Optimal design of retaining walls under seismic loading using a hybrid analytical–numerical approach

Abstract The seismic design of retaining walls is commonly based on analytical approaches such as the Mononobe–Okabe method, which is transparent, computationally efficient, and well aligned with design codes. However, such methods cannot adequately capture the nonlinear soil–structure interaction effects that govern wall deformation during strong ground motion. This study proposes a hybrid analytical–numerical optimization framework that combines code-consistent analytical screening with finite-element dynamic verification to support performance-based retaining wall design. Analytical solutions are used to enforce fundamental stability requirements, including sliding, overturning, and bearing capacity, and to filter infeasible designs at low computational cost. Finite-element analyses are then selectively applied to evaluate seismic wall displacement for designs that satisfy analytical feasibility criteria. Within this framework, several population-based metaheuristic optimization algorithms are implemented and assessed under identical computational budgets. A representative cantilever reinforced concrete retaining wall supporting cohesionless backfill is considered, and the optimization problem is formulated with competing objectives related to material cost and seismic performance. Scalarization and constrained optimization strategies are employed to explore trade-offs between these objectives while maintaining compliance with seismic design provisions. The results clearly indicate that, with the proposed hybrid approach, it is possible to efficiently search the design space with a significantly lower number of unnecessary numerical analyses eliminated, while still representing the formation of deformations under seismic loading via finite-element verification. In summary, this work proposes a decision-support system that efficiently addresses geotechnical optimization problems with constraints by bridging design checks and performance-based analysis.