pca design method - the university of memphis - pca meth… · · 2018-01-15pca design method •...

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 =rateofworkp =contactpressure(psi)h =slabthickness(in)k =modulusofsubgradereaction(psi/in)C =1.0(granularsubbase),0.9(stabilizedsubbase)

.

5

Erosion Model

Notiedconcreteshoulder Tiedconcreteshoulder

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

DirectionDistribution

Factor

PercentTrucks

LaneDistribution

Factor

AverageDaily Traffic(two-way)

TrafficGrowth

Multiplier

9

DesignLife

Growth Factor (AASHTO)

n1 r 1G

r

10

AnnualGrowthRate

DesignLife

Growth Factor (PCA)

Y

2G 1 r

11

AnnualGrowthRate

DesignLife

Lane Distribution Factor

(AD

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)

Freq

uenc

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)

Freq

uenc

y

14

Design Procedure1. 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 StressEquivalent Stress – No Concrete Shoulder

(Single Axle / Tandem Axle)Equivalent Stress – Concrete Shoulder

(Single Axle / Tandem Axle)

16

Load Safety Factor

Traffic Volume LSFHigh

(interstates, multilane highways) 1.2

Moderate(highways and arterials) 1.1

Low(collectors, residential streets) 1.0

Multiplication factor for axle loads

17

Erosion Factor

Erosion Factor – Doweled Joints, Concrete Shoulder(Single Axle / Tandem Axle)

Erosion Factor – No Dowels, Concrete Shoulder (Single Axle / Tandem Axle)

19

Allowable RepetitionsConcrete 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 RepetitionsNo 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


V ADT D G 967512,900 0.5 1.5

26

Lane Distribution Factor

27


V 365 ADT T D L G Y12,900 0.19 0.5 0.81 201.5

V = 10,880,000 trucks

28

Example

Clay subgradek = 100 psi/in

4" untreated subbaseConcrete MR = 650 psi

Doweled JPCPAsphalt Shoulders

29

Modulus of Subgrade Reaction

Design k Values for Untreated Subbases

Design k Values for Cement-Treated Subbases

30

Axle Load Spectrum1,837,000

586,900

422,500307,200

235,800106,900 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

124,90042,870 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

9.5130650

XX

20

Design 1 – Four-lane rural interstate, dowels, asphalt shoulder

35

Load Safety Factor

Traffic Volume LSFHigh

(interstates, multilane highways) 1.2

Moderate(highways and arterials) 1.1

Low(collectors, residential streets) 1.0

Multiplication factor for axle loads

36

9.51306501.2

XX

20


37




38

9.51306501.2

XX

20


30 631036.0

2060.317 206/MR

39

9.51306501.2

XX

20


30 27,00036.0

2060.317

6310 23.4

41

9.51306501.2

XX

20


3028262422

27,00077,000230,000

1,200,000

36.033.631.228.826.4

2060.317

631014,69030,14064,410106,900

23.419.113.15.4

42

9.51306501.2

XX

20


3028262422

27,00077,000230,000

1,200,000unlimited

36.033.631.228.826.4

2060.317

631014,69030,14064,410106,900

23.419.113.15.40.0

= 61.0

44

9.51306501.2

XX

20


45




46

9.51306501.2

XX

20


1920.295 192/MR

52 21,32062.4

47

9.51306501.2

XX

20


1920.295

52 21,32062.4 1,100,000 1.9

49

9.51306501.2

XX

20


1920.295

5248

21,32042,870

62.457.6

1,100,000 1.9

50

9.51306501.2

XX

20


1920.295

5248

21,32042,870

62.457.6

1,100,000unlimited

1.90.0

= 62.9

52

9.51306501.2

XX

20


3028262422

27,00077,000230,000

1,200,000unlimited

36.033.631.228.826.4

2060.317

631014,69030,14064,410106,900

23.419.113.15.40.0

53

Erosion Factor



54

9.51306501.2

XX

20


3028262422

27,00077,000230,000

1,200,000unlimited

36.033.631.228.826.4

2060.317

631014,69030,14064,410106,900

23.419.113.15.40.0

2.59

55

9.51306501.2

XX

20


3028262422

27,00077,000230,000

1,200,000unlimited

36.033.631.228.826.4

2060.317

631014,69030,14064,410106,900

23.419.113.15.40.0

2.59

1,500,000 0.4

57

9.51306501.2

XX

20


3028262422201816

27,00077,000230,000

1,200,000unlimited

36.033.631.228.826.428.021.619.2

2060.317

631014,69030,14064,410106,900235,800307,200422,500

23.419.113.15.40.0

2.59

1,500,0002,200,0003,500,0005,900,00011,000,00023,000,00064,000,000unlimited

0.40.70.91.11.01.00.50

= 6.158

9.51306501.2

XX

20


1920.295

5248

21,32042,870

62.457.6

1,100,000unlimited

1.90.0

59

Erosion Factor



60

9.51306501.2

XX

20


1920.295

5248

21,32042,870

62.457.6

1,100,000unlimited

1.90.0

2.79

61

9.51306501.2

XX

20


1920.295

5248

21,32042,870

62.457.6

1,100,000unlimited

1.90.0

2.79

920,000 2.3

63

9.51306501.2

XX

20


1920.295

5248444036322824

21,32042,870124,900372,900885,800930,700

1,656,000984,900

62.457.652.848.043.238.433.628.8

1,100,000unlimited

1.90.0

2.79

920,0001,500,0002,500,0004,600,0009,500,000

24,000,00092,000,000unlimited

2.32.95.08.19.33.91.80.0

= 38.964

pca design method - the university of memphis - pca meth… · · 2018-01-15pca design method •...

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