Application of arithmetic progression to haul road geometric design

Transactions of the Society for Mining, Metallurgy, and Exploration , 2012, Vol. 332, No. 1, pp. 430-439

Ajak, A.D.

 A complete mining cycle involves digging, loading, hauling and dumping of the materials. Moving the ore from the pit to the crusher or to the waste dump requires access routes, which are termed haul roads. These roads have to be designed, constructed and maintained. A review of the literature indicates a common consensus among researchers that there should be a balance between haul road economics and safety of the road users. However, there is no universally accepted theory on the design of haul road geometry and, in particular, road dimensions. The current industry practice is based on empirical data and rules of thumb developed by engineers. Therefore, this paper will use the overlooked and less valued branch of mathematics, arithmetic progression, to derive a road width equation. It is beyond the scope of this paper to discuss all road design components. The focus will be on the geometric aspects, which more often have a direct impact on road safety. In this paper, the current design practices and techniques for haul road geometrics design will be explored, using arithmetic progression to formulate road width equations, case examples to apply the equation and then validating the results with conventional techniques that have confirmed the reliability of road width equations, thus eliminating use of tables during design.