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Benkelman Beam Rebound AC Overlay Model JOINT CSHRP/MANITOBA BAYESIAN APPLICATION Appendix A Expert Judgement Encoding Package Encoding Package First Generation Bayesian Rebound Model The Department plans to develop a model which will predict the maximum Benkelman Beam Rebound BBR, or deflection, of a flexible pavement after an asphaltic concrete (AC) overlay. The Benkelman Beam Rebound is a measure of pavement strength and simulates the rebound of a pavement under an applied load. Benkelman Beam Rebound values are the maximum spring rebound readings measured in the outerwheel path of a pavement lane. The maximum BBR over a length of pavement is determined as the mean rebound value, plus two standard deviations. BBR values are temperature corrected to 20°C (1). In order to predict the effects of an AC overlay on pavement rebound, the analysis has been broken into two separate models. First, we intend to model and predict the impact of the overlay on pavement rebound immediately after construction, and second, model and predict the change in that rebound over the life of the pavement. Your judgment on the immediate, and long term, impact of the overlay on rebound is being solicited to support the development of these models. Your expert data will be analyzed and combined with limited field data, using Bayesian statistical application and software developed under the CSHRP Program. Your expert judgement should allow us to infer the performance of the overlay beyond the limited four years of field data currently available. Your assistance in providing your expert judgment would be very much appreciated. You are asked to complete the enclosed matrices for each model in Appendix 2 and 3, and provide a description of your experience to accurately characterize your expert judgement in Appendix 1. When completing the encoding forms we would request that you consider your responses within the context a typical Manitoba road section as illustrated in Fig. 1 . All subgrades can be assumed to vary from a high plastic clay to fine sand, and the depths of the overlay layers are specified in the matrix. It is assumed that the Benkelman Beam Rebound values prior to, and after overlay, is an indication of the overall strength of the pavement structure. Please complete the following information in Appendix 13: 1. A description of your experience, and 2. A completed copy of the enclosed matrices for each model. The range for each variable in the model have been described and defined in the encoding package. 1.0 MODEL 1 REBOUND IMMEDIATELY AFTER OVERLAY Model 1 is designed to predict the effects of an overlay on pavement rebound, immediately after construction. Our intent is to use your judgment, in conjunction with the field data, to model and predict the effect of the overlay on the pavement strength immediately after construction. This model will assist us in verifying and validating the current Department design procedure that uses rebound to determine overlay thickness. Model 1 consists of three independent variables (Cumulative Design ESALs, Overlay Thickness, Rebound Before Overlay BBRbo) and a dependent variable (Rebound After Overlay BBRao ). The variables have been defined for you and inference spaces for each identified. The functional form of the equation in Model 1 is as follows:
1.1 Dependent Variable 1.1.1 Benkelman Beam Rebound immediately after overlay, BBR,... The dependent variable in Model 1 is the maximum Benkelman Beam Rebound, BBRao immediately after overlay. The rebound is measured in millimetres (mm), using a Benkelman Beam device which records the maximum rebound of the pavement due to a standard load, during the critical spring season. 1.2 Independent Variables The three independent variables in Model are: 1. Cumulative Design ESALs 2. Overlay Thickness 3. Benkelman Beam Rebound before overlay 1.2.1 Cumulative Design ESALs Cumulative Design Esals represent the total traffic loading that a pavement structure has been designed to carry. ESALs, or Equivalent Single Axle Loads, is an axle group that causes the same equivalent damage as a 8165 kg (80 kilonewtons) single axle. ESALs are used to quantify and combine the damaging effect of different vehicle loadings and axle configurations on a pavement. Typical cumulative design ESALs for Manitoba range from 550,000 to 2,500,000 over a 20 year design life. Therefore, the ESALcumdes ranges to be classified in the matrix for Model fare as follows: *Low Design ESAL 500,000 * Moderate Design 1,250,000 *High Design ESAL 2,500,000 1.2.2 Overlay Thickness Overlay thickness, measured in mm, is designed to increase the structural strength of the pavement. The overlay thickness in the model does not include the existing pavement thickness. The ranges for Overlay thicknesses to be classified in the matrix in Model 1 are as follows: *Thin Overlay 50 mm *Thick Overlay 120 mm 1.2.3 Benkelman Beam Rebound before overlay, BBRbo The Benkelman Beam Rebound before overlay, BBRbo is the variable which is intended to relate the before overlay rebound to the predicted rebound after the new overlay. BBRbo values for pavements in Manitoba range from 0.50 mm to 3 mm. The BBRbo ranges to be classified in the matrix in Model fare as follows:
The encoding matrix for Model 1 is attached in Appendix 2. Please complete this matrix using your expert judgement of pavement rebound immediately after overlay. 2.0 MODEL 2 CHANGE IN DEFLECTION OVER TIME Model 2 is designed to predict the trend, or change over time, in rebound after the overlay. Once again, the intent is to use your judgment in conjunction with the field data to predict the trend in rebound. We have explicitly set the definitions and the inference space for each variable. The functional form of the equation in Model 2 is as follows:
2.1 Dependent Variable 2.1.1 Change in Benkelman Beam Rebound Over Time, BBRot The dependent variable in Model 2 is the change in Benkelman Beam Rebound BBRot, after overlay, over time. BBRot is measured in millimetres. 2.2 Independent Variables Six independent variables are considered in Model 2. These variables are: 1. Age of Overlay 2. Overlay Thickness 3. Benkelman Beam Rebound immediately after overlay BBRao 4. Cumulative ESALs, at time t 5. Environmental factor 2.2.1 Age of Overlay The age of the overlay will influence the overall strength of the asphalt pavement. For Model 2, age is measured in years from the completion of the overlay. Life expectancy of overlays in Manitoba are approximately 1520 years, and Bayesian statistics will allow us to infer the performance of the test site overlays beyond the 4 years of data currently available. The Age of Overlay ranges to be classified in the matrix in Model 2 are as follows: *Young 2 years * Midlife 8 years * Old 15 years 2.2.2 Overlay Thickness Overlay measured in mm, is designed to increase the structural strength of the pavement. Model 2 will be applicable to overlay thicknesses up to 150 mm. In order to establish the relationship between overlay thickness and rebound, two different thicknesses have been used. The Overlay Thickness ranges to be classified in the matrix in Model 2 are as follows: *Thin Overlay 50 mm *Thick Overlay 120 mm 2.2.3 Benkelman Beam Rebound immediately after overlay, BBRao The Benkelman Beam Rebound, BBRao is the rebound immediately after overlay. This variable will be used to establish the base value for rebound, and will be used to define the relationship between the BBRao at overlay, and the rebound over time t. Newly overlayed pavements in Manitoba typically has BBRao ranging from 0.25 mm to 1.5 mm. The BBRao ranges in the matrix in Model 2 is classified as follows:
2.2.4 Cumulative ESALs at Time t, ESALcum,t Cumulative ESALs at time t, ESALcum,t is an indication of the magnitude of traffic loadings on the pavement at any time during its design life. Model 2 uses ESALcum,t as one of the variables to predict pavement rebound at any time, t. Therefore, the range for ESALcum,t in the matrix for Model 2 is classified as follows: *Low Traffic Loading 300,000 *High Volume Road 2,000,000 2.2.5 Environmental Factor, EFACTOR It has been observed that the environment factors of changing temperatures and moisture can have detrimental effects on the performance of asphalt. In an attempt to include environmental factors in Model 2, the Efactor represents a factor that combines high or low precipitation and the duration of thawing during the critical thawing season. The Efactor ranges for the matrix in Model 2 is classified into high or low ranges as follows: *Low Efactor *High Efactor The encoding matrix for Model 2 is attached in Appendix 2. Please complete this matrix using your expert judgement of the change in rebound over time, after an overlay. References: (1) Report by Alberta Transportation Council of Asphaltic Concrete on granular base courses. (2) Manitoba Department of Highways "Pavement Design Manual" (3) "Bayesian Methodology for Verifying Recommendations to Minimize Asphalt Pavement Distress." NCHRP Report 213, June 1979 (4) "Strains due to Load in Frozen and Thawed Flexible Pavements. " University of Minnesota (5) Training Manual in Bayesian Methods and Software. CSHRP, 1994 |
