Using the Levenberg-Marquardt Algorithm to Construct Dynamic Modulus Master Curves

The Dynamic modulus, denoted as |E*|, is one of the most important material properties of hot-mix asphalt (HMA) that is required as an input parameter in the Mechanistic-Empirical Pavement Design Guide (MEPDG) software. To predict HMA modulus value at a given loading time t and temperature T, a |E*| master curve must be constructed based on some existing |E*| test data. For |E*| master curve generation, the MEPDG uses a log sigmoidal model to fit the curve shape and a quadratic-polynomial function for the temperature shift factor determination. Although, there are several mathematical approaches to determine the master curve parameters δ, α, β, γ, a, b, and c, some limitations or problems exist. For example, there are restrictions on the |E*| test temperatures or modulus values and in some methods, the logarithm of the shift factor loga is not exactly zero at the reference temperature (i.e., a ≠ 1), which is not theoretically correct and may cause accuracy problems. In this paper, a new optimization method incorporating the Levenberg-Marquardt algorithm is proposed and a corresponding stand-alone tool for |E*| master curve generation is developed. With this new optimization method, a loga value of zero is guaranteed at the reference temperature and thus, more reliable and accurate solutions for the |E*| master curve generation can be achieved. Further more, the optimization process has less restrictions on the initial value selection or the |E*| test data, which allows for more flexibility and greatly enhances the chances of solution finding. Verification of the proposed method and its associated tool yielded satisfactory results with improved accuracy, flexibility, and robustness.


  • English

Media Info

  • Media Type: DVD
  • Features: Figures; References; Tables;
  • Pagination: 16p
  • Monograph Title: TRB 89th Annual Meeting Compendium of Papers DVD

Subject/Index Terms

Filing Info

  • Accession Number: 01152458
  • Record Type: Publication
  • Report/Paper Numbers: 10-1760
  • Files: TRIS, TRB
  • Created Date: Jan 25 2010 10:48AM