Self-similarity analysis of the elasto-plastic response of underground openings in rock and effects of practical variables

The design of tunnel and shaft excavations in rock is usually based on the assumption that the rock behaves as an elasto-plastic continuum. Much of the current understanding of ground support principles is derived from the analysis of circular openings under conditions of hydrostatic loading. Practical analyses are carried out using numerical modelling for specific geometrical and rock property parameters without benefit of the insight that can be gained from examination of the relationships among these parameters. This insight is especially important for geotechnical design, since the appropriate field-scale values of the parameters are not well known. A good design should consider the practical implications of uncertainties in these values. Presentation of results in dimensionless form also contributes to a better awareness of the critical variables in the analysis.; This thesis examines the mechanics of deformation of an excavation in an elasto-plastic medium. The dimensionless groups of variables that can be assumed to govern the situation are determined. The classical case of a circular opening under hydrostatic loading is considered first and solved for the most general case of softening behavior. The problem is studied analytically using similarity analysis, and the response of the excavation is expressed in dimensionless form so that the representation applies to all possible combinations of the geometrical and mechanical parameters involved in the analysis.; Based on this general solution, the degree of stability of the excavation is examined for the case of circular openings. Gravity effects are included by considering body forces in the self-similar model, and instability criteria are defined in terms of the 'characteristic curve' of the opening. Results are again presented in dimensionless form using 'limit depth charts' (i.e. a graphical representation of stability conditions).; Finally, practical considerations regarding the influence of the shape of the excavation and non-uniformity of the far-field stresses are examined. Solutions obtained numerically for elliptical cavities using the finite difference code FLAC are shown to be of general applicability after expressing the results in terms of the appropriate dimensionless groups.