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Proceedings Papers

Paper presented at the ISRM International Symposium, August 30–September 2, 1989

Paper Number: ISRM-IS-1989-006

... isotropic stress state, i.e. from brittle to ductile. 2 THEORITICAL ANALYSIS 2.1 Possible conditions for the existance of

**straight****line**on the criterion-plot To project a conceptual view of the nonlinear strength criterion, the various possible existing conditions in Eqn.(l) are discussed. As the...
Abstract

ABSTRACT: The strength characteristics of rocks at depth can be, in the first instance, best revealed by conducting triaxial tests in the laboratory. From the available literature, triaxial test data of a large number of rocks has been used to from an empirical non-linear strength criterion, which relates the failure strength, σ1 of rocks to the isotropic stress, σ3 (which is γ.H in the case in-situ condition). The criterion is based upon Mohr-Coulomb approach and its applicability has been examined for a wide range of isotropic stress state from 0.1 MPa to 700.0 MPa (i.e. the equivalent depths of about 5 m to 2800 m from the surface, with the average density of rocks being 2.5 kN/m 3 ), for the rocks of various origins and compressive strengths 1 THE NON-LINEAR FAILURE CRITERION The criterion proposed by Ramamurthy (1986) and Ramamurthy et al. (1985) is based upon Mohr-Coulomb theory and it takes care of non-linear behaviour of intact rocks as well. The investigators observed linear failure envelopes for test results of selected eighty rocks from the earlier published literature and four sandstones tested by them on a plot between log[σ1-σ3)/σ3] and log (σc/σ3) on ordinate and abscissa, respectively, throughout the range of σc/σ3. The slope of the envelopes, α, has been observed to be varying in a narrow range, an a constant value of 0.8 has been suggested by them for all the rocks. The variation observed in the values of B was from 1.8 to 3.0. In the present work, more triaxial data of various rocks from the published literature has been included to establish the validity of the criterion by suggesting possible modifications. The data has been selected, specially for the rocks tested either in a very low or very high range of the confining pressure to cover a wide range of isotropic stress state, i.e. from brittle to ductile. 2 THEORITICAL ANALYSIS 2.1 Possible conditions for the existance of straight line on the criterion-plot To project a conceptual view of the nonlinear strength criterion, the various possible existing conditions in Eqn.(l) are discussed. As the value of B is positive and greater than 1, this equation implies that the deviatoric stress at failure is always more than the compressive strength and is a constant unaffected by the confining pressure. Practically, this stage may occur in a rock under very high confining conditions when (σ1-σ3) does not increase any further by increasing σ3, i.e. ductile condition. (4) α > 1 and B > 1: This condition of the straight line, passing through the point (l,y) where y > 1, and having a slope greater than 1, in the plot suggests that with increasing confining pressure, there is an exponential decrease in the value of (σ1-σ3) throughout the range of σc/σ3, which is not possible. (5) α < 1 and B > 1: The envelope represented by this condition is a straight line passing through a point (1,y) where y > 1.

Proceedings Papers

Paper presented at the ISRM International Symposium, September 12–16, 1988

Paper Number: ISRM-IS-1988-005

...,plane surfaces (rectangles, circles, etc borehole cores,

**straight****lines**- are deduced. The statistical distributions of several correlated practical parameters (number of joints of the set, cut by a given segment; distance, along a given**straight****line**, between a joint of the set and the n-th following...ABSTRACT: The intensity of a joint set quantifies the amount of rock mass fracturing due to that set, without regard to the extent of the individual joints of the set. The general expressions, giving the intensity of a joint set as a function of the sum of the trace lengths of its joints on an observation surface, as well as the formulas for the usual types of observation surfaces - limited adit stretches, plane surfaces (rectangles, circles, etc.), borehole cores, straight lines - are deduced. The statistical distributions of several correlated practical parameters (number of joints of the set, cut by a given segment; distance, along a given straight line, between a joint of the set and the n-th following joint of that set; etc.) are presented, and it is shown that the phenomena of the scale effect on the rock mass deformability are in great part due to the joint distributions. Some practical consequences, regarding problems encountered in the excavation of power plant foundations and underground works, are referred to. RÉSUMÉ: L' intensite d'une famille de diaclases quantifie la partie de la fracturation du massif rocheux due à cette famil le, sans tenir compte de l'extension des diaclases indiv i duelles de la famille. On deduit les expressions generales donnant l' intensite d'une famille de diaclases en fonction de la somme des longueurs de la trace de ses diaclases sur une surface d'observation, ainsi que les formules pour les types usuels de surfaces d'o b servation - tronçons limites de galerie, surfaces planes (rectangles, cercles, etc.), c a rottes de sondage, lignes droites -. On presente les distributions statistiques de plusieurs paramètres pratiques correlatifs {nombre de diaclases de la famille, coupees par un segment de droite donne; distance, le long d'une droite donnee, entre une diaclase de la famille et la enième diaclase suivante de cette famille; etc.),et on montre que les phenomenes de l'effet d'echelle sur la deformabilite des massifs rocheux sont en grande partie dús aux distributions de diaclases. On mentionne quelques consequences pratiques, concernant des problèmes rencontres lors de I'excavation de fondations et ouvrages SOuterrains de centrales energetiques. ZUSAMMENFASSUNG: Die Starke einer Kluftschar quantifiziert das Ausmaß der dieser Schar zu verdankenden Felsdurchtrennung, ohne die Ausdehnung der einzelnen Kluefte der Schar zu beruecksichtigen. Die allgemeinen Gleichungen, die die Starke einer Kluftschar als eine Funktion der Summe der Ausbißlangen ihrer Kluefte auf einer Beobachtungsflache darstellen, sowie die Formeln fuer die gewöhnlichen Beobachtungsflachentypen - begrenzte Stollenstrecken, ebene Flachen (Rechtecke, Kreise, usw.), Bohrlochkerne, Geraden - werden abgeleitet. Die statistischen Verteilungen mehrerer bezueglichen praktischen Parameter (Anzahl der Kluefte der Schar, die durch eine gegebene Strecke geschnitten werden; Entfernung, langs einer gegebenen Geraden, zwischen einer Kluft der Schar und der n-ten folgenden Kluft dieser Schar; usw.) werden vorgestellt, und es wird gezeigt, daß die Phanomene des Maßstabeffektes bei der Felsverformbarkeit zum großen Teil den Kluftverte i lungen zu verdanken sind. Es werden einige praktische Folgerungen erwahnt, die Probleme, die beirn Ausbruch von Kraftwerksgruendungen und unterirdischen Anlagen auftreten,betreffen. 1 INTRODUCTION The intensity of a joint set quantifies the amount of rock mass fracturing due to that set, without regard to the extent of the individual joints of the set. In a homogeneous rock mass the amount of fracturing depends linearly on the con- sidered volume of rock mass, and, therefore, the intensity l of a chosen joint set can be calculated by (Equation in full paper) A j being the area of the joint j of that set, occurring in the rock mass volume V, and N the total number of joints of the set, occurring in this volume. The intensity should, accordingly, be e x pressed in (m 2 /m 3 ), although it is usually expressed in (number of joints/m),as it is often determined by counting the number of joints of the set, which are cut by a segment of unitary length, and whose orientation is normal to the mean attitude of the concerned joint set. This counting will normally yield a value by defect, because any joint having an attitude different from the joint set's mean attitude, will have an intersection with the cylindrical volume of infinitesimal cross section.

Proceedings Papers

Paper presented at the ISRM International Symposium, September 21–24, 1981

Paper Number: ISRM-IS-1981-007

... loading uniaxial compressive stress-deformation curve elasticity clay siltstone strength deformation process moduli compression deformation mechanical behavior plate-bearing test deformation energy application certain stress level

**straight****line**Proceedings of the International Symposium...
Abstract

INTRODUCTION The deformation process of clay siltstone under loading is a cumulative process of energy. Therefore, in order to clarify the deformation process of clay siltstone in compression by plate- bearing test, it is advisable to employ the method of energy analysis. In this paper, the reversible and irreversible energy in the deformation process is calculated from stress-deformation curves. The relationship between the deformation and the time of application of load to clay siltstone is investigated. EXPERIMENTAL PROCEDURES Circular steel bearing plate is applied in testing, The plate has a thickness of 5 cm and a diameter of 32 cm, Its area is about 800 cm%, Three tests, that is, tests (a), (b) and (c), were conducted, In test (a), the deformation of rock is measured immediately after each class of load is applied to it, and then it is read off the scale in every three minutes, It is taken as a controlling standard that the difference between two successive readings in every three minutes is not beyond 1/100 mm, This is called the controlling method of deformation, Tests (b) and (c) are carried out by what is called the controlling method of time, But each is slightly different from the other, In test (b) its deformation is measured after ten minutes of loading and then the next class of load is appliea at once but in test (c) the interval is three minutes, It holds true both in loading and in unloading. At this point these three tests are the same, Tests (a) and (b) arc all single cycle of loading and unloading, while test (c) is multi cycle loading unloading, Other technological requirements and experement conditions, for instance, clean and flat rock surface, accuracy of installation of loading system, rating of measurement instruments and so on, are all the same. When testing is carried out, the natural water content in clay siltstone is 3.1%, testing cavern temperature is between 18.2 ° Ct and 20 ° C, uniaxial compressive strength of clay siltstone is 211 kg/cm 2 . RESULTS AND CONCLUSIONS The stress-deformation curves of test(a), (b) and(c) are obtained by means of the plate-bearing test, as shown in Fig,1 ~ Fig,3,hencc corresponding moduli of elasticity and deformation, as shown in Table 1, In order to make a comparison between them, results in laboratory and normal test in situ in the same testing cavern, where the, area of the plate is 2000 cm 2 , are shown in Table 2. From Table 2 it can be seen that even if the fissure is not developed in clay siltstone and it is more uniform rook, the range of variation of its deformation parameter is very evident as well, (Figure in full paper) The curve was obtained under a single process of loading and unloading as shown in Fig. 4. The reversible and irreversible energy in the deformation process is calculated by measuring areas in the stress-deformation diagram. Total deformation energy u,' applied to the rock mass by an external load is divided into two parts.