Semi‐analytical solution for ultimate bearing capacity of smooth and rough circular foundations on rock considering three‐dimensional strength.

This paper proposes a semi‐analytical solution for the ultimate bearing capacity qu of both smooth and rough circular shallow foundations on rock mass. Specifically, a three‐dimensional (3D) Hoek–Brown (HB) is adopted, in conjunction with equilibrium equations under axisymmetric conditions, to derive the governing equations. The method of characteristics is utilized to solve the stress and failure characteristics mesh to determine the qu. The proposed solution is verified by using it to analyze test foundations. Comparison with an HB criterion‐based solution is performed to highlight the importance of 3D strength. Furthermore, parametric studies are performed to investigate the effects of rock mass properties (intact rock constant mi${m}_{\mathrm{i}}$, geological strength index GSI, intact rock unconfined compressive strength σc) and foundation diameter (B) on the qu, failure surface size, and vertical stress distribution on the foundation base. The results indicate that ignoring the 3D strength and the rock mass weight would lead to underestimation of qu. Besides, the ultimate bearing capacity factor Nσ${N}_{{\sigma}}$ (ratio of qu to σc) increases with mi${m}_{\mathrm{i}}$, GSI and B but decreases with σc${\sigma }_{\mathrm{c}}$. The failure surface size is significantly affected by mi${m}_{\mathrm{i}}$, GSI, B, σc${\sigma }_{\mathrm{c}}$ and rock mass unit weight. The stress distribution on the foundation base has higher variance (higher possibility of stress concentration) at smaller σc${\sigma }_{\mathrm{c}}$, GSI, and larger B, rock mass unit weight. [ABSTRACT FROM AUTHOR]