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BFC 31802 HIGHWAY ENGINEERING (SECTION 5)

RIGID PAVEMENT DESIGN (PCA METHOD) EXAMPLE

The design involves a four-lane interstate pavement with doweled joints and no concrete shoulders. A 100 mm untreated subbase will be placed on a clay subgrade with a k value of 27 MPa/m. Other information include concrete modulus of rupture = 4.5 MPa, design period = 20 years, current AADT = 12,900, annual traffic growth rate = 4% and AADTT = 19% of AADT.

Solution Step 1: Suggest a Trial Thickness for the PCC slab Trial thickness = 240 mm Step 2: Calculate Number of Trucks and determine the LSF Growth factor, G = (1 + r)0.5Y = (1 + 0.04)0.5x20 = 1.5 Assume directional distribution, D is 50:50, therefore D = 0.5 AADT (per direction) is therefore is projected to be 12,900 x 1.5 x 0.5 = 9,675. Lane distribution, L can be estimated from Figure 1, with projected AADT (per direction) = 9,675. Therefore, L = 0.81. AADT (per direction, on design lane) is therefore 9,675 x 0.81 = 7,837. Number of trucks on design lane during design period, T = AADTT x Y x 365 = (0.19)(7,837) x 20 x 365 = 10,869,919 trucks = 10,870 trucks per 1,000 For interstate highways, take load safety factor, LSF as 1.2.

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Step 3: Calculate the Expected Repetitions for single and tandem axles Use adjusted axle load data from Column 3 of Table 3.

SINGLE AXLES

Axle load (kN)

Axles per 1,000 trucks (adjusted) A

Expected repetitions

T A

133 0.58 6,305

125 1.35 14,675

115 2.77 30,110

107 5.92 64,351

98 9.83 106,853

89 21.67 235,553

80 28.24 306,969

72 38.83 422,083

TANDEM AXLES

Axle load (kN)

Axles per 1,000 trucks (adjusted) A

Expected repetitions

T A

231 1.96 21,306

213 3.94 42,828

195 11.48 124,788

178 34.27 372,515

160 81.42 885,036

142 85.54 929,820

125 152.23 1,654,741

107 90.52 983,953

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Step 4: Determine the Equivalent Stress for single and tandem axles Need to find k value of subbase-subgrade. Interpolate from Table 1a (Untreated Base), with k of subgrade = 27 MPa/m and subbase thickness = 100 mm: Therefore, k of subbase-sugrade = 35 MPa/m Interpolate from Table 4a (No Concrete Shoulder), with slab thickness 240 mm and k = 35 MPa/m: Equivalent Stress for: Single axle = 1.44 Tandem axles = 1.35 Step 5: Calculate the Stress Ratio Factor for single and tandem axles Stress Ratio Factor = Equivalent Stress / Modulus of Rupture Stress Ratio Factor for: Single axle = 1.44 / 4.5 = 0.32 Tandem axles = 1.35 / 4.5 = 0.30 Step 6: Determine the Erosion Factor for single and tandem axles Interpolate from Table 5a (Doweled Joints, No Concrete Shoulder), with slab thickness = 240 mm and k = 35 MPa/m: Erosion Factor for: Single axle = 2.61 Tandem axles = 2.80 Step 7: Run Fatigue Analysis by determining Allowable Repetitions and calculating Fatigue Percent Use Figure 2 to determine Allowable Repetitions. Fatigue Percent = 100*(Expected Repetitions/Allowable Repetitions) Sample calculation: For single axle load 160 kN with stress ratio factor 0.32, allowable repetitions (obtained from Figure 5) = 21,000 Fatigue Percent = 100*(6,305/21,000) = 30.0 %

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Step 8: Run Erosion Analysis by determining Allowable Repetitions and calculating Damage Percent Use Figure 3a (Without Concrete Shoulder) to determine Allowable Repetitions. Fatigue Percent = 100*(Expected Repetitions/Allowable Repetitions) Sample calculation: For tandem axle load 277 kN with erosion factor 2.80, allowable repetitions (obtained from Figure 6a) = 890,000 Fatigue Percent = 100*(21,306/890,000) = 2.4 % Step 9: Comment on the adequacy of the thickness based on Total Fatigue Percent and Total Damage Percent. Since the total fatigue percent (85.0%) and total damage percent (42.2%) each does not exceed 100%, therefore the 240 mm slab thickness is adequate for the slab to withstand traffic loading throughout its design period.

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Rigid Pavement Design Worksheet

Project :

Trial Thickness : mm Doweled joints : Yes / No .

Subbase-subgrade, k: MPa/m Concrete shoulder : Yes / No .

Modulus of rupture, MR : MPa Design period : years

Load safety factor, LSF : .

Axle load (kN)

Multiplied by

LSF

Expected repetitions

Fatigue analysis Erosion analysis

Allowable Fatigue Allowable Damage

repetitions percent repetitions percent

1 2 3 4 5 6 7

8. Equivalent stress : . 10. Erosion factor : .

9. Stress ratio factor : .

Single Axles

11. Equivalent stress : 13. Erosion factor :

12. Stress ratio factor :

Tandem Axles

Total = Total =