Superpave Design Aggregate Structure Considering Uncertainty: I. Selection of Trial Blends

The existing method of selecting Superpave trial aggregate blends is deterministic and is based on trial-and-error. The primary purpose of this article is to develop a stochastic optimization model that includes the uncertainties of individual aggregate gradations, primary aggregate (PA) properties, and related specifications. The model can directly determine three different trial blends: (1) a blend close to the minimum specification limits, (2) a blend not close to the specification limits or to the restricted zone (RZ), and (3) a blend close to the maximum specification limits and to the RZ. The constraints of the model include gradation-control specifications, RZ limits, PA properties, and special and unity constraints. The PA properties include coarse aggregate fractured faces, fine aggregate angularity, sand equivalent, and flat and elongated particles. The uncertainty is formulated to ensure that the trial blends satisfy model constraints for a specified confidence level. A binary variable is used to allow the designer to produce a blend that passes below, above, or through the RZ. Application of the model is illustrated using a numerical example. The proposed model, which improves the reliability of trial blends and the efficiency of their selection, should be of interest to practitioners and researchers.