# CE 445

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```					CE 445                    Pavement Management

Notes developed spring 2000

Text: Pavement Management for Local Governments by

Lecture 1 Introduction to Pavement Management
(Handout-Chap 1,2, and 3 of manual)
http://www.pmu.dot.state.nc.us/

Pavement Management System

FHWA – Defines PMS as a set of tools or methods
that can assist decision makers in funding cost effective
strategies for providing, evaluating and maintaining
pavements in a serviceable condition.
AASHTO – Guidelines for Pavement Management
Systems.

Should include:
Inventory
Assessment of conditions
http://www.aot.state.vt.us/images/jpg/PMPaveCondis99.jpg
Needs determination
Prioritization
Budget development
Program
http://www.aot.state.vt.us/images/jpg/PMProSum2000Pav.jpg
Feedback

Objective of PMS
Determine extent and usage of the road system
No miles
Volume
ESALS
% trucks
Accidents
Analyze current network conditions
By political division
By condition vs % system
Develop historical data
Determine condition vs time curve for the road
segments. Useful in making future predictions
Analyze funding options
What is the affect of the decisions related to
maintenance
Assist in marketing the road program
Approach
Network - includes all roads in a political entity. The
type of approach considered in this course
Project - Determines the best solution for a given
project determined from the network analysis

Chap I – Historical Methods

Roads and streets are major investments for most
communities. They must be repaired, rehabilitated and
reconstructed in a timely and cost effective manner.

Examples of management methods used by road
agencies
Historical – Same as last year plus some increase
for inflation

Time based with estimated life - determine how
long between a maintenance activity and cost per sqyd and
calculate the amount of and costs for each year of the
specific activity. For example for a 100 mile system
Seal Coat every 3 years at a cost of \$.50 per sqyd is
100 (5280x24)
Cost ( peryear)                  x0.50  \$245000
3      9
Resurface every 10 years at a cost of \$2.00 per sqyd
100 (5280x24)
Cost ( peryear)                  x2.00  \$281000
10      9
Reconstruct every 50 years at a cost of \$10.00 per
sqyd.
100 (5280x24)
Cost ( peryear)                  x10  \$282000
50     9

For a total annual budget of
Budget  245000  281000  282000  \$808000

Emergency expenditures - sets aside a constant
amount that the engineer estimates will be adequate to
make emergency repairs to the road system. Some time
this is linked with the deferred maintenance strategy

Political – Everyone gets a share based on their
clout. May be partially based on past activities and
distributing the available resource to all the citizens of the
political unit.

Experience of the manager - A knowledgeable
and experienced manager may have the figures developed
in an informal manner and uses this number as the budget
value. Not easily defended and is not very likely in the
present engineering community.

A PMS approach would consider
When is the best time to do maintenance
What is the best maintenance strategy to use and when
should it be used
What is the effect of no maintenance or deferred
maintenance

From this curve it can be seen that if the road condition is
fair it may be able to return the condition to good by doing
a seal coat at a cost of \$0.50 per sqyd compared to doing a
reconstruction at a cost of \$2.00 per sqyd.

Another example is shown below where the present worth
of the strategies can be evaluated
No maintenance
P                P
PWNM 10 yr  Const  2,50(     ,.05,5)  2.50( .05,7)
F                 F
PWNM 10 yr    Const  2.50(.7835  .6139)
PWNM 10 yr  Const  3.49
Preventive maintenance
P                P
PWPM 10 yr  Const  0.10( ,.05,10)  2.5( ,.05,7)
A               F
PWPM 10 yr  Const  0.10(7.722)  2.5(.7107)
PWPM 10 yr  Const  2.54
Obviously the present worth of the cost associated with the
preventive maintenance is lower and is the preferred
option.
The above graphs show the importance of timing and
maintenance strategy. The only problem is to define
the pavement life curves and that is one of the
functions of the PMS program.

Lecture 2 Introduction Continued

Benefits of PMS

Documents existing and future conditions
Plans can be quantified
Alternatives can be compared on some constant
basis
Citizens can be involved in the process and it is
less mysterious

Show video related to PMS = 72,74,76 from LTAP

We have reviewed several elements related to PMS
including the videos and several are starting to reoccur
including
Maintenance activities
What and when
Budget – life cycle costing
Inventory and data base determination
Assessment techniques

One other consideration is in terms of
Project level PMS (explain)
Network level - the one we will work with

Lecture 3 Review of Roadway Cross Section Elements

Roadway X section elements (Chap 2) – related to network
analysis.

X-section
Pavement Type
Flexible
Rigid
Aggregate
Dimensions
Traveled way
Shoulders
Cross slopes
Sidewalks, etc
Drainage – key to good roads
Transverse
Cross slopes
Fore and back slopes
Catch basins
Longitudinal
Ditches
Side
Dimension
False
Curb and gutter
Under drains
Base and sub base
Edge drains

Traffic elements
% trucks
ESAL
Directional split

Lecture 4 Pavement Design Related to Project PMS

(See Chap 3 of the handout)
Many options are available for the engineer designing
pavements that are new or being rehabilitated. Generally
the design process is slightly different for flexible and rigid
pavements. Flexible pavements are designed using the
AASHTO Structural Number concept while rigid
pavements use the AASHTO depth determination
nomographs or analysis from beam on elastic foundation
methods.

Design is a function of

Traffic - usually in terms of ESALs
Materials - CBR, Mr, etc
Environment - seasonal frost, rainfall, drainage
conditions etc.

Design Methods
AASHTO method of design -Guide for Design of
Pavement Structures, 1993. Covers both flexible and rigid
as well as aggregate surfaces. There are computer
programs that do the solutions given the input.
Design standards as developed by SHAs such as
MDOT.
Asphalt Institute design method for flexible
pavements.
PCA method for concrete pavements
COE for government projects

Overlay design is based on the additional thickness
required for future traffic. AASHTO has a procedure

Pavement selection - based on life cycle analysis and
should include fixed cost, annual maintenance,
rehabilitation costs, etc. Life cycle costs are also a function
of interest rate, inflation and other costs associated with
money.

Lecture 5 Maintenance Techniques - Network PMS

Generally maintenance is considered in terms of a set
of general activities with different specific activities related
to each surface type.

Asphalt
Routine-pothole repair, crack and joint sealing
and leveling
Preventive-surface treatments, fog coats, sand
seals and seal coats
Rehabilitation-resurfacing and some
improvement to drainage or improvement of
strength. Usually includes a structural
improvement.
earthwork and resurfacing.
Aggregate
Preventive- ditch cleaning, spot aggregate,
shaping
aggregate.
Reconstruct-geometric changes, safety
improvements, surface improvements
Concrete
Routine- crack sealing, repair of blow outs
Preventive- clean and seal joints

Rehabilitation- slab replacement (50%),
structural overlay
Reconstruction- geometric and safety
improvements, replace pavements, drainage
improvements

Lecture 6 Inventory (Chap 6)
The inventory is the data collection phase of the PMS.
It may be the most important as all other parts of the PMS
are related to the data collected in this phase. This should
include
Dimensions of surface, shoulders and sidewalks
Materials
X-section components
History
Drainage
Section number and identification
Traffic count, etc.

One of the most important elements of the inventory phase
is the determination of the section boundaries. Or how the
roads are divided into manageable sections. There are
several ways this is done. The basic requirement is that
each section has consistent properties in the section.
Section boundaries may be determined by
Change in number of lanes
Change in pavement type
Change in pavement structure
Change in drainage
Traffic volume

Political subdivision
Street intersections
Topographic features
Constructions sections
At a maximum the section is less then 1 mile in length and
the resulting data base will be a function of the number of
sections. A problem is how to treat the intersection of two
streets. Possible solutions are:
Treat intersection as a separate section
Include intersection in a preferred section such as N-S.
Collected Data
Section description- include name and to and from.
May be by latitude and longitude by state wide coordinates
or by mile post.
Functional classification
AASHTO basis
County designation
State trunk line designation
NHS
STP
Act 51 designation
state trunk line
county primary
county local
city major
city minor
Pavement structure- include type and depth if
available.
History and record of maintenance

Cost data related to maintenance activities
Traffic
Parking
Volume
Geometric
Curvature
Vertical alignment
Drainage
Ditch and internal if used
Comments are usually included on the inventory
Several examples of data collection sheets are given in
Chap 6 Figs 6-8,-9 and -10. Data is collected in order of
importance from the arterial to the local access.

Lecture 7 Condition Assessment Chap 7

Before any decisions can be made related to
maintenance activities it is necessary to determine the
condition of the existing facilities. The condition can be
assessed several ways but usually consider:
Structural capacity- load carrying capability of the
pavement section.
Ride quality - the most sensitive to public opinion
Skid resistance - related to safety of the road section
Distress surveys - relates condition to observable
conditions of the pavement.

What ever method is selected to monitor it is
necessary to have a program of regular measurements in
order to get a detailed impression of the progress of the
condition

PC

Tine, years

The curve developed by periodic determination of the
conditions can be used to develop a model that can be used
to predict the behavior of similar pavement sections.
PC  aS  bRC  cSR  dDISS
the coefficients a, b. c and d are determined by statistical
analysis and the independent variables S, RC, SR and DISS
are measurable conditions related to the pavement
condition PC. In the above form it suggests linear analysis
other methods are available.
The pavement condition Vs time curve can also be
used to show the effects of maintenance

Reg Maint

PC

No Maint

Time, Years
Determine results of change in maintenance activities

Rehab and Routine Main
PC

No Main

Time, Years

Track performance of strategies

Preventive main

PC

No main

Time, Years
The time of observations related to condition determines
the expense related to the program as the measurement of
the various conditions is expensive and labor intensive.
Typical frequencies of assessment are
Every year
Every two years ( many states use this time period)
Every five years
Several types of assessment are available
Direct
Roughness testing
Structural testing
Skid resistance
Indirect
Distress
Some of the methods are high tech and some are rather
primitive.

Lecture 8 Data Collection Methods and Equipment

There are many methods used to collect data for
condition assessment. Some are specific to a particular
condition and others are integrated systems. In the
following each condition is treated separately.
Friction Measurement
One of the important elements of a road related to
safety if the ability to develop friction between the tires and
the roadway. The lower the friction the more likely that
accidents will occur. The measurement of friction is basic
and only requires some equipment that will apply a normal
force and measure the shear force required to overcome the
friction. The equation is
F  fN Fr is the measured shear force, N is the normal
r

force and f is the friction factor. Generally, the higher the
friction factor the better the safety characteristics of the
road. Typical methods of measuring the shear force are

Locked wheel trailer device - ASTM E274-85
F  Fr
Fr  fN
F
f 
N

N

F
Fr

Wheel Locked, 40 mph, wet pavement

This device takes a lot of time to collect the data and is
fairly expensive although it is well recognized and used.

Mu-Meter ASTM E 670-87
A trailer that uses the friction relation ship to
determine the friction factor. Wheels on the trailer are
oriented at an angle of 71/2 o to the direction of travel. The
friction force is measured by a transducer between the
trailer and truck.

Laboratory method - British portable tester ASTM E
303
A pendulum device that measures friction between the
We have this device. The problem is the value determined
is good for relative measurements between surfaces but it
does not relate directly to the friction factor observed on
pavements.

Roughness Measurement
Roughness is the variations in the surface along
and transverse to the roadway. It is the primary criteria by
which the traveling public judges the quality of a road. In
Measuring the distortions can be done in several
ways.
Transverse
Rod and level - a traditional survey method. Takes a
long time to do but accuracy is good.
Dip stick - a device that is "walked " across the road
and measures the incremental changes in vertical elevation.
This method is also slow but accurate
Road roughness meter - records dynamic response of
vehicle as it is driven along the roadway. Requires
electronic equipment
Longitudinal
Slope variance method - AASHTO method that
measures the slope change as a standard beam ( 25.5 ft) is
towed along the profile of the road. Measurements are
made at a regular basis and the slope variance is calculated.
SV 
 ( x  x)
i
2

n 1

XI is the measured variance at 1 ft intervals. The speed of
the forward movement is 5 mph = 7.33 fps resulting in a
measurement every 0.14 sec
Note that this value is the slope variance used in the
AASHTO design equation for flexible and concrete roads.
PSI  5.03  1.9 log(1  SV )  0.01 C  P  1.38 RD 2
SV is the slope variance, C and P are cracks, and RD is the
rut depth value
This method is slow and with the advent of better
electronics other method are used that are related to the
response of the vehicle to inertia forces and measured with
accelerometers. The relationship develops as follows
z ( x)  profile  u ( x)  h( x)

u(x) is the height of the vehicle above the pavement, u(x) is
the vertical position at any point in time and is developed
from the basic definitions
dv
a
dt
dx
v
dt
therefore

This requires some electronic instrument that will collect
the data and perform the integration. For example the
South Dakota Profiler
Law Profiler
Others being developed and in use by various agencies

Transverse measurements
Rut depth based on horizontal measurements
Where the rut depth is calculated using the equation
(h1  2h2  h3 )x    dy
RD                        ( )2
4             dx
This is a measure of the rate of change in the slope of the
road with higher values indicating deeper rut depth.
Measurement may be made at small increments of distance
in the x direction and the equation then is a summation
RD   (h  2h  h ) / 4
11     i   i 1

Other electronic devices are available and are becoming
more useable and inexpensive. Also emerging is the area
of laser technology and it is being used to measure rut
depth very accurately.
An example of an integrated vehicle that does most of
the measurements listed above is the ARAN
ARAN® is a multi-functional data collection vehicle which
gathers highway information while travelling at highway
speeds. Videotape of the highway, ditches, and
abutting properties is collected and maintained by the
Pavement Management Section. In addition to the video,
physical properties of the pavement surface are also
collected. The data gathered is analyzed to assign a
Pavement Condition Rating (PCR), predict future
deterioration, and make recommendations on where
http://www.state.me.us/mdot/planning/pavement/pmspage.htm

Structural Evaluation
Evaluation of pavement strength is difficult but there
are many methods that are being used including destructive
and nondestructive.

Nondestructive Methods usually related to the
Static - Plate bearing AASHTO T 222-81 is used
to determine the modulus of subgrade reaction. This value
is determined as
10 psi
ku 
y
The test is time consuming and disruptive to traffic.
Benkleman Beam - ASTM
Uses a swinging beam suspended under a vehicle where the
deflections are measured as the vehicle slowly moves
forward. A tradition method but hard to relate results to a
soil property
Vibratory
Dynaflect Road Rater- uses a set of geophones
set between the wheels of a test trailer. A dropped weight
produces a response in the soils that is measured by the
geophones and from the response it is possible to calculate
soil properties that are related to the strength.
FWD - the falling weight defectometer is a very
popular method of determining the soil properties from
Spectral Analysis of Surface Waves - used by
some researchers but not too popular at present

Destructive Methods
Samples of the roadway materials are taken and the
strength of the materials are evaluated in the laboratory
using conventional triaxial tests or resilient modulus tests

Whatever method is used to evaluate the structural
adequacy of the materials they should produce a result that
can be used in some statistical evaluation of the condition
of the road and can be combined with other values to
produce an overall rating of the roadway
PC  aFR  bRD  cP  dST
pavement condition is a function of friction(FR), rut
depth(RD), structure strength(ST) and profile(P). For this
linear model it is possible to add other independent
variables as they develop.

Lecture 9 Distress Measurement
Many of the PMS procedures that are used at the local
level need an assessment technique that is cheap and easy
to do. The usual process to satisfy this requirement is a
distress survey. The survey is conducted by making visual
observations of the distresses and relating the magnitude,
severity and extent to a maintenance strategy.

The distresses are put into designated categories
Surface defects
Surface distortions
Cracks
Patches and potholes
And evaluated based on the severity and extent

There are several ways that distress surveys are
conducted
Walking survey of 100% of the pavement. All
distresses type, severity and extent are recorded and
mapped. Some times the entire road is video recorded and
analyzed at a later time .
Walking of a sample of the sections of the road with
measurement of distresses.
Riding slow with periodic stops for observations
Riding at normal traffic speed with general
observation
Automated
Film
Video
Laser technology with image analysis

Distress Types Table 8-1
Surface defects
Asphalt            Concrete      Agregrate
Abrasion/polish    spalling      aggregate loss
Bleeding           scaling       dust
Ravelling          d-crack       pot holes
Weathering         crazing
Surface distortions

Bumps              blow up       corrugations
Rippling           pumping       rutting
Shoving            faulting      erosion
Waves              curling
Depressions
Pot holes
Cracks
Longitudinal       corner        not cracked
Transverse         transverse
Shrinkage          punch outs
Slippage           joints
Block
Alligator
Distress
See Pavement Distress Identification Program for more
detail.

Severity
Paser       LTTP                CRS
Slight      low                 N1
Moderate    moderate            N2
Severe      high                N3
Extent
Given as a % of the area or as a measured value for
length and width of cracks

Lecture 10 Pavement Condition Evaluations Forms

Pavement condition evaluation forms should be
appropriate to the level of survey required and should
provide all the data necessary to do a network or project
analysis.
The forms should:
Include an indication of distress type, severity
and extent
Have a standard description of distress type and
accurate definition of severity levels which can be easily
understood by the raters.
Provide standard procedures and frequency
guidelines.
Be easily adapted to computer data entry,
analysis and processing but still be able to be manually
processed.
Provide useful information, be reproducible and
provide facts required
Be easy to understand
Minimize training required
All evaluation procedures are subject to errors such as:
Error of leniency- consistent ratings too high or
too low
Halo effect- tendency of the rater to seek values
near the mean.
Error of central trend - avoid extreme values
Anchoring
There are several forms that illustrate these problems and
they are discussed below
PAVER the rating form developed by the Corp of
Engineers to provide data for their PMS. The rating is
based on a PCI value on a scale of 0 to 100 and is meant to
measure both structural integrity and surface condition.
The pavement is divided into samples and statistical
methods are used to determine how many and which
samples are to be evaluated.
The inspection is completed by walking over each
sample unit recording and measuring the distresses.
The PCI is calculated by
Determine the deduct value for each distress
By using the appropriate curves
Sum the deduct values for all individual
distresses
Calculate a corrected deduct value using
available curves
Find the PCI by subtracting the corrected deduct
value from 100.
The example shows some of the details. For more
detail visit the web site below
http://www.conted.uiuc.edu/support_center/
APWA also promotes and sells PAVER
http://www.pubworks.org/index2.stm
The evaluation process is given in ASTM D6433-99
Asphalt Institute Method. The process is for low volume
asphalt roads and does not account for severity or extent of
the distress. It is based on determining the defect number
associated with a section of pavement and then subtracting
the defects to give a condition rating = 100- sum of defects.
The condition rating is related to a maintenance strategy.
0-30 = reconstruction
30 - 80 = overlay
80 - 100 = routine maintenance
http://www.asphaltinstitute.org/

Texas Method The Texas method involves an assessment
that includes a table with distress type, severity and extent.
The form is completed in the field by checking the
appropriate box and then assigning values to the box
checked by using a key (not shown). The total distress
points are then related to a maintenance strategy as follows:
0 - 10 no maintenance
11 - 49 Routine/preventive maintenance
50 -100 reconstruction/rehabilitation
http://tti.tamu.edu/

Typical score sheet

Distress              Severity   Percentage of area
Type                             1-15% 16-45% 46-100%
Rutting   Low
Medium
Score____ High
Bleeding Low
Medium
High
Score____

Lecture 11 Pavement Condition Decision Process (AHP)

To determine the score associated with each distress is
a difficult job and requires experience or a systematic
process. The process is as follows:
1. List all the distresses that are to be evaluated
Rutting
Transverse cracking
Longitudinal cracking
Raveling
Etc.
2. Assign a maximum deduct value for each distress.
The sum must equal 100
2. Distribute the deduct value to each percentage
range and severity. For example for Rutting with
40 maximum deduct points the deduct values are as
given below

Severity       Extent
Low Med High
Low        0   10     20
Med        10  15     30
High       20   30    40

The distribution of the points can be done by an "expert" or
by some empirical method (See Shahin's Pavement
Management for Airports, Roads and Streets.).

Lecture 12 Distress Index Calculations

A more systematic way of determining the scores
associated with any point distribution scheme is to use a
pair wise comparison method called the Analytical
Hierarchy Process. It requires several steps as follows:
1. Develop a comparative matrix where each decision
factor is compared to each other in term of one of
the factors. For example cracking is four times as
significant as bleeding in promoting asphalt
pavement failure.
       
1   a b
1      
    1 c
a      
1   1
1
b
    c  

in this matrix the a,b and c are the factors and
reflect the weights
2 Determine a column matrix of row products
Row1  1xaxb
1
Row2  x1xc
a
1 1
ROW 3  x x1
b c
3. Determine a column matrix of 1/n power of the row
products
1

Row1  (1xaxb) 3
1
1
Row2  ( x1xc) 3
a
1
1 1
ROW 3  ( x x1) 3
b c

3. Normalize the column matrix of 1/n th power of the
row products
1

(1xaxb) 3
1                     1    1
1           1 1
 (1xaxb)  ( a x1xc) 3  ( b x c x1) 3
3

1
1
( x1xc) 3
a
1            1              1
1           1 1
 (1xaxb) 3  ( x1xc) 3  ( x x1) 3
a           b c
1
1 1
( x x1) 3
b c
1            1              1
1           1 1
 (1xaxb) 3  ( x1xc) 3  ( x x1) 3
a           b c
As an example in table form it might look like this for a
four factor comparison. The factors are friction (FR),
strength (ST), ride quality (RQ) and distress (DT). The job
is to determine the relative weight each factor should have
in predicting pavement failure.

FR ST RQ DT SP                              SP1/4   Normalized
FR 1        1/2 2                  1/4 1/4       0.71    0.16
ST 2        1         2            2/3 8/3       1.28    0.29
RQ 1/2 1/2 1                       1/2 1/8       .59     0.13
DT 4             3/2 2        1      12          1.86           0.42
4.44           1.00

The result above indicates that the most significant factor is
Distress (0.42) then Structure (0.29) then Friction (0.16)
and finally Ride Quality (0.13). An equation to predict
overall pavement condition might be as follows:
PCI  0.16 PCI FR  0.29 PCI ST  0.13 PCI RQ  0.42 PCI DT

In the above it is apparent that the PCI for each of the
distresses is based on 100 and the result is also on a 100
point scale. A more generalized equations is
PCI   w PCI where wI is the weighting factor for factor
i    i

I and PCII is the pavement condition index based on factor
i. Typical examples are
Alaska - PCI=0.5 distress + 0.5 ride
Vermont- PCI = .6 roughness + .25 cracking +.15
rutting

Lecture 13 Distress Index Continued
On the same idea the Asphalt Institute uses the
expression
PCI  100   Defects In this case the defects should reflect
weight, severity and extent.
A formalized approach to the determination of the defects
would be as follows:
1. Develop weights appropriate for each to the
distress types. AHP or "expert" methods are
possible
Alligator cracking      = .5
Block cracking         = .3
Transverse cracking = .1
Longitude cracking = .1
Sum = 1.0
2. Develop a scoring matrix. The weights are
determined from above and the score is the
weight multiplied by the maximum deduct
point for the given distress type

Distress      Weight Max Severity Deduct Value
Type                     High Med      Low Score
Alligator     .5     100 50     30     10
Block         .3       100    30   18       12

Transverse .1          50     5    3        1
Longitude     .1       50     5    3        1

Sum =
PCI = 100 - Sum

For example a pavement section with Low % Alligator
cracking, Med % Block cracking, High % Transverse
cracking and Low % Longitude cracking would have a
Distress value of
Distress = 10 + 18 + 5 +1 =34 and the
PCI = 100 - 34 = 66
The problem here is in selecting the values associated with
the distress and severity types.

Lecture 14 Remaining Service Life

The State of Michigan uses a slightly different method
of evaluating pavements called the Remaining Service Life.
In this process distress points are subtracted from the PCI
until a trigger value is reached and the time from present
until the trigger values is reached is calculate and this call
the remaining service life.
Definitions are:
Design Life- estimate of number of years of service
for a pavement of accumulate a predetermined number of
distress points.
Pavement Live-actual number of years in service from
construction or rehabilitation.
Remaining Service Life-number of years from any
given time for a pavement of accumulate a given number of
distress points.

PCI

Trigger
Value         Design Life    Remaining Service Life
or Pavement
Life
Time

For example using the data in the table and assuming the
PCI values are at a time of 7 years after the pavement is put
in service.

Distress       PCI         Weight
type           7 yrs       factor
Rutting        60          0.5
Alligator      95          0.3
Cracking
Transverse     90          0.1
cracking
Roughness      80          .05
Skid           90          .05
Resistance
Average        83
Sum/5
Average        73
Weighted

The remaining service life is calculated as
RSL  x  Time
x is the intersection of the PCI versus Time curve(straight
line in the drawing above)and time is the time in years from
0 years to the present.
PL (100  TV )
x
100  PCI i
TV is the trigger value and PCII is the PCI for distress I at
the number of years of the pavement life. The calculated
RSL are
7(100  50)
RSLrutting                   7  1.75
100  60
7(100  50)
RSLalligatorr                  7  63
100  95
7(100  50)
RSLtransverse                  7  28
100  90
7(100  50)
RSLroughness                   7  10
100  80
7(100  50)
RSLsurfacefriction                7  28
100  90
7(100  50)
RSLaverage                    7  14
100  83
7(100  50)
RSLweightedr                  76
100  73
The remaining service life depends on what factors are
used to make the calculations. In the given situation the
RSL of 6 years is from the weighted combined average of
PCIs. Other weights would give different results.

The same approach could be used with non-linear
relationships for PCI vs time as shown below.
Remaining Service Life Example
Pavement Condition
Distress              1990       1992       1994    1996   1998          2000     2002     2004
0          2           4      6      8            10       12       14
Rut                    100         85         72      65     60        59.374   62.362   69.062
Alligator              100        100         99      98     95
Transverse             100        100         98      95     90
Roughness              100         95         90      80     65        41.129    6.209   -42.255
Skid                   100        100        100      94     90
Trigger                 50         50         50      50     50           50       50        50

PCI vs Year

100
80
60                                              Rut
40                                              alligator
Transverse
PCI

20
Roughness
0                                              Skid
1990
-20            1995            2000       2005
Trigger
-40
-60
Year

Roughness Equation = 99.929-2.47*X+.179*X^2-.052*X^3
Rut Equation = 100.114-8.714*X+.464*X^2
\

Lecture 15 Pavement Conditions Models

To analyze pavement performance there is a need for
predictive models with the capabilities for considering
rehabilitation alternatives in order to determine:
When to do a certain pavement strategy
What happens after repair
Time vs condition
In many cases the models are developed from historical
evaluations and extrapolated into the future.

Historical data Curve fitted
with Spline function or
Polynomial of nth power

PCI
Data point
Extrapolated data

Present
Time

Or are assumed to be similar to curves developed by other
agencies

For example Washington State DOT uses the following
equation for asphalt overlays
PCI  100  0.1T
2.5
T is the time. When T = 5, PCI = 94
and the time to reach a PCI of 60 is 11years.

There are a series of equations by WADOT that are for
various types of pavement surfacing as given in the
handout.

Several shapes can be determined by using various powers
and slope coefficients
Typical Performance Curve Models
Model PCI = 100-mT^n

T         0.1T^2         PCI          10T^.5      PCI          10T^.5      PCI
0              0         100            0          100           0        100
5            2.5         97.5          50           50    22.36068   77.63932
10             10          90          100            0    31.62278   68.37722
15           22.5         77.5         150          -50    38.72983   61.27017
20             40          60          200         -100    44.72136   55.27864
25           62.5         37.5         250         -150          50         50
30             90          10          300         -200    54.77226   45.22774

120
100
80                                             PCI=100-
PCI

60                                             .1T^2
40                                             PCI=100-
20                                             10T^1.0
0                                             PCI=100-
0              20               40        10T^.5
Time, years

Other methods can be developed as discussed in the FHWA
course on Pavement Management.

Their technique uses a combination of regression analysis
and predetermined models based on availability of actually
data as follows:
For new projects with no actual measured values use
For projects with at least three years of measured PCI
use regression analysis to develop a typical equation
For projection into future use regression results to
present and then use typical model equations
For example:
Time PCI                               PCI calc
Measured                          PCI=100-.1T^2.5
0    100
3    90
5    85
8                                      82
10                                     68
15                                     13

Time              PCI
0           100
3            90
5            85
8            82
10            68
15            13

PCI

150
100
PCI

PCI
50
0
0         5    10    15   20
Time

Regression Analysis
One way to develop models is to use measured values
and develop an equation by regression analysis. There are
several techniques but the easiest is linear regression
y  b0  bi X i  
b0 is the intercept bI is the slope and  is an error term. The
method of least squares minimizes the difference between
the actual data values and the values from the regression
equation resulting in the following equations
x y
x y  n
i                i
i   i
b 
( x )
i                                          2

x  n
2                i
i

and
1
b0      ( y i  bi  x i )
n
Other values of interest are
Total sum of Squares = SSTD
SSTD   ( y  y )     i      avg
2

Error of Sum of Squares = SSE
SSE   ( y  y )  i       i calc
2

Regression Sum of Squares = SSR
SSR   ( y  y )  icalc      avg
2

SSTO = SSR + SSE
Coefficient of Regression (error related to regression
equation)
SSR
R2 
SSTO

For example
Regression Model
y = bo+biX or y = bo + bi(X^n)
Example assumes n = 2.5
Data PT       yi          xi         x^2.5 (xi^2.5)^2    xi^2.5*yi   yavg     ycalc     (yi-yavg)^2 (yi-ycalc)^2 (ycalc-yavg
1        100           0        0          0           0       85    94.29961         225 32.49444876 86.482742
2         90           3    15.59       243     1402.961       85    93.02515          25 9.151531556     64.40303
3         85           5     55.9      3125     4751.644       85    89.72927           0 22.36603733 22.366037
4         82           8      181     32768     14843.59       85    79.50008           9 6.249617029 30.249157
5         68          10    316.2    100000     21503.49       85    68.44589         289 0.198817258 274.03858
Sum                425          26    568.7    136136     42501.68      425         425         548 70.46045193 477.53955
AVG                 85         5.2    113.7

bi=           -0.081757                     R^2 =         0.871423

bi+            94.29961

PCI = 94.3-0.0816X^2.5

Using other values for n produces the following

3.5         Y=92.82-.0079X3.5                                  .84
2.5         Y=94.3-.082X2.5                                    .87
1.5         Y=97.28-.87X1.5                                    .92
3.0         Y=93.45-.025X3.0                                   .85
2.0         Y=95.5-.26X2.0                                     .89
1.0         Y=99.8-2.85X                                       .93                Best

\\portage\balkire\hmsoffice\winword\ce445\linreg.mcd
The PMS package Road ware has a set of default curve for
asphalt, concrete and aggregate surface roads and it is
possible to determine the curve as shown below

Road ware PCI vs Time relationships

Time        PCI      PCI            PCI          PCI
0         10           10          10             10                                      PCI
10
1          9          9.6            8           9.1          8
2          8          9.2    7.171573     8.486386            6                           PCI 10-.4T

PCI
5          7            8    5.527864     6.990669            4
9          6          6.4            4    5.323463            2                           PCI 10-2T^.5
12          5          5.2    3.071797     4.197322            0
14          4          4.4    2.516685     3.486138           -2 0   10          20   30   PCI 10-.9t^.75
17          3          3.2    1.753789      2.46507                       Time
20          2            2    1.055728     1.488326
25          1            0            0   -0.062306

End of this Section. Go to Lecture 16

```
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