Flexible pavements have negligible or low flexural strength. They are flexible under the action of loads. There are several empirical, semi-empirical, and theoretical methods to design a flexible pavement. In this blog, some of the important methods for designing a flexible pavement are explained.

## Flexible Pavement

Before we get into flexible pavement design, it is important to get familiarised with various aspects of flexible pavement. As said, the flexible pavement has little to no flexural strength, and they showcase flexible structural action under the action of loads. If the lower layer of the flexible pavement is undulated, it is reflected back to the surface layer as deformations.

### Flexible Pavement Layers

Typically, flexible pavement consists of four layers as listed below.

Soil subgrade

Sub-base course

Base course

Surface course

### Load Transfer in a Flexible Pavement

The flexible pavement transfers the vertical compressive vehicular road by grain to grain transfer through the points of contact to its lower layers.

The compressive stress is maximum on the surface and is equal to the contact pressure under the wheel. As we go down to the next layers, the stress is spread out in the shape of a truncated cone and hence the lower layers have to withstand only lesser stresses.

Because of this ability to spread out and lower the stresses, only the surface course should be made of high-quality material to withstand high compressive stress and wear & tear by vehicular traffic. The lower layers can be made using lower quality materials as they need to withstand lesser stresses only and there is no vehicular motion.

Bituminous concrete is one of the best flexible pavement materials. Other materials like crushed aggregates, gravel, soil-aggregate mixture, etc. are used in other layers of flexible pavement.

## Flexible Pavement Design

Below given is the list of methods available for designing a flexible pavement.

Empirical method

California bearing ration method (CBR)

Mcleod method

Group index method

Semi-empirical method

Triaxial test method

Theoretical method

Mr. Burmester method

Out of these, empirical methods are the most commonly used methods for designing a flexible pavement.

Group Index Method

A group index is an arbitrary value assigned to soil types based on percent fines, liquid limit, and plasticity index. The GI value is given as,

GI = 0.2a + 0.005ac + 0.01bd

where,

a - that portion of material passing 0.074mm sieve, greater than 35 and not exceeding 75 percent (expressed as whole number 0 to 40)

b - that portion of material passing 0.074mm sieve greater than 15 and not exceeding 35 percent (expressed as whole number 0 to 40)

c - that value of liquid limit in excess of 40 and less than 60 (expressed as whole number 0 to 20)

d - that value of plasticity index exceeding 10 and not more than 30 (expressed as a whole number from 0 to 20)

GI values of soil vary from 0 to 20. The higher the GI value, the weaker is the soil, and for a given traffic load, the greater the pavement thickness required.

Design steps

GI value of the soil is found

Vehicular traffic is g=found and grouped as shown below

The total thickness of pavement (surface, base, and sub-base) is found using the group index chart corresponding to the GI value

## California Bearing Ratio Method

### California Bearing Ratio Test (CBR Test)

Before getting into the details of CBR design it is important to know about the CBR test. The procedure followed in a CBR test is shown below.

The diameter of the CBR mould is 150 mm with a height of 130mm

The specimen of soil subgrade is placed in the mould and a plunger of 50mm diameter is kept on the top surface. It is allowed to penetrate into the specimen

The rate of penetration is 1.25mm per minute

Load is applied for the plunger to penetrate and the load at which penetration is 2.5mm is noted

Further load is applied to reach a penetration of 5mm and the load causing this penetration is noted

The specimen is removed and a standard broken aggregate is filled in the mould

Procedure 4 to 5 is repeated for this standard aggregate and corresponding values are noted.

The standard pressure required for 2.5mm & 5mm penetration for standard aggregate is 70 kg/cm^2 and 105 kg/cm^2 respectively.

The ratio between load or pressure sustained by the specimen at 2.5 mm penetration and load or pressure sustained by the standard aggregate at 2.5 mm penetration is found.

Similarly, the ratio between load or pressure sustained by the specimen at 5 mm penetration and load or pressure sustained by the standard aggregate at 5 mm penetration is found.

The greater of these two ratios is taken as the CBR value of the soil subgrade specimen. Generally, the ratio based on 2.5 mm penetration is higher and is taken as the CBR value.

### CBR Method Concept

This method is based on design charts that are prepared by the California state highway department after performing extensive CBR tests on existing highways. The basis of the design chart is that a material with a given CBR required a certain thickness of pavement layer as cover for a given vehicular load.

### Pavement Thickness Determination by CBR method

First, the soaked CBR value of the soil subgrade is found

An appropriate design curve is chosen by considering the design wheel load

From the chart, for the chosen design curve, the total thickness of pavement required to cover the soil subgrade can be found

To know the thickness of the sub-base course, CBR of the sub-base course is found and by using the same design curve, the total thickness of the pavement required above the sub-base is found. The thickness of the sub-base could be found as the difference between the total pavement thickness and thickness of pavement required above the sub-base.

Similarly, the thickness of all the layers of flexible pavement could be found

## IRC Recommendations for CBR Method

There are two methods recommended by the Indian Road Congress for the design of flexible pavements using the CBR method as listed below.

Based on the number of vehicles

Based on the cumulative standard axle

But the recommendations remain the same for both of these methods as mentioned below. IRC has recommended a CBR design chart for use in India. IRC has also recommended some points on using the CBR method of design which are listed as follows.

The CBR test should be performed on remoulded soils in the lab only

The subgrade soil should be compacted according to Proctor's method at optimum moisture content

For the construction of flexible pavement in heavy rainfall zone, the soil specimen must be soaked in water before testing

The top 50 cm of the subgrade should be compacted to at least 95% of proctor density

At least three samples of the same material and density should be tested. The maximum permissible variation for various CBR values is given below. If the variation is more for the same sample, then six samples must be tested.

The thickness of the wearing course should not be counted in total pavement thickness as they don't serve any structural functionality.

CBR | Error or Variation |

10% | 3% |

30% | 5% |

60% | 10% |

### IRC Method based on Number of Vehicles

An estimate of the traffic must be found at the end of the expected life using existing traffic conditions and probable growth. It is found as,

A = P * [(1+r)^(n+10)]

where,

A - design number of heavy vehicles per day (laden weight > 3 tons)

P - present number of vehicles

r - the rate of growth of vehicles (generally 7.5%)

n - number of years between the last count of traffic and estimated construction completion

10 - represents the design life of the highway

Note:

The design is based on the number of heavy vehicular movements per day. Based on this, the design chart has seven design curves from A to G. Number of vehicles associated with each curve is given in the table below.

Curve Designation | Number of vehicles per day (weight>3 tons) |

A | 0 - 15 |

B | 15 - 45 |

C | 45 - 150 |

D | 150 - 450 |

E | 450 - 1500 |

F | 1500 - 4500 |

G | >4500 |

### IRC Method Based on Cumulative Standard Axle

This is the revised method suggested by IRC and is most commonly used nowadays for flexible pavement design. Instead of the number of vehicles per day, cumulative standard axle load is found. The revised design charts now contain seven curves categorized based on CBR value with the cumulative standard axle on the x-axis and total pavement thickness on the y-axis.

#### Cumulative standard axle

Also called the million standard axles (MSA), it is the total number of standard axles ruing on the flexible pavement during the life of the flexible pavement. It is given as,

MSA = (A * 365 * [(((1+r)^n) - 1) / r] * VDF * LDF) / (10^6)

where,

A - present number of commercial vehicles per day

r - the rate of growth of commercial vehicles (7.5%)

n - the life of flexible pavement (10 to 20 years)

VDF - vehicle damage factor

LDF - lane distribution factor

For single lane, LDF = 1

For double lane, LDF = 0.75

For four lane, LDF = 0.4

VDF = ((V1 * (Wa1/Ws)) + (V2 * (Wa2/Ws)) + (V3 * (Wa3/Ws)) + ...) / (V1 + V2 + V3 + ...)

where,

Vi - the percentage of 'I type' of vehicle

Wai - the weight of that 'I type' vehicle

Ws - 8.2 tons (standard)

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