Optimum Design of Reinforced Concrete Retaining Walls

Introduction

A reinforced concrete (RC) design must satisfy several conditions such as stability under external loads, displacement limitations, strength capacities (flexural, shear, axial, torsional etc.) of the structural members and some other limitations about structural material such as minimum thickness and height of the element, minimum and maximum reinforcement ratios, minimum and maximum spacing between the bars, maximum crack width etc. In addition to the structural, architectural, and material design restrictions; the proposed design must be also economical. For that reason, an engineering design procedure is an optimization problem.

Although the idea of the optimum design is not a new concept in the engineering, due to the limited capacities of the tools used for calculations in the past, the global optimum design may be provided by using the conventional methods. It becomes even more difficult goal, especially in the design of reinforced concrete structures, because of the extremely different strain/stress behaviour and unit costs of the concrete and steel. For that reason, an effective tool like metaheuristic algorithms for the optimum design of reinforced concrete structures should be used.

Metaheuristic algorithms are developed by expressing natural phenomena with mathematical equations for optimization processes. For example, Ant Colony Optimization algorithm (ACO, Dorigo, Maniezzo, & Colorni, 1996) is developed from the behavior of ants in finding the shortest way between their nests and food source is developed, Particle Swarm Optimization (PSO) is developed from the movement of organisms in a bird flock or fish school, the echolocation behavior of micro bats conceptualized the Bat Algorithm and Teaching-Learning-Based Optimization Algorithm (TLBO) is developed from the inspiration of the student-learning-process in a classroom.

In recent years, optimum design of reinforced concrete structures is a very active research topic and in the majority of these studies, the metaheuristic algorithms have been used as methodology. In these studies, optimum cost of retaining wall is investigated under different cases and variables such as the optimum shape of the wall, minimum bending moment, optimum location. Several metaheuristic algorithms; i.e. Genetic Algorithm (GA), Particle Swarm Optimization, Big Bang-Big Crunch Algorithm (BB-BC), Simulated Annealing (SA), Harmony Search (HS) Algorithm, Firefly Algorithm (FA), Teaching-Learning-Based Optimization Algorithm etc. and their improved or modified versions are employed.

Although different inspiration and mathematical expressions used to approach optimum results, metaheuristic methods perform random searches during calculations. For that reason, studies using metaheuristic algorithms as methodology generally search more efficient method for a specific optimization problem. In order to ensure this aim, the proposed methods are generally compared with some other ones for a better optimum result; computation time, average and standard deviation of independent runs.

Optimization via metaheuristic algorithms is an important research area in the structural engineering science. Among research interest of this area, structural design with minimum cost is one of the leading subject. The optimization of the cantilever reinforced concrete retaining wall is covered under this heading. Several applications of metaheuristic methods i.e. SA (Ceranic, Fryer, & Baines, 2001; Yepes, Alcala, Perea, & Gonzalez-Vidosa, 2008), PSO (Ahmadi-Nedushan & Varaee, 2009), HS (Kaveh & Abadi, 2011), BB-BC (Camp & Akin, 2012), GA (Das, Purohit, & Das, 2016; Kaveh, & Behnam, 2013), FA (Sheikholeslami, Gholipour Khalili, & Zahrai, 2014), Charged System Search (Kaveh & Behnam, 2013; Talatahari & Sheikholeslami, 2014), TLBO (Temur & Bekdaş, 2016) can be found in the documentations.