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Proceedings Papers

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

Paper Number: ISRM-IS-2000-513

... strength parameters (Fig. 1). The non-dimensional parameter b controls the de- gree of curvature of the envelope, while the scale parameter A has the dimensions [ s ](1-b) (Charles & Soares 1984b). Previous stability analyses with nonlinear failure

**criterions**were limited to 2-D slopes (e.g. Charles...
Abstract

ABSTRACT: Effects of nonlinearly of strength envelopes on stability analysis of 2-D and 3-D slopes are investigated. Combining the nonlinear strength law with Janbu's method and a minimization process based on dynamic programming makes it possible to determine the minimum factor of safety and critical slip surface for 2-D slopes. The factor of safety equation of a 3-D simplified Janbu method is derived in terms of the same nonlinear strength envelope. In the 3-D case the search procedure is based on dynamic programming and random number generation. Results of some example problems show that a linear approximation of the nonlinear strength envelope leads, under certain conditions, to a significant overestimation of safety factors for both 2-D and 3-D slopes. INTRODUCTION Limit equilibrium methods have been extensively used to evaluate the stability of slopes in engineering practice. In these methods, the factor of safety is commonly defined as a reduction factor on strength, and this factor is an index measuring the relative stability of different potential slip surfaces in a given slope. It is obvious from this definition that the calculated factor of safety is affected by the way which shear strength of soil is evaluated. It has been shown by numerous experimental studies, however, that strength envelopes of many soils exhibit significant nonlinearity, for example, stiff London clay (Atkinson & Farrar 1985), soft clays (Lefebvre, 1981), compacted rock fill (Charles & Soares 1984a). The nonlinearity of strength envelopes can appear over a wide range of normal stresses but it is manifested particularly at low stress levels. Incorporating the above nonlinear strength law into the well known 2-D Janbu method, and using a minimization technique developed by Baker (1980) makes it possible to find the minimum factor of safety in 2-D problems.

Proceedings Papers

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

Paper Number: ISRM-IS-2000-494

...ASSESSMENT OF NEW ZEALAND GREYWACKE ROCK MASSES WITH THE HOEK-BROWN FAILURE

**CRITERION**Stuart A L Read1, Laurie Richards2 and Nick D Perrin3 ABSTRACT Application of the Hoek-Brown failure**criterion**to New Zealand hard greywacke rocks leads to unrealistically high predictions of rock mass strength...
Abstract

ABSTRACT: Application of the Hoek-Brown failure criterion to New Zealand hard greywacke rocks leads to unrealistically high predictions of rock mass strength for better quality rock masses and lower predictions for poorer quality rock masses. To further investigate linkages between rock masses in the field and failure criterion inputs such as the Geological Strength Index ( GSI ), a descriptive engineering geological classification for unweathered greywacke with five classes has been implemented. The results of laboratory triaxial testing of lower quality (Class IV) rocks with extremely-closely spaced defects (c¢=0 kPa, f¢=48°) and assessment of in situ direct shear tests on better quality (Class II) rocks that give similar strengths show further calibration of strength data against the failure criterion is required. INTRODUCTION These Upper Paleozoic to Mesozoic-age rocks are widely spread throughout New Zealand (Figure 1) and are an important source of roading and concrete aggregate as well as being the basement rocks in many of the country's engineering projects. Greywacke rocks are commonly closely jointed as a result of their complex tectonic and geological history. The Hoek-Brown failure criterion (Hoek & Brown, 1997) is an often used method of assessing the strength of closely jointed rock masses, but experience in New Zealand has shown that predictions from this criterion cannot be confidently applied to greywacke rocks. The requirement for a workable failure criterion has led to this research project into the engineering properties of unweathered greywacke. In the first stage of the project, three dam or quarry study sites (Aviemore, Belmont, Taotaoroa – Figure 1) were engineering-geologically mapped and laboratory testing was carried out to define the Hoek-Brown constants for intact rock (Read et al., 1999). This present paper describes further assessment of the failure criterion based on mapping, sampling and laboratory testing largely from Aviemore.

Proceedings Papers

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

Paper Number: ISRM-IS-2000-474

...A SIMPLE

**CRITERION**FOR CREEP INDUCED FAILURE OF OVER-CONSOLIDATED CLAYS Gavan J. Hunter1, Nasser Khalili2 ABSTRACT A simple**criterion**for creep induced failure is proposed for drained loading of over-consolidated clays. The**criterion**is proposed for the prediction of the long-term shear strength...
Abstract

ABSTRACT: A simple criterion for creep induced failure is proposed for drained loading of over-consolidated clays. The criterion is proposed for the prediction of the long-term shear strength for assessment of stability of slopes and for the estimation of the time to the onset of failure (onset of tertiary creep) based on the accumulated strain. The criterion is based on the results of long-term, drained laboratory creep tests on overconsolidated and structured sensitive, strain weakening clays. A summary of the general characteristics of creep is presented followed by the proposed criterion and the results of published laboratory test data that support the criterion. INTRODUCTION Creep induced instability in clayey slopes often occurs at strengths less than the peak strength, with the time to failure ranging from days to tens of years. Several empirical models have been proposed for the prefailure deformation behaviour in such slopes, including the relationships for creep at decreasing and increasing strain rates with time (e.g. see Singh and Mitchell, 1968, and Saito and Uezawa, 1961). Presented in this paper is a strain criterion for the Òfirst timeÓ failure of slopes in over-consolidated clays due to creep under constant shear stress. The basis for the criterion is the process of the creep induced plastic deformations and strain weakening, leading to failure at stress levels below the peak strength. The main aspect of the criterion is that the level of total strain at which the onset of failure due to creep occurs is equivalent to the shear strain to the peak strength on the stress-strain relationship of the soil determined from conventional drained strength test. Hence, the strain (and time) to the onset of failure can be predicted based on the accumulated shear strain.

Proceedings Papers

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

Paper Number: ISRM-IS-2000-604

... medium, leading to analytical solutions under simplified geometry, and has been applied to analyze the displacement behavior of a reinforced tunnel face under spherical symmetry (Wong et al., 2000). strength mechanism tunnel face macroscopic strength

**criterion**homogeneous material**criterion**...
Abstract

ABSTRACT: In this paper, a theoretical stability analysis of a tunnel face, reinforced by fiber-glass inclusions, is proposed. Previous works have already treated the stability of a unreinforced tunnel face in the case of isotropic and homogeneous medium. Based on yield design theory, these studies lead to lower or upper bound estimates of the safety margin. Within the framework of this efficient stability approach, the present work takes into account the effect of reinforcement at the face by the homogenization method. Both the lower and the upper bound approaches are investigated in the cases of a purely cohesive or a cohesive-frictional soil. Examples of design charts are provided to allow a bracketed estimate of the admissible limit loads, depending on the level of reinforcement at the face. INTRODUCTION The construction of tunnels in soft ground often requires face reinforcement. Due to the high longitudinal strength of the bolts, it also increases the stability; their relative brittleness to shearing ensures easy removal during excavation. Practicability of such method has well been demonstrated in the past (Pelizza and Peila, 1993; Wong et al., 2000). Nevertheless, the overall behavior of the reinforced tunnel face is not well understood, and the optimization of bolt-quantity requires adequate design tools. Concerning the modeling of heterogeneous media at the face, numerical methods have been proposed, modeling each of the linear inclusions individually or using either a hypothetical fictive frontal pressure or an isotropic increase of strength (Peila, 1994; Dias, 1999). Over these numerical approaches, the homogenization method of periodical media (De Buhan and Salençon, 1993) allows to replace the heterogeneous mixture (soil + bolts) by an equivalent homogeneous medium, leading to analytical solutions under simplified geometry, and has been applied to analyze the displacement behavior of a reinforced tunnel face under spherical symmetry (Wong et al., 2000).

Proceedings Papers

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

Paper Number: ISRM-IS-2000-402

... ABSTRACT: Many flood protection dikes were damaged in both eastern and western Hokkaido, Japan during large earthquakes in 1993 and 1994 due to liquefaction in the foundations. A

**criterion**based on crest settlement was developed for prioritizing remediation of the diking system to resist...
Abstract

ABSTRACT: Many flood protection dikes were damaged in both eastern and western Hokkaido, Japan during large earthquakes in 1993 and 1994 due to liquefaction in the foundations. A criterion based on crest settlement was developed for prioritizing remediation of the diking system to resist future earthquakes. The potential crest settlement during earthquakes of M=7.5 to M=8.0 was expressed in terms of geometrical properties of the dike cross-section. The procedure used to estimate the settlements was first used to simulate dike failures in eastern Hokkaido. Then, blind prediction tests were carried out for typical dikes in western Hokkaido. These predictions were then checked against actual field performance. The criterion proved to be very effective in predicting the performance of the damaged dikes. INTRODUCTION Flood protection dikes along the Kushiro and Tokachi rivers suffered considerable damage during the 1993 Kushiro-oki earthquake off eastern Hokkaido, Japan. Damage included longitudinal and transverse cracks, slope failures and cave-ins. The more severely damaged dike sections were 6 m – 8 m high, and were constructed of compacted sand fill resting on a comparatively thick peat layer. Figure 1 illustrates a typical failure mode in at a cross-section of the dike on the left bank of the Kushiro River between stations 9K400 and 9K850. The failure mechanism illustrated in Fig. 1 is adapted from Sasaki et al. (1995). In 1994, a major earthquake occurred off the west coast of Hokkaido, the Nansei-oki earthquake, which caused failures of flood protection dikes along several river basins in western Hokkaido. After these earthquakes, the Hokkaido Development Bureau initiated a program of improving the diking systems. Because of the great length of dikes, they wished to develop a criterion for prioritizing the remediation work. One of the approaches they adopted was to use potential crest settlements as a criterion.

Proceedings Papers

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

Paper Number: ISRM-IS-2000-034

... ABSTRACT: This paper is in two parts. The first part presents an overview of the strength of intact rock. A short commentary on various methods of fitting failure criteria to experimental data follows, it is demonstrated that the method of fitting the

**criterion**to the test data has a major...
Abstract

ABSTRACT: This paper is in two parts. The first part presents an overview of the strength of intact rock. A short commentary on various methods of fitting failure criteria to experimental data follows, it is demonstrated that the method of fitting the criterion to the test data has a major effect on the estimates obtained of the material properties. The results of a recent analysis of a large data base of test results is then presented. This demonstrates that there are inadequacies in the Hoek-Brown empirical failure criterion as currently proposed for intact rock and, by inference, as extended to rock mass strength. The parameters mi and s c are not material properties if the exponent is fixed at 0.5. Published values of mi can be misleading as mi does not appear to be related to rock type. The Hoek-Brown criterion can be generalised by allowing the exponent to vary. This change results in a better model of the experimental data. Analysis of individual data sets indicates that the exponent, a, is a function of mi which is, in turn, closely related to the ratio of s c /s t . A regression analyis of the entire data base provides a model to allow the triaxial strength of an intact rock to be estimated from reliable measurement of its uniaxial tensile and compressive strengths. The method proposed is the most accurate of those methods that do not require triaxial testing and is adequate for preliminary analysis. Analysis is presented that shows applying the Hoek-Brown criterion to most rocks results in systematic errors. Simple relationships for triaxial strength that are adequate for slope design are presented. The second part of this paper presents a discussion of the application of the Hoek-Brown criterion to estimating the shear strength of rock masses for slopes.

Proceedings Papers

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

Paper Number: ISRM-IS-2000-035

... between these blocks. This method was modified over the years in order to meet the needs of users who applied it to problems that were not considered when the original

**criterion**was developed (Hoek 1983, Hoek and Brown 1988). The application of the method to poor quality rock masses required further...
Abstract

ABSTRACT: This paper presents a review of the estimation of rock mass strength properties through the use of GSI. The GSI classification system greatly respects the geological constraints that occur in nature and are reflected in the geological information. A discussion is given regarding the ranges of the Geological Strength Index for typical rock masses with specific emphasis to heterogeneous rock masses. INTRODUCTION Reliable estimates of the strength and deformation characteristics of rock masses are required for almost any form of analysis used for the design of surface excavations. Hoek and Brown (1980a, 1980b) proposed a method for obtaining estimates of the strength of jointed rock masses, based upon an assessment of the interlocking of rock blocks and the condition of the surfaces between these blocks. This method was modified over the years in order to meet the needs of users who applied it to problems that were not considered when the original criterion was developed (Hoek 1983, Hoek and Brown 1988). The application of the method to poor quality rock masses required further changes (Hoek, Wood and Shah, 1992) and, eventually, the development of a new classification called the Geological Strength Index (Hoek 1994, Hoek, Kaiser and Bawden 1995, Hoek and Brown 1997, Hoek, Marinos and Benissi, 1998), extended recently for heterogeneous rock masses (Marinos and Hoek, 2000). A review of the development of the criterion and the equations proposed at various stages in this development is given in Hoek and Brown (1997). ESTIMATE OF ROCK MASS PROPERTIES The basic input consists of estimates or measurements of the uniaxial compressive strength (—ci) and a material constant (mi) that is related to the frictional properties of the rock. Note that both tables are updated from earlier versions (Marinos and Hoek, 2000).

Proceedings Papers

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

Paper Number: ISRM-IS-2000-045

...

**criterion**used. An example is given to illustrate the capability of the proposed numerical procedure. INTRODUCTION In their natural state most soils are somewhat anisotropic. Due to the mode of deposition and subsequent loading of soil masses, measurements have shown that the particles tend to adopt a...
Abstract

ABSTRACT: This paper describes a new technique for computing lower bound limit loads in anisotropic media under conditions of plane strain. Although limit analysis has been applied extensively to homogenous and isotropic soils, as well as soils with a variation of cohesion with direction, it is well recognised that natural soil deposits also exhibit a variation of friction angle with direction. A finite element formulation or the lower round theorem is presented which allows for the variation of soil strength with direction. In order to achieve this, the conventional Mohr-Coulomb yield criterion used. An example is given to illustrate the capability of the proposed numerical procedure. INTRODUCTION In their natural state most soils are somewhat anisotropic. Due to the mode of deposition and subsequent loading of soil masses, measurements have shown that the particles tend to adopt a preferred orientation. It is this preferred particle orientation which results in a variation of soil properties as the angle of the major principal stresses varies during shear deformation. While the measurement of this inherent anisotropy is difficult, its effects have been shown via laboratory tests on samples cut at different angles. While existing data would seem to suggest that the variation of cohesion (undrained shear strength) with orientation due to soil anisotropy is more significant than the effects of friction angle, the effect of friction angle variation should not be ignored. Arthur and Menzies (1972) and Arthur and Phillips (1975) measured inherent anisotropy in prepared sand samples using a consolidated-drained shear test. They noted that a slightly higher friction angle (typically ill the order of 2–3 degrees) occurs when the direction of the major principle stress coincides with the direction of sand deposition as compared to when the major principal stress is perpendicular to the direction of deposition.

Proceedings Papers

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

Paper Number: ISRM-IS-2000-633

... ABSTRACT: This paper discusses the application of the Convergence-Confinement method of tunnel design to rock masses that are assumed to obey the Hoek-Brown failure

**criterion**. The basis of the Convergence-Confinement method and the interpretation of the three basic components of the method...
Abstract

ABSTRACT: This paper discusses the application of the Convergence-Confinement method of tunnel design to rock masses that are assumed to obey the Hoek-Brown failure criterion. The basis of the Convergence-Confinement method and the interpretation of the three basic components of the method _the Longitudinal Deformation Profile (LDP), the Ground Reaction Curve (GRC) and the Support Characteristic Curve (SCC)_ are presented. A closed form solution for the construction of the GRC considering a general form of the Hoek-Brown failure criterion for rock is presented. An example illustrating the application of the solution to the construction of the GRC using the closed-form solution is discussed and results compared with those from the classical Hoek-Brown criterion as implemented in the finite difference code FLAC 3D . INTRODUCTION Estimation of the support required to stabilize excavations in rock is subject to considerable uncertainty. Although general geological information supplemented by limited borehole cores is usually available in advance of excavation, the ground exposed at the face can differ considerably from that anticipated, especially with respect to deformability and strength. These conditions dictate that the excavation support system be one that can accommodate variations in ground conditions while acting to stabilize the excavation. Given these constraints and uncertainties, it is valuable to have a general, albeit simplified, appreciation of the nature of the interplay between the (variable) rock mass and the installed support, and the effect of variation in assumed rock properties on the support loads. The Convergence-Confinement method is such a tool; it allows a quick estimation to be made of the loads transmitted to the support behind the face of a tunnel. By using the method, the engineer can get a ‘practical feel’ for the response to be expected for different support systems under variable rock conditions.

Proceedings Papers

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

Paper Number: ISRM-IS-2000-612

.... reservoir geomechanics acoustic emission technique delay time core specimen Reservoir Characterization

**criterion**stress determination MPa loading relation variation soft sedimentary rock drift wall Upstream Oil & Gas calculation specimen Kaiser effect determination situ stress stress...
Abstract

ABSTRACT: In this paper we evaluate the possibility of the acoustic emission (AE) technique to measure in situ vertical stresses around an excavated drift using the Kaiser effect, which is characterized by an increase in AE when escalating stress exceeds the previous maximum stress. Rock cores were obtained from horizontal boreholes drilled into the wall of a drift excavated in soft sedimentary rock. This allowed the vertical stress variation with distance from the drift wall to be determined up to a depth of 5 m. The vertical stresses determined using rock cores varied with distance and reached a maximum of 4 – 5 MPa at a distance of 2 – 3 m from the drift, when the highest concentration of stress was expected. The vertical stress variation was consistent with calculations by the three dimensional FEM program, ANSYS. Furthermore, the stress measured by the over coring method just about agreed with the stress determined by the AE and DRA methods. The AE and DRA methods described in this paper should be applicable to in situ stress measurement with reasonable accuracy even in soft sedimentary rock. A delay time of up to 101 days did not affect the determination of in situ stress in soft sedimentary rock. INTRODUCTION The reliable evaluation of in situ stress is important in the analysis and design of underground excavations, particularly for evaluating the stability of underground structures to prevent failure or collapse of underground openings. Although a number of techniques have been proposed and developed to determine in situ stress, the task is not easy and all methods suffer from deficiencies and limitations. The main deficiencies of established techniques, such as the over coring and hydraulic fracturing methods, is that they are usually expensive and time consuming.

Proceedings Papers

Paper presented at the ISRM International Symposium, September 10–12, 1990

Paper Number: ISRM-IS-1990-012

... excavation tunnel deformation

**criterion**variation lining carnallite tachyhydrite Static and Dynamic Considerations in Rock Engineering, Brummer (ed.) © 1990 Balkema, Rotterdam. ISBN 90 6191 1532 Micro-Computer modelling and practical design/monitoring of large underground excavations C.Douat...
Abstract

ABSTRACT: An approach to the study of four practical problems of rock engineering using a micro-computer program is presented. The intent is to illustrate how a computer model, in these cases involving simple elastic behavior of the rock medium, sufficed to provide useful practical insight for the design. More sophisticated elastic/inelastic analysis, although available in the computer program, was felt to be not warranted in these cases, due principally to the absence of data on the mechanical properties of the rock mass. Specifics of the calculations and computations are minimized in this paper, but are explained in detail in several of the listed references. INTRODUCTION The development of powerful, relatively inexpensive, micro-computers and computer programs able to model rock engineering problems has given engineers a potentially very valuable design tool. The microcomputer can be located at the job-site, even in remote locations, allowing the actual behavior of the rock to be compared with predictions; and design change options to be examined, with minimum delay. However, the arrival of the microcomputer has not changed the rock. The large-scale heterogeneities and discontinuities, the variability and uncertainty of in-situ conditions remain, and must be considered in the design. Also, one has usually very limited detailed information on the mechanical properties of the rock mass prior to excavation, i.e., rock engineering problems are usually "data-limited." As has been noted, A rock mass is a complex assemblage of different materials and it is very unlikely that its behavior will approach the behavior of the simple models which engineers and geologists have to construct in order to under stand some of the processes which take place when rock is subjected to load. Hoek and Brown (1980) "Understand" is a key word in this statement. Flexible, 'user-oriented' computer programs are now available which can help the engineer develop an understanding of how a structure in or on rock is performing, and indicate possibilities for improving the design. Empirical design rules based on successful designs for (apparently) similar projects, are valuable and should be used as a check on a proposed design. They can not provide the understanding-and the associated awareness of possibilities for improving the design-that can come from the proper use of models. Starfield and Cundall (1988) have presented valuable guidelines on the use of models in rock mechanics, and note that Simplification is a crucial part of rock mechanics modelling. A model is an aid to thought, rather than a substitute for thinking..... They further advise.....plan the modelling exercise in the same way as you would plan a laboratory experiment. In particular, the modeler should ask, why am I building a model; how can I justify the particular model I am using; what did I learn from the modelling exercise? We have attempted to follow this approach to modelling and offer four examples as illustrations. All of them are, to varying degrees, "data-limited" and were studied using the two-dimensional finite-difference computer code, FLAC, (See References) on a microcomputer.

Proceedings Papers

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

Paper Number: ISRM-IS-1989-165

... plastic region will depend on the assumptions of (a) the yield

**criterion**; (b) the use of associated or non-associated flow rule; and (c) the dilatancy angle~. Under the axisymmetric plane strain condition, the strains and the displacements are expressed as ur f r _Lu 8r r' - 0 where the subscript r, 8 and...
Abstract

ABSTRACT: Closed-form solutions of stresses and displacements around a circular opening in a thermal elasto-plastic medium subjected to a hydrostatic initial stress are given. The solutions have been derived using the equation of equilibrium, compatibility condition, along with the stress-elastic thermal strain relationship, yield criteria, plastic potential and a flow rule. The effects of temperature, support pressure, and strength parameters on the distribution of stresses, displacements and strains are illustrated in the parametric studies. Conclusions of direct engineering significance are outlined. 1 INTRODUCTION Study of the thermo-mechanical behaviour of rock materials under elevated temperature is a relatively new challenge to engineering rock mechanics. Recent design and development of energy and resource related underground structures such as nuclear power plants, high-level radioactive waste repositories, oil extraction and storage facilities require adequate understanding of thermo-mechanical properties and behaviour of rocks at relatively low pressure but high temperature environments. Within the last decade, studies have been carried out on thermally-induced microcracks in rock (e.g. Lo and Wai, 1982), and the effects of temperature on the thermo-mechanical properties of rocks have been studied extensively (e.g. Durham and Abey, 1981, nage and Heard, 1981, Mongelli et al, 1982, Drury et al, 1984). Several studies have been made to compare theoretical models with laboratory and field experimental results (e.g. Johnson and Gangi, 1980, Witherspoon 1981, Chan et al., 1980, Van Sambeek et al, 1980, Gregory and Kim, 1981). It has been recognized that in general the temperature prediction by thermo-mechanical models is satisfactory. However, the models used in the theoretical analyses overestimates stresses and displacements from 20 to as much as 100%. The discrepancy has been attributed to: difficulty in field instrumentation; existing discontinuities in rock (faults, joints); and the validity of the theoretical models used. In the thermo-elastic analyses, it has been shown that tangential stress is highly compressive at the tunnel surface and tensile in the vicinity of a heat front in many instances (Lo et al, 1982, Ogawa, 1986). In this paper solutions of thermal elasto-plastic stresses and displacements are proposed and the results of parametric studies will be presented. 2 DEFINITION OF THE PROBLEM The problem is defined in Figure 1. Consider a circular opening with a radius a being excavated in an infinite thermal elasto-plastic medium which is subjected to isotropic initial stresses Po. The excavation removes the boundary stresses around the circumference of the opening, and the inside of the opening is filled with a liquid or gas so that the opening is subjected to an instantaneous constant increase in temperature V and support pressure Pi. As time increases, the temperature of the medium increases, thus causing thermal stresses and displacements. In the vicinity of the opening, the induced stresses by excavation and by thermal loading may exceed the strength of the material, leading to the development of a plastic zone with a radius b, where b - b(t). It is required to obtain the thermal elasto-plastic stresses and displacements around the opening.

Proceedings Papers

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

Paper Number: ISRM-IS-1989-167

... material model is described as follows: Linear elasticity up to a linear Mohr-Coulomb failure

**criterion**. After reaching the Mohr-Coulomb**criterion**the material fails with a sudden volume increase. The broken material then behaves fol- lowing soil-mechanics with no further volume change. The given...
Abstract

Abstract: At the coal-mine of "Les Houilleres de Blanzy", France, extraction galleries are constructed at a depth of approximately 700 m, entirely in coal of very poor mechanical properties. To understand the problem of the severe convergence that occurs in these galleries a mathematical simulation is made, using a simplified shape (cylindrical tunnel) of the underground opening. The material model is described as follows: Linear elasticity up to a linear Mohr-Coulomb failure criterion. After reaching the Mohr-Coulomb criterion the material fails with a sudden volume increase. The broken material then behaves following soil-mechanics with no further volume change. The given mathematical simulation is an exact solution of the above problem. The thus calculated deformations are in good agreement with the convergence observed underground. The presence of a large zone of broken material around the gallery is verified by in situ observations and measurements. Therefore, it can be concluded that the simplifications made are acceptable. It is obvious that man-made measures are necessary to avoid or limit the problems related to the strong convergence. Some experiments carried out are described shortly. As a preparation to an underground experiment, the possibility of injecting the broken coal with resin is analyzed. A circular area around a gallery could be injected. A material model is described for injected coal (Mohr-Coulomb envelope with a small cohesion) and again an exact solution is found for the stress distribution and deformations. Calculations show that only a small improvement of the material property, by means of injection, already gives a strong stabilizing effect on the galleries. It remains to be seen if this is applicable in practice. 1. Introduction The underground coalmine of "Les Houilleres de Blanzy" is located in the coal basin of Blanzy, between Rozelay and Montceau les Mines. This formation belongs to the north-east section of the Massif Central, France. The Blanzy formation is generally folded in the north-east/south- west direction. The basin is a depression of 100 Km long, 10 Km wide with a minimum depth of 1500 m, see fig. 1. The coal found in this region belongs to the upper carbon period. The coal was subjected to tectonic movements and metamorphism at low pressures and high temperature. The result of this geological history is that coal seams occur of thicknesses up to 40 m which are of very poor mechanical properties. The production method used in this mine (a special retreating longwall caving method) requires that extraction galleries are constructed entirely in the coalseam and are maintained until the face has passed. During this period (0.5–2 years) strong convergence occurs in the galleries and up to five reopenings are required. In the past, several attempts are made to avoid or reduce the problems related to this strong convergence. See [1] and [2]. Extremely strong arches were constructed and coal was extracted from between those arches to limit the pressure on them. In principle this method worked but it was much to laborious.

Proceedings Papers

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

Paper Number: ISRM-IS-1989-003

... ductile behaviors is observed by the increase of the confining pressure. Upstream Oil & Gas normal stress minimum principal stress minimum stress Reservoir Characterization strength strain energy stress state metals & mining

**criterion**experiment fracture strength triaxial...
Abstract

ABSTRACT: To clarify the effect of the intermediate principal stress on the strength and deformational behavior of rocks, three sandstones, marble, and shale were deformed under true triaxial stress state in which the intermediate principal stress is not equal to the minimum nor to the maximum principal stress. Failure strength increased with the relative increase of the intermediate principal stress except for the stress state where the intermediate principal stress approaches to the maximum stress. The relative increase of intermediate principal stress induced also changes the deformation of rock from the ductile mode to the more brittle mode. The difference between the intermediate principal strain and minimum principal strain increased markedly with increment of the intermediate principal stress. The fracture stability of rock specimen was suggested by the concept of the effective shear strain energy stored around the closed microcracks. The deformational anisotropy was indicated by the preferred orientation of stress-induced open microcracks. 1 INTRODUCTION: The Physical behavior of rock under triaxial stress state is essentially important for the underground mining and for the utilization of underground spaces for example, tunnels, electric powerhouse, storages of gas and oil, open pit mine, and high level waste repository and so on), because the act of excavations changes the stress fields and other physical and mechanical environments of rocks around the underground open space. The underground rock body is subjected to the initial stress prior to excavation. In many cases, it can be adequately assumed that the vertical normal stress is equal to the weight of the overlying rock mass, usually, 25–27MPa/Km on the average. The magnitude of the horizontal stresses lie widely between 0.5 and 3.5 times as large as the vertical normal stress at the depth shallower than 1000m(Brown and Hoek,1978). These observations suggest that the three principal stresses are different each others for many cases of initial. In order to investigate the mechanical characteristics of rocks around the underground openings, we have to adopt the testing equipment with which three different principal stresses can be reproduced precisely. The so-called triaxial compression test has been proved to be the most adequate and convenient testing method for the study of the mechanical characteristics of rocks for wide variety of confining pressures. In the conventional triaxial compression test, the longitudinal axial load is applied parallel to the axis of a cylindrical rock specimen through steel end pieces and the other stresses(confining pressure) are the cylinder by a fluid medium. The relatively homogeneous stress distribution can be produced in the specimen with the conventional triaxial test(confining pressure test). However, the intermediate principal stress is fixed equal to the minimum principal stress(compression test under confining pressure), in fewer cases, to the maximum principal stress(extension test under confining pressure), because the stress state in the confining pressure test is essentially axially symmetrical. According to the confining pressure experiments, failure strength increased remarkably with increase of the confining pressure, and relative transition from brittle to ductile behaviors is observed by the increase of the confining pressure.

Proceedings Papers

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

Paper Number: ISRM-IS-1989-018

... Reservoir Characterization drilling operation pore pressure wellbore integrity strength History specimen Wellbore Design triaxial loading shale Upstream Oil & Gas

**criterion**critical state borehole instability stress level weald clay peak strength mechanical behaviour...
Abstract

ABSTRACT: Drilling problems are frequently encountered throughout the Tertiary section in the North Sea. The problems are mainly to be associated with smectitic shales and tuffaceous sediments. Typical problems are drill tool sticking and lost circulation. The causes of borehole instability can be both of chemical and mechanical nature. Possible causes are fracturing of the formation, borehole collapse and creep or swelling in the borehole wall. Borehole instability take place even with inhibitive oil-based mud systems, so part of the problem is clearly of a mechanical nature. In the paper, we present an experimental investigation of mechanical strength and elastic parameters of shales at stress levels corresponding to depths of wellbore instabilities. Four different clays were selected as analogue materials to those encountered in North Sea Tertiary formations. The pre-failure, peak strength and post failure behaviour of these shale materials have been studied. INTRODUCTION Borehole instability has been a significant contributor to unproductive drilling time during the history of drilling for hydrocarbons. As a consequence, drilling costs have been unacceptably high. This fact has led the oil drilling industry to allocate increasing resources on trying to understand, alleviate and solve the problem of borehole instability. While drilling, unstable boreholes cause a variety of problems. The problems are most likely caused by fracturing of the formation, borehole collapse, large deformations and creep in the borehole wall and destructive rock-fluid interactions between the formation and the mud-system. These destructions result in excessive washing and reaming, hole "packing off", lost circulation and stuck pipe, and in the worst case losing the hole. Observations of drilling problems on the Statfjord field indicate that initial tight hole sections after some time may develop into an oversized borehole. This situation is probably due to further collapse in the borehole Wall. For the purpose of keeping the wellbore mechanically stable, increased mud weight has proven to enhance the situation. Using conventional methods for estimating pore pressures, it has been shown that troublesome shales very often are "overpressured", i.e. its pore pressure has attained a higher pressure level experienced at an earlier stage in the rocks stress history. This means that these shales normally are drilled "underbalanced". Another factor that has proven to reduce borehole instability is to minimize the sail angle through the particular hole sections of troublesome shales. Optimization of casing setting depths with respect to geology/ lithology, formation strength and pore pressure, will also be a contribution to reduced borehole instability problems during drilling. As of today, oil based muds are regarded to be the most inhibitive mud with respect to highly reactive clays, which often is dominant in troublesome shales. Use of oil based mud will reduce the destructive chemical effects of interactions between the rock and the mud. The result is that the wellbore will be closer to the gauge size, which in turn contributes to optimum hole cleaning and improved drilling conditions. To be able to predict potentially instable formations, it is of vital importance to know certain rock parameters.

Proceedings Papers

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

Paper Number: ISRM-IS-1989-004

... parameter's single hexagonal pyramidal failure surface suitable extensively to rock-like materials, which thought the effects of both the intermediate principal stress and the hydrostatic pressure at one time, and formed the correspondent

**criterion**for rock-like materials. 1 INTRODUCTION: In the...
Abstract

ABSTRACT: Having carefully researched the B. Paul's strength theory and systematically demonstrated it by experiments through the analysis of the characteristics of the failure strength of rock-like materials under the general triaxial stress states, we put forward the idea of the three parameter's single hexagonal pyramidal failure surface suitable extensively to rock-like materials, which thought the effects of both the intermediate principal stress and the hydrostatic pressure at one time, and formed the correspondent criterion for rock-like materials. 1 INTRODUCTION: In the underground winning and the open pit mining, such the problems as the steadiness and the fracturing failure of rock-masses under the general triaxial stress will all be met undoubtedly. To ensure the safety of mining, we must research the criterion for failure of rock-masses under the general triaxial stress states and determine under what triaxial stress states rock-masses may be fractured. So a great many of rock mechanics workers over the world have systematically researched the characteristics of the failure strength of rock-like materials under the general triaxial stress states and have put forward a variety of criteria for failure of rock like materials (1–5). By comprehensive analysis of these criteria for failure, we have discovered that these criteria for failure of rock- like materials either neglect the intermediate principal stress or the hydrostatic pressure, or are too complex to use, therefore, it's essential to go further into a criterion for failure of rock-like materials which thinks the effects of both the intermediate principal stress and the hydrostatic pressure at one time and has so simple mathematical expression that it's convenient in use. 2 THE B.PAUL'S STRENGTH THEORY: In order to research the criterion for failure of rock-like materials, B. Paul (2) has put forward the idea of the three parameter's single hexagonal pyramidal failure surface suitable extensively to rock-like materials which thought the effects of both the intermediate principal stress and the hydrostatic pressure at one time by spreading the well known Tresca Yield Surface in the plasto-elasticity, and has point out that the failure loci on the cross section perpendicular to the hydrostatic axis in the same pyramidal failure surface have different sizes with the distance from the vertex and have all threefold symmetry. Figure 1 gives the general space-formation of the three parameter's single hexagonal pyramidal failure surface in the three-dimension principal stress space, and Figure 2 gives the failure loci on the vertical section through the hydrostatic axis of the failure surface and the failure loci on the cross section perpendicular to the hydrostatic axis of the failure surface. 3 EXPERIMENTAL DEMONSTRATION: 3.1 Experimental procedure Limestone and fine-grain sandstone and median-grain sandstone concerned in the experiment were all obtained from the region around Nanton Coal Mine in Chongqing and could be regarded as the macroscopic homogeneous isotropic materials, and its values of physical-mechanical coefficient are listed in Table 2. 3.2 The failure loci on the vertical section By the measured failure strength of specimens under the general triaxial stress states.

Proceedings Papers

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

Paper Number: ISRM-IS-1989-005

... conditions, close to those, acting within the massif, are described. The program on mechanical tests of rocks is carried out, depending upon the calculated qualitative changes of principal stresses and three-di- mensionally stressed states near the mine workings. The developed ener- gy

**criterion**of rock...
Abstract

ABSTRACT In present work the systematic investigations on the mechanical characteristics of rocks under tree-dimensionally stressed state conditions, close to those, acting within the massif, are described. The program on mechanical tests of rocks is carried out, depending upon the calculated qualitative changes of principal stresses and three-dimensionally stressed states near the mine workings. The developed energy criterion of rock strength includes the deformation forces, acting under the deformation conditions, the shape and volume changing, their limiting values and the Nadai-Laudet parameter, taking into account three-dimensionally stressed state types. 1 INTRODUCTION The rock and rock massives loading conditions have a pronounced dimensional character. The relations between three principal stresses, characterizing mechanical state of rock massif near the mine workings are changed naturally. It defines the corresponding massif deformations and failure. The investigating the complex rock massif deformation and failure processes would be more successful under the natural conditions. However, the single tests only are possible in this case because of substantial production problems. The thorough preparation work for mine tests includes the necessary laboratory and analytical study. In present work the systematic investigations on the mechanical characteristics of rocks under the three-dimensionally stressed state conditions, close to that, acting within the massif, are described. this study allows to reveal the most characteristic features of geo-mechanical processes, proceeding Within the massif and to determine the main process parameters changing trends. 2 VOLUME LOADING OF THE MASSIF As for the gentle sloping rock bed in front of the face, all three principal stresses, acting in geo-mechanical processes, which proceed in the above mentioned zone within mine workings, are compressive, and three-dimensionally stressed state in different massif areas varies from summarized compression to summarized tension (Norel 1983). Three principal stresses, defining the three-dimensionally stressed state within the massif, are varied qualitatively as follows. When approaching the face, the maximum compressive stress, directed vertically relative to the working plane and defined as б3, increases from the vertical compressive stress value within unmined massif zone up to the peak value, which equals in the maximum compressive stress zone (where Kk is the concentration index) and then falls down to the strength index value at the face edge. The intermediate compressive stress, directed over the length of the face and defined as б1, varies from λp3 within unmined massif zone to the 1/2 (б1+ б3) value in maximum compressive stresses. 3 TESTS PROGRAM The program on mechanical tests of rocks is carried out depending upon the calculated qualitative changes of principal stresses and three-dimensionally stressed states near the mine workings. Before analyzing the test results, some statements on deformed media mechanics. being used in this work (Nodai 1969) should be considered because there is always the algebraic inquality б1≥б2≥б3 for three triaxial principal stresses. In this case the compressive stresses and deformations are negative; tensile stresses. 4 TENSOR DECOMPOSITION Tensor decomposition for three main types of three-dimensionally stressed states has allowed the more clear understanding of physical foundations of the summarized compression.

Proceedings Papers

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

Paper Number: ISRM-IS-1989-006

... 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**...
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, August 30–September 2, 1989

Paper Number: ISRM-IS-1989-002

... strain rates of d /dt=10- 2 -10-¹ 2 S-¹: brittle yield and dilation at low σm, ideally elastoplastic and non-dilative behavior at high σm' transition from viscoelastic to viscoplastic creep as r rises, of steady-state cracking (with an-nealing), rate dependence of the yield

**criterion**, and primary creep...
Abstract

ABSTRACT: The elastoviscoplastic behavior of saltrocks may be interpreted in terms of a number of different fundamental deformation mechanisms that act at different rates at different shear and normal stress levels. The paper presents a new approach to a constitutive law for these materials, recognising the complex behavior, and making distinctions between different types of yield criteria and viscous flow laws. An attempt is made to develop this behavior as an analogue to the behavior of rock at high temperatures and stresses, where viscous mechanisms became possible. It is empasised that an appreciation of the dominant deformation mechanisms acting at particular conditions will guide the form of macroscopic constitutive laws for non-saltrocks. INTRODUCTION: Understanding rock behavior at great depth and elevated temperature requires quantification of deformation processes which do not occur in ordinary conditions. Study of these time-dependent (creep) processes requires high temperature (T) and stress (σm¹) tests at slow strain rates (dE/dt). Shear stresses (r=(σ¹-σ 3 )/2) and pore pressures must also be controlled. It may be of practical interest to explore analogues which display similar mechanisms at lower T, σm¹, and r conditions. Salt and potash may be useful analogues in some conditions. Halite (NaCl) and sylvite (KC1) display different deformation processes depending on σm¹, T, and r, but in conditions accessible in the laboratory and the field (σm¹ <70MPa; r<40MPa; T<150°C). Provided that it can be shown that mechanisms are similar, analogies may be developed to other rock types. The critical issues are that behavioral fields, activation energies, and mechanism transition points be quantified to permit comparisons and extrapolations; deformation maps (Frost and Ashby, 1982) are essential for this purpose. A behavioral model for saltrocks will be described and treated as an analogue to the behavior of rocks at great depth. Emphasis is on the effects of stress and strain rate on mechanisms in saltrocks. Saltrocks display most aspects of brittle viscous- ductile behavior at strain rates of d /dt=10- 2 -10-¹ 2 S-¹: brittle yield and dilation at low σm, ideally elastoplastic and non-dilative behavior at high σm' transition from viscoelastic to viscoplastic creep as r rises, of steady-state cracking (with an-nealing), rate dependence of the yield criterion, and primary creep with recovery. YIELD BEHAVIOR: Elastoplastic (EP) yield is the conventional yield criterion (Y) of rock mechanics. Fig. 1 shows Brazilian and triaxial test data giving a curved criterion with these features: at low σ 3 , brittle behavior with dilatancy and debonding, small to failure, dependency of Y on σ3, UCS about 12 times To; at high σ3, cataclastic flow without σ3 dependence, dilatancy supression, crystal rupture; and, at intermediate confining stresses, transitional behavior. Typically, for halite, the transition to fully cataclastic plastic yield occurs at σ3= 10–20 MPa, σ1-σ3]EP≈ 35- 40 MPa, with rate effects. Consider a test at low σ3: if r<Y, steady state creep will occur, but r>Y can be applied for short times before strain-weakening. Thus, Y is a lower bound, defined as the lowest τ for strain-weakening yield in any time.

Proceedings Papers

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

Paper Number: ISRM-IS-1989-007

... be taken into con- sideration at present), and to examine certain laws governing. separately, the brittle railure and the brittle-ductile transition in sandstones. 2 LINEAR STRENGTH

**CRITERION**FOR SANDSTONES An induced stress theory or brittle railure or rocks has been developed CKwa~niewski. 19S6b...
Abstract

ABSTRACT: Results of the conventional triaxial compression tests on ultimate strength as well as on the mode of deformation or ninety-five (101) various sandstones from the territories or Asia. Europe, North America and Africa have been compiled in the paper. The rocks analyzed include arenites, wackes as well as pyroclastic sandstones or the porosity from 0.2 % to 55.9 % and of the uniaxial compressive strength from 4.6 MPa to 260 MPa. Most of them come from coal basins and oil fields from depths of up to 5000 m. Specimens or these rocks have been tested by different investigators at confining pressures up to 300 MPa, at room temperature, with strain rates from 10 5 to 10 -4/s. For seventy-one (75) sandstones, experimental data have been collected which express the major principal stress at failure in a function or confining pressure in the brittle field. The data have been used for the purpose of assigning to these rocks, and verifying quantitatively, the new linear strength criterion or brittle failure. Some or the sandstones analyzed preserved the brittle character even at pressures or 300 MPa. However, most or them underwent a transition into transitional and even ductile state already at much lower pressures. The data from the experimental studies or the deformational behaviour in the conditions or conventional triaxial compression have been collected for fifty-nine (62) sandstones. The data were used to determine the criterion of transition from the brittle into transitional state, and from the transitional into ductile state, and to estimate values or the coefficient or internal friction at strength failure, specific to the B-T and T-D transitions. 1 INTRODUCTION Sandstones belong to the rocks which commonly accompany accumulations or solid, liquid and gaseous fossil fuels in the earth's crust. It is among sandstones that coal seams most frequently occur. The sandstones are also reservoir rocks for oil and natural gas. A knowledge of the mechanical properties of these rocks and of their behaviour a depths is thus very important for an efficient and safe extraction of the natural energy resources. Rocks subjected to differential stress may fracture, fault with or without loss of cohesion, or flow, depending upon rock type and environmental factors such as confining pressure, pore pressure, temperature, strain rate and moisture, At shallow depths in the earth's Crust, at the relatively low pressures and temperatures, it is the brittle failure which is the dominant mechanism of rock failure. The brittle failure or rock is characterized by small strains at the ultimate strength, momentary loss of cohesion, separation into two or more parts, violent and remarkable stress drop, release of stored elastic strain energy, and occurrence of the acoustic effect. However, brittle failure is not the only response of rocks to loading and other external factors. In the conditions of higher pressures and temperatures, and lower strain rates, which are typical for deeper parts or the earth's crust, rocks lose the brittle character and, acquiring an ability to deform to large strains without gross-fracturing.