Hybrid system reliability and monotonicity framework for gravity retaining walls using ANN and SCM method

This study presents a system reliability analysis of a gravity retaining wall (R-Wall) subjected to varying seismic conditions using a sequential compounding method integrated with deterministic and artificial intelligence approaches. Three primary failure modes, sliding (SL), overturning (OT), and bearing capacity (BC), were evaluated under five horizontal seismic coefficients (KH = 0.10 to 0.18) through deterministic analysis and validated using Artificial Neural Network (ANN) models. The reliability index (B), calculated using the First-Order Second Moment (FOSM) method, revealed that overturning is the most critical failure mode, with B declining sharply beyond KH = 0.12. In contrast, SL and BC retained relatively higher B values (9.38–4.46 and 13.45–6.87, respectively). The overall Bsystem decreased drastically from 5.99 to 0.13, indicating increasing structural vulnerability under stronger seismic loads. ANN models with architectures 4-15-1 (SL and OT) and 7-15-1 (BC) showed excellent predictive performance (R2 > 0.999, RMSE < 0.005), closely replicating deterministic and system reliability outcomes. Monotonicity analysis further quantified the influence of input parameters on wall stability, highlighting kH and ob as dominant contributors, while rb had minimal effect. Across all cases, the ANN model effectively captured complex nonlinear relationships, offering valuable insights for optimized and safer design of retaining structures under seismic loading.