Non linear elasto-plastic analysis of cylindrical cavity in rock mass using a Hoek-Brown criterion

Abstract

This paper aims to present an elastic, perfectly plastic, constitutive model based on the Hoek-Brown failure criterion and with non-associative plasticity. The objective is to apply the model to the non-linear analysis of geotechnical problems like excavations in rock mass. The computational implementation was carried out with a computational program called ANLOG (Non-Linear Analysis of Geotechnical Problem) system based on a displacement formulation of the finite element method. Due to the non-linear nature of the constitutive model, the study adopts an incremental iterative Newton-Raphson procedure with automatic load increments to guarantee the global level equilibrium. In addition, to guarantee the consistency condition at the local level, the study adopts, for the stress integration, an explicit algorithm with automatic sub-increments of strain. To validate the computational implementation and applicability of the numerical model, the study uses theoretical results to compare with ones obtained with the numerical simulation of cylindrical cavity in rock mass.Keywords: Hoek-Brown failure criterion, finite element method, elastoplasticity, stress integration algorithm, cylindrical cavity, tunnel, rock mass. Resumo Esse artigo apresenta um modelo constitutivo elástico perfeitamente plás-tico com plasticidade associada e com base no critério de resistência de Hoek--Brown. O objetivo é aplicar esse modelo para análise não linear de problemas geotécnicos como escavações em maciços rochosos. As implementações computacionais foram realizadas no sistema ANLOG (Análise não linear de obras geotécnicas) com base na formulação em deslocamento do método dos elementos finitos. Devido à natureza não linear do modelo constitutivo, o estudo adota um procedimento incremental iterativo do tipo Newton-Raphson com incrementos