A traffic survey conducted on a road yields an average daily traffic count of 5000 vehicles. The axle load distribution on the same road is given in the following table:

Axle load |
Frequency of traffic (%) |

18 |
10 |

14 |
20 |

10 |
35 |

8 |
15 |

6 | 20 |

The design period of the road is 15 years, the yearly traffic growth rate is 7.5% and the load safety factor (LSF) is 1.3. If the vehicle damage factor (VDF) is calculated from the above data, the design traffic (in million standard axle load, MSA) is ____________

This question was previously asked in

GATE CE 2014 Official Paper: Shift 1

__Concept:__

The design traffic in terms of the cumulative number of standard axles to be carried during the design life of the road as per IRC 37:2012 is:

\(N = \frac{{365 \times \left[ {{{\left( {1 + r} \right)}^n} - 1} \right] \times A \times D \times F}}{r}\)

Where,

N = Cumulative number of standard axles to be cater for in the design in (msa)

A = Initial traffic in the year of completion of construction in terms of the number of commercial vehicles per day.

\(A = P{\left( {1 + r} \right)^x}\)

x = number of years between the last count and the year of completion of construction

P = Number of commercial vehicles as per the last count

r = annual growth rate of commercial vehicles in decimal, n = design life of pavement in years

D = Lane distribution factor, F = Vehicle damage factor

__Calculation:__

Calculation of VDF: -

Axle load (ton) |
Frequency (%) (Ni) |
Equivalency factor Fi \({F_i}\; \rm = \;{\left( {\frac{{Actual\;load}}{{Standard\;lod}}} \right)^4}\) |

18 |
10 |
\({\left( {\frac{{18}}{8}} \right)^4}\; = \;25.62\) |

14 |
20 |
\({\left( {\frac{{14}}{8}} \right)^4}\; = \;9.378\) |

10 |
35 |
\({\left( {\frac{10}{8}} \right)^4}\; = \;2.44\) |

8 |
15 |
\({\left( {\frac{{8}}{8}} \right)^4}\; = \;1\) |

6 | 20 | \({\left( {\frac{{6}}{8}} \right)^4}\; = \;0.316\) |

\(\begin{array}{l} \sum {N_i}\; = \;100\% \\ \therefore \;VDF\; = \;\frac{{10 \times 25.62 + 20 \times 9.378 + 35 \times 2.44 + 15 \times 1 + 20 \times 0.316}}{{100}} \end{array}\)

= 5.50

\(N = \frac{{365 \times \left[ {{{\left( {1 + r} \right)}^n} - 1} \right] \times A \times D \times F}}{r}\)

Where r = Rate of growth = 7.5 %

n = design life = 15 yrs

A = Anticipated traffic = 5000 CV/day

D = VDF = 5.50

F = lane distribution factor = 1

L = lane safety factor = 1.3

\(\therefore \;CSA\; = \;\frac{{365}}{{0.075}} \times \left[ {{{\left( {1 + 0.075} \right)}^{15}} - 1} \right] \times 5000 \times 5.50 \times 1 \times 1.3\)

= 340.80 msa