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 q_u 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 q_u. 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 (Formula presented.), geological strength index GSI, intact rock unconfined compressive strength σ_c) and foundation diameter (B) on the q_u, 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 q_u. Besides, the ultimate bearing capacity factor (Formula presented.) (ratio of q_u to σ_c) increases with (Formula presented.), GSI and B but decreases with (Formula presented.). The failure surface size is significantly affected by (Formula presented.), GSI, B, (Formula presented.) and rock mass unit weight. The stress distribution on the foundation base has higher variance (higher possibility of stress concentration) at smaller (Formula presented.), GSI, and larger B, rock mass unit weight.