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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) 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 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 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. Roadway elements 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 Total count (AADT) % 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. Reconstruction-reworking the grade including earthwork and resurfacing. Aggregate Routine- blading, pot hole repair Preventive- ditch cleaning, spot aggregate, shaping Rehabilitation- scarify, and compact, add 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 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 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 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 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 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 11 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. 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 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 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 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 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 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 76 100 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 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 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 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 \\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 Roadware 10-.4T 10-2T^.5 10-.9t^.75 12 0 10 10 10 10 PCI 10 Roadware 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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