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MODELLING PAY FACTOR IN HOT-MIX ASPHALT PAVEMENT CONSTRUCTION BASED ON BETA DISTRIBUTION, MONTE CARLO SIMULATION AND LIFE-CYCLE COST ANALYSIS ing. Vittorio Nicolosi ing. Mauro D’Apuzzo Department of Civil Engineering University of Rome “Tor Vergata” Italy Department of Mechanics, Structures and Environment; University of Cassino Italy ing. Pietro Lorenzetti Pavement Management Middle East 2009, Dubai UAE

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V. Nicolosi, P.Lorenzetti, M. D’Apuzzo. 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 construction Slide 2 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.

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V. Nicolosi, P.Lorenzetti, M. D’Apuzzo. Modelling Pay Factor in hot-mix asphalt pavement construction based on beta distribution, Monte Carlo simulation and life-cycle cost analysis BASIC CONCEPTS Slide 3 Major types of transportation construction specifications: Method Specifications or Prescriptive Specifications End-Result Specifications Quality Assurance Specifications Performance- Related Specifications Performance- Based Specifications Report of the AASHTO Highway Subcommittee on Construction Quality Over the past few decades, many transportation Agencies developed from "Method Specifications" to "Quality Assurance Specifications".

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V. Nicolosi, P.Lorenzetti, M. D’Apuzzo. Modelling Pay Factor in hot-mix asphalt pavement construction based on beta distribution, Monte Carlo simulation and life-cycle cost analysis Slide 4 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)." Difference PRS uses QCs (e.g. asphalt content, air voids, aggregate gradations, etc.) PBS uses FEP (e.g. resilient modulus, creep properties, and fatigue) BASIC CONCEPTS

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V. Nicolosi, P.Lorenzetti, M. D’Apuzzo. Modelling Pay Factor in hot-mix asphalt pavement construction based on beta distribution, Monte Carlo simulation and life-cycle cost analysis BASIC CONCEPTS OF PERFORMANCE SPECIFICATION Slide 5 Material Properties AS-DESIGNED Material Properties AS-CONSTRUCTED Performance Prediction Methodology Performance AS-DESIGNED Performance AS-CONSTRUCTED Life Cycle Cost Analysis Pay Factor AS-DESIGNED Cost vs. AS-CONSTRUCTED Cost Two types of models are required: Performance-prediction Models Maintenance-cost Models

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V. Nicolosi, P.Lorenzetti, M. D’Apuzzo. 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 construction 6 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 pavement’s 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.

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V. Nicolosi, P.Lorenzetti, M. D’Apuzzo. Modelling Pay Factor in hot-mix asphalt pavement construction based on beta distribution, Monte Carlo simulation and life-cycle cost analysis Maintenance & Rehabilitation Input Pay Adjustment framework based on LCCA 7 Construction factors (Materials properties, Layers thickness) Environmental factors Traffic Subgrade properties Pavement performance prediction Fatigue Rutting Friction Life-Cycle Cost evaluation Rut depth Fatigue cracking M&R required Future costs estimation (Rehabilitation & Mantenaince Costs, User costs, etc.) RRR Costs RRR Policies PAY FACTOR Assessment

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V. Nicolosi, P.Lorenzetti, M. D’Apuzzo. Modelling Pay Factor in hot-mix asphalt pavement construction based on beta distribution, Monte Carlo simulation and life-cycle cost analysis Framework for pavement performance prediction 8

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V. Nicolosi, P.Lorenzetti, M. D’Apuzzo. Modelling Pay Factor in hot-mix asphalt pavement construction based on beta distribution, Monte Carlo simulation and life-cycle cost analysis Maintenance & Rehabilitation Policy 9

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V. Nicolosi, P.Lorenzetti, M. D’Apuzzo. 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 the LCCA approach 10 where: C p is the lot bid price LCC des is the Life Cycle Cost in the as designed scenario LCC cons is the Life Cycle Cost in the as constructed scenario Initial construction cost M & R cost Pavement Residual value

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V. Nicolosi, P.Lorenzetti, M. D’Apuzzo. Modelling Pay Factor in hot-mix asphalt pavement construction based on beta distribution, Monte Carlo simulation and life-cycle cost analysis AS-DESIGN scenario Materials quality attributes variability 11 Materials perfectly meet all standard specifications Materials properties meet a range around standard specifications Materials properties are stochastic variables either in “as design” and “as constructed” scenarios AS-CONSTRUCTED scenario Materials 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);

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V. Nicolosi, P.Lorenzetti, M. D’Apuzzo. Modelling Pay Factor in hot-mix asphalt pavement construction based on beta distribution, Monte Carlo simulation and life-cycle cost analysis Materials QC variability 12 Beta distribution was chosen to model the M&C variability Disadvantages is 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 DISTRIBUTION Advantages Defined in a finite range; Different shapes from left skewed to symmetrical to right skewed; Support the calculation of an inverse probability distribution function BETA DISTRIBUTION

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V. Nicolosi, P.Lorenzetti, M. D’Apuzzo. Modelling Pay Factor in hot-mix asphalt pavement construction based on beta distribution, Monte Carlo simulation and life-cycle cost analysis Conventional Acceptance Q.ty Characteristics standards tolerate a wide spread of pavement performances At a design stage, it’s 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 Factor Influence of performance variability on PF 13

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V. Nicolosi, P.Lorenzetti, M. D’Apuzzo. Modelling Pay Factor in hot-mix asphalt pavement construction based on beta distribution, Monte Carlo simulation and life-cycle cost analysis Variable definition: Asphalt concrete properties affecting pavement performances (for each AC layer) 1.Thickness 2.Bitumen content 3.Level of Compaction 4.Fine Aggregate fraction 5.Filler fraction (In a 3 layers pavement: 3*5 = 15 AC parameters to be examined) Material variability modelling in the on PF prediction 14

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V. Nicolosi, P.Lorenzetti, M. D’Apuzzo. Modelling Pay Factor in hot-mix asphalt pavement construction based on beta distribution, Monte Carlo simulation and life-cycle cost analysis A simple Monte Carlo random generation scheme would have been too cumbersome (at least 3 15 = 14’348’907 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 15

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V. Nicolosi, P.Lorenzetti, M. D’Apuzzo. Modelling Pay Factor in hot-mix asphalt pavement construction based on beta distribution, Monte Carlo simulation and life-cycle cost analysis Framework of the Latin Hypercube approach in the input data generation Material variability modelling in the on PF prediction 16

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V. Nicolosi, P.Lorenzetti, M. D’Apuzzo. Modelling Pay Factor in hot-mix asphalt pavement construction based on beta distribution, Monte Carlo simulation and life-cycle cost analysis Framework for the PF prediction formula 17 Influence of performance variability on PF PF prediction function is inherently project-specific !

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V. Nicolosi, P.Lorenzetti, M. D’Apuzzo. Modelling Pay Factor in hot-mix asphalt pavement construction based on beta distribution, Monte Carlo simulation and life-cycle cost analysis Section layout WEARING COURSE (Asphalt Concrete) BINDER COURSE (Asphalt Concrete) BASE COURSE (Asphalt Concrete) SUBBASE COURSE (Cement treaded granular material) SUBGRADE (Site Soil) Case study: Input parameters 18 Layer Surface course (HMA) Binder course (HMA) Base course (HMA) AS -DESIGNED LayersNominal dimension 5070150 ThicknessUnilateral Tolerance 1.52.14.5 [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 values 5.254.754 ContentUnilateral Tolerance 0.3 [%]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 241423222366 RelativeNominal values 98.5 CompactionUnilateral Tolerance 1.5 [%]GBD Parameters (*) (97, 100, 1.5, 1.5) AS -CONSTRUCTED LayersMean value 50.2067.20145.5 ThicknessStandard Deviation 9.510.523.0 [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) BulkMean value 2340.02286.32297.0 DensityStandard Deviation 8.012.009.5 [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 5.274.803.97 ContentStandard 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) Mixes Volumetric properties

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V. Nicolosi, P.Lorenzetti, M. D’Apuzzo. Modelling Pay Factor in hot-mix asphalt pavement construction based on beta distribution, Monte Carlo simulation and life-cycle cost analysis WEARING COURSE (Asphaltic Concrete) BINDER COURSE (Asphaltic Concrete) BASE COURSE (Asphaltic Concrete) SUBBASE COURSE (Cement treaded granular material) SUBGRADE (Site Soil) Case study: Input parameters 19 Aggregates gradation properties Layer Surface course (HMA) Binder course (HMA) Base course (HMA) AS -DESIGNED FineNominal values 6.526.423.6 AggregateUnilateral Tolerance 3.0 [%]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 values 6.54.04.2 contentUnilateral Tolerance 1.5 [%]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 -CONSTRUCTED FineMean value 6.5427.8025.70 AggregateStandard 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 8.403.553.85 contentStandard 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) section layout

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V. Nicolosi, P.Lorenzetti, M. D’Apuzzo. Modelling Pay Factor in hot-mix asphalt pavement construction based on beta distribution, Monte Carlo simulation and life-cycle cost analysis TRAFFIC DATA: Case study: Input parameters 20 Vehicle typeAxle typeAxles load [kN]% on heavy traffic strem 1) Light truckS + S 10 2025.83 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 truck S + S + S + S S + S + T 40 90 80 80 8.1 7) Truck with trailer and Articulated truck S + S + S + S S + T + T 60 100 100 100 16.55 8) Truck with trailer and Articulated truck S + T + S +S S + T + T 40 80 80 80 80 4.54 9) Truck with trailer and Articulated truck S + T + S +S S + T + T 60 90 90 100 100 9.26 10) Truck with trailer and Articulated truck S + S + TR 40 100 80 80804.54 11) Truck with trailer and Articulated truck " S + S + TR 70 110 90 90909.26 12) DumpersS + S + TR 4 0 130 130 1301300.06 13) Dumpers "S + S 50 803.41 S=single axle, T= tandem axle, TR= tridem axle AADTT = 1200 heavy vehicles /day Gf = 1% (per year)

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V. Nicolosi, P.Lorenzetti, M. D’Apuzzo. Modelling Pay Factor in hot-mix asphalt pavement construction based on beta distribution, Monte Carlo simulation and life-cycle cost analysis Case study: Input parameters 21 SEASON Average 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] Winter46271815.5 Spring129578515.5 Summer2311650712 Autumn148354714 CLIMATE DATA

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V. Nicolosi, P.Lorenzetti, M. D’Apuzzo. Modelling Pay Factor in hot-mix asphalt pavement construction based on beta distribution, Monte Carlo simulation and life-cycle cost analysis Case study: pavement performance input parameters Input parameter for the first 20 pavement samples generated: AS – Constructed Iter. Ticknes sSurfaceCoarseFatiguelifeRutting[mm] N[cm] D [daN/mc] Va [%] Pb [%] Fine aggregate [%] Fille r [%] Retain ed P 4 Retained P 3/8 YearN. Vehicle HMA layersSubgrade 15.0612395.0685.68 5.237.738.3544.4818.286970372.713.57 25.0342398.8085.33 5.388.107.8944.3513.663576462.173.36 34.9642372.5536.75 5.094.837.5343.7714.970075952.363.50 44.8232375.4856.19 5.435.779.7143.4216.376981782.293.50 55.1192383.3056.27 5.136.689.0041.5112.055328002.173.33 64.9942379.5586.15 5.344.978.4740.0214.969811122.343.40 75.0752369.3166.86 5.108.028.0842.8312.658408992.163.39 84.9192394.7015.70 5.237.639.5139.0911.653674362.203.34 Iter.MAINTENANCE COSTTOTAL COST RESIDUAL VALUE LLC N.[€/mq] 110.1729.575.45 24.12 211.7731.174.91 26.26 311.3030.705.06 25.64 410.8230.225.22 25.00 512.4231.824.72 27.10 611.3130.715.05 25.66 712.1731.574.79 26.78 812.5531.954.68 27.27 98.7228.126.05 22.07 1010.4629.865.34 24.52

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V. Nicolosi, P.Lorenzetti, M. D’Apuzzo. Modelling Pay Factor in hot-mix asphalt pavement construction based on beta distribution, Monte Carlo simulation and life-cycle cost analysis Case study: PF methodology applied 23 M & R policy Pavement Input Parameters Pavement Performance Evaluation Life Cycle Cost Analysis Payment Adjustment Factor Evaluation

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V. Nicolosi, P.Lorenzetti, M. D’Apuzzo. Modelling Pay Factor in hot-mix asphalt pavement construction based on beta distribution, Monte Carlo simulation and life-cycle cost analysis Probability density function of life cycle cost for the as-design / as-constructed cases and LCC Case study: LCC evaluation 24

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V. Nicolosi, P.Lorenzetti, M. D’Apuzzo. Modelling Pay Factor in hot-mix asphalt pavement construction based on beta distribution, Monte Carlo simulation and life-cycle cost analysis Case Study: PF evaluation WorstBetter Risk % undertaken

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V. Nicolosi, P.Lorenzetti, M. D’Apuzzo. Modelling Pay Factor in hot-mix asphalt pavement construction based on beta distribution, Monte Carlo simulation and life-cycle cost analysis About the key study: The algorithm is robust and effective The correlation between the PF and the asphalt layers properties is confirmed The 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 26 Conclusions About the methodology: All asphalt layers properties variability are considered into the algorithm The variability is simulated by a BETA distribution with defined range limits The maintenance policy could be customized The PF is a random variable The specific PF is calculated by the accepted level of risk

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V. Nicolosi, P.Lorenzetti, M. D’Apuzzo. Modelling Pay Factor in hot-mix asphalt pavement construction based on beta distribution, Monte Carlo simulation and life-cycle cost analysis Thank you for joining … ing. Vittorio Nicolosi ing. Mauro D’Apuzzo Department of Civil Engineering University of Rome “Tor Vergata” Italy Department of Mechanics, Structures and Environment; University of Cassino Italy ing. Pietro Lorenzetti p.lorenzetti@syscomconsulting.com

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