Optimisation of Reinforced Concrete Cantilever Retaining Wall Cross-Section Using Physics-Informed Neural Networks

Abstract

The design of reinforced concrete cantilever retaining walls is a fundamental task in geotechnical and structural engineering to ensure stability in areas with significant ground elevation differences. Conventional design approaches based on classical earth pressure theories (e.g., Rankine, Coulomb) and iterative stability checks are often time-consuming, rely heavily on engineering judgment, and may lead to conservative, non-optimal solutions in terms of material use. This study proposes a novel optimisation framework using Physics-Informed Neural Networks (PINNs) to automate and enhance the cross-sectional design of cantilever retaining walls. Unlike traditional data-driven machine learning models, the proposed PINN embeds governing physical principles and technical constraints such as earth pressure theory, sliding and overturning stability, bearing capacity limits, and simplified structural strength requirements directly into the loss function. The model predicts key geometric parameters, including stem thickness (top and base), toe length, heel length, and base thickness, aiming to minimise concrete volume while satisfying all stability and strength criteria. The PINN is implemented in PyTorch and trained using the AdamW optimiser. Validation is performed through conventional design calculations and comparison with industry-standard software. Case studies demonstrate that the PINN can achieve up to 10–25% reduction in concrete volume compared with traditional designs, while maintaining required safety factors. The results highlight the potential of physics-informed deep learning as an efficient and reliable tool for preliminary retaining wall design, enabling engineers to explore optimal and code-compliant solutions rapidly.