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Lower bound limit analysis of unsupported vertical circular excavations in rocks using Hoek‐Brown failure criterion
Author(s) -
Kumar Jyant,
Rahaman Obaidur
Publication year - 2020
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.3051
Subject(s) - limit analysis , hoek–brown failure criterion , geological strength index , yield surface , parametric statistics , mathematics , upper and lower bounds , yield (engineering) , rotational symmetry , stability (learning theory) , structural engineering , geotechnical engineering , limit (mathematics) , radius , smoothing , rock mass classification , geology , geometry , engineering , finite element method , mathematical analysis , materials science , computer science , statistics , computer security , metallurgy , constitutive equation , machine learning
Summary The stability of vertical unsupported circular excavations in rock media, obeying generalized Hoek‐Brown yield criterion, has been investigated by using the lower bound finite elements limit analysis. An axisymmetric analysis, composed of a planar domain with a mesh of three‐noded triangular elements, has been carried out. The optimization problem is dealt with by using the semidefinite programming technique avoiding the need of either smoothing the yield surface or making any assumption associated with the circumferential stress ( σ θ ). A detailed parametric study has been executed, and the effects of different input material parameters, namely, geological strength index ( GSI ), yield parameter ( m i ), and the disturbance factor ( D ) on the results have been studied. For different height to radius ratios of the excavation, the computed results are presented in the form of nondimensional stability numbers. Failure mechanisms have also been investigated for a few typical cases. The results from the analysis have been compared with that evaluated separately with the application of the software OptumG2.