Multi-Parametric Optimization of Stone Gravity Retaining Walls Under Static and Seismic Loading

This paper presents a multi-parametric optimization framework for trapezoidal stone gravity retaining walls subjected to static and pseudo-static seismic loading. The wall is treated as a no-tension gravity structure, and the base width, top width, and embedment depth are optimized by minimizing the wall self-weight. The objective function is constrained by overturning, eccentricity, sliding, and bearing-capacity requirements, as well as by lower geometric bounds. The analytical formulation is implemented directly in an optimization model and includes Coulomb-type active earth pressure, Mononobe–Okabe seismic pressure, mobilized passive resistance, wall inertia, and bearing capacity. Two foundation scenarios are considered: Scenario A, with identical foundation and retained soil properties, and Scenario B, with competent foundation soil. The parameter grid combines five retained-soil heights, six soil friction angles, four passive-resistance mobilization factors and four seismic accelerations, evaluated for two foundation scenarios and three loading branches (static and two opposite-sign vertical seismic branches), producing 2160 optimized designs. The results reveal distinct mechanically controlled design regimes. In Scenario A, low friction angles are governed mainly by bearing capacity and sliding, whereas eccentricity dominates as friction increases. In Scenario B, sliding and bearing cease to govern, and the optimum is controlled predominantly by eccentricity, with overturning appearing in a limited low-wall domain. The positive and negative vertical seismic branches produce different design demands, with the negative branch becoming progressively more critical as seismic intensity increases. The optimized base-width-to-height ratio further shows that weak foundation conditions can lead to markedly more massive wall geometries, whereas stronger foundation soil enables substantially more compact solutions.