ing. Vittorio Nicolosi

MODELLING PAY FACTOR IN HOT-MIX ASPHALT PAVEMENT CONSTRUCTION BASED ON BETA DISTRIBUTION, MONTE CARLO SIMULATION AND LIFE-CYCLE COST ANALYSISing. Vittorio Nicolosiing. Mauro DApuzzoDepartment of Mechanics, Structures and Environment; University of Cassino Italying. Pietro LorenzettiPavement Management Middle East 2009, Dubai UAE

V. Nicolosi, P.Lorenzetti, M. DApuzzo. Modelling Pay Factor in hot-mix asphalt pavement construction based on beta distribution, Monte Carlo simulation and life-cycle cost analysis

The Pay Adjustment concept in pavement constructionSlide *Quality of the construction process is a major factor in determining pavement performance under traffic loading and defined environmental conditions.To improve the construction process, quality control/quality assurance (QC/QA) procedures and pay incentives have to be instituted (i.e. transportation construction specifications) Contractor pay-adjustment incentives aim to: encourage the contractor to construct pavements with significantly improved performance in comparison to those meeting minimum specification requirements; provide a rational alternative when inadequate/adequate construction performances need to be economically evaluated.


BASIC CONCEPTSSlide *Major types of transportation construction specifications:Method Specificationsor Prescriptive Specifications End-Result Specifications Quality Assurance Specifications Performance-Related Specifications Performance-Based Specifications Report of the AASHTO Highway Subcommittee on Construction QualityOver the past few decades, many transportation Agencies developed from "Method Specifications" to "Quality Assurance Specifications".


Slide *Quality Assurance Specifications Performance-Related Specifications Performance-Based Specifications Specifications that use quantified Quality Characteristics (QCs) and Life Cycle Cost (LCC) relationships that are correlated to product performance. AASHTO

Quality Assurance Specifications describe the desired level of fundamental engineering properties (FEP) that are predictors of performance and appear in primary prediction relationships (i.e. models that can be used to predict stress, distress, or performance from combinations of predictors that represent traffic, environment, supporting materials, and structural conditions)."DifferencePRS uses QCs (e.g. asphalt content, air voids, aggregate gradations, etc.)PBS uses FEP (e.g. resilient modulus, creep properties, and fatigue)BASIC CONCEPTS


BASIC CONCEPTS OF PERFORMANCE SPECIFICATIONSlide *Material PropertiesAS-DESIGNEDMaterial PropertiesAS-CONSTRUCTEDPerformance Prediction MethodologyPerformanceAS-DESIGNEDPerformanceAS-CONSTRUCTEDLife Cycle Cost AnalysisPay FactorAS-DESIGNED Cost vs. AS-CONSTRUCTED CostTwo types of models are required:Performance-prediction Models Maintenance-cost Models


The Pay Adjustment concept in pavement construction*The Pay Factor (PF) is the reduction or amplification coefficient that has to be applied to the pavement lot bid price to correctly remunerate the pavements contractor according to the quality of the pavement constructed

A new pay factor assessment method, based on Life Cycle Cost Analysis, is now proposed

The Pay Factor (PF) assessed by LCCA approach compensate the potential higher Rehabilitation & Maintenance costs suffered by the Road Agency (within a defined analysis period) as a consequence of the lower quality pavement provided by the Contractor.


Maintenance & RehabilitationInputPay Adjustment framework based on LCCA *Construction factors (Materials properties, Layers thickness) Environmental factorsTraffic Subgrade propertiesPavement performance predictionLife-Cycle Cost evaluationFuture costs estimation(Rehabilitation & Mantenaince Costs, User costs, etc.)RRR CostsRRR PoliciesPAY FACTORAssessment


Framework for pavement performance prediction*


Maintenance & Rehabilitation Policy*

Modificare la larghezza della casella per cambiare quella del paragrafo. L'altezza della casella cambia automaticamente in funzione del testo.

FatigueCrackedArea/Section

Ruth depth

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No actiontaken

< 15 mm

Surface layerreconstruction

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Asphalt layersreconstruction

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15 mm


The Pay Adjustment concept in the LCCA approach*where:Cp is the lot bid priceLCCdes is the Life Cycle Cost in the as designed scenarioLCCcons is the Life Cycle Cost in the as constructed scenarioInitial construction costM & R costPavement Residual value


AS-DESIGN scenarioMaterials quality attributes variability*Materials perfectly meet all standard specificationsMaterials properties meet a range around standard specificationsMaterials properties are stochastic variables either in as design and as constructed scenariosAS-CONSTRUCTED scenarioMaterials properties from multiple measurements within an entire Lot Variability of relevant M&C characteristics in pay-adjustment procedures are traditionally modelled basing on normal distribution (sym Gauss bell);


Materials QC variability*Beta distribution was chosen to model the M&C variabilityDisadvantagesis defined in an infinite range while M&C characteristics assume values in a finite range.has a symmetric shape while in the construction process skewed distributions are sometimes produced by system errors.NORMAL DISTRIBUTIONAdvantagesDefined in a finite range;Different shapes from left skewed to symmetrical to right skewed;Support the calculation of an inverse probability distribution functionBETA DISTRIBUTION


Conventional Acceptance Q.ty Characteristics standards tolerate a wide spread of pavement performancesAt a design stage, its important to evaluate the effect that deviation from target quality construction specifications will have on Pay-Adjustment/Pay Factor.The PF framework proposed assess a correlation between material attributes variability and the consequent Pay FactorInfluence of performance variability on PF*


Variable definition:Asphalt concrete properties affecting pavement performances(for each AC layer)ThicknessBitumen contentLevel of CompactionFine Aggregate fractionFiller fraction

(In a 3 layers pavement: 3*5 = 15 AC parameters to be examined)Material variability modelling in the on PF prediction*


A simple Monte Carlo random generation scheme would have been too cumbersome (at least 315 = 14348907 simulations). Therefore a constrained random generation scheme has been employed (Latin Hypercube, LH).According to the LH generation method, relevant variables are split into equal-probability non overlapping intervals and permutations are performed in order to generate the input datasets for the Monte Carlo simulation.This procedure allows a dramatic reduction of the overall amount of simulations to be performed, still achieving a remarkable accuracy of the results gained. Material variability modelling in the on PF prediction*


Framework of the Latin Hypercube approach in the input data generationMaterial variability modelling in the on PF prediction*


Min, Max, Mean and St-Dev:- asphalt layer thickness- asphalt binder content - relative compaction / density- fine and filler aggregate fraction

Sampling variable Xk(based on Generalized Beta Distribution)

Pairing Valuesby random selection of a permutation Permutation set No.1 Permutation set No.2 .. Permutation set No. k

- Marshall air void (mix design)

As designed

Coarse aggregate gradationSub-fraction percentage- % retained at sieve size 19 mm- % retained at sieve size 9.5 mm- % retained at sieve size 4.75 mm

- asphalt layer thickness- asphalt binder content- relative compaction / density

Min, Max, Mean and St-Dev:- fine aggregate percentage- filler percentage

Sub-fraction %

- fine aggregate fractionfiller aggregate fraction

Air Void [%]

GENERATION OF INDEPENDENT VARIABLES VECTORS

Aggregate Gradation Data- Mean percentage of sub-fraction xx by total corse aggregate weith [%]- Deviation of percentage of sub-fraction xx by total coarse aggregate weith [%]

INPUT DATA

Evaluation of derived parameters

Vectors of input characteristics for asphalt concretes (i=1 to h is the layers number)Vector 1: (Thickness)i ,1, (Binder content)i,1 , (Air Void)i , (Ret. Sieve 19)i,1 , (Ret. Sieve 9.5)i ,1 , (Ret. Sieve 4.75)i,1 , (Pas. Sieve .075)i ,1 ....Vector m: (Thickness)i ,m , (Binder content)i ,m , (Air Void)i , (Ret. Sieve 19)i ,m , (Ret. Sieve 9.5)i,m , (Ret. Sieve 4.75)i ,m, (Pas. Sieve .075)i,m

Coarse aggregate fraction


Framework for the PF prediction formula *Influence of performance variability on PFPF prediction function is inherently project-specific !


Section layoutCase study: Input parameters*Mixes Volumetric properties

LayerSurface course (HMA)Binder course (HMA)Base course (HMA)AS -DESIGNEDLayersNominal dimension 50 70 150 ThicknessUnilateral Tolerance 1.52.1 4.5 [mm]GBD Parameters (*)(48.5, 51.5, 1.5)(67.9, 72.1, 1.5, 1.5)(145.5, 154.5, 1.5, 1.5)BinderNominal values5.254.754ContentUnilateral Tolerance0.30.30.3[%]GBD Parameters (*)(4.95, 5.55, 1.5, 1.5)(4.45, 5.05, 1.5, 1.5)(3.70, 4.30, 1.5, 1.5)Density [kg/ m3]Target value 2414 2322 2366 RelativeNominal values98.598.598.5CompactionUnilateral Tolerance1.51.51.5[%]GBD Parameters (*)(97, 100, 1.5, 1.5)(97, 100, 1.5, 1.5)(97, 100, 1.5, 1.5)AS -CONSTRUCTEDLayersMean value 50.20 67.20 145.5 ThicknessStandard Deviation 9.5 10.5 23.0 [mm]GBD Parameters (*)(47.0, 52.9, 4.650, 3.923)(65.0, 70.5, 2.234, 3.351)(139.0, 153.0, 3.814, 4.401)Bulk Mean value 2340.0 2286.3 2297.0 DensityStandard Deviation 8.0 12.00 9.5 [kg/ m3]GBD Parameters (*)(2314,2, 2366.0, 4.708, 4.748)(2250.5, 2325.6, 4.181, 4.590)(2279.0, 2318.1, 1.477, 1.731)BinderMean value 5.274.803.97ContentStandard Deviation 0.170.200.21[%]GBD Parameters (*)(4.75, 5.75, 3.946, 3.657)(4.27, 5.25, 2.676, 2.291)(3.55, 4.47, 1.708, 2.051)


Case study: Input parameters*Aggregates gradation properties section layout

LayerSurface course (HMA)Binder course (HMA)Base course (HMA)AS -DESIGNEDFineNominal values6.526.423.6AggregateUnilateral Tolerance3.03.03.0[%]GBD Parameters (*)(3.5, 9.5, 1.5, 1.5)(23.4, 29.4, 1.5, 1.5)(20.6, 26.6, 1.5, 1.5)FillerNominal values6.54.04.2contentUnilateral Tolerance1.51.51.5[%]GBD Parameters (*)(7.0, 10.0, 1.5, 1.5)(2.5, 5.5, 1.5, 1.5)(2.7, 5.7, 1.5, 1.5)AS -CONSTRUCTEDFineMean value 6.5427.8025.70AggregateStandard Deviation 1.451.551.45[%]GBD Parameters (*)(3.60, 9.98, 1.754, 2.049)(24.56, 31.45, 1.843, 2.077)(22.30, 28.95, 2.176, 2.080)FillerMean value 8.403.553.85contentStandard Deviation 0.810.710.75[%]GBD Parameters (*)(6.80, 10.10, 1.525, 1.621)(2.22, 5.10, 1.427, 1.663)(2.15, 5.65, 2.157, 2.283)


TRAFFIC DATA:Case study: Input parameters*AADTT = 1200 heavy vehicles /day Gf = 1% (per year)

Vehicle typeAxle typeAxles load [kN]% on heavy traffic strem 1) Light truckS + S 10 20 25.83 2) Light and medium truckS + S 40 808.4 3) Light and medium truckS + S 50 1105.02 4) Heavy truckS + T 40 80 800.83 5) Heavy truckS + T 60 100 1004.2 6) Truck with trailer and Articulated truckS + S + S + SS + S + T 40 90 80 80 40 90 80 808.1 7) Truck with trailer and Articulated truckS + S + S + SS + T + T 60 100 100 100 60 100 100 100 16.55 8) Truck with trailer and Articulated truckS + T + S +SS + T + T 40 80 80 80 80 40 80 80 80 804.549) Truck with trailer and Articulated truckS + T + S +SS + T + T 60 90 90 100 100 60 90 90 100 1009.2610) Truck with trailer and Articulated truckS + S + TR 40 100 80 8080 4.5411) Truck with trailer and Articulated truck "S + S + TR 70 110 90 90909.2612) Dumpers S + S + TR 4 0 130 130 1301300.0613) Dumpers " S + S 50 803.41S=single axle, T= tandem axle, TR= tridem axle


Case study: Input parameters*CLIMATE DATA

SEASONAverage air temperature Tm [C]Average daily variation in the air temperature Ag [C]Average daily radiation I[kCal / gg]Average wind speed v[m/sec]Winter46271815.5Spring129578515.5Summer2311650712Autumn148354714


Case study: pavement performance input parametersInput parameter for the first 20 pavement samples generated: AS Constructed

Iter.TicknessSurfaceCoarseFatiguelifeRutting[mm]N[cm]D [daN/mc]Va [%]Pb [%]Fine aggregate [%]Filler [%]Retained P 4Retained P 3/8YearN. VehicleHMA layersSubgrade15.0612395.0685.685.685.237.738.3544.4818.286970372.713.5725.0342398.8085.335.335.388.107.8944.3513.663576462.173.3634.9642372.5536.756.755.094.837.5343.7714.970075952.363.5044.8232375.4856.196.195.435.779.7143.4216.376981782.293.5055.1192383.3056.276.275.136.689.0041.5112.055328002.173.3364.9942379.5586.156.155.344.978.4740.0214.969811122.343.4075.0752369.3166.866.865.108.028.0842.8312.658408992.163.3984.9192394.7015.705.705.237.639.5139.0911.653674362.203.34

Iter.MAINTENANCE COSTTOTAL COSTRESIDUAL VALUELLCN.[/mq][/mq][/mq][/mq]110.1729.575.4524.12211.7731.174.9126.26311.3030.705.0625.64410.8230.225.2225.00512.4231.824.7227.10611.3130.715.0525.66712.1731.574.7926.78812.5531.954.6827.2798.7228.126.0522.071010.4629.865.3424.52


Case study: PF methodology applied*

M & R policyPavement Input ParametersPavement Performance EvaluationLife Cycle Cost AnalysisPayment Adjustment Factor Evaluation


Areacracked

Ruth depth

< 10 %

Ruth depth

10 %

Do Nothing

< 15 mm

Surface layerreconstruction

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< 15 mm


15 mm


Probability density function of life cycle cost for theas-design / as-constructed cases and DLCCCase study: DLCC evaluation*


Case Study: PF evaluationWorstBetterRisk %undertaken


About the key study:

The algorithm is robust and effectiveThe correlation between the PF and the asphalt layers properties is confirmedThe algorithm is a further step from a performance-related approach to a performance-based specification Could be a powerful tool to enhance the pay factor assessment risk management *ConclusionsAbout the methodology:

All asphalt layers properties variability are considered into the algorithmThe variability is simulated by a BETA distribution with defined range limitsThe maintenance policy could be customizedThe PF is a random variableThe specific PF is calculated by the accepted level of risk


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Over the past few decades, many transportation Agencies have moved from "Method Specifications" to "Quality Assurance Specifications". More recently, national research efforts have focused on the development and implementation of "Performance Related Specifications" and "Performance Based Specifications".Method Specifications = "Specifications that require the Contractor to produce and place a product using specified materials in definite proportions and specific types of equipment and methods under the direction of the Agency. . The principal disadvantages of Method Specifications include: 1) The Agency controls each step of the Contractor's operation; 2)The Contractor may not be allowed to use the most economical or innovative procedures and equipment to produce the product sought; 3) Materials Acceptance is based on inspection for "substantial conformance; 4)Decisions based on test results of individual Field Samples can increase disputes and confrontation between the Contractor and Agency; 5) Contractor payment is not linked to product quality or long-term performance.End-Result Specifications = "Specifications that require the Contractor to take the entire responsibility for producing and placing a product. The Agency's responsibility is to either accept or reject the final product or to apply a price adjustment commensurate with the degree of compliance with the specifications. . It is difficult to enforce such a specification and the implications are involved with legal procedures and concepts rather than sound engineering considerations.Quality Assurance Specifications = "Specifications that require Contractor Quality Control and Agency Acceptance activities throughout production and placement of a product. Final acceptance of the product is usually based on a statistical sampling of the measured quality level for key Quality Characteristics.. Quality Assurance Specifications: a) Recognize the inherent Variability of materials; b) Assign Quality Control (QC) sampling, testing, and inspection to the Contractor; c) Include Acceptance sampling, testing, and inspection by the Agency; d) Identify the specific Quality Characteristics to be measured for Acceptance; e) Provide price adjustments related to quality level of the product.

*Performance-Related and Performance Based Specifications may be considered as improved Quality Assurance Specifications.Performance-Based Specifications are different from Performance-Related Specifications in that they specify the desired levels of the actual fundamental engineering properties FEPs (not the Acceptance Quality Characteristics AQCs ) that are predictors of performance. The fundamental engineering properties specified (e.g., resilient modulus, creep properties, and fatigue properties) are used in performance prediction relationships (i.e., mathematical models) that can be used to predict stress, distress, or performance from combinations of predictors that represent traffic, environmental, and structural conditions. *In the Performance Specification a predictive methodology is used to predict the performance of a pavement structure according to two scenarios: one is the hypothetical as-designed scenario, which assumes that the materials perfectly meet all design specifications; the second is the realistic as-constructed scenario where the materials actually used is sampled and tested, and theirs properties are used to predict as-constructed performance. Finally, cost models are used to estimate the cost to the Agency specific to each scenario. The difference between the as-designed and as-constructed life cycle cost is then used as a basis for calculating a pay factor (i.e. a bonus or penalty).*Quality Assurance Specifications use Limits of Acceptance (LOA) derived using mathematical probability principles and the actual Normal Variability of local materials. Therefore materials properties have to be assumed random variable in as design scenario.In as-constructed scenario information about materials are gained from the multiple measurements within an entire Lot; individual measurements are not the most significant item. Therefore materials properties are random variables and usually represented by average and standard deviation of statistical distribution.*Variability of relevant M&C characteristics in pay-adjustment procedures are traditionally modelled basing on normal distribution; however little evidence has been found to support that assumption in the real world. While this approach is mathematically simple, normal distribution approximations present same limitations. As matter of fact normal random variable is defined in an infinite range while M&C characteristics assume values in a finite range both in the design (AQCs tolerance) and construction process. Moreover normal distribution has a symmetric shape while in the construction process skewed distributions are sometimes produced by system errors.Therefore beta distribution have been chosen for this work to model the M&C variability, because they satisfy the following requirement (Lin et al. 1997):The capability of modelling distribution with a finite range (not always from - to +);The capability of accommodating different shapes from left skewed to symmetrical to right skewed;The capability of supporting the calculation of an inverse probability distribution function which determines the distribution values corresponding to a given confidence level.The generalized beta distribution (GBD) is used in various engineering problems (e.g. Perth Method in project management), it has four parameters: a, and b (location and scale parameters), which are respectively, the minimum and maximum values of the random variable, and g and h which are the shape parameters.*The mix volumetric properties are generate as follows:- starting from a target mix recipe, the initial value of aggregate content by volume, V*a, is evaluated;- bitumen content by aggregate weight, B%, and Level of Compaction, LC are randomly generated, according to specification limits;- on-site void content, Vsite, is calculated by means of expression [15];- on-site bitumen content by volume, Vbsite, is calculated by means of expression [16].Aggregate gradation is generate as follows:- filler and fine aggregate fractions are randomly generated within the specifications limits according to a Beta distribution density function; - coarse aggregate fraction is automatically derived once filler and fine aggregate fraction are defined, since the overall sum of the three major fraction must yield 100; they refer to the ASTM standard P19 (3/4) P9,5 (3/8) P4,75 (sleave n4) P0,075 (filler)- within the coarse aggregate fraction, n-1 sub-fractions are randomly generated according to a triangle-shaped probability density function or a beta distribution.*Refer to slide 7: independent variables LCCp / LCCc >>> differenza Delta_LCC una variabile aleatoria (ipotesi semplificativa, sempre beta) con una sua varianza, media e lavore minimo e massimo >>> varianza = differenza delle varianze >>> servono quattro equazioni: differenza media, differenza varianza, valore minimo delle differenze, valore massimo delle differenze. Abbiamo generato la Montecarlo >>> abbiamo le distribuzioni LCCp e LCCc >>> da quelle ricaviamo la funzione della distribuzione della probabilit >>> lavoriamo sulle funzioni. Quindi quando facciamo le differenze lavoriamo sulle funzioni, non sulle distribuzioni. La differenza di fatto il PayFactor che si cercava.The framework previously described, has been applied to determine the pay adjustment in an case study case, in which the AQC are fixed basing on the Italian specification. Pavement layout examined is comprised by three asphalt layers on a 400 mm thick granular foundation layer resting on a subgrade whose Resilient Modulus is 90 Mpa.The target value (or mean value in the as-constructed) and the variability of M&C factors, used in the example for the as-designed and as-construction cases, are illustrated in Table*The framework previously described, has been applied to determine the pay adjustment in an case study case, in which the AQC are fixed basing on the Italian specification. Pavement layout examined is comprised by three asphalt layers on a 400 mm thick granular foundation layer resting on a subgrade whose Resilient Modulus is 90 Mpa.The target value (or mean value in the as-constructed) and the variability of M&C factors, used in the example for the as-designed and as-construction cases, are illustrated in Table*An Annual Average Daily Truck Traffic (AADTT) of 1200 vehicles/day and a compound growth factor equal to 1% is assumed in the design lane. *Quale rischio si vuole accettare. Con PF=1 >> va tutto a vantaggio dellimpresa pi mi abbasso pi va a vantaggio dellamministrazione. Sulle ordinate c il rischio percentile > sulle ascisse il valore del PayFactor corrispindente.

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