J.P. Harrison

Development of a local degradation approach to the modelling of brittle fracture in heterogeneous rocks

Abstract At the microscopic scale (say, of the order of grain size), rock is a heterogeneous material whose brittle fracture is a complicated progressive process caused by isolated microstructural changes, known also as dissipative processes. These processes are particularly difficult to predict and model in the compressive field. This paper develops a novel numerical methodology for the simulation of these isolated processes, particularly in compressive fields, such that the resulting non-linear macroscopic behaviour can be predicted. The core of the model is elemental degradation. As suggested by laboratory investigations, the microscopic processes involved in rock fracture can be classified into a combination of brittle and ductile processes. The former cause degradation in both local material elasticity and strength, with the extent of degradation being determined by the degree of bond breakage in forming crack surfaces or the like. The latter, however, lead only to plastic deformation. Thus, when brittle processes dominate the deformation of a material, more degradation occurs than if ductile processes dominate. Elemental degradation is represented by a new parameter termed the degradation index, which is introduced in this research and defined as the ratio of the degradation occurring at a certain confining stress level to the corresponding degradation occurring under uniaxial conditions. In combination with an elasto-plastic constitutive relation, the degradation model yields an elastic–brittle–plastic elemental constitutive behaviour. In the model, failure of an element causes disturbance of the local stress field, which may lead to progressive failure of surrounding elements. An explicit finite difference scheme is used to implement the degradation model. An engineering application of the degradation model to the plane strain analysis of mine pillar behaviour is presented. In terms of isolated fracture processes and the corresponding macroscopic mechanical behaviour, the degradation model produces simulation results that are similar to field observations. That is, the fracture process of a squat pillar begins with the initiation of local failure at random sites, and progresses through extension of these failed sites, coalescence of the extended sites, and slabbing or spalling of the ribsides, until development of large shear fractures ultimately occurs. The results suggest that the degradation model is a powerful approach to the study of macroscopic brittle behaviour encountered in rock mechanics and rock engineering. The application of the degradation model to the simulation of brittle fracture of rock specimens in laboratory compression tests is the subject of a companion paper.

Application of a local degradation model to the analysis of brittle fracture of laboratory scale rock specimens under triaxial conditions

Abstract Development of brittle fracture and the associated macroscopic behaviour of rock specimens in laboratory tests are simulated using a local degradation model for brittle fracture in heterogeneous rocks. We examine this subject because laboratory uniaxial and triaxial tests are widely used in the rock mechanics community to both characterise rock behaviour and to interpret fracture phenomena observed in natural rock, such as the Earths crust, and developed around rock engineering structures. In addition, numerous historical efforts related to the detailed study of this subject have made available a great deal of information for use both as model input data and comparison results. A series of numerical experiments have been performed to investigate the influence of a number of parameters on rock fracture. In particular, rock fracture under various confining stresses has been explored. The results show that the degradation algorithm is capable of reproducing many characteristics associated with brittle fracture in heterogeneous rocks, including: the development of fracture from the elemental scale to the macroscopic scale; fracture pattern as a function of confining pressure; variation of fracture plane angle with respect to confining pressure; the complete stress–strain curve and corresponding strain energy dissipation characteristics; dependence of the stress–strain curve on confining pressure; and loading–unloading hysteresis loops. Independent investigations into the effect on rock fracture of (i) the degradation parameter embodied with the model and (ii) the Weibull shape parameter used to introduce heterogeneity distribution are described. The results indicate that the degradation parameter controls the degree of degradation relative to confining pressure. As this parameter increases, and the elemental degradation decreases, the number of failed sites generated prior to the formation of macroscopic fracture plane increases, and both the peak and ultimate strengths of the model increase. The Weibull parameter influences the formation of the final fracture plane. As this parameter increases, reducing the heterogeneity, the number of diffused failed sites and the angle of the eventual fracture plane to the major principal stress tends to decrease, and the brittleness of the resulting stress–strain curve increases. It is suggested that values in the range 2–4 are appropriate for this parameter in representing elemental strength distribution of rock materials.

A semi-automated methodology for discontinuity trace detection in digital images of rock mass exposures

Abstract The in situ measurement of discontinuity geometry at rock mass exposures is a slow process, it can be hazardous, and often a large proportion of the exposure is inaccessible. Photogrammetry is a safer method with which to measure discontinuity geometry, and by removing the issues of inaccessibility it provides greater access to the exposure. The use of digital images — rather than customary analogue photographic images — for photogrammetry retains these benefits, while offering the prospect of an automated, and hence fast, method of discontinuity detection and discontinuity geometry analysis. This paper presents a methodology for semi-automated discontinuity trace detection in greyscale digital images of rock mass exposures. The methodology detects discontinuity traces as individual objects, which is a necessary precursor to automated discontinuity geometry analysis. The methodology initially considers a rock mass exposure digital image as a discrete surface, the elevation of which is given by pixel brightness levels. By doing so, a discontinuity trace can be likened to a topographic ravine and therefore some pixels within a discontinuity trace can be found by locating the so-called ‘ravine pixels’. A series of digital image processing techniques are then applied to group and transform these ravine pixels into linear structures that are more suited to computer decision-making, and this results in what we call ravine-line segments. A novel method is presented that links these ravine-line segments together to achieve discontinuity trace detection. The method considers three criteria during the linking process to help ensure acceptable discontinuity detection. These criteria involve the nature of the image search, the angles used to control the shape of a discontinuity trace, and the brightness of the pixels in the rock mass exposure image. Case studies show the discontinuity trace maps that result when the methodology is applied to several rock mass exposure images, and a comparison is made between a discontinuity trace map produced by the methodology and several drawn by hand.

Selection of the threshold value in RQD assessments

The use of rock quality designation (RQD) as an engineering measure for classifying discontinuous rock masses is widespread.

Automated tracing of rock mass discontinuities from digital images

Abstract The successful design of an engineered structure, either on or within a discontinuous rock mass, is largely dependent on our ability to reliably characterise discontinuity and rock mass geometry. Customary sampling methods for the collection of discontinuity measurements, using in situ scanline and window techniques, are inadequate in providing reliable characterisation and slow. Digital photogrammetry provides the means for the rapid collection of large quantities of discontinuity data. This paper presents initial results from a novel algorithm, coded in C, to automatically detect discontinuities from digital images of rock exposures. The basis of the method is that a digital image of a rock exposure is considered as a grey scale topographic surface, on which dark pixels represent low elevation and light pixels high elevation. Generally, discontinuities which intersect a near-planar rock face form dark linear features, and these can be regarded in three dimensions as topographic ravines. The algorithm we have developed considers the curvature of this surface and using this detects pixels which coincide with discontinuities.