D. Jones. R. Wu. J. Lea. Q. Lu. Phone: Phone:

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1 CalME: A New Mechanistic-Empirical Design Program for Flexible Pavement Rehabilitation P. Ullidtz, corresponding Dynatest International Naverland, DK 00 Glostrup, Denmark Phone: pullidtz@dynatest.com J. Harvey University of California Pavement Research Center Department of Civil and Environmental Engineering University of California, Davis, California, USA Phone: jtharvey@ucdavis.edu I. Basheer Division of Pavement Management California Department of Transportation (Caltrans) 00 Folsom Blvd. Sacramento, California, USA Phone: () -0 imad.basheer@dot.ca.gov D. Jones University of California Pavement Research Center Department of Civil and Environmental Engineering University of California, Davis, California, USA Phone: 0 djjones@ucdavis.edu R. Wu University of California Pavement Research Center Department of Civil and Environmental Engineering University of California, Davis, California, USA Phone: -- rzwu@ucdavis.edu J. Lea University of California Pavement Research Center Department of Civil and Environmental Engineering University of California, Davis, California, USA Phone: 0 jdlea@ucdavis.edu Q. Lu University of California Pavement Research Center S. th St., Bldg. -T University of California, Berkeley Richmond, CA 0, USA Tel: () -, Fax: () - qlu@ucdavis.edu Word count: words, 0 words: Total words. TRB 0 Annual Meeting CD-ROM

2 0 0 0 Mechanistic-Empirical Design of Asphalt Overlays using CalME ABSTRACT A computer program, known as CalME, has been developed for analysis and design of new flexible pavements and rehabilitation of existing pavements. The paper describes the overlay design procedure and the calibration of the models for reflection cracking and permanent deformation through Heavy Vehicle Simulator (HVS) tests. To simplify the input process the program includes databases for traffic loading, climatic conditions and standard materials. A companion program was developed for backcalculation of layer moduli, and the results may be automatically imported into the CalME database. The program incorporates the existing, empirical California Department of Transportation (Caltrans) design methods as well as an incremental-recursive analysis procedure based on the mechanistic-empirical method. The effects of different pavement preservation and rehabilitation strategies on pavement damage may be studied with several options for triggering timing of placement. The influence of within-project variability on the propagation of damage can be evaluated using Monte Carlo simulation. The program also permits importation of the results of HVS or track tests into the database and simulation of the experiments on the computer. This is very useful for the calibration of the mechanistic-empirical models, but may also be used for an in-depth interpretation of accelerated pavement testing results. An HVS experiment that was used for calibration of the reflection cracking and the permanent deformation models is described. INTRODUCTION CalME is a computer program developed by Caltrans for analysis and design of rehabilitation, using asphalt overlays, and of new flexible pavements. It is currently configured for California practice. It includes the existing Caltrans empirical design methods, a classical mechanistic-empirical (ME) method, and an incremental-recursive ME-based procedure using the time-hardening approach for modeling and simulating pavement response and performance. The models for new design, and their calibration using Heavy Vehicle Simulator (HVS) tests, are described in Ullidtz et al., 00. The present paper presents a quick summary of the program and an overview of the models used for rehabilitation design and their calibration using HVS testing. CalME was developed beginning in the late 0s using research products from the SHRP program (-), subsequent Caltrans sponsored research and development, and gathering of models and data from research programs around the world. CalME was developed to fill the following needs for an ME analysis tool for use in California: Emphasis on rehabilitation and pavement preservation (a term invented later), which account for more than 0 percent of Caltrans pavement program, rather than new pavements. Emphasis on use of in-situ pavement testing data for existing pavements (namely Falling Weight Deflectometer [FWD] data) as opposed to sampling and laboratory testing. TRB 0 Annual Meeting CD-ROM

3 0 0 0 Able to consider reflection cracking, rutting in overlays and modified asphalt mixtures, particularly rubber- and polymer-modified mixes. Capable of simulating damage and predicting pavement response (deflections, strains, stresses) throughout the pavement life as opposed to only the initial and final conditions. Compatible with calibration using accelerated pavement testing data (made possible by the previous item). Able to consider variability through Monte Carlo simulation with reasonable run times. Source code available to Caltrans and partner agencies for understanding and modification. Development was continued by Caltrans early in this decade when it was determined from available information that the National Cooperative Highway Research Program (NCHRP) Mechanistic Empirical Pavement design Guide (MEPDG) flexible pavement models did not fully meet these criteria. Caltrans ultimate goal is that CalME or its models and ideas become part of multi-state or national long-term research and development programs. OVERLAY DESIGN WITH CalME An important input for design of an asphalt overlay is the structural condition of the existing pavement. The material types, the layer thicknesses and resilient moduli must be determined. A companion program called CalBack has been developed for backcalculation of layer moduli from FWD data (for details see Lu et al., 00). CalBack stores the material types, test temperatures, layer thicknesses and backcalculated moduli in a database, from which the information is automatically imported into CalME. The variability of the layer moduli is calculated by CalME for use with the Monte Carlo simulation option. For existing asphalt pavements with surface cracking the typical distance between the cracks must be recorded. For jointed Portland cement concrete (PCC) pavements the distance between the joints is required for use in the reflection cracking model. Traffic Data The required traffic input is the axle load spectrum from a Weigh In Motion (WIM) station. CalME has a database with axle load spectra from all WIM stations in California, and the appropriate WIM station is selected from a list by the user. For Californian conditions a procedure has been developed to obtain axle load spectra for highways without WIM information (Lu and Harvey, 00, Lu 00). Climate California has been divided into a number of climate zones, for the purpose of flexible pavement design (Harvey et al. 000). For each zone the surface temperature each hour during a period of 0 years has been precalculated, for a range of pavement structures, and included in the CalME database. CalME calculates the temperatures at the required depths based on interpolation between EICM simulations for representative structures TRB 0 Annual Meeting CD-ROM

4 (Ongel et al, 00) using an algorithm that reduces the size of the database and speeds retrieval. 0 0 Figure Basic input parameters for rehabilitation design. In the caption of the form shown in Figure the climate zone (Mountain, High Desert) and the WIM station (WIM00) are indicated. Both of these are chosen by the user from a list. The design life for the initial treatment is selected by the user (default 0 years shown). The number of axle loadings in the design lane during the first year of the design period and the annual growth rate in percent are imported from the traffic database. The values may be changed by the user. Materials Library In Figure, the layer names, thicknesses and moduli are imported from the CalBack database. Each name is associated with a large number of model parameters describing the master curve, fatigue properties, permanent deformation susceptibility, and other model parameters appropriate for the material type. The CalME database has a library of standard pavement materials based on their specification class, with default data based on laboratory and field testing for representative materials. When imported from a CalBack database the names are preceded by Old- to indicate that these are existing materials. The moduli are the mean values, and for asphalt materials the values displayed are for the annual average temperature and to a loading time of msec. The remaining information in the table and the information in the Rehabilitation frame is related to the Caltrans empirical design methods. Caltrans Empirical Method The present Caltrans rehabilitation design method is based on the 0 th percentile deflection value (D0), corresponding to the California deflectograph load. This is calculated from the temperature adjusted layer moduli in CalBack. The CalME architecture is amenable to inclusion of other empirical methods for initial design and comparison purposes. TRB 0 Annual Meeting CD-ROM

5 The Tolerable Deflection at Surface and the required Percent Reduction in Deflection, for the design traffic, is calculated in accordance with the Caltrans Highway Design Manual (Caltrans 00). A list of rehabilitation alternatives is then presented (see Figure ). Clicking on the line of one of the alternatives will add this alternative to the structure shown in Figure. The solution with Mill, for example would remove all of the existing asphalt layer (0 mm thick) and 0 mm of the aggregate base (AB) and replace it with mm of Dense Graded Asphalt Concrete (DGAC). 0 Figure List of Rehabilitation alternatives from Caltrans rehabilitation design. Classical ME Method In Figure, the Classical Design method uses the Asphalt Institute design criteria (although other criteria may be used). The user may select this method to check the residual life of the existing structure. This method may also be used to design an overlay for fatigue cracking and overall pavement rutting (subgrade strain criteria). Incremental-Recursive Analysis In Figure, this method is labeled as Recursive. The incremental-recursive procedure does not propose a rehabilitation design, but may be used to determine how a given design performs with respect to rutting and cracking in each layer. For instance, selecting the 0 mm DGAC solution from Figure, and running the incremental-recursive analysis (with no lateral traffic wander and including reflection cracking) would result in a total permanent deformation (RD) of. mm and cracking density (Cr) of 0. m/m after 0 years, which would be satisfactory for typical design limits of mm of permanent deformation and 0. m/m of cracking. TRB 0 Annual Meeting CD-ROM

6 Figure Performance versus time with 0 mm DGAC overlay ( years between vertical bold lines). Simulations are carried out to two times the design life plus one year, or years in this example (Figure ), to limit truncation of data for the Monte Carlo simulations. Monte Carlo Simulation The simulation in Figure is based on the mean values of all parameters. CalME has a Monte Carlo simulation option, where the input includes the distribution of a number of important structural parameters. This makes it possible to determine the influence of within-project variability on the propagation of damage. The variability of layer moduli is calculated from the backcalculated values imported from the CalBack database. For each of the Monte Carlo runs the parameters are selected randomly from the distributions. Wes0FLM_MC... Cracking, m/msq Years Figure Cracking severity as a function of time (0 simulations), mean and ± one standard deviation. TRB 0 Annual Meeting CD-ROM

7 Wes0FLM_MC Percent >= 0. m/msq Years Figure Crack propagation as a function of time (0 simulations). Figure shows the development of cracking severity over time. The heavy curve is the mean cracking severity for the 0 Monte Carlo simulations, the thin curves indicate the mean value plus and minus one standard deviation, and the horizontal line is the limit. The mean cracking severity will reach the limit after years. Figure shows the propagation of the cracked area within the project through progressive crack development in sub-sections, with cracking having a cracking severity of 0. m/m or more within a sub-section. Less than % of the area will reach the limit within the design life of 0 years. Twenty simulations of years each for this structure took approximately 0 minutes on a 00 model Xs Lenovo laptop computer. Maintenance and Rehabilitation Scheduling CalME offers the user the ability to schedule one or more maintenance and rehabilitation (M&R) or pavement preservation activities. An example is shown in Figure where 0 mm has been milled and inlaid with HMA at year 0 and simulation of cracking (red line) and rutting (blue line) is continued for another 0 years. TRB 0 Annual Meeting CD-ROM

8 0 0 Figure Performance prediction with 0 mm mill and fill with HMA after 0 years. M&R strategies may also be set up based on the pavement condition in terms of level of permanent deformation and/or cracking of the wearing course rather than a fixed year, which permits consideration of different pavement preservation actions and trigger criteria. CALIBRATION OF MODELS One of the facilities of CalME is that the results of HVS or track tests can be imported into the CalME database. The test may then be simulated, hour by hour for the duration of the test, and the predicted responses and performances can be compared to the measured values from pavement instrumentation; thus facilitating the calibration of the CalME models. The HVS project used for calibration of overlay models was divided into two phases. In the first phase, six test sections of a uniform pavement were trafficked with the HVS to induce fatigue cracking on the asphalt concrete layer. The original pavement consisted of approximately 0 mm of DGAC on a design thickness of mm of aggregate base (AB) on a clay subgrade. The AB consisted of 0% recycled building waste material with a high percentage of crushed concrete. Reactive cement was found in the AB. In the second phase, selected overlay mixes were placed both on the trafficked and untrafficked sections to evaluate reflection cracking as well as permanent deformation. The test sections were instrumented with Multi Depth Deflectometers (MDDs) and thermocouples. At regular intervals during the HVS tests the resilient deflections were recorded at several depths using the MDDs and at the pavement surface using a Road Surface Deflectometer (RSD, similar to a Benkelman beam). The permanent deformations were also recorded by the MDDs and the pavement profile was measured using a laser profilometer. Any distress at the surface of the pavement was recorded. During HVS testing the temperature was controlled using a climate chamber. Falling Weight Deflectometer (FWD) tests were carried out before and after the HVS tests. Details on the HVS and the instrumentation can be found in Harvey et al., and on the overall study in Jones et al, 00a and 00b. TRB 0 Annual Meeting CD-ROM

9 0 0 Elastic Parameters and Calculation of Response Elastic parameters of the materials were backcalculated from the last FWD tests before commencement of the HVS loading. For asphalt layers, the master curve was obtained from frequency sweep tests on beams in the laboratory. With the exception of the original DGAC layer the agreement between the backcalculated moduli and the laboratory master curves was good. For the subgrade, the change in stiffness with changing stiffness of the pavement layers and with changing load level was obtained from FWD backcalculated values. These parameters were used with a layered elastic response model to calculate stresses, strains and deflections in the pavement structure, for each hour of the tests. Reflection cracking damage was calculated using the method developed by Wu (00). In this method the tensile strain at the bottom of the overlay over an existing crack is estimated using a regression equation developed using many D and D finite element calculations. This tensile strain is used with the fatigue equation to calculate damage in the asphalt layers. The tensile strain at the bottom of the overlay, in ìstrain, is calculated from the following equation assuming a dual wheel on a single axle: a b lnls expb H b H b E Ean E bn n an E E E E a E b E u o an, E bn, E un, E n, s s s Es LS H H LS H a H u n, a an, a un a Equation un un n where E a and H a are the overlay modulus and thickness, respectively, E u and H u are the underlayer modulus and thickness, respectively, E b is the modulus of the base/sub-base, E s is the modulus of the subgrade, LS is the crack spacing, ó o is the tire pressure, and a is the radius of the loaded area for one wheel, and constants are as follows: á = 0, â = -0., â = -0., â = -., a = 0., b = 0., b = -0., b = -0.0, b = 0.0. Prediction of Damage in Asphalt To predict reflection cracking, the resulting principal tensile strain at the tip of the crack from Equation was used with the model for the master curve of the damaged asphalt, which has the format: log E Equation exp log tr where ä, á, â, and ã are constants, tr is reduced time in sec and ù is the damage, calculated from: TRB 0 Annual Meeting CD-ROM

10 0 0 MN MNp MNp A Equation ref E E ref A' SE SE where E is the modulus of damaged material, E i is the modulus of intact material, MN is the number of load repetitions in millions (N/ ), ìå is the strain at the bottom of the asphalt layer, SE is the strain energy, and A, A, á, â, ìå ref, E ref, and SE ref are constants (not related to the constants of Equation ). The initial (intact) modulus, E i, corresponds to a damage, ù, of 0 and the minimum modulus, E min = ä, to a damage of. The parameters of Equation were determined from four point bending beam fatigue tests in the laboratory. ref Prediction of Damage in Aggregate Base (AB) The recycled base showed some cementing characteristics (un-hydrated cement released from the crushed concrete) and CalME can calculate damage in lightly cemented layers. Before the HVS tests the material might reach a modulus of more than 00 MPa, which during the HVS loading could drop to about 0 MPa. To ensure that the stresses and strains were correctly calculated for the duration of the experiment, it was necessary to model this performance. A crushing model was developed based on a model used in a Nordic HVS experiment on weak cement treated bases (Thoegersen et al., 00). The model was changed to use the vertical stress at the top of the layer, instead of the tensile strain at the bottom, resulting in the following damage function for the aggregate base: z E MN ref Ei Equation Damage function for recycled aggregate base. Where ù is the damage, MN is the number of load applications in millions, ó z is the vertical, normal stress at the top of a layer, ó ref is a permissible stress, E is the modulus of the material (= ( - ù) E i ), E i is the initial modulus of the material, and á, â, and ã are calculated in the same way as for the HVS-Nordic model. The initial modulus (E i ) was backcalculated from the last FWD test before the HVS experiment, and the value of the permissible stress (ó ref ) was chosen so that the final modulus of the base would be close to the modulus determined for the layer from the first FWD test after the HVS experiment, and that the calculated RSD and MDD deflections would be close to the measured values. The base layer was originally constructed in three lifts and for the simulations it was subdivided into three layers. The model was used on each of the layers, resulting in the lowest modulus being at the top of the base. Dynamic TRB 0 Annual Meeting CD-ROM

11 Cone Penetrometer tests confirmed this to be the case. Extension of this type of model to full-depth in-place recycling and no modification or modification with cement and/or foamed asphalt is a next step in development. Simulation of Pavement Response The deflections normally increase considerably during an HVS test, as a result of damage to the bound layers (asphalt and re-cementing AB in this case). This means that the stresses and strains in the pavement layers, which are used in calculation of the pavement performance, also change during the test. To ensure that the pavement response calculated by CalME was reasonably correct for the duration of the test, the surface deflections and the deflections at the depths of the MDD modules were calculated by CalME and compared to the RSD and MDD measurements. 0 Figure Measured (RSD) and calculated (Calc) surface deflection versus load applications. Figure shows a comparison of surface deflection under a 0 kn wheel load, for the test section with a mm MB (modified binder containing up to % recycled tire rubber) overlay. Even though the monitored test section is only m long the measured surface deflections vary considerably over the area of the test section, sometimes by as much as a factor of. The coefficient of variation on the RSD measurements varies from less than % to more than 0%. It may be noticed that the deflection increases by more than 0% within the first one million load applications. The drop in deflection after one million load applications is due to the pavement temperature being reduced from 0 ºC to ºC. The deflections calculated by CalME are seen to be in reasonably good agreement with the average of the RSD deflections. TRB 0 Annual Meeting CD-ROM

12 Measured and calculated surface deflections, MB 0 Deflection, mm RSD Monte Carlo Number of load applications 0 Figure. Monte Carlo simulation of the MB section In Figure the Monte Carlo option in CalME was used for the MB section. It shows that the predicted scatter in surface deflection using the Monte Carlo approach is similar to the scatter of the measured values. Permanent Deformation Once the pavement response had been successfully simulated it was possible to calibrate the permanent deformation models. Permanent deformations were measured both during the rutting experiment and during the reflection cracking experiment. The permanent deformation (down rut) in the asphalt layers was calculated from: dp K Equation h i i i where K is a calibration factor determined from HVS testing, h i is the thickness of layer i, and ã i i is the inelastic (permanent) shear strain in layer i, determined from: i exp A exp ln Equation N lnn e exp ref where ã e is the elastic (resilient) shear strain, ô is the shear stress, N is the number of load repetitions, ô ref is a reference shear stress (0. MPa), and A, á, â, and ã are constants determined from the Repeated Simple Shear Tests at Constant Height. The summation in Equation is done for the top 0 mm of the asphalt. Permanent deformation due to post compaction was not calculated. Permanent deformations of the TRB 0 Annual Meeting CD-ROM

13 unbound layers were calculated using the model given in Ullidtz, et al. (00) and were found to be relatively small for all tests. The same calibration factor (K =.) was used for all of the tests, even though the rutting experiment was done using uni-directional loading, at a temperature of -0 C at a depth of mm, and the reflection cracking experiment was with bi-directional loading, at temperatures of -0 C. Rutting study, uni-directional, -0 C at 0 mm Calculated down rut, mm MB mm RAC-G mm DGAC 0 mm MB mm MB 0 mm MAC mm = 0 0 Measured down rut, mm Figure Measured and calculated down rut during rutting study. Reflection cracking study, bi-directional, 0 C Calculated down rut, mm MB mm RAC-G mm DGACa 0 mm DGACb 0 mm MB mm MB 0 mm MAC mm = 0 0 Measured down rut, mm Figure Measured and calculated down rut during reflection cracking study. TRB 0 Annual Meeting CD-ROM

14 0 The measured and the simulated down rut during the rutting study are shown in Figure. For all of the tests the calculated down rut is % lower than the measured values, with an R of 0. and a standard error of estimate of. mm. For the reflection cracking study (Figure ) the calculated down rut is % below the measured values, the R is 0. and the standard error of estimate is 0. mm. Cracking A reasonably good fit could be obtained for the reflection cracking density using the following equations: m / m Cr. o Equation. where Cr is the cracking in m/m, ù o is a constant determined from the crack density (0. m/m ) at crack initiation. ù i is the amount of damage at crack initiation and is calculated from: i 0 Equation h AC mm where h AC is the combined thickness of the asphalt layers. Figure compares the observed reflection cracking on the overlay sections to the reflection damage predicted using Equation, as a function of the reflection damage calculated from Equation and Equation. Note that some of the sections did not crack, which was predicted by CalME. TRB 0 Annual Meeting CD-ROM

15 Cracking, m/m MB mm RAC-G mm DGAC 0 mm a DGAC 0 mm b MB mm MB 0 mm MAC mm Calc mm Calc 0 mm Reflection damage Figure Surface cracking as a function of reflection damage. Figure shows the predicted reflection cracking severity as a function of the observed severity. The predicted cracking levels were in good agreement with observed values. Predicted reflection cracking versus observed cracking Calculated cracking, m/m y =.0x R = Observed cracking, m/m Figure Predicted reflection cracking severity as a function of observed severity. TRB 0 Annual Meeting CD-ROM

16 0 0 0 CONCLUSIONS CalME has been found to be a useful tool for progressing from the presently used empirical models to mechanistic-empirical models for design of rehabilitation, maintenance and pavement preservation overlays and new asphalt pavements. The use of pre-established databases for traffic loading, climatic conditions and standard materials simplify the input process. For overlay design the results of backcalculated FWD data may be automatically imported and different maintenance and rehabilitation strategies may be quickly analyzed. Laboratory data can also be used for input. Reliability-based designs can also be performed by utilizing the Monte Carlo option in CalME which allows studying the influence of within-project variability on the progression of pavement damage. The Monte Carlo simulations have run times on typical personal computers that are feasible for engineering practice. The facility for importing accelerated pavement testing results (e.g. HVS or track tests) into the CalME database and simulating the experiment on the computer, has been found useful for calibrating the models used in CalME. These calibrations increase the confidence in the models, but the facility may also be used to enhance the interpretation of HVS experiments. Even though great efforts are taken to ensure uniform conditions for all experiments, it is impossible to avoid variations in materials, subgrade support or in climatic conditions during testing. Once the experiments have been imported into CalME, virtual experiments may be carried out with exactly identical conditions for all of the tests. Future enhancement of CalME includes: calibrating the developed pavement roughness model (based on variability), investigating the influence of temperature on fatigue damage, and the importance of rest periods and the correct modeling of the effects of time and temperature on hardening of materials. Several models for including these effects have been developed but not yet evaluated. Additional calibration using track tests and in-situ pavement sections (for example SPS sections in California) is also required. Particularly valuable will be the information gathered into the new California Pavement Management System. Inclusion of additional materials parameters for full-depth recycling with and without modification with cement and/or foamed asphalt and asphalt emulsion and other recycled materials will be performed as funding becomes available. ACKNOWLEDGEMENT This paper describes research activities that were requested and sponsored by the California Department of Transportation (Caltrans), Division of Research and Innovation. Caltrans sponsorship is gratefully acknowledged. The contents of this paper reflect the views of the authors and do not reflect the official views or policies of the State of California or the Federal Highway Administration. REFERENCES Caltrans. Highway Design Manual. Chapter 0: Flexible Pavements. Edition Jul, pp.-. TRB 0 Annual Meeting CD-ROM

17 0 0 0 Harvey, J. T., du Plessis, L., Long, F., Shatnawi, S., Scheffy, C., Tsai, B-W., Guada, I., Hung, D., Coetzee, N., Reimer, M. and Monismith, C. L. Initial CAL/APT Program: Site Information, Test Pavement Construction, Pavement Materials Characterizations, Initial CAL/APT Test Results, and Performance Estimates. Report for the California Department of Transportation. Report No. RTA-W-. Pavement Research Center, CAL/APT Program, Institute of Transportation Studies, University of California Berkeley, June. Harvey, J.T., A. Chong, J. Roesler. Climate Regions for Mechanistic-Empirical Pavement Design in California and Expected Effects on Performance. Pavement Research Center, CAL/APT Program, Institute of Transportation Studies, University of California, Berkeley. June 000. Jones, D., Harvey, J., and Monismith, C. Reflective cracking study: Summary report. Davis & Berkeley, CA: University of California Pavement Research Center. (UCPRC- SR-00-0), 00a. Jones, D., Tsai, B., Ullidtz, P., Wu, R., Harvey, J. and Monismith, C. Reflective Cracking Study: Second-Level Analysis Report. Davis & Berkeley, CA: University of California Pavement Research Center. (UCPRC-SR-00-0), 00b. Lu, Q. Estimation of Truck Traffic Inputs Based on Weigh-in-Motion Data in California, Davis & Berkeley, CA: University of California Pavement Research Center. (UCPRC-TM-00-0), January 00. Lu, Q., Ullidtz, P., Basheer, I., Ghuzlan, K. & Signore, J.M. CalBack: Enhancing Caltrans Mechanistic-Empirical Pavement Design Process with New Back-Calculation Software, Journal of Transportation Engineering, ASCE, Vol., No., pp. -, July 00. Lu, Q., and J. Harvey. Characterization of Truck Traffic in California for Mechanistic Empirical Design. Transportation Research Record: Journal of the Transportation Research Board, National Research Council, No., 00, pp.. Ongel, A. and Harvey, J.T. 00. Analysis of 0 Years of Pavement Temperatures using the Enhanced Integrated Climate Model (EICM). Draft report prepared for the California Department of Transportation. Pavement Research Center, Institute of Transportation Studies, University of California Berkeley, University of California Davis. UCPRC-RR-00/0. Thoegersen, F., Busch, C. and Henrichsen, A. Mechanistic design of semi-rigid pavements - An incremental approach. Fløng, Denmark: Danish Road Institute. (Report ). 00. Ullidtz, P, Harvey, J., Tsai, B-W. and Monismith, C. Calibration of Mechanistic- Empirical Models for Flexible Pavements Using the California Heavy Vehicle TRB 0 Annual Meeting CD-ROM

18 Simulators, Transportation Research Record, Journal of the Transportation Research Board, No. 0, 00, pp. 0-. Wu, R-Z. Finite Element Analyses of Refective Cracking in Asphalt Concrete Overlays. Doctoral dissertation. Department of Civil and Environmental Engineering, University of California, Berkeley, 00. TRB 0 Annual Meeting CD-ROM