Selection of roadway grades that minimize earthwork cost using linear programming

Roadway grades are normally established to satisfy the geometric specifications of the road. Once the grades are established, the earthwork allocations that minimize the cost are determined. This paper presents a model that links these two activities. The model selects the roadway grades that minimize the cost of earthwork and satisfy the geometric specifications. The geometric specifications pertain to the elements of the vertical alignment, elevation of grade line at specified stations, horizontal and vertical alignment relations, and type of vertical curve. The model enumerates all technically feasible grades and solves the linear programming problem to minimize earthwork allocation cost for those grade alternatives that satisfy borrow pit and landfill capacity constraints. The model incorporates important earthwork details and guarantees obtaining the global minimum earthwork cost. Application of the model is illustrated by a numerical example and model extensions to accomodate other design and construction aspects are presented.