ing. Vittorio Nicolosi

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

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. The Pay Adjustment concept in pavement construction

3. Major types of transportation construction specifications: BASIC CONCEPTS Report of theAASHTO Highway Subcommittee on ConstructionQuality Performance-Based Specifications Performance-Related Specifications Quality Assurance Specifications End-Result Specifications Method Specifications or Prescriptive Specifications Over the past few decades, many transportation Agencies developed from "Method Specifications" to "Quality Assurance Specifications".

4. Quality Assurance Specifications BASIC CONCEPTS 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)

5. BASIC CONCEPTS OF PERFORMANCE SPECIFICATION Performance Prediction Methodology Material Properties AS-DESIGNED Performance AS-DESIGNED Performance AS-CONSTRUCTED Material Properties AS-CONSTRUCTED Life Cycle Cost Analysis • Two types of models are required: • Performance-prediction Models • Maintenance-cost Models PayFactor AS-DESIGNED Cost vs. AS-CONSTRUCTED Cost

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. The Pay Adjustment concept in pavement construction

7. Fatigue M&R required Rut depth Rutting Fatigue cracking Friction Pay Adjustment framework based on LCCA Input Pavement performance prediction Maintenance & Rehabilitation Future costs estimation (Rehabilitation & Mantenaince Costs, User costs, etc.) Construction factors (Materials properties, Layers thickness) Environmental factors Life-Cycle Cost evaluation Traffic Subgrade properties PAY FACTOR Assessment RRR Costs RRR Policies

8. Framework for pavement performance prediction

9. Maintenance & Rehabilitation Policy

10. The Pay Adjustment concept in the LCCA approach where: Cp is the lot bid price LCCdes is the Life Cycle Cost in the as designed scenario Initial construction cost Pavement Residual value M & R cost LCCcons is the Life Cycle Cost in the as constructed scenario

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

12. Materials QC variability Beta distribution was chosen to model the M&C variability NORMAL DISTRIBUTION BETA DISTRIBUTION • 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. • 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

13. Influence of performance variability on PF 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

14. Material variability modelling in the on PF prediction • Variable definition: • Asphalt concrete properties affecting pavement performances • (for each AC layer) • Thickness • Bitumen content • Level of Compaction • Fine Aggregate fraction • Filler fraction • (In a 3 layers pavement: 3*5 = 15 AC parameters to be examined)

15. Material variability modelling in the on PF prediction A simple Monte Carlo random generation scheme would have been too cumbersome (at least 315 = 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.

16. Material variability modelling in the on PF prediction Framework of the Latin Hypercube approach in the input data generation

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

18. 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 Mixes Volumetric properties Section layout

19. 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 section layout Aggregates gradation properties

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

21. Case study: Input parameters CLIMATE DATA

22. Case study: pavement performance input parameters Input parameter for the first 20 pavement samples generated: AS – Constructed

23. Case study: PF methodology applied Pavement Input Parameters Pavement Performance Evaluation M & R policy Life Cycle Cost Analysis Payment Adjustment Factor Evaluation

24. Case study: DLCC evaluation Probability density function of life cycle cost for the as-design / as-constructed cases and DLCC

25. Case Study: PF evaluation Worst Better Risk % undertaken

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 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

27. Thank you for joining … ing. Vittorio Nicolosi ing. Pietro Lorenzetti Department of Mechanics, Structures and Environment; University of Cassino Italy ing. Mauro D’Apuzzo Department of Civil Engineering University of Rome “Tor Vergata” Italy p.lorenzetti@syscomconsulting.com