23 - PCA Method

Prévia do material em texto

PCA Design Method
PCA Design Method
• Two failure modes considered:
– Fatigue failure due to slab flexure
– Erosion failure due to foundation compression
• Edge loads produce the worst stresses
– Fatigue based on tensile stress due to edge loads
• Corner loads produce the worst deflections
– Erosion based on deflections due to corner loads
2
Miner’s Hypothesis
3
Fatigue Model
.
4
Erosion Model
.
P =	rate	of	work	
p =	contact	pressure	(psi)
h =	slab	thickness	(in)
k =	modulus	of	subgrade	reaction	(psi/in)
C =	1.0	(granular	subbase),	0.9	(stabilized	subbase)
.
5
Erosion Model
No	tied	concrete	shoulder Tied	concrete	shoulder
6
Design Parameters
1. Concrete modulus of rupture (MR)
2. Modulus of subgrade reaction (k)
3. Design traffic volume
4. Axle load spectrum
7
Modulus of Subgrade Reaction
Design k Values for Untreated Subbases
Design k Values for Cement-Treated Subbases
8
Design Traffic Volume
           V 365 ADT T D L G Y
Direction
Distribution
Factor
Percent
Trucks
Lane
Distribution
Factor
Average
Daily Traffic
(two-way)
Traffic
Growth
Multiplier
9
Design
Life
Growth Factor (AASHTO)
     
  
n1 r 1
G
r
10
Annual
Growth
Rate
Design
Life
Growth Factor (PCA)
  
Y
2G 1 r
11
Annual
Growth
Rate
Design
Life
Lane Distribution Factor
(A
D
T)
 (D
) (
G
)
12
Axle Load Spectrum
0
100
200
300
400
500
600
3000-6999 7000-7999 8000-
11999
12000-
15999
16000-
17999
18000-
19999
20000-
21999
22000-
23999
24000-
25999
26000-
29999
Single Axle Load (lbs)
Fr
eq
ue
nc
y
13
Axle Load Spectrum
0
50
100
150
200
250
6000-
11999
12000-
17999
18000-
23999
24000-
29999
30000-
31999
32000-
33999
34000-
35999
36000-
37999
38000-
39999
40000-
41999
Tandem Axle Load (lbs)
Fr
eq
ue
nc
y
14
Design Procedure
1. Choose a trial slab thickness (h).
2. For each axle load class:
a) Determine Ni for fatigue failure.
b) Divide ni by Ni to determine fatigue damage factor di.
c) Determine Ni for erosion failure.
d) Divide ni by Ni to determine erosion damage factor di.
3. Sum fatigue and erosion damage factors over all of the 
axle load classes.
4. If both sums are less than 1 (life) your design is good; 
otherwise you need to increase your slab thickness.
15
Equivalent Stress
Equivalent Stress – No Concrete Shoulder 
(Single Axle / Tandem Axle)
Equivalent Stress – Concrete Shoulder 
(Single Axle / Tandem Axle)
16
Load Safety Factor
Traffic Volume LSF
High 
(interstates, multilane highways) 1.2
Moderate
(highways and arterials) 1.1
Low
(collectors, residential streets) 1.0
Multiplication factor for axle loads
17
18
Erosion Factor
Erosion Factor – Doweled Joints, Concrete Shoulder
(Single Axle / Tandem Axle)
Erosion Factor – No Dowels, Concrete Shoulder 
(Single Axle / Tandem Axle)
19
Allowable Repetitions
Concrete Shoulder 20
Erosion Factor
Erosion Factor – Doweled Joints, No Concrete Shoulder
(Single Axle / Tandem Axle)
Erosion Factor – No Dowels, No Concrete Shoulder 
(Single Axle / Tandem Axle)
21
Allowable Repetitions
No Concrete Shoulder 22
Example Problem
23
Example
Four-lane rural interstate
Two-way ADT = 12,900 
Trucks (T) = 19%
Growth rate (r) = 4%
D = 0.5 (assumed)
Design life (Y) = 20 years
24
Traffic Growth Multiplier
   
Y 102G 1 r 1.04 1.5   
25
Design Traffic Volume
      V ADT D G 9675
12,900 0.5 1.5
26
Lane Distribution Factor
27
Design Traffic Volume
           V 365 ADT T D L G Y
12,900 0.19 0.5 0.81 201.5
V = 10,880,000 trucks
28
Example
Clay subgrade
k = 100 psi/in
4" untreated subbase
Concrete MR = 650 psi
Doweled JPCP
Asphalt Shoulders
29
Modulus of Subgrade Reaction
Design k Values for Untreated Subbases
Design k Values for Cement-Treated Subbases
30
Axle Load Spectrum
1,837,000
586,900
422,500
307,200
235,800
106,900 64,410 30,140 14,690 6,310
0
200,000
400,000
600,000
800,000
1,000,000
1,200,000
1,400,000
1,600,000
1,800,000
2,000,000
12 14 16 18 20 22 24 26 28 30
Single Axle Load (kips)
31
Axle Load Spectrum
1,356,000
1,227,000
984,900
1,656,000
930,700 885,800
372,900
124,900
42,870 21,320
0
200,000
400,000
600,000
800,000
1,000,000
1,200,000
1,400,000
1,600,000
1,800,000
16 20 24 28 32 36 40 44 48 52
Tandem Axle Load (kips)
32
33
34
9.5
130
650
X
X
20
Design 1 – Four-lane rural interstate, dowels, asphalt shoulder
35
Load Safety Factor
Traffic Volume LSF
High 
(interstates, multilane highways) 1.2
Moderate
(highways and arterials) 1.1
Low
(collectors, residential streets) 1.0
Multiplication factor for axle loads
36
9.5
130
650
1.2
X
X
20
Design 1 – Four-lane rural interstate, dowels, asphalt shoulder
37
Equivalent Stress
Equivalent Stress – No Concrete Shoulder 
(Single Axle / Tandem Axle)
Equivalent Stress – Concrete Shoulder 
(Single Axle / Tandem Axle)
38
9.5
130
650
1.2
X
X
20
Design 1 – Four-lane rural interstate, dowels, asphalt shoulder
30 631036.0
206
0.317 206/MR
39
40
9.5
130
650
1.2
X
X
20
Design 1 – Four-lane rural interstate, dowels, asphalt shoulder
30 27,00036.0
206
0.317
6310 23.4
41
9.5
130
650
1.2
X
X
20
Design 1 – Four-lane rural interstate, dowels, asphalt shoulder
30
28
26
24
22
27,000
77,000
230,000
1,200,000
36.0
33.6
31.2
28.8
26.4
206
0.317
6310
14,690
30,140
64,410
106,900
23.4
19.1
13.1
5.4
42
43
9.5
130
650
1.2
X
X
20
Design 1 – Four-lane rural interstate, dowels, asphalt shoulder
30
28
26
24
22
27,000
77,000
230,000
1,200,000
unlimited
36.0
33.6
31.2
28.8
26.4
206
0.317
6310
14,690
30,140
64,410
106,900
23.4
19.1
13.1
5.4
0.0
 = 61.0
44
9.5
130
650
1.2
X
X
20
Design 1 – Four-lane rural interstate, dowels, asphalt shoulder
45
Equivalent Stress
Equivalent Stress – No Concrete Shoulder 
(Single Axle / Tandem Axle)
Equivalent Stress – Concrete Shoulder 
(Single Axle / Tandem Axle)
46
9.5
130
650
1.2
X
X
20
Design 1 – Four-lane rural interstate, dowels, asphalt shoulder
192
0.295 192/MR
52 21,32062.4
47
48
9.5
130
650
1.2
X
X
20
Design 1 – Four-lane rural interstate, dowels, asphalt shoulder
192
0.295
52 21,32062.4 1,100,000 1.9
49
9.5
130
650
1.2
X
X
20
Design 1 – Four-lane rural interstate, dowels, asphalt shoulder
192
0.295
52
48
21,320
42,870
62.4
57.6
1,100,000 1.9
50
51
9.5
130
650
1.2
X
X
20
Design 1 – Four-lane rural interstate, dowels, asphalt shoulder
192
0.295
52
48
21,320
42,870
62.4
57.6
1,100,000
unlimited
1.9
0.0
 = 62.9
52
9.5
130
650
1.2
X
X
20
Design 1 – Four-lane rural interstate, dowels, asphalt shoulder
30
28
26
24
22
27,000
77,000
230,000
1,200,000
unlimited
36.0
33.6
31.2
28.8
26.4
206
0.317
6310
14,690
30,140
64,410
106,900
23.4
19.1
13.1
5.4
0.0
53
Erosion Factor
Erosion Factor – Doweled Joints, No Concrete Shoulder
(Single Axle / Tandem Axle)
Erosion Factor – No Dowels, No Concrete Shoulder 
(Single Axle / Tandem Axle)
54
9.5
130
650
1.2
X
X
20
Design 1 – Four-lane rural interstate, dowels, asphalt shoulder
30
28
26
24
22
27,000
77,000
230,000
1,200,000
unlimited
36.0
33.6
31.2
28.8
26.4
206
0.317
6310
14,690
30,140
64,410
106,900
23.4
19.1
13.1
5.4
0.0
2.59
55
Allowable Repetitions
No Concrete Shoulder 56
9.5
130
650
1.2
X
X
20
Design 1 – Four-lane rural interstate, dowels, asphalt shoulder
30
28
26
24
22
27,000
77,000
230,000
1,200,000
unlimited
36.0
33.6
31.2
28.8
26.4
206
0.317
6310
14,690
30,140
64,410
106,900
23.4
19.1
13.1
5.4
0.0
2.59
1,500,000 0.4
57
9.5
130
650
1.2
X
X
20
Design 1 – Four-lane rural interstate, dowels, asphalt shoulder
30
28
26
24
22
20
18
16
27,000
77,000
230,000
1,200,000
unlimited
36.0
33.6
31.2
28.8
26.4
28.0
21.6
19.2
206
0.317
6310
14,690
30,140
64,410
106,900
235,800
307,200
422,500
23.4
19.1
13.1
5.4
0.0
2.59
1,500,0002,200,000
3,500,000
5,900,000
11,000,000
23,000,000
64,000,000
unlimited
0.4
0.7
0.9
1.1
1.0
1.0
0.5
0
 = 6.1
58
9.5
130
650
1.2
X
X
20
Design 1 – Four-lane rural interstate, dowels, asphalt shoulder
192
0.295
52
48
21,320
42,870
62.4
57.6
1,100,000
unlimited
1.9
0.0
59
Erosion Factor
Erosion Factor – Doweled Joints, No Concrete Shoulder
(Single Axle / Tandem Axle)
Erosion Factor – No Dowels, No Concrete Shoulder 
(Single Axle / Tandem Axle)
60
9.5
130
650
1.2
X
X
20
Design 1 – Four-lane rural interstate, dowels, asphalt shoulder
192
0.295
52
48
21,320
42,870
62.4
57.6
1,100,000
unlimited
1.9
0.0
2.79
61
Allowable Repetitions
No Concrete Shoulder 62
9.5
130
650
1.2
X
X
20
Design 1 – Four-lane rural interstate, dowels, asphalt shoulder
192
0.295
52
48
21,320
42,870
62.4
57.6
1,100,000
unlimited
1.9
0.0
2.79
920,000 2.3
63
9.5
130
650
1.2
X
X
20
Design 1 – Four-lane rural interstate, dowels, asphalt shoulder
192
0.295
52
48
44
40
36
32
28
24
21,320
42,870
124,900
372,900
885,800
930,700
1,656,000
984,900
62.4
57.6
52.8
48.0
43.2
38.4
33.6
28.8
1,100,000
unlimited
1.9
0.0
2.79
920,000
1,500,000
2,500,000
4,600,000
9,500,000
24,000,000
92,000,000
unlimited
2.3
2.9
5.0
8.1
9.3
3.9
1.8
0.0
 = 38.9
64