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 Thi ckness for the PCC slab
Trial thickness = 240 mm Step 2: Calculate Number of Trucks and determine the LSF 0.5Y
0.5x20
Growth factor, G = (1 + r) = (1 + 0.04) = 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.
1
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
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
TANDEM AXLES
2
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 %
3
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
Subbase-subgrade, k :
Doweled joints : Yes
Load safety factor, LSF :
Concrete shoulder : Yes
MPa/m
Modulus of rupture, MR :
/ No
Design period :
MPa
. / No .
years
.
Axle load (kN)
Multiplied by LSF
Expected repetitions
1
2
3
Fatigue analysis Allowable repetitions 4
8. Equivalent stress :
.
9. Stress ratio factor :
.
Fatigue percent 5
Erosion analysis Allowable repetitions 6
10. Erosion factor :
Damage percent 7 .
Single Axles
11. Equivalent stress :
13. Erosion factor :
12. Stress ratio factor : Tandem Axles
Total =
Total =
5
