AbstractThe ability of shallow bridge foundations to dissipate earthquake energy via rocking has gained significant attention by bridge engineers owing to recent efforts to quantify the performance of rocking footings. This paper presents a new formulation for estimating the moment capacity of rocking bridge foundations resting on all types of soils under varying saturation and surface flux boundary conditions. The proposed formulation uses the moment capacity equation originally employed for saturated soils, classical effective shear strength parameters, and a representation of the soil–water retention curve (SWRC) to accommodate partially saturated conditions that may commonly exist below the shallow foundations of bridge substructures. A closed-form equation is incorporated in this formulation for the matric suction and effective saturation profiles to directly implement surface flux boundary conditions when analyzing the moment capacity of rocking foundations supported on partially saturated soils. The formulation implements a new method to predict the air entry suction for partially saturated soils, representing a key step towards improving the accuracy of moment capacity. A parametric study is performed to investigate the sensitivity of the moment capacity to primary design variables and various surface flux boundary conditions. The analyses demonstrate that flow conditions have a negligible and strong influence on the moment capacity of coarse- and fine-grained soils, respectively. Predictions from the proposed formulation were compared against two sets of experimental data obtained from large-scale shaking table (on sand) and snap-back (on plastic silt) tests and indicated good agreement with experiments.