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Proceedings Papers

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

Paper Number: ISRM-IS-2000-429

... computed. The STEPSIM4 process is repeated for a large number (usually 2000 to 5000) of failure paths and the ensuing statistical distribution of shear strengths is computed (i.e. a mean and

**standard****deviation**with respect to effective friction angle and cohesion). It complements existing geotechnical...
Abstract

ABSTRACT: A "step-path" method for determining the statistical shear strength along critical failure paths through jointed rock slopes is reviewed. The computed shear strength is a function of both sliding and "stepping-up" along sets of suitably orientated geological discontinuities within slopes and of shearing through either the intact rock or rock mass substance where such critically orientated discontinuities are absent. Details of STEPSIM4 (Monte-Carlo based software developed for this analysis), input rock mechanics parameters, ensuing strength outputs and several illustrative examples are presented. STEPSIM4 facilitates a more realistic assessment of slope stability risks. It is a software tool that provides an avenue for combining hard factual data with data that may be only approximate or judgmental. Some inputs may be the user''s best estimates, provided that the outputs are then viewed accordingly. STEPSIM4 complements the existing geotechnical approaches. It does not replace commonsense, site-specific experience and good engineering judgment. INTRODUCTION Background Rock masses are systems comprising intact rock and geological discontinuities. As conceptually shown in Figure 1, high rock slope failures may involve several mechanisms. Many landslides exhibit composite failure modes. Sliding may occur along large numbers of "relatively" short, adversely dipping, geological discontinuities within the rock mass. This process is often accompanied by dilation of the mass as the failure path "steps up" on other subvertical discontinuity sets within the mass and by shearing through and/or tensile failure of the intact rock and/or rock mass "bridges" between the discontinuities. Geotechnical assessment of the mean and the likely statistical variability in the shear strength parameters for composite failure paths such as the conceptual one shown in Figure 1 is not always a straightforward task. The STEPSIM4 "step-path" method provides an avenue for assessing the statistical shear strength along potential two-dimensional failure paths through rock masses.

Proceedings Papers

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

Paper Number: ISRM-IS-2000-014

... attenuation relation return period Magnitude rupture seismic hazard analysis probabilistic approach Artificial Intelligence variability evaluation recurrence interval

**Standard****Deviation**STATE OF THE PRACTICE OF SEISMIC HAZARD EVALUATION Norman A. Abrahamson l INTRODUCTION The main use of seismic...
Abstract

INTRODUCTION: The main use of seismic hazard analyses is to develop rock outcrop or stiff soil ground motions for use in design. The quantitative descriptions of the ground motions can be in terms of simple scalar values (e.g. peak acceleration, peak velocity, peak displacement, response spectral values, or Arias intensity) or it can be in terms of time histories of acceleration, velocity, and displacement. Typically, the design ground motions are then used in geotechnical and/or structural engineering analyses. This paper does not address site-specific site response analyses. Site response is addressed in the accompanying theme lecture paper by Dobry. The topic of this paper is the state-of-the-practice of seismic hazard analysis. The actual practice of seismic hazard analysis varies tremendously from poor to very good. The large variability in practice is not simply a reflection of project budgets; a large variation in practice exists for similar projects. Although the basic methodologies used in seismic hazard analysis are well established, as represented by short courses and seminars on seismic hazard analysis as well as numerous seismic hazard reports, these basic methodologies are generally not well understood. Usually, the state-of-the-practice is defined as what the "average" practitioner would do. This applies to both those conducting the seismic hazard evaluation and those applying the results in an engineering analysis. In general, the high end of the practice is very good, but the results are often not well understood by the engineers who need to apply them. To address with this situation, we first discuss the some of the shortcomings of the current practice, and then discuss the state-of-the-practice at the high end. As a start, we describe many common misunderstandings regarding the development and interpretation of design ground motions that contribute to poor practice.

Proceedings Papers

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

Paper Number: ISRM-IS-2000-184

... variability is modeled as a random field, which can be described concisely by the coefficient of variation (COV) and the scale of fluctuation. The COV of inherent variability for various test measurements is given in histograms to illustrate its population distribution. The means and

**standard****deviations**of...
Abstract

ABSTRACT: This paper focuses on the typical inherent variabilities for the basic properties of natural geomaterials. The issue of measurement error, which is closely related, is noted when necessary. The results of an extensive literature review on inherent variability are presented. This variability is modeled as a random field, which can be described concisely by the coefficient of variation (COV) and the scale of fluctuation. The COV of inherent variability for various test measurements is given in histograms to illustrate its population distribution. The means and standard deviations of the COV are shown with the total number of data groups, and the shapes of the histograms are discussed. The scale of fluctuation is discussed elsewhere. INTRODUCTION The presence of uncertainties and their significance in natural geomaterials (soils and rocks) has long been appreciated, at least in a qualitative manner. However, in the overwhelming majority of geotechnical texts and courses, after making the observation that uncertainty is an important factor, it is then relegated to a minor position, and the remainder of the text/course is evaluated in a traditional deterministic fashion. The reasons for this unfortunate state of affairs range from the point that it is "easier" to do deterministic evaluations to the fact that it is somewhat difficult to embrace uncertainty easily and directly because it is complex in geotechnical problems. After all, uncertainties arise in the loads, geologic site interpretations, geotechnical properties, computation models, etc. Quantifying all of these components is a monumental task. To help mitigate this problem, this paper focuses on the typical inherent variability in some test measurements of natural geomaterials. This variability commonly is modeled as a random field, which can be described concisely by the COV (= standard deviation / mean) and the scale of fluctuation (Vanmarcke, 1977).

Proceedings Papers

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

Paper Number: ISRM-IS-1988-005

... chosen segment and the normals to the mean attitude of thE joint set. The Poisson distribution with the par- ameter (I I cost) has the mean"fJ', given by W'=llcos£ (19) and the

**standard****deviation**aN' given by aN = VI I cos £ (20) For small values of the parameter (I I cos the Poisson distribution is...
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, September 12–16, 1988

Paper Number: ISRM-IS-1988-072

... bolt rock bolt waste repository repository fracture rock burst Reservoir Characterization distribution curve

**Standard****Deviation**variation mathematical model support system underground support Rock Mechanics and Power Plants. Romana fed) e 1988Balkema. Rotterdam. ISBN 90 6191 8278 Design...
Abstract

ABSTRACT: Variations in actual rock mass properties and inaccuracies in measuring these properties require that the design of underground supports for a nuclear waste repository be based upon statistical "probability of failure" calculations. A review of the material properties of the basalt at the Hanford, WA, site illustrates these variations. A statistical approach to a design based upon a normal distribution curve is discussed and a hypothetical calculation presented. The effects of high temperatures on the long-term structural behavior of rock and rock support systems are critical because high-level nuclear waste repositories in the United States must withstand temperatures up to 2000 C (3920 F). A second critical factor is that it must be possible to retrieve waste materials for up to so years after the last waste is emplaced. The applicability of using conventional rock supports in waste repositories is discussed and some designs are suggested. INTRODUCTION The safe burial of high-level nuclear wastes is the subject of numerous studies. Most are inconclusive because existing geotechnical methods cannot accurately measure or predict water flow, in situ rock stresses, rock mass properties of a given host rock, or ground movements that would take place over an extended time. Current philosophy in the United States is that failures are unacceptable because a failure could damage canisters and release radioactivity. The design of supports for nuclear waste repositories in the United States is further complicated by the waste having to be retrievable for so years after the last emplacement. Generally, engineers have little experience with the high temperatures expected in underground repositories over a long time; temperatures could increase enough to jeopardize the integrity of the canisters. Because the repository must be Ventilated, the repository must be free from blockages. Rock supports should minimize rock movement beyond the yield point to minimize fracturing, which increases rock permeability and could lead to water transport of radionuclides from failed canisters. These shortcomings, along with the limitations of mathematical models, reduce the reliability of design studies because good results depend upon accurate physical data. The results of an investigation of the proposed high-level waste repository site at Hanford, WA, provides an example of the problems involved and underlines the design difficulties. In spite of these difficulties, however, repositories must still be designed, and the shortcomings in engineering and geological design data must be overcome. DESIGN CONSIDERATIONS 2.1 Rock Mass Properties Studies of waste repository sites show that rock mass properties can vary widely. These variations can be represented by a distribution curve. Rock mass properties as typically used in design studies are: the intact compressive strength of the rock, the allowable stress in emplacement rooms and boreholes, the maximum in situ stress and its direction, and bulk density. Poor measurements of these properties result partly from natural fractures, physical and chemical heterogeneities, limitations of testing procedures, and difficulty in obtaining an adequate number of representative samples. Because the host rock is influenced by its surroundings, the rock properties must be measured in situ rather than in a laboratory, and this requires specialized equipment.

Proceedings Papers

Paper presented at the ISRM International Symposium, August 31–September 3, 1986

Paper Number: ISRM-IS-1986-031

... hydraulic fracturing normal stress hydraulic test determination mayet Upstream Oil & Gas montagne focal mechanism fracture plane plane Cornet

**Standard****Deviation**stress field equation Proceedings of the International Symposium on Rock Stress and Rock Stress Measurements/Stockholm/I-3...
Abstract

Abstract.: A method for determining the complete regional stress field is presented. It is based on measurements of the normal stress supported by preexisting fracture planes (with various dip and strike) by means of hydraulic tests. The solution does not involve the stress field in the immediate vicinity of the well. Two examples concerning granitic rocks are presented. The first one involves fourteen tests between 100m and 973m, the second one sixteen tests between 50m and 620m. For the second case, a stress discontinuity is observed around 300m Deep results are coherent with focal mechanisms of microseismic events. Résumé: Une méthode de me sure de contrainte, basée sur la détermination de la contrainte normale supportée par des fractures naturelles (de pendages et azimuts variés) est présentée. La solution ne fait pas intervenir le champ de contrainte au voisinage des forages utilisés. Cette méthode est illustrée par les résultats de deux campagnes d''essai en massif granitique. La première concerne quatorze mesures entre 100m et 973m, la seconde seize essais entre 50m et 620m. Dans le deuxième cas, une discontinuité du champ de contrainte est mise en évidence autour de 300 m. Les résultats des essais profonds sont cohérents avec les mécanismes au foyer d''évènements microsismiques. 1. Introduction The hydraulic fracturing stress determination technique is now well established (see e.g. Hubbert and Willis.1957.: Scheidegger, 1962, Fairhust, 1964· Haimson and Fairhurst, 1969 / Haimson 1978; Haimson, 1983, Hickman and Zoback 1983). This method is based on analysis of pressure time records obtained in packed off zones of boreholes where the rock is homogeneous, linearly elastic and isotropic with respect to both its elastic characteristics and its "strength". When the borehole axis is parallel to one of the principal stress directions it provides ways to evaluate the magnitude and the direction of the two principal stresses which are perpendicular to the borehole axis. In order to alleviate the constraining assumptions underlying the classical theory of hydraulic fracturing, Cornet (1980, 1982) and Cornet and Va1ette (1984) have proposed conducting hydraulic tests on preexisting fractures with various dip and strike for determining the complete regional stress tensor (H.T.P.F stress determination method). Bertrand et al, (1983) and Rummel and Baumgartner (1984) have reported successful stress measurements obtained with the H.T P.F. method. Their computational procedures are somewhat different from that proposed by Cornet and Valette (1984), but they also rest on the same hypothesis that the regional stress field is continuous and is a linear function of depth. In the present paper the H.T.P.F. method described by Cornet and Valette is illustrated by field results obtained in two granite area of central France, namely Auriat and Le Mayet de Montagne. In the first case a solution is presented for the stress field, which fits measurements taken between 150m and 980m. In the second (Le Mayet de Montagne), it is found that the stress field is not continuous in the depth range where measurements were conducted (50m, 620m).

Proceedings Papers

Paper presented at the ISRM International Symposium, August 31–September 3, 1986

Paper Number: ISRM-IS-1986-036

... Characterization geothermal reservoir crystalline rock rock mass Differential Strain Curve analysis situ stress stress measurement compression

**Standard****Deviation**dry rock site core sample Magnitude Proceedings of the International Symposium on Rock Stress and Rock Stress Messuremeots/Stocknotm/t-a...
Abstract

ABSTRACT: We measured in situ stresses in a Hot Dry Rock geothermal reservoir using hydraulic fracturing of the rock mass as well as the novel technique of differential strain curve analysis (DSCA). We found that the DSCA method gave reliable stress estimates for deep rock masses, as well as provided complete stress tensor information from single core samples. Our results also showed the existence of unexpected and substantial changes of stress state: the stress state rotates from a normal faulting to a strike-slip faulting system within 1 km depth change. Nous avons mésuré des contraintes in situ dans un réservoir souterrain de roche chaude et sèche en employant Le procédé par fracturation hydraulique du massif rocheux ainsi que la nouvelle méthode d ''analyse differentielle de la courbe de déformation. Nous trouvons que cette méthode donne des évaluations fiables pour les matériaux rocheux prof''onda et qu''elle fournit les informations entières du tenseur contrainte d''un échantillon unique de carotte. Nos résultats montrent aussi l''existence de changement imprévus et importants de l''état de contraintes: I''etát de contraintes se tourne de la formation normale de failles à un systeme de faille à rejet horizontal dans le changement de profondeur dans les limits de 1 km. Wir haben in-situ Spannungen in einem Erdreservoir von heissem trockenem Tiefengestein gemessen und wir haben die neue Methode der Differentialanalyse von Dehnungskurven benutzt. Wir finden, dass diese Methode zuverlässige Spannungsabschätzungen für Tieigebirgsmassen gibt und vollstandige Angaben über den Spannungstensor von einer einzigen Kernprobe liefert. Unsere Ergebnisse zeigen auch die Existenz von unvorhergesehenen und beträchtlichen Veränderungen des Spannungszustandes: Der Spannungszustand dreht sich von einer normalen Sprungbildung bis zu einem Seitenverschiebeungssystem in einer Tiefenveränderung innerhalb 1 km. 1. INTRODUCTION As part of the development of a Hot Dry. Rock geothermal reservoir, we estimated in situ stresses using hydraulic fracturing methods and the novel technique of differential strain curve analysis (DSCA). This geothermal project is being conducted by Los Alamos National Laboratory with funding from the United States Department of Energy, Japan''s New Energy Development Organization and West Germany''s Ministry for Science and Technology. The experimental site is located on the western flank of the Valles Caldera at Fenton Hill, New Mexico, USA. The age of caldera formation is about 1.1 m.y. with volcanism occurring between about 10 m.y. and 0.1 m.y. ago. Two wells, one of which is sidetracked and redrilled into a different geometry, penetrate the geothermal reservoir region which extends from about 3 km depth to about 4.5 km depth. The geology (Laughlin et al. 1983) consists of Precambrian metamorphic and igneous intrusive rocks with temperatures ranging from 200–320°C. The great depth of the reservoir, coupled with the presence of numerous pre-existing fractures, makes conventional hydraulic fracturing stress measurement difficult to carry out. The depth, coupled with the high temperatures, produces conditions too severe to use the borehole tools necessary for finding and isolating unfractured intervals as is conventionally done (e.g. Bredehoeft et aI, 1976). Consequently, an additional method for estimating stresses at these severe conditions was sought, and the method of differential strain curve analysis (DSCA) of core samples was chosen to provide additional information on the state of stress. Ren and Roegiers (1983) used this technique successfully to estimate the state of stress in deep boreholes drilled for petroleum exploration and production. 2. DIFFERENTIAL STRAIN CURVE ANALYSIS Based on the theoretical work of Walsh (1965), Simmons et al. (1974) developed an experimental method for measuring total microcrack volumes and orientations in rock samples in the laboratory. Samples are prepared with foil strain gages attached in appropriate orientations. After being jacketed, the sample is loaded hydrostatically to a pressure sufficient to close essentially all the crack porosity: 200 MPa or so. Projecting the asymptotic slope of the strain pressure curves back to zero pressure, as Walsh described, gives the contribution of crack closure to the strain recorded by each gage. With a minimum of six appropriately oriented gages, this crack strain contribution can be resolved into a strain tensor with both the three principal crack strains and their directions determined (e. g. Solkolnikoff 1956). Under suitable conditions, this crack strain tensor can be interpreted to give the in situ stress state. A necessary condition is that the great majority of microcracks present in the sample are due to the relief of the in situ stress during and following cutting of the core sample. A further assumption necessary is that microcrack porosity oriented in any given direction is produced in proportion to the magnitude of the effective compressive stress that was relieved in that direction. In other words, if the in situ stresses in the x and y directions are in the ratio of 1: 2, then the crack strains measured in these directions must also be in the ratio of 1:2.

Proceedings Papers

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

Paper Number: ISRM-IS-1982-049

... with assigning the

**standard****deviation**of the different data of the final result to the**standard****deviation**of the initial data. ZUSAMMENFASSUNG: Die Materialkonstanten beteiligen sich nicht mit gleichem Gewicht in der Ausbildung der Spannungs-, Verformungs- und Verschiebungszustande. Der Vortrag...
Abstract

SUMMARY: The material constants do not participate equally in developing the stress-, strain- and displacement stage generated when installing the support in underground openings, and excavations. The paper describes a method taking into calculation also the uncertainty of surrounding rocks with assigning the standard deviation of the different data of the final result to the standard deviation of the initial data. ZUSAMMENFASSUNG: Die Materialkonstanten beteiligen sich nicht mit gleichem Gewicht in der Ausbildung der Spannungs-, Verformungs- und Verschiebungszustande. Der Vortrag gibt eine Methode, die auch die Ungewissheit der Gebirgsumgebung ln Betracht zieht, die Standarddeviation der einzigen Daten des Endergebnisses der Standarddeviation den Ausgangsdaten zuordnend. RESUME: Les constantes du material ne participent pas egalement au developpement de la situation des tensions, deformations et deplacements qui se forment quand Ie soutenement des galeries et des cavites des mines est effectue. L''auteur donne la description d''une methode prenant en calculation aussi l''incertitude du terrain enveloppe, assignant la deviation des differents donnees a la deviation des donnees initiales. When designing the support of underground roadways and openings there occurs generally an oversizing not to be determined that can not be justified by aiming at safety. This results on one hand from the fact that there is an uncertainty in the number of the nature parameters used for design, in the way of mea- suring them and in the reliability of the data obtained. On the other hand the design methods used do not adequately describe the behaviour of support with unduly idealizing the environment and using algorithms excessively simplifying and without Considering exactly all boundary conditions. In order to increase reliability and economic efficiency some processes correct the support parameters based on the high number of measurements and investigations carried out during execution with extrapolating the subsequent construction phases not known primarily. The rock mechanical parameters can be detected by investigation results obtained by means of borings and samplings. These characteristics can show significant dispersion. In developing the arising stress, strain and displacement condition the material properties do not participate equally. We show a method which by taking into calculation also the uncertainty of the surrounding rocks tries to represent the environment in the most adequate way with illustrating the support method enabling the coaction of rock and support. Based on the parameter testing by the finite element method /FEM/ there can be established which data prove to be important from the point of view of the support design. In the practice spatial problems are encountered both in mining and tunelling. The three dimensional testings of a given range requires one order higher computer capacity, calculating time /cpu/ and very sophisticated data preparation also a Hookean elasticity model compared to the plain /two dimensional/ testing. Therefore where it is not absolutely necessary using spatial programs is generlly avoided. For the overwhelming majority of the cases occuring in pactice the plain testings are sufficient. However for special cases, e.g. the immediate surrounding of junctions, longwalls, parts near the face and very frequently changing soil and ground conditions, the three dimensional calculations prove to be indispensable. The real situation can be well approximated by plain strain and therfore this model gives a good solution at an approximate distance of one and half road diameter from the face. In order to investigate into the plain problems arising in our Institute isoparametric elements are used. The corresponding spatial element is the isoparametric hexahedron with 10 junctions applied for our spatial programs. Thus a high calculation accuracy can be reached with a relatively small number of elements andjunctions. For their employing we have well composed and proved programs. The FEM computation is based on continuum mechanical approach and therefore our loadings and boundary conditions have to be fixed in compliance with it.