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
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