New Limit Equilibrium Solution for the Bearing Capacity of Bucket Foundations in Sand

Abstract This paper presents a new limit equilibrium solution for the ultimate bearing capacity of bucket foundations in sand subjected to combined horizontal–vertical-moment loading. Closed-form expressions are derived for all reaction components, i.e., the lateral resistance, base shear, and distributed moment generated by vertical shear stresses. A key outcome is a general analytical formulation of the lateral bearing coefficient, function of soil angle of shearing resistance, and caisson–soil interface friction angle, derived directly from equilibrium considerations rather than empirical calibration, making the solution broadly applicable to any rigid cylindrical foundation element mobilizing passive and active pressures. This allows us to furnish fully analytical three-dimensional (3D) interaction domains at failure, which are easy to compute and suitable for (1) direct use in ultimate limit state (ULS) checks; (2) simplified design procedures; and (3) macroelement formulations. The proposed expressions, for both reaction components and the resulting failure domains, are validated against extensive 3D finite-element analyses with different constitutive laws, independent numerical studies from the literature, and small-scale physical tests, showing excellent agreement across stress distributions and global failure envelopes. A simplified lower-bound formula is also proposed to support preliminary design in routine engineering.