ABSTRACT: When considering the rock stress component of rock mechanics design, the basic procedure is to consider the pre-existing stress-state in the rock mass and then estimate the disturbance to this stress state as a result of engineering excavation. Failure criteria are applied to the final stress state to establish whether failure will occur. However, during the evolution of the stress state, the failure locus may be reached before the anticipated failure state and, in this case, failure will occur unexpectedly. This indicates that the complete stress path (defined as the variations in magnitudes and orientations of the stress tensor components resulting from engineering-induced or natural changes) must be considered. We list a set of stress path principles with their corollaries and then introduce a new and powerful method for simultaneously illustrating changes in the six independent components of the stress tensor. This method plots the magnitudes of the principal stresses above their orientational paths on the hemispherical projection, to provide a three-dimensional stress path locus for each of the three principal stress components. In connection with this presentational device, we illustrate a number of concepts associated with the stress path in rock engineering. For example, we show how the minor principal stress approaches zero at an unsupported excavation face, the interchange of the trajectories of two principal stresses when their magnitudes become equal, and the influence of the bounds on the principal stresses given by strength criteria. RESUME: Si on s’interesse à la composante “contrainte” lors d’un dimensionnement en mécanique des roches, la méthode de base consiste à considérer l’état de contrainte pré-existant dans le massif rocheux, puis d’estimer la perturbation à cet état générée par l’excavation projetée. Des critères de rupture sont appliqués à l’état de contrainte final pour établir si une rupture va se produire. Cependant, lors de l’évolution de l’état de contrainte, la surface critique peut être atteinte ce qui provoquera une rupture anticipée et, dans ce cas, cette dernière sera inattendue. Cela indique que le chemin de contrainte complet (défini par les variations de l’intensité et de l’orientation des composantes du tenseur des contraintes liées à des causes anthropiques ou naturelles) doit être pris en compte. Nous présentons un ensemble de règles pour les chemins de contraintes ainsi que leurs corollaires et, ensuite, nous introduisons une méthode, nouvelle et puissante, pour présenter simultannement les changements des six composantes du tenseur des contraintes. Cette méthode consiste à tracer l’intensité des contraintes principales sur le chemin d’orientation des contraintes à l’aide d’une projection hémisphérique afin d’obtenir le lieu, en trois dimensions, de chaque contrainte principale. En relation avec cet outil de représentation, nous illustrons certains concepts associés au chemin de contrainte en ingénierie au rocher. Par exemple, nous montrons comment la contrainte mineure tend vers zero à la surface d’une excavation sans soutenement, le changement de direction des deux contraintes principales quand leur intensité deviennent égales, et l’influence des conditions aux limites sur les contraintes fournies par un critère de rupture. ZUSAMMENFASSUNG: Bei ingenieurmassigen Taetigkeiten in Felsgesteinen ist es noetig die ungestoerten Gesteins Stress Componenten, die vor einem anthropogen Eingriff im Gestein vorhanden waren, zu kennen und erst dann Vorhersagen ueber Stoerung des Stress Zustandes, der durch einen ingenieurmaessigen Eingriff hervorgerufen wird, herzuleiten. Kriterien fuer das Versagen werden im letzten Stadium, des Stress Zustandes angewendet, um zu erfahren ob ein Versagen wohl eintreten wird. Es ist jedoch zu beachten, dass waehrend des Stress Aufbaus ein oertliches Versagen eintreten kann, welches vor dem eigentlichen, erwarteten Versagens Zustand auftritt. Diese Moeglichkeit weist darauf hin, dass der gesammte “Stress Path” (definiert durch die Variationen der Stress Tensor Komponenten in Richtung und Groesse, hervorgerufen durch ingenieurmaessig hervorgerufene oder natuerlich Vorgaenge) betrachtet werden muss. Wir fuehren eine Liste der “Stress Path” Prinzipien auf und stellen dann eine neue und wirksame Methode zur gleichzeitigen Darstellung der sechs unabhaegigen Komponenten des Stress Tensors vor. Diese Methode stellt die Groesse der “Principal Stresses” in Abhaengigkeit von ihrem rauemlichen Weg auf einer hemispherischen Projektion dar und erlaubt hiermit eine drei dimensionale Darstellung fuer jeden Ort des “Stress Path’s” in die drei Haupt Stress Komponenten. Im Zusammenhang mit der hier gegebenen Darstellungsart, verdeutlichen wir eine Reihe von Konzepten in der Felsmechanik. Wir zeigen zum Beispiel, wie der “Minor Principal Stress” Null zustrebt an einer Wand von einer nicht abgestuetzten Ausschachtung, den Austausch von Trajektorien zweier “Principal Stresses” wenn ihre Groessen sich gleichen, und den Einfluss der Groesse von “Principal Stresses” bei gegebenen Kriterien des Festgkeits Versagens.
Discussion: T. L. Gibbs,* (Honorary Vice-President and Fellow): In terms of the Pneumoconiosis Compensation Act of 1962, a Pneumoconiosis Risk Committee was established whose function it is to estimate (by whatever means the committee deems fit) in respect of every controlled mine the pneumoconiosis risk to which persons employed in a dusty atmosphere at that mine are exposed. In estimating such risk the committee may estimate different risks in respect of individual mines or parts of mines or classes or groups of mines or occupations or localities at mines. The pneumoconiosis risk may be reviewed and re-estimated at any time. The Act provides further that the General Council for Pneumoconiosis Compensation shall apportion the levy imposed on owners of controlled mines on the basis of the pneumoconiosis risk determined by the risk committee and the numbers of persons employed in a dusty atmosphere. The task of the risk committee is a most responsible one and also a very difficult and complex one in view of the many different types of mines, rock formations, dust conditions, etc. Quite obviously, comparisons between mines cannot be made on dust concentrations alone as different mineral dusts have different toxicity or pneumoconiosis response factors. However, with its present knowledge, the risk committee is satisfied that the risk at mines, other than coal mines, is related to the mean quartz-equivalent dust concentration to which persons are exposed and the estimation of risks is based on this relationship. From the above, it will be clear that the work done by Dr du Toit on the problem of basing the current rate of levies to provide for pneumoconiosis compensation on the current dust hazard at mines has been of immense value to the risk committee. Up to now the risk committee has not been able to obtain complete and accurate information on the dust exposure of persons at all mines - and, in fact, it is doubtful whether it will be economic or practicable to obtain this in the foreseeable future - but reasonable assessments have been possible from routine dust sampling in some cases and from periodic comprehensive dust surveys in others. As a temporary measure the risks of some mines were estimated initially on a group basis relating to average dust conditions and the type of rock and mineral mined, but as more information became available, differentiation between individual mines became possible. It is the aim of the risk committee to eventually apply such a differentiation in all cases and to ensure that within the bounds of practicability each mine pays for its risk and for its risk only. In this connection, the relationship between the levies and the amounts actually paid out in compensation are examined regularly. In conclusion, I wish to add my congratulations to the author on his excellent paper. His findings will assist materially in the just administration of that very important piece of beneficial legislation, the Pneumoconiosis Compensation Act. G. K. Sluis Cremer MD (Visitor): Dr du Toit has made a valiant attempt to relate dust hazard and the rate of collecting funds for the purpose of paying compensation for Pneumoconiosis. In doing so he has had to make a number of assumptious, some of which touch on the medical aspects of pneumoconiosis. It is worth discussing whether these assumptions are justifiable. Pneumoconiosis is defined in our Pneumoconiosis Act as permanent disease of the cardio-respiratory organs which is caused by the inhalation of mineral dust. To a non-medical person this definition has probably a clear cut meaning. The doctors however have to deal with such conditions as silicosis and asbestosis where there is a well defined dose response relationship to the inhalation of quartz and asbestos respectively and on the other hand chronic bronchitis where the relationship to dust inhalation is poorly defined and where certainly no clear dose response relationship has emerged after many investigations in this country and overseas. Nevertheless since 1953 about half of our certifications for Pneumoconiosis are on the grounds of chronic bronchitis i.e. the X-rays show no evidence of silicosis, asbestosis or other relevant disease. This fact must affect Dr du Toit's computations. The next assumption we should examine is the manner in which toxicity factors have been allocated to the various mineral species. These allocations have in part been based on a restricted number of animal experiments carried out overseas but mostly in South Africa by Webster at the Pneumoconiosis Research Unit. To extrapolate the findings in a relatively small number of animal experiments to the expected reactious in man is a notoriously dangerous exercise. Furthermore the bracketing together of all silicates (except asbestos) and the insoluble metal oxides is entirely unacceptable. Talc (a hydrated silicate of magnesium) and muscovite mica (a silicate of aluminium and potassium) cause pneumoconiosis in their own right. On the other hand
I have read with interest all the papers dealing with heat transfer and the setting of heat stress limits that have appeared during the past two decades. Scientifically speaking, most of them can be rated as being of a high standard, and some of them have been acclaimed internationally as masterpieces of logical and calculated reasoning. Weathering of ore minerals A short course on 'The Weathering of Ore Minerals and the Textural Evaluation of Base Metal Gossans' is to be given by Dr I.M. Reynolds in Grahamstown from 4th to 6th October, 1982.
For the past 12 years, the Universities of Stellenbosch and Cape Town have hosted an annual symposium to discuss research topics in Minerals Processing. Since 1987, this meeting has been held under the auspices of the Western Cape Branch of the South African Institute of Mining and Metallurgy, and has enjoyed much national and international support. In 1993, in place of the usual Symposium, the Branch and Universities collaborated with CSM Associates Ltd and Minerals Engineering Journal is organizing the international Minerals Engineering '93 Conference in Cape Town.
Visualising and Understanding the Stress Path for Rock Mechanics Modelling and Testing, and Rock Engineering Design