Keywords: structural optimization, harmony search algorithm, cantilever retaining walls, reinforced concrete, cost optimization, discrete variables.

Optimum cost design of reinforced concrete cantilever retaining walls the harmony search algorithm is presented in this paper. The reinforced concrete cantilever retaining wall is the most common type among the retaining wall structures. The wall has a simple geometry, consisting of a base slab, a key and a stem, which is made in the form of an inverted T or L. In the formulation of the optimum design problem the height and thickness of stem, length of toe projection and the thickness of stem at base level, the length and thickness of base , the depth and thickness of key and the distance from toe to the key are treated as design variables. The values of these design variables are to be selected from a design pool which contains a list of discrete numbers starting from the minimum value and increasing with a certain increment up to the maximum value for each variable. The design constraints are implemented according to the provisions of ACI 318-05. The optimum design satisfies the factor of safety for failure modes, strength, serviceability and other required limitations to attain practically acceptable shapes. The design of retaining walls is implicit in the domain of the soil-structure interaction problem. The main target of the problem is to explore the conditions supporting the backfill safely, and to ensure that both the structure and the soil surrounding do not fail and that the deformations take place are within acceptable limits. Accordingly, the following failure modes should be considered; overturning stability, sliding stability, failure in bearing capacity, no tension condition in the foundation, and failures related to the moment and shear capacities of the four components of wall, namely, the stem, toe, heel, and key. The objective function is taken as the overall cost of the retaining wall. The optimum design problem formulated according to ACI 318-05 is found to be a discrete programming problem. The solution of the design problem is obtained by using the harmony search algorithm (HS) which is one of the recent additions to metaheuristic techniques. The HS algorithm has been successfully applied to wide variety of engineering optimization problems. The HS algorithm does not require any initial values for the design variable and uses a random search instead of a gradient search, so derivative information is unnecessary. In addition, the HS algorithm uses few parameters which are initially specified and consists of simple steps which make it easy to implement. A Number of design examples is presented to demonstrate the efficiency and robustness of the algorithm presented.

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