OPTIMAL COST DESIGN OF CANTILEVER RETAINING WALLS

Abstract

The paper pertains to the optimal cost design of a cantilever soil retaining structure of a given height satisfying some structural and geotechnical design constraints. The cost function and design restrictions are nonlinear functions of the design variables necessitating the problem to be formulated as a nonlinear programming problem. Sequential unconstrained minimization technique along with Powell’s algorithm for multidimensional search and quadratic interpolation technique for one-dimensional search has been adopted. The constrained optimization problem is converted to an unconstrained one by using extended penalty function method and developing a composite function that readily allows even an infeasible initial design vector in the analysis. As the objective functions and the design constraints are not explicit expressions of the design variables, non-gradient based minimization algorithm was chosen. The adopted method has been found to be quite efficient in finding the minima, which is established by the fact that for decreasing sequence of the penalty parameter, the minimization of the composite function leads to the minimization of the objective function. Sensitivity analysis has also been carried out. It was observed that on varying the stem top width from 20 to 30 cm, the percentage increase in cost ranges from 9 % to 15 %.