Heat Transfer

A one-dimensional, coupled heat and moisture flow model called the Integrated Climatic Model (ICM) was developed in the late 1980s by Lytton et al. to simulate temporal variations in the temperature, moisture, and freeze/thaw conditions internal to the pavement and their impact on key pavement material properties (Lytton et al, 1993). This program is recognized as the most comprehensive model addressing the effects of climate on pavements.

The Enhanced Integrated Climatic Model (EICM) (Zapata and Houston, 2008) is an improved version of ICM that was developed for the Federal Highway Administration (FHWA) and adopted as the climatic model in the Mechanistic-Empirical Pavement Design Guide (MEPDG) software developed under National Cooperative Highway Research Program (NCHRP) Project 1-37A (ARA, 2004). EICM is intended to help predict or simulate the changes in behavior and characteristics of pavement and unbound materials in conjunction with varying environmental conditions over years of service.

EICM was found to be too slow and complex to be run within CalME. Instead, CalME uses a simplified thermal model to predict a pavement’s temperature profile during its service life. The model is based on surface temperatures generated by EICM and a constant deep soil temperature. Specifically, CalME divides California into nine climate zones, each of which is represented by a “super weather station” that has thirty years (Ongel, 2004) of historical weather data ranging from 1961 to 1990 that can be used as inputs to EICM to calculate pavement surface temperatures over that same thirty-year period. CalME assumes that pavement temperature at a depth of four meters remains constant and sets this value as the annual average surface temperature. CalME then solves for pavement temperature profile by using a 1-D Finite Element formulation with a finite difference time step (Lea, 2012).

CalME further assumes that pavement temperatures are cyclic and that the 30-year period is longer than the temperature cycle. Accordingly, CalME uses the 30 years of historical temperature data to represent future pavement temperatures and repeats itself every thirty years. This is a simplification, and it is believed that the error introduced is minimal.

Solving for pavement temperature profile with known top (surface) and bottom (i.e., 4 meter depth) temperature history is essentially a heat transfer problem, which is governed by the following partial differential equation (in 1D) called Fourier’s Law of conduction:

where:          T is temperature that varies with time t and depth z

          a is the thermal diffusivity

CalME starts with an initial uniform temperature profile using the average annual surface temperature as the fixed value. It solves the above heat conduction equation hour by hour. It uses a year of simulation to stabilize the solution and remove the effect of the assumed initial temperature profile. The only model parameter required here is a, i.e., the thermal diffusivity of the material in each layer.

Lytton, R.L., D.E. Pufahl, C.H. Michalak, H.S. Liang, and B.J. Dempsey. An Integrated Model of the Climatic Effects on Pavements, Report No.: FHWA-RD-90-033. 1993. Prepared by U.S. Department of Transportation, Federal Highway Administration: McLean, VA.

Zapata, C.E., W.N. Houston, and National Cooperative Highway Research Program. Calibration and Validation of the Enhanced Integrated Climatic Model for Pavement Design, Report No.: NCHRP Report 602. 2008. Prepared by Transportation Research Board of the National Academies: Washington, DC.

ARA Inc., Guide for Mechanistic-Empirical Design of New and Rehabilitated Pavement Structures, ERES Consultants Division, ARA Inc. 2004. Prepared by the National Cooperative Highway Research Program, Transportation Research Board, National Research Council.

Ongel, A., and J.T. Harvey. Analysis of 30 Years of Pavement Temperatures using the Enhanced Integrated Climate Model (EICM). Report No.: UCPRC-RR-2004/05. 2004. Prepared by Pavement Research Center, Institute of Transportation Studies, University of California Berkeley, University of California Davis.

Lea, J.D., and J. Harvey, editors. Simplified Thermal Modeling Approach Used in CalME. In Proceedings of the Transportation Research Board 91st Annual Meeting. 2012.