Optimization of Retaining Ditch Height for Gentle Slope Turning in Inclined Coal Seam Open-pit Mines

Inclined coal-seam open-pit mines with internal dumping commonly reserve an end-side retaining ditch when turning from horizontal advance to along-strike excavation. Selecting a single fixed ditch level is straightforward but ignores year-to-year variability in stripping volumes and haulage distances, which can inflate the combined transportation and secondary stripping costs. This study proposes a two-stage optimization framework for planning the ditch-height trajectory during the turning period. First, a maximum economic ditch height is derived via an economic-compensation model that balances the revenue from overlying coal recoverable after turning against the added costs of longer haulage and increased external dumping, with cost/revenue streams discounted using a compound-interest formulation. Second, within this upper bound, a total-cost minimization model couples annual stripping transportation costs during turning with the secondary stripping cost after turning. The model enforces annual waste-volume balance among inner dumping, ditch storage, and external dumping, preferred waste-flow directions, bounds on ditch height, and limits on height differences between adjacent years. Haulage distances are calculated from centroid locations of stripping and dumping stages extracted from 3DMine, and the resulting dynamic program is solved using a sequential recursion method. A seven-year case study (2023-2029) outputs an optimized fluctuating ditch scheme with yearly ditch heights of 214.5, 190.5, 206.7, 201.3, 189.6, 181.2, and 166.0 m, reducing the cumulative cost by 148.32 million CNY compared with the conventional constant-level ditch plan. The framework offers a practical decision tool for parameterizing retaining ditches and improving the overall economics of gentle-slope turning in inclined coal-seam open-pit mines.