Lower bound limit analysis for an axisymmetric problem in rock mass using power cone programming

Abstract

AbstractBy using the lower bound finite elements limit analysis (LB‐FELA) and the power cone programming (PCP), a methodology has been introduced to solve an axisymmetric stability problem with the usage of the generalized Hoek and Brown (GHB) yield criterion‐ applicable for rock mass. The formulation involves the application of the GHB yield criterion in its native form without any smoothing and it does not require any assumption associated with the circumferential stress (σθ). The efficacy of the proposed formulation in a rock mass has been demonstrated by determining (i) the bearing capacity of a circular footing, (ii) the stability numbers for an unsupported vertical cylindrical excavation, and (iii) the vertical uplift capacity of a circular horizontal anchor. The obtained solutions have been compared with that reported in literature. Failure patterns for each problem have also been explored. For the anchor problem, for no solution is reported with the usage of the GHB criterion, the influences of different material yield parameters (GSI, mi, and σci), unit weight of rock mass (γ), and the embedment ratio (H/B) of the anchor on the uplift capacity have been comprehensively examined.