Keywords: heuristic optimization, structural design, road vaults.

The design of reinforced concrete vaults is a key aspect of the construction of road, railways and hydraulic artificial tunnels. Alternative rectangular section frame tunnels [1] require less expensive scaffolding and formwork but are only functional for up to 5.00 m of earth cover. This paper examines the application of three methods of heuristic optimization for the analysis of reinforced concrete road vaults used in the construction of underpasses. The structure is defined by 49 discrete design variables that include the thickness of the vault, the thickness of the bottom and top sections of the lateral walls, the depth of the foundation slab, the toe of the slab, the concrete grades of the three elements and 41 variables that define a standard reinforcement set up.

The objective function is the cost of the structure expressed as the sum of the unit prices by the construction measurements. Penalty functions are used for infeasible solutions. Structural constraints account for the verification of flexure and shear limit states in the vault elements and the foundation slab. The traffic loading considered is in accordance with national prescriptions and includes a 4 kN/m² distributed load plus a 600 kN heavy vehicle. Earth fill pressures are taken for partial filling heights of ¼, ½, ¾ and total height and three horizontal pressure coefficients of 0.20, 0.33 and 0.50 are considered.

The three heuristic methods used are the global best descent local search (GB), the simulated annealing (SA) [2] and the threshold acceptance (TA) [3]. All methods are applied to a structure of 12.40 m of diameter of the vault, 3.00 m of height of the lateral walls and a total height of the fill of 1.00 m above the vault. The paper presents two original moves of neighbourhood search and an algorithm for the automatic calibration of the parameters of the simulated annealing and the threshold acceptance methods. These two moves are then applied to the automatic design and economic optimization of the structural vaults of structural concrete. The TA algorithm appears to be more efficient that the GB and the SA algorithms. Optimum structures are quite slender as regards the vault, with a relation of depth to span ratio of about 62. The optimization method indicates savings of about 10% with respect to a traditional design.

1

C. Perea, J. Alcala, V. Yepes, F. Gonzalez-Vidosa, A. Hospitaler, "Design of reinforced concrete bridge frames by heuristic optimization", Adv Eng Softw, 39(8), 676, 2008. doi:10.1016/j.advengsoft.2007.07.007

2

S. Kirkpatrick, C.D. Gelatt. and M.P. Vecchi, "Optimization by simulated annealing", Science, 220(4598), 671-680, 1983. doi:10.1126/science.220.4598.671

3

G. Dueck and T Scheuer, "Threshold accepting: A general purpose optimization algorithm superior to simulated annealing", Journal of Computation Physics, 90, 161-175, 1990. doi:10.1016/0021-9991(90)90201-B

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