Optimum design of cantilever walls retaining linear elastic backfill by use of genetic algorithm

Retaining walls are used in many geotechnical engineering applications, e.g. supporting deep excavations, bridge abutments, harbor-quay walls, anchored retaining walls, etc. Although they are generally simple structures, their static and dynamic interaction with the supporting and/or retained soil is a subject of ongoing research. Apart from this, seismic design of retaining walls is primarily based on rules of thumb and the designer's experience, in order to set the initial dimensions and make the necessary checks to comply with the design codes. In addition, the calculation of the seismic earth pressures is done in a rather simplistic way which may lead to either conservative or unsafe designs. In the present study, after a comprehensive literature review, optimum design is performed for cantilever walls retaining soil layers of two different heights, using numerical two-dimensional simulations and a genetic algorithm. Numerical simulations are performed using the finite element code ABAQUS [1] whereas for optimization purposes, the genetic algorithm provided with MATLAB [2] is utilized. For the calculation of the seismic earth pressures, linear elastic soil, retaining wall stem and wall foundation are assumed. The optimization procedure involves four design variables that have to do with the wall geometry, while the soil and wall material parameters and the frequency range of interest are kept fixed. Structural and geotechnical constraints as well as upper and lower bounds for the design variables are imposed to ensure technical feasibility of the solutions. The results on the optimum solutions are presented and comparisons are made with the corresponding results according to conventional seismic design methods. The numerical results of the study provide a clear indication of the direct dynamic interaction between the retaining wall and the surrounding soil, whereas the complexity of the optimization problem itself is evident. This justifies the necessity for a more elaborate consideration of the optimum design of retaining walls, especially if material and geometric non-linearities are taken into account.