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A pavement designer has arrived at a design traffic of 100 million standard axles for a newly developing national highway as per IRC:37 guidelines using the following data: design life = 15 years, commercial vehicle count before pavement construction = 4500 vehicles/day, annual traffic growth rate = 8%. The vehicle damage factor used in the calculation was
  • a)
    1.53
  • b)
    2.24
  • c)
    3.66
  • d)
    4.14
Correct answer is option 'A'. Can you explain this answer?
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Design Traffic Calculation:
To calculate the design traffic for the pavement, we need to consider the design life, initial vehicle count, and annual traffic growth rate.

Given data:
- Design life = 15 years
- Commercial vehicle count before pavement construction = 4500 vehicles/day
- Annual traffic growth rate = 8%

Step 1: Calculate the total traffic for each year:
To calculate the total traffic for each year, we need to consider the annual traffic growth rate.

Total traffic for year 1 = Initial vehicle count = 4500 vehicles/day

Total traffic for year 2 = Total traffic for year 1 + (Annual traffic growth rate x Total traffic for year 1)
= 4500 + (0.08 x 4500)
= 4500 + 360
= 4860 vehicles/day

Similarly, we can calculate the total traffic for each subsequent year.

Step 2: Calculate the cumulative traffic for each year:
To calculate the cumulative traffic for each year, we need to sum up the total traffic for that year and all the previous years.

Cumulative traffic for year 1 = Total traffic for year 1 = 4500 vehicles/day

Cumulative traffic for year 2 = Total traffic for year 2 + Cumulative traffic for year 1
= 4860 + 4500
= 9360 vehicles/day

Similarly, we can calculate the cumulative traffic for each subsequent year.

Step 3: Calculate the design traffic:
The design traffic is defined as the cumulative traffic for the last year of the design life.

Design traffic = Cumulative traffic for the last year of the design life

In this case, the design life is 15 years. Therefore, we need to calculate the cumulative traffic for year 15.

Step 4: Calculate the vehicle damage factor:
The vehicle damage factor is used in the calculation of pavement design traffic. It is given by the formula:

Vehicle damage factor = (Design traffic / 10^6)^(1/3)

Using the calculated design traffic, we can now calculate the vehicle damage factor.

Calculation:
Design traffic for year 15 = Cumulative traffic for year 15

To calculate the cumulative traffic for year 15, we can use the formula for the sum of an arithmetic series:

Cumulative traffic for year 15 = [(Total traffic for year 1 + Total traffic for year 15) / 2] x 15

Substituting the values, we get:

Cumulative traffic for year 15 = [(4500 + Total traffic for year 15) / 2] x 15

Solving this equation will give us the cumulative traffic for year 15.

Finally, we can calculate the vehicle damage factor using the formula mentioned earlier.

Answer:
The correct vehicle damage factor is given as option A) 1.53.
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A pavement designer has arrived at a design traffic of 100 million sta...
2.24
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A pavement designer has arrived at a design traffic of 100 million standard axles for a newly developing national highway as per IRC:37 guidelines using the following data: design life = 15 years, commercial vehicle count before pavement construction = 4500 vehicles/day, annual traffic growth rate = 8%. The vehicle damage factor used in the calculation wasa)1.53b)2.24c)3.66d)4.14Correct answer is option 'A'. Can you explain this answer?
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