Punching Analysis of Underlying Karst Rock Foundation Considering Self-Weight of Rock Mass

The 3D equation of the ultimate bearing capacity P_b of the karst cave foundation under self-weight γ is established using the associated flow law in the upper limit method of limit analysis on the basis of the Hoek-Brown strength criterion and the punching failure mode of the karst cave foundation. In combination with the variational principle, the equation of the punching failure line and the ultimate bearing capacity expression of the karst cave foundation are derived. The ultimate bearing capacity P_b and critical hole diameter of the karst cave foundation under self-weight are calculated by programing. The theoretical rationality is verified by indoor model tests. The research shows that: (1) The influence of the rock RMR value and uniaxial compressive strength σ_c on the ultimate bearing capacity of the karst cave foundation has nothing to do with the consideration of the self-weight γ factor. Both factors increase with the increase in uniaxial compressive strength σ_c and RMR value, and vice versa. These factors decrease with the increase in self-weight γ; however, the change is obscured; (2) The ultimate bearing capacity of the karst cave foundation P_b basically linearly increases with the increase in the thickness of the roof h of the cave; when considering the self-weight σ and thickness of the roof h, the change of the ultimate bearing capacity P_b of the karst cave foundation mainly depends on the difference between the increment of the internal dissipative and gravity power; (3) When RMR < 40, self-weight γ has a great influence on the critical span D of the cave, and when RMR>60, self-weight has a small influence on the critical span D of the cave; (4) When RMR ≤ 40, the influence of self-weight γ on the ultimate bearing capacity P_b must be considered; when RMR ≥ 70, self-weight γ must be considered when calculating the ultimate bearing capacity P_b of the karst cave foundation because the error is generally within 3%.