In the present work, numerical limit analyses techniques are used to determine the collapse load factor of rock masses, considered as discontinua and equivalent continua in the Cosserat sense. The Cosserat type equivalent continuum has, as its most relevant feature in the context of the present work, the possibility of incorporating toppling (rotational) modes of failure. The two implementations are described in the paper. Validation, illustrative and comparative examples are presented.
In many geotechnical problems such as the ones found in bearing capacity of foundations, retaining structures, slope stability and underground excavations, a primary objective consists in the determination of a collapse load, a maximum load the geotechnical system is able to support before it collapses. These loads are generally determined by limit equilibrium methods or elasto plastic finite element analyses. In the present work, use is made of numerical limit analysis, an alternative, often very advantageous technique in relation to the ones described but in general seldom used in practice. The paper is divided into three parts. The first part of the paper formulates the general limit analysis problem under the framework of mathematical programming. The second part is devoted to the formulation of a true discontinuum formed by a set of discrete rigid blocks. The last part describes the formulation of limit analysis applied to Cosserat continuum representing a regularly fractured rock mass. The work presented in the paper is part of a broader study on applications of numerical limit analysis to geotechnical problems ( Araujo et al, 1996; Araujo et al, 1997)