Keywords: ant colony, optimization, concrete structures, piers.

This paper deals with the economic optimization of reinforced concrete bridge piers with rectangular hollow sections typically used in railway construction of prestressed concrete viaducts. It uses the heuristic optimization by the ant colony algorithm reported in previous publications [1,2]. The evaluation of solutions follows the Spanish Code for structural concrete. Design loads are in accordance to the European regulations for railway bridges. Fifteen continuous viaducts are studied with span lengths of 40, 50 and 60m and pier heights of 20, 30, 40, 50 and 60m. The total number of variables varies from 83 for the 20 m height piers to 195 for the 60m height piers. The size of the solution space varies from a minimum of 1.59*10⁴⁵ for the 20m height piers to a maximum of 2.77*10⁵¹ for the 60m height piers. Variables for the column include geometrical values for the width of the pier, the thicknesses of the walls at different cross-sections, the concrete grades at different heights and the reinforcement of the column following a decreasing in height setup. As for the footing, 5 variables define the geometry and 11 the reinforcement. All variables are discrete in this analysis. The most important parameters are the vertical height, the transverse dimension of the pier which is 6.80m and the vertical and horizontal loads on the top bearings and the partial coefficients of safety. Main reactions include two vertical reactions spaced 5.00m apart and horizontal reactions due to bearings friction and wind. Structural restrictions considered followed standard provisions for these piers, except for the ULS of buckling which has been dealt with by the method reported by Manterola.

The proposed ant colony optimization (ACO) algorithm follows an original formulation of the path followed by ants that includes both the trace followed by former ants and the random selection of new paths. The ACO algorithm was programmed in Compaq Visual Fortran Professional 6.6.0. Typical runs reduced to 524 minutes in a Pentium IV of 2.8 GHz. The research includes results for a) the optimum column width, b) the cross section area at the bottom of the piers, c) the amount of kg/m of reinforcing steel at the bottom section of the piers, d) the overall amount of kg/m of reinforcing steel in the columns, e) the amount of kg of reinforcing steel in the footings, f) the total amount of kg/m of reinforcing steel in the whole piers, g) the overall amount of cubic metres per metre concrete in the columns, h) the amount of cubic metres of concrete in the footings, and i) the total amount of cubic metres per metre of concrete in the whole piers. In addition, the total cost of the piers is also reported. Finally, results indicate that ant colony optimization is a clear option for improving the design costs of real reinforced concrete structures. It is concluded that the results presented are of much value for the preliminary design of the piers of prestressed concrete viaducts for high speed railway lines.

1

F.J. Martinez, V. Yepes, A. Hospitaler, F. Gonzalez-Vidosa, "Ant colony optimization of RC bridge piers of rectangular hollow section", in "Proceedings of the Ninth International Conference on the Application of Artificial Intelligence to Civil, Structural and Environmental Engineering", B.H.V. Topping, (Editor), Civil-Comp Press, Stirlingshire, United Kingdom, paper 38, 2007. doi:10.4203/ccp.87.38

2

F.J. Martinez, F. Gonzalez-Vidosa, A. Hospitaler, V. Yepes, "Heuristic optimization of RC bridge piers with rectangular hollow sections", submitted for publication, November 2008.

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