1. Flexible pavement design
Flexible pavements are so named because the total pavement structure deflects, or flexes, under loading.
Design procedures
For flexible pavements, structural design is mainly concerned with determining appropriate layer thickness and composition.
The main design factors are stresses due to traffic load and temperature variations.
Two methods of flexible pavement structural design are : Empirical design and mechanistic empirical design.

2. Empirical design
An empirical approach is one which is based on the results of experimentation or experience.
CBR method is widely known and will be discussed.
Mechanistic-Empirical Design
Empirical-Mechanistic method of design is based on the mechanics of materials that relates input, such as wheel load, to an output or pavement response. In pavement design, the responses are the stresses, strains, and deflections within a pavement structure.

3. Traffic and Loading
Equivalent single wheel load
To carry maximum load with in the specified limit and to carry greater load, dual wheel, or dual tandem assembly is often used. Equivalent single wheel load (ESWL) is the single wheel load having the same contact pressure, which produces same value of maximum stress, deflection, tensile stress or contact pressure at the desired depth.

4. Boyd and Foster method
where P is the wheel load, S is the center to center distance between the two wheels, d is the clear distance between two wheels, and z is the desired depth.

6. Example 1
Find ESWL at depths of 5cm, 20cm and 40cm for a dual wheel carrying 2044 kg each. The center to center tyre spacing is 20cm and distance between the walls of the two tyres is 10cm.

7. Repetition of Loads
It is required to carry out traffic surveys for accounting the factor of repetition for wheel loads in the design of pavement. Such collected data are converted to some constant equivalent wheel loads. Equivalent wheel load accounting for repetition of load are those which require same thickness and strength of pavements.
If the pavement structure fails with N1 number of repetition of load W1 and for the same failure criteria if it requires N2 number of repetition of load W2, then W1N1 and W2N2 are considered equivalent.
An equivalent axle load factor (EALF) defines the damage per pass to a pavement by the ith type of axle relative to the damage per pass of a standard axle load.

8. McLeod has given a procedure for evolving equivalent load factors for designing flexible pavements.
McLeod assumes that the pavement thickness which are deigned for a given wheel load would support repetition of such load during the life of pavement. For one load application, the pavement thickness so required is only one fourth the pavement thickness designed for 106 load repetitions.

10. Wheel Load kg
Repetition to failure, Number
Equivalent to 2268 kg
Equivalent Load factors
2268
105000
1.0 1
2722
50000
2.1 2
3175
22500
4.7 4
3629
13000
8.2 8
4082
6500
16.3 16
4536
3300
32.0 32
4993
1700
61.76 62
5443
1000
105.0
105
Equivalent load factors are employed to convert daily traffic count for each category of wheel load for design purposes.

11. Example:
Calculate design repetitions for 20 year period for various wheel loads equivalent to 2268 kg wheel loads using the following traffic survey data on a four lane road.
Wheel Load kg
Average Daily Traffic
(both directions)
Percent of total traffic volume
Equivalent Load factors
2268
Total volume
(considering traffic growth)
215
13.17 1
2722
15.30 2
3175
11.76 4
3629
14.11 8
4082
6.21 16
4536
5.84 32

12. Design repetitions equivalent of 2268 kg wheel load per lane = /4
Wheel Load kg
A. D. T.
(both directions)
Percent for each load
Days/year
Number of years
Equivalent Load factors
Design repetitions equivalent of 2268 kg load 1 2 3 4 5 6
7=(2×3×4×5×6)
2268
215
13.17/100
365 20
2722
15.30/100
3175
11.76/100
3629
14.11/100 8
4082
6.21/100 16
4536
5.84/100 32
Total estimated repetitions (two directions) =
Design repetitions equivalent of 2268 kg wheel load per lane = /4

13. Design of Flexible Pavement by California Bearing Ratio Method:
Design curves correlating CBR value with total pavement thickness cover were developed by California State Highway Department for wheel loads of 3175 kg and 5443 kg representing light and heavy traffic. Later the design curve for 4082 k wheel load was obtained by interpolation for medium traffic.

14. CBR Testing Machine Definition:
It is the ratio of force per unit area required to penetrate a soil mass with standard circular piston at the rate of 1.25 mm/min. to that required for the corresponding penetration of a standard material.

15. Equipments For CBR Test
Cylindrical mould :
Inside dia 150 mm , height 175 mm,
detachable extension collar 50 mm height
detachable perforated base plate 10 mm thick. 
Spacer disc 148 mm in dia and 47.7 mm in height along with handle. 
Metal rammers. Weight 2.6 kg with a drop of 310 mm (or) weight 4.89 kg a drop 450 mm. 
Weights. One annular metal weight and several slotted weights weighing 2.5 kg each, 147 mm in dia, with a central hole 53 mm in diameter. 
Loading machine.
capacity of atleast 5000 kg , movable head or base that travels at an uniform rate of 1.25 mm/min.
 Metal penetration piston 50 mm dia and minimum of 100 mm in length. 
Two dial gauges reading to 0.01 mm. 
Sieves mm and 20 mm Sieves.

16. Penetration of plunger (mm)
Load vs Penetration
The standard loads adopted for different penetrations for the standard material with a C.B.R. value of 100%
Penetration of plunger (mm)
Standard load (kg)
2.5
5.0
7.5
10.0
12.5
1370
2055
2630
3180
3600

17. Permissible Variation in CBR Value
Maximum Variation in CBR Value 5
+_ 1
5-10
+_ 2
11-30
+_ 3
31 and above
+_ 4

19. Following figure shows different curves based on traffic volume
Following figure shows different curves based on traffic volume. This design chart is similar to the one followed in U.K.

20. It is possible to extend the CBR design curves for various loading conditions, using the following expression developed by U.S. Corps of Engineers:
However these expressions are applicable only when the CBR value of the sub-grade soil is less than 12 percent.
Here,
t = pavement thickness, cm
P = wheel load, kg
CBR = California Bearing Ratio, percent
p = tyre pressure, kg/cm2
A = area of contact, cm2

21. Determination of pavement thickness.
Example:
The CBR value of sub-grade soil is 5% calculate total thickness of pavement using:
(i) Design curve developed by California State Highway Department.
(ii) Design chart similar to the one followed in U.K.
(iii) Design formula developed by U.S. Corps of Engineers.
Assume 4100 kg wheel load or medium traffic or 200 commercial vehicles per day. Tyre pressure 6 kg/cm2.

22. Solution:
38cm
(ii) 37.5 cm
(iii)
t = 35.5 cm

23. Example:
Design the pavement section using CBR charts similar to the one used in U.K.CBR values and traffic details are as under:
(i) Soil sub grade with 4% CBR,
(ii) Compacted soil with 7% CBR,
(iii) Poorly graded gravel with 20% CBR,
(iv) Well graded gravel with 95% CBR,
(v) Minimum thickness of bituminous concrete surfacing may be taken as 5 cm.
(vi) Number of vehicles for design3260 veh/day.

24. Solution: Soil Sub-grade CBR = 4% 15 cm compacted Soil CBR = 7%
19 cm poorly graded gravel CBR = 20%
13 cm well graded gravel CBR = 95%
8 cm bituminous surfacing
21 cm
40 cm
55 cm

25. Example: Find out the total thickness of a flexible pavement to carry an average traffic of about 250vehicles exceeding 3 tonne loaded weight. The CBR value of the sub-grade is 4%. Assume the wheel load as 4100kg and tyre pressure as 6kg/cm2. Compare results as obtained by California State Highway charts and by U.S. Corps of Engineer formula.