 56
20 10 39 62 51 56
12 56 90 58 64
25 12 45 72 58 64
16 80 128 72 80
30 12 37 60 58 64
16 66 106 72 80
35 12 32 51 58 64
16 57 91 72 80

60. TYPICAL ARRENGEMENTS OF JOINTS

61. RECOMMENDED DIMENSIONS OF DOWEL BARS FOR
RIGID PAVEMENTS FOR AN AXILE LOAD OF 10.20 T
Slab
thickness
(cm)
Dowel bar details
Diamete
r (mm)
Length
(mm)
Spacing
(mm)
20 25 500 250
25 25 500 300
30 32 500 300
35 32 500 300

62. DESIGN OF SLAB THICKNESS
• The THREE different LOAD combinations
producing stresses for Pavement design are
– 1) Flexural stress due to TRAFFIC Loads,
– 2) Stress due Temperature Gradient and
– 3) Combination of Flexural stress and
Temperature stresses

63. DESIGN PARAMETES
• 1) Allowable Flexural Stress > 40 kg/sqcm
• 2) Elastic modulus of CC=300000 kg/sqcm.
• 3)Poisons ration of CC = 0.150
• 4) Coefficient of Thermal Expansion = 0.00001
• 5) Effective Modulus of Sub grade k-value),
• ( k- value >4 kg/sqcm/cm and < 30 kg/cucm)
• 6) Growth rate of Traffic = 7.50 %,

64. DESIGN PARAMETES
• 7) Traffic pattern in CVPD and Tonnage,
• Legal Axle Load for Single Axle = 10.20 T
• Legal Axle Load for Tandem Axle = 19.00 T
• Legal Axle Load for Tridem Axle = 24.00 T
• 8) Spacing of Contraction joint
• 9)Width of the Slab
• 10)Design Period,
• 11) Load safety factor
• Express ways & NH = 1.20
• State Highways & MDR = 1.10
• Residential roads = 1.00

65. DESIGN PARAMETES
• 12) Maximum temperature differential
of the Region.
• The Design is Trial and error Method

66. CHEMISTRY OF CEMENT & ENGINEERS REACTION

67. CEMENT CHEMISTRY(ACTION)

68. ENGINEERS REACTION

69. THANK YOU