tBeam—A Fast Model to Estimate Energy Consumption Due to Pavement Structural Response: Theoretical and Validation Manual

One of the most important contributors to the environmental impacts from use of highways is the energy exerted by vehicles, particularly routes that carry higher volumes of traffic. Part of this energy is consumed by response of the vehicle’s tires and suspension to pavement surface roughness and macrotexture. Another part of the energy consumed is by energy dissipation due to the structural response of the pavement itself under the moving load. This document is the theoretical and validation manual tor tBeam, standalone software for the analysis of energy dissipation in pavements under moving vehicles. tBeam was developed as part of the improvement of modeling capabilities for environmental life cycle assessment of pavements being conducted the University of California Pavement Research Center for the California Department of Transportation. The energy consumed due to structural response are controlled by the structural properties of the pavement which are dependent on the time of day, the season, and the condition (damage) of the pavement. The energy dissipation also depends on the speed and weight of each moving wheel load. As a result, estimating the lifetime energy dissipated in a pavement structure requires multiple analyses considering the thousands of permutations of these variables for a given segment of the highway network. Therefore, models for pavement-vehicle energy dissipation must balance two opposing needs: obtaining a reasonably accurate estimate of the dissipated energy, and high numerical efficiency. For numerical efficiency, the tBeam software employs a one-dimensional finite-element based solution of a wheel traveling at a constant velocity on a viscoelastic beam-foundation system, and a further reduction of numerical effort is obtained by formulating the model relative to a moving coordinate system attached to the wheel. The one-dimensional solution is, by nature, an approximation to the three-dimensional world. This approximation can be improved by incorporating a “correction factor,” which is based on comparisons with pavement simulations accounting for the double curvature observed in loaded pavements. In this report prediction disparity for a single structure is studied. The results show a clear trend where the correction factor decreases with rising temperature, and increases with higher velocity. The present study was insufficient to establish a law for the correction factor even for the single case studied. The correction factor ranged from about 1.25 at low temperature and high velocity to about 0.6 for high temperature and low velocity. The first part of this report presents the underlying theory for tBeam and implementation details. The second part presents closed form solutions for specialized pavement-foundation systems. The third component of the report presents some of the validation simulations undertaken to demonstrate the performance of tBeam, including comparisons with closed form solutions provided in this report, and recommendations for further development of tBeam.