Flexible pavement design Example
EXAMPLE NO:1
A flexible pavement is constructed with 4 in. of hot mix asphalt wearing surface, 8 in of aggregate-bituminous base and 8 in of crushed stone sub-base. The subgrade has a soil resilient modulus of 10,000 psi and M2 and M3 are equal to 1.0 for the materials in the pavement structures. The overall standard deviation is 0.5, the initial PSI is 4.5 and the TSI is 2.5. Daily traffic has 1080 20-kips single axles, 400 24-kip single axles, and 680 40-kip tandem axles. How many years would you estimate this pavement would last if you wanted to be 90% confident that your estimate was not too high, and if you wanted to be 99% confident that your estimate was not too high?
Solution:
Given Data:
D1 = 4 inch D2 = 8 inch D3 = 8 inch
Mr = 10,000 psi M2 = M3 = 1.0 So = 0.5
PSI = 4.5 ∆ PSI = 2.0 TSI = 2.5
Loads:
Single Axle = 20 kip
Single Axle = 24 kip
Tandem Axle = 680 40-kip
Design Size =?
R = 90 % (b). 99%
SN = a1D1 + a2D2M2 + a3D3M3 ------------ (1)
Putting values in Equ. (1)
SN = (0.44)(4) + (0.30)(8)(1) + (0.11)(8)(1) = 5.039 = 5
From Table 4.2 and 4.3
20 kip single axle equivalent = 1.51
24 kip single axle equivalent = 3.03
40 kip tandem axle equivalent = 2.08
Thus; total daily 18 kip EASL
Daily W18 = 1.51(1080) + 3.03(400) + 2.08(680) = 4257.2 18-kip ESAL
(a) At R = 90%, Zr = -1.282
Now, By using AASHTO Design Equation:
W18 = 26,128,077
So;
Year = 
= 16.82 years
= 16.82 years
(b) At R = 99%, Zr = -2.362
After solving equation, W18 comes and to be:
W18 = 7,854,299
So;
Year = 
= 5.05 years
= 5.05 years
PROBLEM 4.5
Truck A has two single axles. One axle weighs 12,000 lb and the other weighs 23,000 lb. Truck B has an 8000 lb single axle and a 43,000 lb tandem axle. On a flexible pavement with a 3 in hot mix asphalt wearing surface, a 6 in soil-cement base, and an 8 in crushed stone subgrade, which truck will cause more pavement damage? (Assume drainage coefficients are 1.0)
Solution:
Given Data:
Truck A:
One single axle = 12 kip
2nd single axle = 23 kip
Truck B:
One single axle = 8 kip
One tandem axle = 43 kip
And
D1 = 3 inch of HMA; a1 = 0.44
D2 = 6 inch Soil cement base; a2 = 0.20
D3 = 8 inch Crush Stone; a3 = 0.11
M1 = M2 = M3 = 1.0
Calculation:
SN = a1D1 + a2D2M2 + a3D3M3 ------------ (1)
Equation (1) becomes:
SN = (0.44)(3) + (0.2)(6)(1) + (0.11)(8)(1) = 3.4
Now:
18 kips ESALs for vehicle: (Using Table 4.2 and 4.3)
Truck A:
12 kip single axle = 0.222
23 kip single axle = 2.574
Total 18-kip ESAL = 2.796
Truck B:
8 kip single axle equivalent = 0.047
43 kip tandem axle equivalent = 2.706
Total 18-kip ESAL = 2.753
RESULTS:
Truck A will cause little more damage but both damages caused by trucks are near to each other.
PROBLEM 4.6
A flexible pavement has a 4 in hot mix asphalt wearing surface, a 7 in dense-graded crushed stone base, and a 10 in crushed stone subbase. The pavement is on a soil with a resilient modulus of 5000 psi. The pavement was designed with 90% reliability, an overall standard deviation of 0.4 and a ∆PSI of 2.0. The drainage coefficients are 0.9 and 0.8 for the base and subbase, respectively. How many 25-kips single axle loads can be carried before the pavement reaches its TSI?
Solution:
D1 = 4 inch of HMA; a1 = 0.44
D2 = 7 inch of Dense grade crushed stone; a2 = 0.18
D3 = 10 inch of crushed stone; a3 = 0.11
Mr = 5000 psi
Reliability = R = 90 %
Standard Deviation = So = 0.4
∆ PSI = 2.0
TSI = 2.5
M1 = 1, M2 = 0.9, M3 = 0.8
25 kip single axle load
Calculations:
SN = a1D1 + a2D2M2 + a3D3M3 ------------ (1)
Equation (1) becomes:
SN = (0.44)(4) + (0.18)(7)(0.9) + (0.11)(10)(0.8) = 3.77
PSI = 4.5
Zr = -1.282
W18 = ?
After solving AASHTO Design equation:
Log10 W18 = Zr So + 9.36[log10 (SN+ 1)] – 0.20 + (log10[
]/(0.40 + [
]5.19) + 2.32log10(Mr) – 8.07
]/(0.40 + []5.19) + 2.32log10(Mr) – 8.07
W18 = 935439.937
18-kip ESAL for vehicle:
25 kip single equivalent = 3.469 (18-kip ESAL)
Total passes of 25 kip ESAL single axle load to reach TSI = 
= 269656.94 Passes
= 269656.94 Passes
PROBLEM 4.7
A highway has the following pavement design traffic:
|
Daily Count
|
Axle Load
|
|
300 (Single Axle)
|
10,000 lb (44.5 kN)
|
|
120 (Single Axle)
|
18,000 lb (80.1 kN)
|
|
100 (Single Axle)
|
23,000 lb (102.3 kN)
|
|
100 (Tandem Axle)
|
32,000 lb (142.3 kN)
|
|
30 (Single Axle)
|
32,000 lb (142.3 kN)
|
|
100 (Triple Axle )
|
40,000 lb (177.9 kN)
|
A flexible pavement is designed to have 4 in of sand mix asphalt wearing surface, 6 in of soil cement base, and 7 in of crushed stone subbase. The pavement has a 10-year design life, a reliability of 85% an overall standard deviation of 0.30, drainage coefficients that are 1.0 an initial PSI of 4.7, and TSI of 2.5. What is the minimum acceptable soil resilient modulus?
Solution:
Given Data:
D1 = 4 inch of sand mix asphalt; a1 = 0.35
D2 = 6 inch sand cement base; a2 = 0.20
D3 = 7 inch crushed stone; a3 = 0.11
Design life = 10 year
R = 85%
Overall standard deviation So = 0.30
M2 = M3 = 1.0 PSI = 4.7 (critical)
TSI = 2.5 Mr =?
Calculations:
SN = a1D1 + a2D2M2 + a3D3M3 ------------ (1)
Equation (1) becomes:
SN = (0.35)(4) + (0.2)(6)(1) + (0.11)(7)(1) = 3.37
Calculating 18-kip ESALs:
Daily W18 = 0.11208(300) + 1(120) + (100)(2.5782) + 100(0.88826) + 30(9.871) + 100(0.546)
= 851.023 18-kip ESAL
Zr = -1.036
∆ PSI = 2.2
By using AASHTO Design equation:
We get;
Mr = 9009.803 psi
PROBLEM 4.8
Consider the conditions in Problem 4.7. Suppose the state has relaxed truck weight limits and the impact has been to reduce the number of 18,000-lb single axle loads from 120 to 20 and increase the number of 32,000-lb single axle loads from 30 to 90. Under these revised daily counts, what is the minimum acceptable soil resilient modulus?
Solution:
Given Data:
D1 = 4 inch of sand mix asphalt; a1 = 0.35
D2 = 6 inch sand cement base; a2 = 0.20
D3 = 7 inch crushed stone; a3 = 0.11
Design life = 10 year
R = 85%
Overall standard deviation So = 0.30
M2 = M3 = 1.0 PSI = 4.7 (critical)
TSI = 2.5 Mr =?
No. of 18,000 lb single axle loads = 20
No. of 32,000 lb single axle loads = 90
Calculations:
SN = a1D1 + a2D2M2 + a3D3M3 ------------ (1)
Equation (1) gives:
SN = 3.37
Calculating 18-kip ESALs:
Daily W18 = 0.11208(300) + 1(20) + 100(2.5782) + 100(0.88826) + 90(9.871) + 100(0.54623)
= 1343.283
Total W18 = 1343.283 x 10 x 365 = 4902982.95
By using AASHTO design equation:
Mr = 10968.76 psi
PROBLEM 4.9
A flexible pavement was designed for the following traffic with a 12-year design life:
|
Daily Count
|
Axle Load
|
|
1300 (Single Axle)
|
8000 lb (35.6 kN)
|
|
900 (Tandem Axle)
|
15,000 lb (66.7 kN)
|
|
20 (Single Axle)
|
40,000 lb (177.9 kN)
|
|
200 (Tandem Axle)
|
40,000 lb (177.9 kN)
|
The highway was designed with 4 in of hot mix asphalt wearing surface, 4 in of hot mix asphaltic base, and 8 in of crushed stone subbase. The reliability was 70%, overall standard deviation was 0.5, ∆PSI was 2.0 (with s TSI of 2.5), and all drainage coefficients were 1.0. What was the soil resilient modulus of the subgrade used in design?
Solution:
D1 = 4 inch of HMA; a1= 0.44
D2 = 4 inch HMA; a2 = 0.40
D3 = 8 inch crushed stone; a3 = 0.11
Reliability = 70%
So = 0.5 ∆PSI = 2
TSI = 2.5 M1 = M2 = M3 = 1
Calculations:
SN = a1D1 + a2D2M2 + a3D3M3 ------------ (1)
Equation (1) gives:
SN = 4.24
Axle Loads (Table 4.2 and 4.3)
Single 8-kips = 0.03932
Tandem 15-kips = 0.04308
Single 40-kips = 22.164
Tandem 40-kips = 2.042
Calculating 18-kip ESALs:
Daily W18 = 1300(0.03932) + 900(0.04308) + 20(22.164) + 200(2.042) = 941.568
So;
Total W18 = 941.568 x 365 x 12
= 4124067.84
Zr = -0.524
Now, from design equation of AASHTO.
Mr = 5250.31 psi
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