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 m(i), geological strength index GSI, intact rock unconfined compressive strength sigma(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 N-sigma (ratio of q(u) to sigma(c)) increases with m(i), GSI and B but decreases with sigma(c). The failure surface size is significantly affected by m(i), GSI, B, sigma(c) and rock mass unit weight. The stress distribution on the foundation base has higher variance (higher possibility of stress concentration) at smaller sigma(c), GSI, and larger B, rock mass unit weight.