traffic and axle loads - the university of memphis - traffic...serviceability limit p i p f p t p...

Traffic and Axle Loads

Typical Axle Combinations

Single Axle Tridem AxleTandem Axle

Typical Weight Limits

Weigh Stations

Axle Load Histogram

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

Freq

uenc

y

Single Axle Load (lbs)

Axle Load Histogram

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

Freq

uenc

y

Tandem Axle Load (lbs)

Standard Axle Load

Single Axle, Dual Wheels

9 kips

9 kips

LOAD EQUIVALENCY

Mazda Miata

1 consumption per passageMM

dN

Curb weight = 2300 lb

Assume NM = 12,000,000

Ford Excursion

1 consumption per passageFF

dN

Curb weight = 6300 lb

Assume NF = 200,000

“Standard” Vehicle

1 consumption per passageSS

dN

Assume NF = 1,000,000

Curb weight = 4300 lb

Mazda Equivalency Factor

11

M M SM

S S M

d N NFd N N

1,000,000 0.08312,000,000

MF

Ford Equivalency Factor

11

F F SF

S S F

d N NFd N N

1,000,000 5.0200,000

FF

MECHANISTIC METHOD

Pavement Life (Fatigue)

21

kf tN k

AsphaltTensileStrain

AsphaltFatigue

Life

LEF (Fatigue)

1 si

i

kNLEFN

2

1

kst

k 2

2

kit

k sitt

3 ≤ k2 ≤ 6

Pavement Life (Rutting)

43

kf cN k

SubgradeCompressive

Strain

SubgradeFatigue

Life

LEF (Rutting)

3 si

i

kNLEFN

4

3

ksc

k 4

4

kic

k sicc

3.5 ≤ k4 ≤ 4.5

Pavement Life (Rigid)

4

225,000

t

fNMOR

ConcreteModulus of

Rupture

ConcreteTensile Strain

LEF (Rigid)

sts

ii

MORNLEFN

4

it MOR

4

4

itst

LEF Summary

4 4 4 4

18

i i it t c i

i s s st t c

LLEFL

18-kipStandardAxle Load

MeasuredAxle Load

AASHTO METHOD

AASHTO LEF

18

10 10 22 18

18 1log 4.79log 4.33log

xt t t

t x x

W G GLW L L

Flexible Pavements

18

10 10 22 18

18 1log 4.62log 3.28log

xt t t

t x x

W G GLW L L

Rigid Pavements

AASHO Road Test

Source: http://www.fhwa.dot.gov

Pavement Performance

p

log W

i i fWp p p p

failure

pi

pf

Pavement Performance

p

log W

failure

pi

pf

(failure)

Pavement Performance

p

log W

x

xi i f

x

Wp p p p

pi

pffailure

Pavement Performance

x

xt

i ft ix

p p pW

p

Wt x

Serviceability Limit

pi

pf

pt

p

x

failure

log W

x

Flexible Pavement Performance

x

x

x

tt 4.2 4.2 1.5

Wp

Wt x

Serviceability Limit

4.2

1.5

pt

p

x

failure

log W

x

Flexible Pavement Performance

x

xtt

x

Wp 4.2 4.2 1.5

3.232

5.19 3.232

0.0810.41

xx

L LSN L

9.365.93 4.332

4.792

10 1

xx

SN LL L

Example

Calculate the serviceability index pt for a flexible pavement with a structural number of 6 that has been subjected to 20 million 18-kip axle loads.

Step 1

Calculate 18 (the number of 18-kip single-axle loads needed to reach the pf = 1.5 failure limit):

9.365.93 4.332

4.792

9.36 4.335.93

4.79

10 1

10 6 1 1 51,866,61518 1

xx

SN LL L

Step 2

Calculate 18 (the rate at which the performance curve will approach 18 = 51,866,615 axle loads):

3.232

5.19 3.232

3.23

5.19 3.23

0.0810.41

0.081 18 10.4 0.4456 1 1

xx

L LSN L

Step 3

Calculate the performance index pt after 20 million 18-kip loads have been applied to the pavement:

0.445

4.2 4.2 1.5

20,000,0004.2 2.7 2.4351,866,615

x

xtt

x

Wp

Flexible Pavement Performance

x

xtt

x

Wp 4.2 4.2 1.5

xt t x xW p , , f

AASHTO LEF

18 18 18, ,, ,

x

t ts

x t t x x

W f pNLEFN W f p

Flexible Pavement Performance

x

xtt

x

Wp 4.2 4.2 1.5

x

xtt

x

W4.2 p4.2 1.5

x

t

tt10 x 10

xG

W4.2 plog log4.2 1.5

Pavement Performance

xtt x 10

x

WG log

10 10log log x

tt x

x

G W

10 10log log x

tt x

x

GW

Pavement Performance

10 10log log x

tt x

x

GW

1010loglog10 10

txtx x

GW

10t

x

x

G

t xW

Example

How many 18-kip axle loads are needed to reduce the serviceability index of a flexible pavement with a Structural Number of 5 from pi = 4.5 to pt = 2.5?

Step 1

Calculate 18 (the number of 18-kip single-axle loads needed to reach the pf = 1.5 failure limit):

9.365.93 4.332

4.792

9.36 4.335.93

4.79

10 1

10 5 1 1 12,253,66418 1

xx

SN LL L

Step 2

Calculate 18 (the rate at which the performance curve will approach 18 = 12,253,664 axle loads):

3.232

5.19 3.232

3.23

5.19 3.23

0.0810.41

0.081 18 10.4 0.5005 1 1

xx

L LSN L

Step 3

Calculate W18 (the number of 18-kip axle loads) needed to reach a serviceability limit of pt = 2.5:

10

18 18

18

10

4.2log4.2 1.5

18 18

4.2 2.5log4.2 1.5

0.500

10 10

12,253,664 10 4,857,763

t

t

pG

tW

Question

How many 12-kip axle loads are needed to reduce the serviceability index to the same pt = 2.5 limit?

Step 1

Calculate 12 (the number of 12-kip single-axle loads needed to reach the pf = 1.5 failure limit):

9.365.93 4.332

4.792

9.36 4.335.93

4.79

10 1

10 5 1 1 75,458,30512 1

xx

SN LL L

Step 2

Calculate 12 (the rate at which the performance curve will approach 12 = 74,458,305 axle loads):

3.232

5.19 3.232

3.23

5.19 3.23

0.0810.41

0.081 12 10.4 0.4295 1 1

xx

L LSN L

Step 3

Calculate W (the number of 12-kip axle loads) needed to reach a serviceability limit of pt = 2.5:

10

12 12

12

10

4.2log4.2 1.5

12 12

4.2 2.5log4.2 1.5

0.429

10 10

75,458,305 10 25,666,939

t

t

pG

tW

Question

What is the LEF for a 12-kip single axle load applied to a pavement with SN = 5 if pt = 2.5?

18

12

4,857,763 0.18925,666,939

t

t

WLEF

W

AASHTO LEF

1818 1818 1810 10

10

t

t t

x

txx

GG G

tG

t xx

WLEF

W

xLEF e EALF

10t

x

x

G

t xW

AASHTO LEF

18 1818 10

t t

x

x

G Gt

t x

WLEF

W

18

18 18

1 10

t t

x x

G Gt x

t

WLEF W

AASHTO LEF

18

1818

log log log

xt t tx

t x

W G GW

1: log xx

NOTE this is not ee

This is basically the equation in the textbook

AASHTO LEF

18

10 10 22 18

18 1log 4.79log 4.33log

xt t t

t x x

W G GLW L L

Flexible Pavements

18

10 10 22 18

18 1log 4.62log 3.28log

xt t t

t x x

W G GLW L L

Rigid Pavements

Rigid Pavement Performance

x

xtt

x

Wp 1.54.5 4.5

5.20

8.46 3.52

22

3.6311

.0

x

x LDL L

7.352

5.85 3.28

62

4. 210 1

x

x

LL LD

Rigid Pavement Performance

x

xtt

x

Wp 1.54.5 4.5

x

xtt

x

Wp1

4.54.5 .5

x

t

tt10 x 10

xG

Wplog log1.5

4.54.5

TRUCK LOAD FACTORS

Question

What is the LEF for a 12-kip single axle load applied to a pavement with SN = 5 if pt = 2.5?

18

12

4,857,763 0.18925,666,939

t

t

WLEF

W

AASHTO Equivalency Factors

NOTE: This table is for SN = 5.0 and pt = 2.5 ONLY

Individual Truck Load Factors

12,000 32,000 32,000

ESAL = ??

AASHTO Equivalency Factors

NOTE: This table is for SN = 5.0 and pt = 2.5 ONLY

Individual Truck Load Factors

0.189 0.857 0.857

ESAL = 1.903

Average Truck Load Factors

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

Freq

uenc

y

Single Axle Load (lbs)

Single Axle LoadsPer 1000 Trucks

Average Truck Load Factors

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

Freq

uenc

y

Tandem Axle Load (lbs)

Tandem Axle LoadsPer 1000 Trucks

Single AxlesLoad Group

(lbs)Axle Count

per 1000 trucks LEF ESALs3000-6999 557 0.005 2.79

7000-7999 140 0.027 3.78

8000-11999 493 0.088 43.38

12000-15999 154 0.360 55.44

16000-17999 75 0.796 59.70

18000-19999 33 1.24 40.9

20000-21999 5 1.83 9.15

22000-23999 2 2.58 5.16

24000-25999 1 3.53 3.53

26000-29999 1 5.39 5.39

TOTAL = 229.2

Tandem AxlesLoad Group

(kips)Axle Count

per 1000 trucks LEF ESALs6000-11999 227 0.010 2.3

12000-17999 162 0.037 6.0

18000-23999 108 0.150 16.2

24000-29999 140 0.429 60.1

30000-31999 58 0.757 43.9

32000-33999 25 0.97 24.3

34000-35999 6 1.23 7.4

36000-37999 3 1.54 4.6

38000-39999 1 1.89 1.9

40000-41999 1 2.29 2.3

TOTAL = 169.0

Average Truck Load Factor

229 169 0.401000 f

ESALsTVehicles

Average number of ESALs per truck

SIMPLIFIED METHODS

FHWA Truck Classes

FHWA Class 4

Source: WSDOT Pavement Guide Interactive CD-ROM

FHWA Class 5

Source: WSDOT Pavement Guide Interactive CD-ROM

FHWA Class 6

FHWA Class 7

FHWA Class 8

Source: WSDOT Pavement Guide Interactive CD-ROM

FHWA Class 9

Source: images.encarta.msn.com

FHWA Class 10

Source: WSDOT Pavement Guide Interactive CD-ROM

FHWA Class 11

FHWA Truck ClassesClass Type EALF1 Motorcycles negligible2 Passenger Cars negligible3 Other Two-Axle, Four-Tire Single Unit Vehicles negligible4 Buses 0.575 Two-Axle, Six-Tire, Single Unit Trucks 0.266 Three-Axle Single Unit Trucks 0.427 Four or More Axle Single Unit Trucks 0.428 Four or Less Axle Single Trailer Trucks 0.309 Five-Axle Single Trailer Trucks 1.2010 Six or More Axle Single Trailer Trucks 0.9311 Five or Less Axle Multi-Trailer Trucks 0.8212 Six-Axle Multi-Trailer Trucks 1.0613 Seven or More Axle Multi-Trailer Trucks 1.39

Typical Traffic Data

Source: WSDOT Pavement Guide Interactive CD-ROM

WSDOT Simplified System

WSDOT Category FHWA Classes Assumed EALF

Single Units 4, 5, 6, 7 0.40

Double Units 8, 9, 10 1.00

Trains 11, 12, 13 1.75

Daily ESALs = 0.40(single units) + 1.00(double units) + 1.75(trains)

Source: WSDOT Pavement Guide Interactive CD-ROM

TDOT Simplified System

VehicleType

FHWAClass

FlexibleEALF

RigidEALF

Cars & Motorcycles 1, 2 0.001 0.001

Pickups, Panel Vans 3 0.004 0.005

Buses 4 0.300 0.300

2-axle, 6-tire Singles 5 0.170 0.170

3-axle or more Singles 6, 7 0.700 1.000

4-axle Combos 8 0.700 0.780

5-axle or more Combos 9 -11 1.100 1.780

DESIGN ESALS

Design ESALS

• Goal is to determine how many ESALS willbe applied to the most heavily used trafficlane over the design life of the pavementand design the entire pavement system forthat level of traffic.

Design ESALS

fESAL 365 ADT T T D L G

Truck LoadFactor

LaneDistribution

Factor

DirectionDistribution

Factor

GrowthFactor

PercentTrucks

AverageDaily Traffic(two-way)

Design ESALS

fESAL 365 ADT T T D L G

Truck LoadFactor

LaneDistribution

Factor

DirectionDistribution

Factor

GrowthFactor

AverageDaily Truck

Traffic

Design ESALS

m

m m mi 1

ESAL 365 L D N T G

DirectionDistribution

Factor

DailyTruck Count(two-way)

GrowthFactor

TruckLoad

Factor

LaneDistribution

Factor

Traffic GrowthCOMPARISON OF GROWTH IN VOLUME AND

LOADINGS ON THE INTERSTATE SYSTEM

70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 00 020

100

200

300

400

500

600

700

PE

RC

EN

T G

RO

WTH

(3-Y

EA

R M

OV

ING

AV

ER

AG

E)

RURALAVERAGE DAILYLOAD

RURALAVERAGE DAILYTRAFFIC

YEARSource: Truck Weight Study and HPMS

Growth Factor

1 1G 0

ng for gg

Lane Distribution FactorsNumber of Lanesin Each Direction

Percent of Loadsin Design Lane

1 100

2 80-100

3 60-80

4 50-75

Lane Distribution Factor

95