Optimal Segmentation of Walls Built on Slopes

Walls built on slopes are often designed with horizontal segments requiring the digging of ditches in which the depth increases with the length of the segment, while the effective (lowest) height of the wall above the ground decreases. The optimal length of the segment is determined by minimizing the total costs—consisting of the fixed cost per segment, cost of digging and cost of builidng for a given required effective height. Models with linear and non-linear digging and building costs for slopes having constant angle of inclination are developed.