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					CE 445                    Pavement Management

Notes developed spring 2000

Text: Pavement Management for Local Governments by
Federal Highway Administration, 1985

Lecture 1 Introduction to Pavement Management
    (Handout-Chap 1,2, and 3 of manual)

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

Should include:
   Assessment of conditions
    Needs determination
    Budget development

Objective of PMS
    Determine extent and usage of the road system
         No miles
         % trucks
    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
    Assist in marketing the road program
     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
           Historical – Same as last year plus some increase
for inflation
                Last Year X (1+ adjustment%/100)

           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
                              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

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
     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
          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
     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

Roadway elements
        Pavement Type
              Traveled way
              Cross slopes
              Sidewalks, etc
    Drainage – key to good roads
              Cross slopes
              Fore and back slopes
              Catch basins
              Curb and gutter
              Under drains
                   Base and sub base
                   Edge drains

     Traffic elements
          Total count (AADT)
          % trucks
          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

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
     Asphalt Institute design method for flexible
     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

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.

         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
         Reconstruction-reworking the grade including
         earthwork and resurfacing.
         Routine- blading, pot hole repair
         Preventive- ditch cleaning, spot aggregate,
         Rehabilitation- scarify, and compact, add
         Reconstruct-geometric changes, safety
         improvements, surface improvements
         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

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
     Dimensions of surface, shoulders and sidewalks
     X-section components
     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
           Act 51 designation
                state trunk line
                county primary
                county local
                city major
                city minor
     Pavement structure- include type and depth if
     History and record of maintenance

    Cost data related to maintenance activities
          Vertical alignment
          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


                      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


               No Maint

                              Time, Years
Determine results of change in maintenance activities

                                                              Rehab and Routine Main

                   No Main

                              Time, Years

Track performance of strategies

                                                Preventive main


                          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
                Roughness testing
                Structural testing
                Skid resistance
Some of the methods are high tech and some are rather

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

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 



            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
     A pendulum device that measures friction between the
surface and the pad.
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

      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
addition roughness can lead to accelerated wear because
wheel loads that are displaced can lead to harmonic forces
that lead to more distortions.
           Measuring the distortions can be done in several
      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
    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)

                 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
     x   adtdt

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
 pavement expenditures should be made.

     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
defection basin developed during a loading or impulse.
          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 is the deflection under the 10 psi loading
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
          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
accelerometers placed on the roadway
          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
         Patches and potholes
And evaluated based on the severity and extent

     There are several ways that distress surveys are
     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
           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
          Pot holes
          Longitudinal       corner        not cracked
          Transverse         transverse
          Shrinkage          punch outs
          Slippage           joints
See Pavement Distress Identification Program for more

           Paser       LTTP                CRS
           Slight      low                 N1
           Moderate    moderate            N2
           Severe      high                N3
     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
     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
          Be easily adapted to computer data entry,
analysis and processing but still be able to be manually
          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
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
           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

APWA also promotes and sells PAVER

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

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

     Typical score sheet

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

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
           Transverse cracking
           Longitudinal cracking
      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
              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
           Row2  x1xc
                  1 1
          ROW 3  x x1
                  b c
    3. Determine a column matrix of 1/n power of the row

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

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

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

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

Lecture 13 Distress Index Continued
     On the same idea the Asphalt Institute uses the
     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
               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.


  Value         Design Life    Remaining Service Life
                or Pavement

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
       Transverse     90          0.1
       Roughness      80          .05
       Skid           90          .05
       Average        83
       Average        73

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 )
           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

           60                                              Rut
           40                                              alligator

            0                                              Skid
          -20            1995            2000       2005

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

               Data point
                                                     Extrapolated data


Or are assumed to be similar to curves developed by other

For example Washington State DOT uses the following
equation for asphalt overlays
     PCI  100  0.1T
                      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

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

                        80                                             PCI=100-

                        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
default equations (WADOT for example)
     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



                           0         5    10    15   20

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

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

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

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

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

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

N           Equation                                           R2                 Comments

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

      A Mathcad program can be found at the following link
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
            Roadware 10-.4T         10-2T^.5     10-.9t^.75          12
        0         10           10          10             10                                      PCI
        1          9          9.6            8           9.1          8
        2          8          9.2    7.171573     8.486386            6                           PCI 10-.4T

        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