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Keywords: strain tensor

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Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the 49th U.S. Rock Mechanics/Geomechanics Symposium, June 28–July 1, 2015

Paper Number: ARMA-2015-221

..., three dimensional photogrammetry and multi- sensor displacement monitoring, are also used nowadays to monitor displacement. If a strain calculation method is developed, the data may be used to calculate distributions of three dimensional

**strain****tensors**in the slope or highwall. Without a strain...
Abstract

Abstract All rock excavations by means of natural gravity caving, mechanical excavation or blasting cause redistribution of the static stress and strain in the remaining rock mass. It is critical to measure the change of the strain state. Such a measurement can serve as quantification of the damage and of the effectiveness of a blast design or an excavation method. Secondly, the measurement can be used to monitor slope or mine structure stability to improve the mine safety. At present, there is no method available to calculate strain changes over a large area of a rock slope or an underground structure. New technologies developed over the last few decades; such as GPS, radar systems, three dimensional photogrammetry and multi-sensor displacement monitoring, are also used nowadays to monitor displacement. If a strain calculation method is developed, the data may be used to calculate distributions of three dimensional strain tensors in the slope or highwall. Without a strain calculation method, the data can only give displacement change at discrete monitoring spots. This paper presents a method for measuring the change of the static strain state at a remaining rock mass or ground associated with operations of excavations, such as blasts, mechanical means or gravitational caving of a portion of the ground. The method is based on measuring coordinates of selected points with recent accurate survey techniques before and after an excavation. The paper also shows that for small deformation the different reference points for survey before and after an excavation can be used, which provides great convenience in practical measurement. The calculation of the strain change is done by solving a set of simultaneous equations for the displacement gradients. With the number of survey points larger than the minimum number required, the number of the independent equations is greater than the number of unknowns and minimizes measurement errors.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the The 42nd U.S. Rock Mechanics Symposium (USRMS), June 29–July 2, 2008

Paper Number: ARMA-08-285

... reservoir thermal stress floor rock

**strain****tensor**compressive stress layered rock mass tensile stress principal stress st principal stress numerical modeling diagram sandstone boundary rock mass Von Mise stress 1 Introduction The underground rock mass will be fractured when it is under high...
Abstract

ABSTRACT: A numerical modeling was carried out to investigate the stress changes of a layered rock mass when it is heated. The aim of this project was to understand rock fracturing characteristics associated with underground coal gasification at a coal mine. The model contains three coal seams which are sandwiched between a number of sandstone and mudstone layers. The finite element software ANSYS was used to for this modeling. The modeling had two steps: thermal transmission modeling and thermal stress calculation. The results show that the high temperature generated by underground coal burning induced thermal stress which exceeded the strength of the rock mass. The modeling also simulated the propagation of coal burning development in a coal seam and the rock mass responses to the burn front. 1 Introduction The underground rock mass will be fractured when it is under high temperature environment because the thermal expansion of the rock mass is constrained and can?t take place freely. When the thermal stress exceeds the strength of the rock mass, micro cracks will be produced. Thermal cracking in rock mass played an important role in engineer practices, such as dealing with nuclear waste storage [1], rock drilling [2], exploitation of crude oil [3], geothermal exploitation [4] and underground coal gasification [5] and so on. The temperature of underground coal burning in UCG (underground coal gasification) is above 1000° [6, 7]. This high temperature will produce a high thermal gradient and stress field in the surrounding rock mass. When the thermal stress exceeds the strength of the rock mass, the rocks will fracture. If the fracture was significant, it will affect the gasification process in UCG. In order to keep the gasification process working normally, we need to know the thermal stress distribution of layered rock mass under high temperature environment. Because of the complexity of rock mass and UCG process, the integrity theoretical analysis is very difficult. However, the numerical simulation not only can simulate the complexity mechanics of rock mass, but also can predict engineering problems. Therefore, the numerical modeling of UCG was set up and the finite element software ANSYS was used for this modeling. The software ANSYS can solve high precision nonlinear and coupled field problems, such as thermal-mechanical process. In rock engineering, ANSYS can be used to analyze large structural displacements and problems related to stress-strain and plastic behavior [8]. Therefore, it can be used in the study of thermal stress fields in rock mass. 2 Assumption for modeling thermal stress of layered rock mass The thickness of coal seams is much smaller than its width and length. In order to reduce the calculation time, this numerical model was regard as a 2D model and plane strain was calculated. The UCG was a coupled phenomenon involving thermal, hydrological, mechanical and chemical processes. However, in this study, the modeling was carried out only to investigate the stress changes of a layered rock mass when it is heated. The aim of this project was for the understanding of rock fracturing characteristics with thermal stress.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the The 32nd U.S. Symposium on Rock Mechanics (USRMS), July 10–12, 1991

Paper Number: ARMA-91-675

... reservoir geomechanics cement

**strain****tensor**loading Reservoir Characterization behavioure sandstone UNIAXIAL stress Upstream Oil & Gas damage behaviour uniaxial loading damage variable irreversible deformation micro-experimental study damge deformtion behavioure rock damage deformation...
Abstract

1 INTRODUCTION ABSTRACT: In this paper, damage deformation behaviour in Chongqing sandstone is observed by using of acoustic emission (AE) technique and micro-experimental technique. Micro-experimental results are shown as follow: a) Under the beginning of loading, the deformation is mainly that holes, cracks and cements are compressed; b) When uniaxial stress is 47MPa, the original holes, cracks and other defects are still state, no crack is developped; c) When uniaxial stress is 82MPa, the micro-cracks link up through the interface of granular, and micro-cracks direction are parallel to compression stress direction. The micro-experimental results of crack growing, developping, linking up are close to AE experimental results. Experiments find that cracks growing, developping, linking up of rock in deformation have volumetric dilatancy. Clearly, internal structure damage of rock is focus to its volumetric dilatant behaviour on macro. According to analysis on damage deformation behaviours of rock, a new damage variable is defined by damage volumetric deformation of rock in deformation. The new damage variable can better describe the damage deformation behaviours of rock. In the recent 20 years, the damage mechanics is developed and it is applied in rock mechanics which makes the studies of rock have a new field and new method. Krajcinovic, D & Fonsek, G. U. [1981], Holcomb, D. J. & Costin, L. S. [1986]. Lland, K.E. [1980] Xie heping & Chen Zida [1987], Resende, L. & Martin, J. B. [1984], Lemaitre, J. [1985], Vakulenko, A. A. & Kachanov, M. L. [1971], Dragon, A. & Mroz, z. [1979] and Kyoya, T. & Ichikawa. Y., Kawamoto, T. [1985] introduce a continuum damage concept proposed by Kachanov, L. M. [1958] into rock mechanics. Damage mechanics in rock is studied and some effective rock damage theory is gotten. Rock material properties and work condition are different from metal material, which makes damage theory built by use of metal damage mechanics method cannot effectively describe the damage deformation behaviours of rock. In the present paper, the damage deformation behaviours of rock are observed by use of micro-experimental technique and Acoustic emission technique. According to experimental results and damage deformation behaviours analysis of rock, a new rock damage variable is defined. 2 MICRO-EXPERIMENTAL OBSERVATION OF ROCK DAMAGE All rocks have clearly damage characteristic in macroscope or microscope. Fig.2 is electron microscope photograph of mudstone before deformation. From two rock micostructure in Fig.l and Fig.2 we can clearly find there are many holes, micocrcracks, interfaces and other defects in rocks. Fist let us observe electron microscope photograph of Chongqing sandstone under loading. At the beginning of loading, the deformation is mainly that holes cracks and cements of rock are compressed, some cements are crushed because of partly stress concentration. When uniaxial stress is 47MPa, the original holes, cracks and other defects are still state, no crack is developped ( Fig.3a ) . When uniaxial stress is 72 mpa , micro open cracks have formed in the interface of granular and micro-cracks direction are parallel to compression stress direction (Fig.3b).

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the The 25th U.S. Symposium on Rock Mechanics (USRMS), June 25–27, 1984

Paper Number: ARMA-84-0959

... ABSTRACT ABSTRACT We have instrumented well-controlled free-face blasts with six- component borehole strain gages, in order to determine the complete

**strain****tensor**as a function of time due to explosive loading. The**strain****tensors**have been diagonalized to determine the principal strain time...
Abstract

ABSTRACT ABSTRACT We have instrumented well-controlled free-face blasts with six- component borehole strain gages, in order to determine the complete strain tensor as a function of time due to explosive loading. The strain tensors have been diagonalized to determine the principal strain time-histories, and further processed to determine the octahedral shear strains as a function of time. Principal strain time-histories, when compared with a computer model, indicate the arrival of various direct and reflected phases. Strong shear strains coincide with the expected arrival time of shear waves. These shear waves are probably instrumental in the fragmentation of confined rock due to explosive loading, and should be incorporated in models of the fragmentation process. INTRODUCTION Many mining operations rely on blasting to initially fragment rock masses for subsequent processing. In certain applications, (i.e., oil shale retort formation, blasting operation success is critical to resource recovery. In more conventional mining operations, blasting is still the most energy-efficient means of fragmenting rock. Optimal use of explosive energy in mining operations requires a thorough understanding of the underlying physical principles. Both pressurization due to rapidly expanding explosive gases, and strain waves generated by the interaction of the gases with the borehole walls undoubtedly affect fragmentation. Although the effect of expanding gases was once deemed most important, in the past few years the importance of strain waves and their interaction with flaws has received increased attention. Because the controversy over which effect is predominant is thoroughly reviewed by Winzer et al. (1983), we will only briefly discuss previous strain measurement studies here. Analytical predictions of the strain wave from an explosive column have become progressively more sophisticated, from the initial work of Sharpe (1942), through models of Heelan (1953), Jordan (1962), and Favreau (1969). Plewman and Starfield (1965) proposed a novel numerical approach in which a cylindrical explosive column is modeled as a linear series of spherical charges detonated with delays corresponding to the detonation velocity of the explosive. The resultant waveform is then a repeated summation of the strain waves generated by a spherical charge, appropriately lagged, and attenuated according to path- length differences. The U.S. Bureau of Mines did an extensive series of field studies in the 1950's and 60's to determine the response of rock to explosive [e.g., Duvall and Atchison (1957); Atchison and Tournay (1959)]. Comparing some of the strain-gage records obtained with the numerical model of Plewman and Starfield, Starfield and Pugliese (1968) found generally good agreement. The model simulated neither an s-wave from the explosive column nor any reflections. The tests were done in quarry floor, so that reflections from a vertical free face were not present, rock movement was somewhat confined, and the rock was only damaged from preceding blasts. It is noteworthy that no significant tensile strains were observed in the original records or the models. We have worked almost entirely with bench blast configurations, because that is the usual operating condition in quarries. In a typical bench blast, complicated strain histories in the affected rock may arise from several causes. First, strain waves generated by the explosive column will have a broad pulse-width due to the finite detonation velocity of the explosive. This is evident from the work discussed above. Second, the rock through which the waves will propagate will have discontinuities due to jointing, layering, and damage from previous blasts, which may attenuate strain wave

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the The 18th U.S. Symposium on Rock Mechanics (USRMS), June 22–24, 1977

Paper Number: ARMA-77-0009

... displacement, and therefore all the components of the stress and

**strain****tensors**, are independent of ¿. This kind of deformation is a particular case of a kind referred to as antiplane-strain. In this paper, it is shown how this condition can be modeled very simply without resorting to a full three-dimensional...
Abstract

ABSTRACT ABSTRACT The geothermal energy program has resulted in an increased interest in the deformation and stability of relatively large diameter holes drilled deep into crystalline rocks in regions where the geothermal gradient is high. Knowledge of the response of the rock surrounding such holes can be gained providing that an adequate model can be constructed. For complete generality the model should be capable of analysis of a hole which is arbitrarily orientated with respect to the principal axes of the initial stress field and also any planes of elastic symmetry of the rock. Under these conditions the deformation of the rock around the hole will not, in general, be in plane strain. Taking the ¿ axis as the axis of the hole then, providing the hole is long, the axial strain will be constant and the axial displacement will be a linear function of ¿. The other components of displacement, and therefore all the components of the stress and strain tensors, are independent of ¿. This kind of deformation is a particular case of a kind referred to as antiplane-strain. In this paper, it is shown how this condition can be modeled very simply without resorting to a full three-dimensional analysis. The formulation of a finite element code making use of this approach is presented very briefly and shown to give results in good agreement with those obtained analytically. Finally, some calculations of stresses and displacements around chilled holes deep in hot, dry crystalline rock are introduced. INTRODUCTION Drilling a borehole in any rock will result in disturbance of the initial stress and temperature states. When the hole is deep and the rock hot, these disturbances may be of practical significance as far as borehole closure and stability are concerned. Reviewing the literature, it is clear that this problem has not been extensively studied for the conditions that are likely to be encountered when drilling deep into hot, dry rock of the crystalline basement. Analysis of stresses around borehole has been mainly related to drilling in soft rock. In some cases the influence of the bottom of the hole is taken into account, but more commonly the hole is considered to be long and. an analysis conducted on the basis that the deformation will be in plane-strain. Often it is further assumed that the axial stress will be the intermediate principal stress and that it has no effect upon the strength of the rock. Whether these simplifications are reasonable depends-upon the nature of the rock and also the initial state of stress. To be completely general, however, full account should be taken of: The magnitude and orientation of the principal initial stresses Material anisotropy The orientation of the hole If all these factors are taken into account a conventional two-dimensional analysis assuming the deformation to be in plane-strain will not be adequate. In particular, such an analysis would not represent axial, or out of plane, displacements and associated stresses.