Excavation-induced damage around underground opening in brittle rock

Excavation of an underground opening in a highly stressed brittle rock mass can lead to instability in form of surface spalling. This mode of failure results from a sequence of events triggered by the high compressive stress that could exist near the walls of an opening: microcracks grow and coalesce near the boundary of the excavation to form a surface-parallel macrocrack which subsequently buckles when a critical stress is reached. Furthermore, uniaxial and triaxial tests of brittle rock specimens show that the response is highly nonlinear and complex.; This thesis consists of three parts: (i) development of a micro-mechanical damage model for brittle rocks, (ii) calculation of the damage zone around a circular tunnel in a far-field isotropic stress, and (iii) analysis of the stability of a near-surface parallel crack.; First, we will deal with the development of a constitutive model aimed at reproducing the complex brittle response observed in the laboratory. The model is formulated for plane-strain condition under compressive stres field. The source of inelastic response is sliding of pre-existing microcracks and growth of tensile cracks (wing cracks) at their tips. The initial cracks are assumed to be uniformly distributed. Using the concept of average strain and assuming no interaction between microcracks, the total strain is given by superposition of all individual microcracks. An incremental constitutive relations is obtained based on the framework of thermodynamics with internal variables. Simple examples based on an elastoplastic model with sliding cracks and a damage model for tensile crack propagation are given as a “road map” for the development of the proposed model. For the sliding wing crack mechanism, the slip along the plane of initial flaw and the length of the wing crack will be treated as internal variables. The sliding and propagation criteria are established on the basis of physical mechanisms. Evolution of the internal variables depends on the current state of stresses and internal variables, and on the incremental stress path. It is shown that this model is capable of capturing many of the important characteristics of the brittle response.; In the second part, an application of the constitutive model to the simple case of a circular tunnel subject to a hydrostatic stress field will be presented. The solution to this problem is reduced to solving a first order ordinary differential equation using the Biot Hodograph Method.; The last part is concerned with the determination of the far-field compressive buckling stress of a near-surface parallel crack, in the limiting case when the crack is situated close to the free surface. In other words, we restrict consideration to the practical case h/l $\ll$1, here l is the crack half-length and h is the distance between the crack and boundary. The problem is simplified as the layer between the crack and the free surface can then be treated as a beam under given loads. For the case h/l $\ll$ 1, the critical buckling stress takes a very simple asymptotic form. As buckling is taking place, the crack starts to open asymmetrically, thus causing an increase of both mode I and mode II stress intensity factors. The stress intensity factors in the post-buckling regime can be calculated using a nonlinear analysis of buckling.