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Proceedings Papers

Paper presented at the ISRM International Symposium, November 19–24, 2000

Paper Number: ISRM-IS-2000-609

... variable method (Muskhelishvili, 1964). complex variable solution boundary condition

**expression**tunnel trough depth tunnel boundary settlement trough tunnel lining equation displacement shallow tunnel ovalization Verruijt expansion contraction coefficient circular tunnel A...
Abstract

ABSTRACT: The solution is obtained through the use of complex variables and a conformal mapping onto a circular ring. The boundary conditions are that the surface of the half plane is completely free of stress and that the tunnel undergoes a prescribed displacement corresponding to an ovalization of the tunnel. When the solution is compared to a previously published approximation, it appears that the approximation suffers from an inaccuracy in the boundary conditions for compressible soils. From the solution it is evident that the settlement trough at the soil surface is much narrower than in the case of a uniform contraction of the tunnel cavity. For a shallow tunnel, the stresses accommodating an ovalization of the tunnel cavity do not correspond to an ovalization of the tunnel lining, suggesting that in practice pure ovalization of shallow tunnels is unlikely to occur. INTRODUCTION In this paper an exact analytical solution for the ovalization of a tunnel in a linearly elastic half-plane is presented. Although soil behavior can only be roughly approximated by linearly elastic models, this solution can be used as a tool to gain insight into the fundamental nature of the problem and as a benchmark for numerical procedures based on more sophisticated models of soil behavior. The paper is divided into five sections; the first two sections deal with the mathematical details of the solution, the third section discusses issues encountered during the validation, and the last two sections present the results and conclusions. STATEMENT OF THE PROBLEM General Solution The problem of a circular tunnel in an elastic half-plane with a stress free upper surface and a prescribed displacement at the tunnel boundary was solved by Verruijt (1997) through use of the complex variable method (Muskhelishvili, 1964).

Proceedings Papers

Paper presented at the ISRM International Symposium, November 19–24, 2000

Paper Number: ISRM-IS-2000-207

... geometric characteristic characteristic evaluation rock mass numerical method mean value deformability modulus displacement discontinuity open crack numerical analysis discontinuity assumption analytical solution natural discontinuity crack length specimen MPa

**expression**fracture density...
Abstract

ABSTRACT: The purpose of this paper is to suggest a numerical method for the evaluation of the deformability modulus of discontinuous rock masses. The study is conducted by assuming that the fracture density and the length of cracks, contained in a rock mass, depend on a negative exponential statistical distribution. Compressive tests are simulated on rock volumes containing open and closed flat cracks through a numerical computation code based on the Displacement Discontinuity Method. It proved impossible to determine the deformability modulus of the Representative Volume Element (RVE) in numerical terms. However, for a set of specimens containing even as few as 9 open cracks, the mean value of the deformability modulus is seen to approach the value determine d for the RVE analytically. Based on this observation, the calculation method is applied to determine the deformability modulus of specimens containing closed cracks. The numerical results show that the deformability modulus of a rock mass decreases as function of the fracture density and the maximum crack length if it is compared to that of rock material. INTRODUCTION The evaluation of the value of the deformability modulus to be assumed for the rock mass is a difficult task when a continuous equivalent approach is used. As a matter of fact, the values obtained through laboratory tests on small specimens, containing only micro- fractures, are different from those obtained through large scale tests on the rock masses containing natural discontinuities of different orders of magnitude. For this reason laboratory values cannot be directly assumed in the analysis of real rock structures. For engineering purposes, empirical correlations are used linking quality indices of the rock mass with the value of the deformability modulus determined in situ (Bieniawski, 1976; Barton et al., 1974).

Proceedings Papers

Paper presented at the ISRM International Symposium, November 19–24, 2000

Paper Number: ISRM-IS-2000-183

... s tr y , 1 6 4 6 A b ik o , A b ik o - s h i ,C h ib a- k e n 2 7 0 - 1 1 9 4 J ap a n Figure 2 : Failure envelopes of various materials tested as

**expressed**by the proposed criterion o f p e r v i o u s z o n e a n d c o r e z o n e m a t e r i a l s a r e s h o w n i n F i g u r e 1 . T h e d i m e...
Abstract

ABSTRACT: 1) A new failure criterion, (τ/τR) α = 1 – σ/σt, is proposed based on the results of triaxial compression tests on rock and granular materials of various types. In this criterion, τ and σ are shearing stress and normal stress, respectively, τR and σt are τ- and σ- intercepts, respectively. ‘α’ is a failure envelope exponent. It is demonstrated that this criterion can express in the unified manner, the failure criterion of rock and granular materials of a wide range of types from hard rock to sand. 2)It is shown that the non-linear deformability of these materials can be expressed by D/D o = R 1/a , where D is a deformability, D o is its initial value and R is the relaxation factor. 3) One proposed technique is to apply the above-mentioned equations to numerical analysis of deformation behavior of rock masses during excavation. INTRODUCTION In the excavation of large caverns or tunnels, rock masses undergo deformation, leading to a failure in some cases. The most important factors affecting the behavior of such rock masses are 1) failure criterion for rock mass and 2) non-linear deformability of rock mass. The authors studied the results of triaxial compression tests on a wide range of rock and granular materials, such as, hardrock, soft rock, concrete, sand, and others. A unique solution is obtained which can express in a comprehensive and unified manner, the failure criterion and non - linear deformation characteristics of these materials of different types. Proposal of a Technique for Expressing the Non - linear Deformability of Various Materials The phenomenon in which a rock mass is subjected to an external force and the stress - strain relationship becomes non - linear, thereby causing a local failure can be considered in the following manner.

Proceedings Papers

Paper presented at the ISRM International Symposium, November 19–24, 2000

Paper Number: ISRM-IS-2000-185

... of suction caisson under uplift loading is included, and results of finite element modelling are presented. A simplified method for the estimation of the uplift capacity for suction caissons is described, based on the results of the finite element study. The

**expressions**developed in this paper take...
Abstract

ABSTRACT: Suction caissons are being used increasingly for the anchorage of large compliant offshore structures. Uplift capacity of the suction caissons under inclined loading is a critical issue in these applications, and reliable methods of predicting the capacity under this form of loading are required in order to produce reliable designs. An extensive theoretical investigation has been carried out of suction caissons in uniform soils subjected to inclined uplift loading for cases where the behaviour of the seabed soil is undrained. A brief review of previous research on the behaviour of suction caisson under uplift loading is included, and results of finite element modelling are presented. A simplified method for the estimation of the uplift capacity for suction caissons is described, based on the results of the finite element study. The expressions developed in this paper take into account the influence of the aspect ratio of the caisson, the point of application and angle of inclination of the loading, and the undrained shear strength of the soil. INTRODUCTION Suction caissons often provide a cost effective alternative for catenary, taut leg, tension leg moorings and jacket structures, compared to conventional piles and drag anchors, particularly in areas such as the North Sea, the Gulf of Mexico and North-West Shelf in Western Australia, and for water depths in the 300m to 3000m range. Suction caissons are normally cylindrical units made of concrete or steel. A suction caisson can penetrate partly into the soil under its own weight. Further penetration can be achieved by pumping the water out of the caisson, creating an inside under-pressure relative to the outside water pressure (active suction). The installation phase is where the suction caissons gain many of the advantages over piled foundations, as the suction installation can take place in a relatively short time.

Proceedings Papers

Paper presented at the ISRM International Symposium, November 19–24, 2000

Paper Number: ISRM-IS-2000-041

...SHEAR STRENGTH OF GEOMATERIALS - A BRIEF HISTORICAL PERSPECTIVE Richard H.G. Parry 1 ABSTRACT Although the shear strength

**expression**proposed by Coulomb (1776) for masonry, brick and earth, made up of cohesion and friction components, is still in general use today, it was not until Terzaghi (1936...
Abstract

ABSTRACT: Although the shear strength expression proposed by Coulomb (1776) for masonry, brick and earth, made up of cohesion and friction components, is still in general use today, it was not until Terzaghi (1936) presented the principle of effective stress that it could be used with confidence in most soils and soft or jointed rocks. The Griffith (1921, 1924) crack theory, while inadequate in itself, has provided a starting point for developing empirical expressions for the shear strength of hard intact rocks. Many factors influence the shear strength of soils and rocks, such as drainage conditions, rate of strain or shear displacement, degree of saturation, stress path, anisotropy, fissures and joints. A brief review is attempted here of the more salient advances which have been made in understanding and quantifying the influence of these various factors. INTRODUCTION Until the 20th Century such assessments were necessarily qualitative, based mostly on experience or rule of thumb. The problem is that soil and rock come in an infinite number of guises, and while experience and rule of thumb may often have sufficed in the past, there were no doubt many instances, mostly long forgotten, when they proved inadequate and even misleading, leading to failures. The advances in understanding the strength of engineering materials which occurred in the 19th Century did not extend to soils and rock masses. A fundamental understanding of the strength of soils and soft rocks had to await an understanding of effective stress, first expressed formally by Terzaghi in 1936 and for which he is justifiably regarded as the Father of Soil Mechanics. A different, more empirical approach has been required in the case of hard rocks for which it is recognised that their strength is dominated by the presence of imperfections.

Proceedings Papers

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

Paper Number: ISRM-IS-1989-082

... reservoir geomechanics displacement borulev coefficient Reservoir Characterization Upstream Oil & Gas dimension contour excavation

**expression**metals & mining excavation contour formula stability failure process Rock Excavation Destruction propagation destruction...
Abstract

ABSTRACT: The paper presents the results of experimental laboratory studies focusing on the physics of failure. Different stages of failure of a rock mass around excavations are established, and assessment of its state is carried out. Conditions of stability of such a rock mass subject to the action of blast loads are proposed. Excavation stability is also shown to depend on duration of blast impulse. Analytical relationships are presented to assess the rates of rock block fall when destructing excavations with blast loads. The rate of rock block fall is found to depend on rock strength characteristics, blast impulse parameters and velocity of joint propagation. A brief analysis of problems connected with design of rock excavations for combined action of static and dynamic loads is done. In the contemporary mining industry powerful explosions are practiced to raise the rate of the mineral resources mined, as well as that of boring, blasting and the work connected with breaking down and removal of a considerable volume of rock. Such explosions generate in the rock mass seismic blast waves, which affect the rock excavations and can cause their failure. Therefore, studying the process of rock excavation destruction and working out methods for determining the parameters of that process has become an urgent problem. The polarized-optical method based on physical modelling has certain advantages in studying wave propagation processes in a homogeneous rock mass (Khesin, 1975; Borulev et al., 1986; Sinitsin et al., 1985). In order to conduct experimental studies with physical models it is necessary to decide the questions of modelling, choosing model materials, experimental techniques and interpretation of the results obtained. Borulev et al. (1986) and Sinitsin et al. (1985) give criterial relations between the basic parameters of the failure process of the homogeneous isotropic rock mass. Their derivation is based on the statistical strength theory using Griffith's criterion for determining the moment when joint displacement starts. Using similarity criteria requires satisfying the relations established for the dimensions of joints, the density of their distribution in the rock mass, their propagation velocity, the specific surface energy in the natural and model material. It has been found that the process of failure in models of industrial glass is adequate (with allowance for the geometric scale) to that of the surrounding rock mass. The main result of the experimental laboratory studies is visual observation of failure dynamics in transparent models (Borulev et al. 1986; Sinitsin et al. 1985; Borulev et al., 1988). Formation of different failure zones in the surrounding rock mass determines the degree of its destruction, which is characterized by the failure coefficient m.. The value of the coefficient is¹ found in Table 1, where the index i denotes the degree of destruction. A procedure and a program for computing the parameters of the failure process of rock excavations induced by seismic blast waves have been developed on the basis of the investigation results. The mathematical base is the statistical strength theory and brittle fracture mechanics.

Proceedings Papers

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

Paper Number: ISRM-IS-1988-005

..., 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...
Abstract

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, August 31–September 3, 1986

Paper Number: ISRM-IS-1986-010

... rock mass or several of its units are thinly layered and the thickness and deformability properties of the horizontal layers vary appreciably with depth. Reservoir Characterization Thickness plane

**expression**coordinate system reservoir geomechanics variation gravitational loading rock...
Abstract

ABSTRACT: This paper presents four models for the stress distributions induced by gravity in anisotropic, stratified and regularly jointed rock masses. These rocks are assumed to be laterally restrained. It is shown that the nature of the stress field induced by gravity is strongly affected by rock mass structure. It is also found that a decrease in rock mass anisotropy and a stiffening of rock masses with depth can generate stress distributions comparable to empirical distributions proposed in the literature. RESUME: Ce papier présente quatre modèles pour la distribution des contraintes induites par la gravité dans des massifs rocheux anisotropes, stratifiés et fracturés. La roche ne peut pas se déformer latéralement. On montre que l''état de contrainte induit par gravité est fortement relié à la structure du massif rocheux. On montre aussi qu''une diminution du caractère anisotrope et de la compressibilité des massifs rocheux avec la profondeur peuvent créer des distributions de contraintes comparables à celles proposées dans la litérature. ZUSAMMENFASSUNG: Dieser Beitrag stellt vier Modelle vor für die Druckverteilung, die durch die Gravitation in anisotropischen, geschichteten und rissigen Felsmassen erzeugt wird. Es wird angenommen, daβ der Fels seitlich fixiert ist. Es wird gezeigt, daβ die durch die Gravitation erzeugten Druckverteilung stark von der Felsstruktur abhängt. Man kann darüberhinaus nachweisen, daβ eine Abnahme in der Felsanisotropie und eine Versteifung der Felsmassen mit zunehmender Tiefe Druckverteilungen erzeugt die vergleichbar mit empirischen Verteilungen sind und in der Literatur vorausgesagt werden. 1. INTRODUCTION In this paper, four models are proposed for the influence of anisotropy caused by rock fabric elements such as foliation, bedding or joints on gravity-induced stresses. At the outset, the constitutive relations for linear anisotropic elastic media and the thermodynamic constraints on the constants appearing in these relations are reviewed. Then, having established the general constitutive background, the four models are presented. The first and most general model describes gravity induced stresses in an anisotropic rock mass and provides a framework for the succeeding three models. The second and third models describe gravity-induced stresses in horizontally layered rock where layer thicknesses and elastic properties vary with depth. The last model describes gravity-induced stresses in a regularly jointed rock mass where joints are either parallel or normal to the ground surface. We conclude with a discussion of the implications of the results of each model with respect to measured stresses. 4. STRESSES DUE TO GRAVITATIONAL LOADING OF AN ANISOTROPIC ROCK MASS Consider the equilibrium of a flat-lying horizontal elastic rock mass of uniform-density p under gravity alone. The rock mass is assumed to be'' laterally restrained and orthotropic in an x,y,z coordinate system such that the x and y-axes are horizontal and the z-axis is positive downwards with the plane z = 0 coinciding with the ground surface (Fig. 1). At each point in the rock mass, three planes of elastic symmetry exist, each plane being normal to a coordinate axis. The constitutive model for the rock mass is described by equation (2) where because of symmetry and lateral restraint yxy'' Yxz'' Yyz'' EX and Ey vanish. If the rock mass is transversely isotropic in planes perpendicular to the ground surface. unequal horizontal stresses will be induced in the x and y directions. From this brief discussion of stresses due to gravitational loading of anisotropic elastic rock, it can be concluded that inclusion of anisotropy broadens the range of permissible values of gravity-induced horizontal stresses. In fact, as shown in Figure 2, it is thermodynamically admissible for the horizontal stress to exceed the vertical stress for certain ranges of anisotropic rock properties. Also, for vertical anisotropy, equation (14c) implies that horizontal stresses are no longer equal and the gravity induced stress state becomes truly triaxial. 5. GRAVITY STRESSES IN A HORIZONTALLY STRATIFIED ROCK MASS WITH DISCRETE LAYERS The first model is limited to rock masses with uniform and homogeneous anisotropic properties. However, it can be generalized to include the heterogeneous character of a horizontally stratified rock mass. The rock mass consists of several horizontal strata; each one being thick enough to be regarded as homogeneous and transversely isotropic or isotropic and to have its thickness and deformability properties taken into account. Consider the equilibrium of a flat lying horizontal stratified rock mass under gravity alone. The rock mass consists of n horizon. 6. GRAVITY STRESSES IN A HORIZONTALLY STRATIFIED ROCK MASS WITH MANY THIN LAYERS. In the second model, the rock mass consists of several discrete horizontal mechanical units, each one being thick enough to be regarded as homogeneous and transversely isotropic or isotropic and to have its thickness and deformability properties taken into account. In this model, the overall rock mass or several of its units are thinly layered and the thickness and deformability properties of the horizontal layers vary appreciably with depth.

Proceedings Papers

Paper presented at the ISRM International Symposium, May 26–28, 1982

Paper Number: ISRM-IS-1982-071

...-situ deformation tests have shown that the rock masses yield the law of anisotropic elasto-plastic media. In some cases, the anisotropic behaviour does not obviously

**express**and the rock masses can be approximately treated as the isotropic elasto-plastic media. This paper presents a method dealing with...
Abstract

SUMMARY: In calculating the stresses in the lining of a pressure tunnel with circular cross-section, it is generally assumed that the deformability of rock masses follows the theory of elasticity. However, this assumption does not often consist with the real characteristics of rock masses. In-situ deformation tests have shown that the rock masses yield the law of anisotropic elasto-plastic media. In some cases, the anisotropic behaviour does not obviously express and the rock masses can be approximately treated as the isotropic elasto-plastic media. This paper presents a method dealing with the calculation of the lining stresses considering the elasto-plastic stress-strain relationship based on some in-situ test results. The rock masses are treated as the linear strain hardening media. The critical interior water pressure for creating the plastic deformation of rock masses is given. It is also discussed how to determine the mechanical parameters of rock masses. ZUSAMMENFASSUNG: Bei der Berechnung der Spannungen fuer die Auskleidung eines Druckstollens mit kreisförmigem Querschnitt wird allgemein angenommen, dass die Verformungen des Gebirges der Elastizitatstheorie folgen. Diese Annahme stimmt jedoch oft nicht mit den wirklichen Verhaltnissen im Gebirge ueberein. In-situ Verformungsmessungen haben gezeigt, dass das Gebirge dem Stoffgesetz des anisotropen, elasto-plastischen Mediums folgt. In einigen Fallen zeigt sich kein offensichtlich anisotropes Verhalten und das Gebirge kann annaherungsweise wie ein isotropes elasto-plastisches Medium behandelt werden. Diese Arbeit stellt eine Methode vor, die sich mit der Ermittlung der Spannungen in der Auskleidung aus elasto-plastischen Spannungs-Dehnungs-Beziehungen beschaftigt, die auf Ergebnissen von in-situ Tests basieren. Das Gebirge wird wie ein sich linear verfestigendes Medium behandelt. Der fuer die Entstehung der plastischen Verformungen verantwortliche kritische wasserinnendruck wird angegeben. Weiterhin wird das Problem der Ermittlung der mechanischen Gebirgskennwerte diskutiert. RESUME: Dans le calcul des contraintes dans le revetement d''une galerie sous-pression, on suppose que la deformation des massifs rocheux suit la theorie d''elasticite. Cependant, cette hypothese ne s''applique pas toujours aux caracteristiques reelles des massifs rocheux. Des essais de deformation in-situ ont montre que les massifs rocheux repondent a la loi des substances elasto-plastiques anisotropes. Dans quelques cas, le comportement anisotrope ne s''exprime pas d''une facon evidente et les massifs rocheux peuvent etre traites approximativement comme les milieux elasto-plastiques isotropes. Cette etude presente une methode qui traite du calcul des contraintes dans le revetement en considerant la relation contrainte- deformation elasto-plastique basee sur quelaues resultats d''essais in-situ. Les massifs rocheux sont traites comme les substances durcies a deformation lineaire. La pression d''eau interne critique pour produire la deformation plastique des massifs rocheux est donnee. Aussi s''agit-il d''une discussion sur la facon de determiner les parametres mecaniques des massifs rocheux. Introduction Concerning with the theory applied to the calculation of the stresses in pressure tunnel lining with circular cross section, it is generally assumed that the rock masses are elastic media. The contact force between the rock masses and lining follows Winkler''s law. But a lot of in-situ rock mechanics tests show that the rock masses are not pure elastic media and the isotropic linear elastic theory can only be applied in a few cases. The mechanical behaviors of rock masses are very complicated. It is not only affected by the micro-structure and mineral crystals, but also by the macro-structural planes, such as faults, joints and beddings. In hydraulic engineering, the later is more important than the former and strongly affects the deformation and strength characteristics of rock masses. It is the reason, that both the in-situ elastic modulus and yeilding stresses are lower than that obtained from the laboratory tests using rock samples. The deformation of a discontinuity under normal stresses should approach a certain limit. The discontinuity should be compacted under compression until it no longer affects the total deformation of the rock masses, while it should get apart as the tension stress exceeds its tensile strength. Its shearing deformation is a function of both shearing and normal stresses.

Proceedings Papers

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

Paper Number: ISRM-IS-1981-103

..., possessing viscous-elastic properties, the relationship between stress tensor and deformations can be

**expressed**in the following integral form [3], (4]: (Equation in full paper) For a function, describing creeping of the rocks under consideration a modified**expression**for the Abel's nucleous in the case of...
Abstract

Deformations, arising in weak rocks subjected to the action of external forces, are functions of the time too. The theory of Voltera-Rabotnov [1], [2] will be used for determination of these rheological deformations. For the case of nonhomogeneous, multicomponent and anisotropic rocks, possessing viscous-elastic properties, the relationship between stress tensor and deformations can be expressed in the following integral form [3], (4]: (Equation in full paper) For a function, describing creeping of the rocks under consideration a modified expression for the Abel's nucleous in the case of multicomponent and anisotropic media has been accepted in the following form: The integration constants c 1 are determined by respective boundary conditions. For the case under consideration, the boundary conditions are: It will be noticed that expressions for rheological displacements, when the rocks possess orthogonal anisotropy, transversal isotropy and complete isotropy are obtained as particular cases. For orthogonal-anisotropic rocks, in the expressions for rheological displacements (12) it should be put: For transversal-isotropic rocks, except for conditions (15) and (14), the following equations are valid too: Thus obtained expressions for rheological deformations (12) makes Possible experimental determination of the rheological parameters δ ij and α ij for various cases of rheological anisotropy at rock creeping. For this purpose, experimental mea- surements of longitudinal deformations U j of a rock sample of parallelipiped Shape, with given lengths and subjected to pure compression along coordinate axes Xi should be carried out. These measurements should be taken for two various moments of time t 1 and t 2 . Thus, for determination of the rheological parameters α ij and δ ij a definite system of equations is obtained. On the base of the so determined numerical values of the rheological parameters α ij and δ ij , by formulae (12), the rheological displacements at creeping at a given moment of the time and for an arbitrary point of the rock massif can be determined.

Proceedings Papers

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

Paper Number: ISRM-IS-1981-101

... Upstream Oil & Gas Frictional Resistance rock cutting rake angle diagram strength tool edge metal friction cross-section amonton frictional mechanism mechanism Nishimatsu

**expression**obliquity friction resistance initiation asperity macroscopic failure crack...
Abstract

INTRODUCTION In studies that been carried out at LNEC On the frictional resistante of particles of granular materials [1] analyses were made of the main mechanisms referred to by several authors to explain the classic Amon- tons' s friction laws, and recentlythe stick-slip of geologic materials, such as the interlocking mechanism attributed to Coulomb [2], the adhesion mechanism proposed by Terzaghi [3] and the brittle failure mechanism presented by Byerlee [4]. Nevertheless it seems that some phenomena of failure and wearing observed in the contact and sliding of geologic materials, such as the Ploughing of contact surfaces, cannot be explained only on basis of those mechanisms. Jaeger [5] suggests that in addition to the mechanisms of failure of saliences pro- Posed by Byerlee there should occur a further mechanism of failure on rather flat surfaces parallel to the direction of sliding. In fact this becomes clear enough when sliding occurs with materials of different hardness, and the harder one scratches or ploughes out the softer material [5, p, 117]. Bearing i n mind what happens with metals of different hardness, in which the mechanism by which the harder metal Ploughes out the softer one is perfectly identified [2], this suggestion seems reasonable and worth to be analysed. On the other hand the recent development of studies on rack cutting, mainly related to tunnel-boring machines [6], has shown-same analogy between rock cutting by means of tracks opened by the tools of the boring machine and the ploughing mechanism used in the theorization of metallic friction. This-analogy provides a new outlook regarding the problem of the friction of geological materials, which may be of interest. These are thus the guidelines for and the motivation behind the present work. PLOUGHING MECHANISM IN METALLIC FRICTION It is a well-established concept that the frictional resistance of metal surfaces can be considered as the sum of two terms. One represents adhesion, that is, the shearing of the metallic junctions established at the true points of contact between the surfaces, the area of these contacts being small as compared to the apparent area of the surfaces, or large as compared to the mollecular dimensions. The other term expresses the ploughing process. The mechanism by which these two terms participate in the process of metal friction is briefly as follows [2, p.90]. Let us consider sliding between surfaces of two metals of different hardness. A given asperity of the harder metal sinks into the surface of the softer one until the contact area is sufficient to withstand load N applied to the asperity. If A is the projection of the area of contact thus generated and q is the yield stress of the sfter metal, we shall obtain. The force T required to make the asperity slide in a direction parallel to the surface will be the sum of two terms as already said: one, T s , is the force required to over-some the shearing strength s resulting from the metallic junctions

Proceedings Papers

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

Paper Number: ISRM-IS-1981-112

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**expression**for the settlement of foun4ation due to closure of discontinui- ties, Sd' can be written as n S =E 4z d 1=1 JT(2 + ~i (6 ) R X zi ) (1 + 9 I'F FR 1 2 (1 + OvKi~ Ki) where n - the IlIDber of dipcontinuities present in an effeotive depth equal to twioe the d1smeter of the foundation, R = i/rF f...
Abstract

INTRODUCTION Major civil engineering structures such as dams, bridges, tall buildings, towers, etc. are generally founded on a rock mass if intact or competent rook is located at a reasonable depth below the ground level. However, the ooncept of founding a structure on rock whenever the soil above the rook has inadequate engineering characteristics, end without regard for the nature, type end behaviour of rock, has become quite outdated (Kulhawy, 1980 and Goodman, 1980). This is because any rock mass generally contains discontinuities whose deformation behaviour under load is quite different from that of intact rock. For important structures such as mentioned above, the settlement of foundations becomes a governing factor in design since excessive total and differential settlements endanger the safety or utility of the structure. Thus the ultimate bearing capacity at which the foundation rook will fail has less engineering significance (Farmer, 1978; Chappe11 end Maurice, 1980). The settlement comprises mainly of two parts. The first part is due to the deformability of intact rook material while the second part is due to the compressibility of discontinuities'. A major contribution to the settlement canes from the closure of discontinuities since discontinuities are usually more oompressib1e than intact rook. It i8 not on4r the presence of discontinuities that makes the prediction of foundation behaviour more difficult but also the random nature of their location, strength and deformation properties. The random variability of the deformation properties of intact rock is also important. If a design does not incorporate this complexity and variability it may prove either unsafe orover-conservative. In this context it is appropriate to quote Fairhurst (1976):"..rock does have characteristics of variability end, to a degree, unpredictability of variation, that we neglect at our peril". Present work is concerned with incorporating the random variability in the aforesaid parameters to improve the predietion of settlement and Monte Carlo simulation method is adopted. LITERAT URE REVIEW Several methods have been in use for the estimation of settlement of foundation on rook, a majority of which use the principles of elastioity either directly or indirectly (Timoshenko and Goodier, 1951; Hobbs, 1975; Chappell and Maurice, 1975; Farmer,1978; Hungr and Coates, 1978; etc.). Some methods estimate the foundation settlement by direct extrapolation from field load tests (Waldorf et.a1., 1963; Hobbs, 1975) or by empirical correlations between the modulus reduction factor and RQD(Peck et a1., 1974, Kulhawy 1978,etc.). However it is noticed that the current methods for the estimation of settlement do not incorporate the random variability in the geometrical and deformation properties of discontinuities and that in the deformation properties of intact rock. Adopting second moment probability methods the authors in their earlier work (1980) have proposed two models to study the influence of random variability: in each parameter. In the first model the discontinuous rock mass is idealized as a system with equivalent continuum properties (Kulhawy,1978). The inherent random variability in the spac1rJgand the stiffness of horizontal discontinuities and that in the Young's modulus of rock material are considered.

Proceedings Papers

Paper presented at the ISRM International Symposium, September 27–29, 1978

Paper Number: ISRM-IS-1978-024

... Upstream Oil & Gas dynamic stress detonation

**expression**Reservoir Characterization criterion characteristic impedance damage criterion tensile strength dynamic tensile strength particle velocity criteria charge weight rock mass ground vibration strength Rock mechanics...
Abstract

Summary After reviewing the classic criteria of structural damage due to ground vibrations caused. by rock, blasting, their assumptions, and limitations are pointed out, particularity when dynamic stability analysis, are to be performed. A new criteria, based on the balance between the magnitude of the dynamic stresses carried by the vibrating wave and the dynamic strength of the medium is proposed. Due to its simplicity and direct application to field conditions of rock blasting, the method seems appropriate, to predict failure in any type of structure, provided their dynamic properties are known. Confirmation of the allowable limits of vibration proposed by the empirical, criteria is accomplished and examples of application of the new criterion to, dam structures and rock volumes situated in the proximity of blasting works are presented.