Optimization-based seismic stability assessment of rockfill dams considering friction angle sensitivity and probabilistic uncertainty

Abstract

Rockfill dams draw nearly all of their shear resistance from the internal friction angle (ϕ) of the fill, yet design practice still treats ϕ as a fixed input and rarely traces how its variability propagates into seismic safety and construction cost. This study quantifies that propagation and asks whether the resulting safety–cost trade-off can be resolved numerically rather than through heuristic factors of safety. Limit equilibrium analysis, supported by the nonlinear Hoek–Brown strength description and cross-checked against slice-based solutions in GEO5 (Bishop, Fellenius–Peterson, Spencer, Janbu, and Morgenstern–Price), generated a 42-point parametric data set spanning ϕ = 30–60° and horizontal seismic coefficients kh = 0–0.4. Monte Carlo simulation with 10,000 realizations quantified the uncertainty in the factor of safety (FS); Newmark sliding-block analysis estimated permanent seismic displacement; four regression models were trained as surrogates for the area-ratio response; and genetic algorithm and NSGA-II searches explored the design space. Raising ϕ from 30° to 60° increased FS by 96% under static loading and by 102–103% at kh = 0.3–0.4, while the normalized area ratio A/A(ϕ = 30°) fell by up to 81%. Gradient boosting proved the most reliable surrogate, retaining R² = 0.992 under leave-one-out cross-validation against 0.902 for the linear baseline, although this advantage disappeared under extrapolation beyond the sampled seismic range. The Pareto front is convex and contains a transitional band, near ϕ ≈ 58° with kh ≤ 0.15, where a modest increase in fill volume buys a disproportionate gain in FS; beyond it, additional material returns little.