# Multiparametric Analysis of a Gravity Retaining Wall
## 1 Introduction  
Highways and local road networks are the most important land infrastructure in the European Union. Retaining walls make up a significant proportion of the fixed assets of the highways and local road networks and are vital elements. Their failure can have serious economic consequences. According to Eurocode 7 [1], a retaining wall is defined as an earth retaining structure supporting at least 2 m of ground, i.e., the soil level in front of the wall is \(\geq\)2 m lower than the soil level behind the wall. Such structures fall into geotechnical category 2 or 3 of Eurocode 7 and must be designed by a suitably qualified person. The report COST Action 345 [2] collects information on the number and type of retaining structures in European countries and highlights the importance of the annual cost of maintaining, repairing, renewing and replacing these structures. In the United Kingdom, the average length of retaining walls per km of whole road systems is about 11.1 m/km. The majority of retaining walls in the United Kingdom are gravity retaining walls, about 85%. The other 15% are reinforced concrete retaining walls. Ninety-five percent of all retaining walls measure less than 6 m in height. The average replacement cost per m for a retaining wall in the United Kingdom, Spain and Denmark is estimated at 1550, 560 and 4390 EUR/m respectively. In geotechnical engineering, gravity retaining walls are used to secure slopes that do not have long-term stability for providing lateral soil load resistance. This paper deals with masonry retaining walls consisting of stones with bedded concrete of lowcompressive strength. In designing gravity retaining walls, stability conditions such as sliding, overturning, eccentricity and bearing capacity are evaluated using selected wall dimensions. If the initially selected dimensions do not satisfy the stability conditions, new dimensions are selected and reevaluated until the stability conditions are satisfied. Even if the conditions are met, it is not certain that the determined wall dimensions will ultimately result in the most economical wall design. Optimization is required to satisfy all conditions and obtain the lowest possible cost. Calculations used to determine the external and internal stability of masonry walls should be carried out according to the Eurocode 7 standard. The final design of a gravity retaining wall should be simple to construct, quick to build and the best economic solution to the problem. In the recent past, many heuristic optimization algorithms have been used in the field of civil engineering. However, not many of them have been applied in the field of geotechnical engineering. Concrete retaining walls have been optimized to the optimal design using eleven population-based metaheuristic algorithms; all the algorithms used quickly converged to high-quality optimal designs [3; 4; 5; 6]. Optimizations for reinforced concrete retaining walls, in terms of cost and weight, have been made by several authors [7; 8; 9; 10; 11]. Gravity retaining walls of stone masonry or unreinforced concrete have also been investigated [12; 13]. Stability analyses of gravity retaining walls, for different wall-back types, have been performed but not optimized [14]. In a detailed comparative study, different optimization methods were shown for geotechnical problems and their effects on the variation of studied parameters [15]. Multiparametric optimizations on different civil engineering structures have been studied by several authors [16; 17; 18]. [PERSON] et al. [19] discussed a comparative study of an optimal design for composite steel-concrete floor structures based on the multiparametric mixed-integer nonlinear programming (MINLP) approach.