Determination of Optimum Bitumen Content in Marshall Mix Design Method Using a Nonlinear Programming Model

The general aim of Hot Mix Asphalt Design is selection of the most suitable and economic mixture of aggregate and bitumen which can maintain the properties of asphalt mixture in a definite range. Until now different methods have been developed for Hot Mix Asphalt Design including Marshal Method, Modified Marshal Method, HVeem Method and Superpave Method. At the time being, the Hot Mix Asphalt Design is based on the Marshal Method in Iran. In Marshal Method, the optimum bitumen content is based on the mean of the bitumen content which obtained from highest Marshal stability, highest density and the most suitable air voids in Asphalt content. This bitumen content is not necessarily the optimum bitumen content. In this paper a nonlinear programming model is developed to determine the optimum bitumen content from Marshal or modified Marshal Method. To do that, first of all the equations which relate the effective parameters in Hot Mix Asphalt Design such as density of mixture, Marshal stability, flow, Asphalt content, air voids, VMA, void filled with bitumen versus bitumen content using method of least squares and from a quadratic polynomial equation. Then based on these equations and using a nonlinear multi objective programming model, the optimum bitumen content is determined in such a way that given hot mix Asphalt has all of the requirement mentioned in the design guide and has a highest density and Marshal Stability. Since the optimum bitumen content is definitely between the maximum and minimum bitumen content used in the test (4 to 7 percent), it is possible to first determine all allowable solutions (bitumen contents which satisfy all of the constraints), then evaluating objective function in each allowable solutions. The most optimum value of objective function and also optimum bitumen content can be determined.To evaluate the presented model a program was written in MATLAB. Then based on results obtained from a Marshall mix design method and using the above model, the optimum bitumen content was determined. Finally, application of this method is described using an example and then optimum bitumen content was determined based on the results of a real Marshal test.