طراحی اسکله پل بلند با بهینه سازی کلونی مورچه ها

This paper describes a methodology for the analysis and design of Reinforced Concrete (RC) tall bridge piers with hollow rectangular sections, which are typically used in deep valley bridge viaducts. Piers are usually considered tall when the shaft has a height of 50 m or more. Three different types of rectangular hollow tall piers have been studied for road piers of 90.00 m in height: RTRA90, RLON90 and RLT90. RTRA90 has the two side walls inclined, RLON90 has the two frontal walls inclined and RLT90 has all four walls inclined. The procedure used in the present study to solve the combinatorial problem is a variant of the ant colony optimization. RTRA90 leads to the most economical pier, both in column and foundation cost, since it is the most efficient set up for horizontal loads. Regarding the cost of the vertical column only, i.e. excluding the foundation, the cost of RTRA90 and RLON90 are similar, but the cost of the column RLT90 is higher due to its larger unit cost of interior formwork.

Bridge piers are crucial for the design of prestressed concrete viaducts, especially when the piers are tall, since they can make up more than 50% of the total cost of the viaduct. Fig. 1 shows a frontal and a side elevation of a hollow rectangular tall bridge pier. Tall bridge piers include a bottom foundation, which can be either a surface footing as in Fig. 1 or include deep piles; the main hollow shaft with inclined walls; and the top block end part that sustains the reactions due to the pair of pot bearings of the bridge deck. Piers are usually considered tall when the height of the shaft reaches 50 m or more. Shafts shorter than 50.00 m are generally considered as high piers. High piers do not generally require inclined walls because a constant cross-section is sufficient and facilitates the construction procedure. The construction sequence is normally done in shaft stages of approximately 5.00 m in height. The main parameters affecting their design are the pier height, the vertical and horizontal loads transferred by the bridge deck and the permissible ground stress. The behavior of a tall pier resembles that of a loaded cantilever. Rectangular hollow cross-sections are most frequently used for tall piers (see Fig. 2). These sections efficiently distribute the weight of an area and resist axial loading and the bending moments due to the eccentric traffic loading, together with the bending due to the horizontal loads at the top of the pier and along the column. Additionally, the high radius of gyration of rectangular hollow cross-sections improves the strength against instability due to second order effects. Piers are generally calculated to sustain the actions prescribed by the loading code considered in the analysis [1] and must comply with the limit states prescribed by the concrete code under consideration [2].An engineering model for the optimum design of high piers with constant cross-sections was developed in a previous study [3], which described the optimization model in terms of cost function, design variables, parameters and structural constraints. The optimization methodology was based on two types of algorithms: population algorithms (ant colony and genetic) and neighborhood-based algorithms (simulated annealing and threshold accepting). The ant colony algorithm appeared to be more robust and was chosen for the present study of optimum design of tall piers. While the initial publication concentrated on the development of an automatic design model for high piers, the present publication upgrades and generalizes the model so as to cater to the analysis and design of tall piers of any height and variable cross-sections. It is worth noting that high piers can be designed by a combination of simplified buckling methods, spreadsheet calculations and elemental software for cross-section computations which are available to most postgraduate specialists. On the other hand, tall piers require specialized software which is rarely available. Most traditional procedures for structural concrete adopt initial designs based on cross-section dimensions, steel reinforcement and material grades arising from sanctioned common practice. The selection of initial solutions in the traditional approach is followed by the analysis of the structure and checking the passive reinforcement. Should the dimensions, reinforcement or material grades be insufficient, the structure is redefined on a trial-and-error basis. This process is not automatic and leads to safe designs, but the cost of the reinforced concrete (RC) pier is, consequently, highly dependent upon the experience of the structural designer. Modern artificial intelligence procedures define the structure based on the design variables, automatically calculate and validate the structure and then redefine it by means of an optimization algorithm that controls the flow of a large number of iterations in the search for the optimum structure. This optimum structure has to satisfy the limit states prescribed by concrete codes. Heuristic optimization methods are a clear alternative to experience based methods. However, it is worth mentioning that experience is crucial for the development of computer design models since design involves more than a mere application of codes of practice. This means that experience will move beyond preliminary design decisions to the judgment required to develop computer design models like the one used for the present study. The recent development of heuristic methods, such as genetic algorithms, simulated annealing, threshold accepting, tabu search and ant colonies, among others [4], [5], [6], [7] and [8], is linked to the evolution of personal computers. The first studies on heuristic structural optimization were applied to steel structures by Jenkins [9] and Rajeev and Krishnamoorthy [10]. These studies applied genetic algorithms to the optimization of the weight of steel skeletal structures. Regarding RC structures, early applications include a pioneering optimization of RC beams by Coello et al. [11], and the application of genetic algorithms to prestressed concrete beams by Leite and Topping [12]. Another early work includes a study on genetic algorithms applied to concrete members by Kousmousis and Arsenis [13]; as well as a study on genetic algorithms applied to RC columns by Rafiq and Southcombe [14]. Recently, there have been a number of RC applications on RC beams and RC building frames [15], [16], [17] and [18]. More recently, our research group has applied several metaheuristic algorithms to the optimization of walls, bridge frames, building frames, high bridge piers, vaults and pedestrian bridges [3], [19], [20], [21], [22], [23] and [24]. The objective of the present publication is to guide designers to a methodology for the optimum modeling of tall piers. This methodology would reduce the time needed for preliminary design, analysis and overall design of tall bridge piers. The method followed consisted in formulating the optimization problem, modeling the structure on the basis of design variables, choosing the ant colony optimization algorithm and description of numerical examples.

Three different types of rectangular hollow piers have been studied for tall road piers of 90 m in height: RTRA90, RLON90 and RLT90, defined in Section 2.2. RTRA90 has the two side walls inclined, RLON90 has the two frontal walls inclined and RLT90 has the four walls inclined. The optimization procedure used in the present study is a variant of the ant colony optimization described in Section 3 and requires the definition of the initial values for αα and ββ in expression (4). Numerical results indicate that the main cost difference between the shafts is due to the differences in the unit price of the internal formwork, which is larger for 4 inclined walls (RLT90) than for two inclined walls only (RTRAN90 and RLON90). The difference of this cost is due to the fact when the four walls are not vertical, it is necessary to employ a crane and other auxiliary means for taking the interior formwork down to the ground and vary its dimensions for the next stage of the column. This maneuver increases the unit cost of the internal formwork. On the other hand, the cost of columns RTRA90 and RLON90 is similar, and hence it is not relevant for the column cost the choice of which two parallel walls are not vertical. Nevertheless, RLON90 is the pier with the largest cost due the cost of its footing. RTRA90 is the most economic pier, its column being the cheapest and its footing being the cheapest as well. This so since the wind force is the biggest horizontal force and the wind direction coincides with the direction of variable wall widths for RTRA90.