Question

(18%) An engineer wants to design a flexible pavement which has a 4-inch sand-mix asphalt wearing surface, 11-inch soil cement base, and a 11-inch crushed stone subbase. It is designed to withstand 400 22-kip single-axle loads and 800 34-kip tandem axle loads per day. The subgrade CBR is 8, the overall standard deviation is 0.45, the initial PSI is 4.2, and the final PSI is 2.5. What is the probability that this pavement will have a PSI above 2.5 after 25 years? (Drainage coefficients are 1.0.) **Round up the SN value to nearest integer**

Answer 1

So first find the design # ESAL's on the faciity during the design life. We know the truck loads.

Assume no growth in traffic (since we are not given any infromation about growth rate). But design life is 25 years. so the ESAL loading for 1st year * 25 = total design ESAL load. this is calculated as follows

Assume lane distribution factor and directionality factor are 1

Calculate Truck Factors for different loadings

Truck Factor (per truck) for 22kip single axle loads = 22*1000/18000 = 1.222

Truck Factor (per truck) for 34kip single axle loads = 34*1000/18000 = 1.889

So ESAL's due to 22 kip trucks = 1.222 * 400 * 365 * 25 = 4461111

So ESAL's due to 34 kip trucks = 1.889 * 800 * 365 * 25 = 13788889

So total ESALS on the roadway during the design life = 18250000

Assume that layer coefficients for asphalt wearing surface is 0.35, for soil cement base it is 0.20 and for crushed stone sub-base it is 0.11.

Based on an empirical equation M_R = 10.33 *CBR, so for CBR = 8, MR = 82.64 MPA = 11983psi

So we have our three layers as follows

So Structural Number SN= 5

Now use the flexible pavement design formula to calculate the thickness. This formula is known to be

where SN = 5

W₁₈ = predicted number of 18 kip loads i.e ESALs = 18250000

Z_R = standard normal deviate = we NEED TO FIND THIS OUT

S₀ = combined standard error of traffic prediction and performance predictions given to be 0.45

S_N = Structural number (an index that is indicative of the total pavement thickness required) = a₁D₁ + a₂D₂m₂ + a₃D₃m₃ where D is in inches, we are given that m1 = m2 = m3 = 1 This is calculated to be 6 (ROUNDED OFF)

a = layer coefficients Assume that layer coefficients for asphalt wearing surface is 0.35, for soil cement base it is 0.20 and for crushed stone sub-base it is 0.11. and D is the thickness in inches. All drainage coefficients are 1

Delta PSI = difference between initial design serviceability index P₀ and terminal design serviceability index P_t

= 4.2 - 2.5 = 1.7

M_R = subgrade resilient modulus (in psi) = 11983 psi.

So calculate and find our Zr value. We get Zr = -3.72

So based on Zr tables, this means the reliability is close to 100%

There probability of terminal service index falling below 2.5 is zero.

Alternatively probability of terminal service index being above 2.5 is 1.

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