3

STABILITY ASSESSMENT

Consistent with the definition of failure given in the Introduction, stability refers to several different phenomena related to the degradation of the rock adjacent to the walls of a borehole, or larger circular opening, as a result of the tangential stress concentrations. True dynamic instability that results in the violent fracture of the rock (as in a rock burst) is rare. Because it can be shown (Zheng et al., 1989) that the rock surrounding a circular opening provides a very stiff “loading system,” dynamic instability would occur only for very brittle, Class II rocks (Wawersik and Fairhurst, 1970), unless instability is associated with the behavior of contained fluids as in a gas outburst. An unstable excavation is used here to mean a circular opening in which the tangential stress concentration is sufficient to cause the rock to deform inelastically or fail. As a result of this inelastic deformation, the damaged rock may fall into the open space, thereby changing either the size and, more commonly, the cross-sectional shape from that of a circle. Sometimes the damaged rock remains in place so the excavation more or less retains its original cross section. For the remainder of this chapter, instability will be used to imply that the ratio of rock stress to rock strength exceeds the elastic limit producing either a zone of degraded rock adjacent to the circular cross section or resulting in a substantial change in cross section of the originally circular borehole. Frequently, the cross sections of boreholes or tunnels are observed to elongate in the direction of the minimum principal stress as a result of preferred failure in orientations that produce a breakout.

A puzzling consequence of this is that the elongated shape becomes stable, i.e., further degradation of the rock and further changes in the cross section cease, although the magnitudes of the stress concentrations at the edge of the elongated or breakout cross section must be



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Stability, Failure, and Measurements of Boreholes and Other Circular Openings 3 STABILITY ASSESSMENT Consistent with the definition of failure given in the Introduction, stability refers to several different phenomena related to the degradation of the rock adjacent to the walls of a borehole, or larger circular opening, as a result of the tangential stress concentrations. True dynamic instability that results in the violent fracture of the rock (as in a rock burst) is rare. Because it can be shown (Zheng et al., 1989) that the rock surrounding a circular opening provides a very stiff “loading system,” dynamic instability would occur only for very brittle, Class II rocks (Wawersik and Fairhurst, 1970), unless instability is associated with the behavior of contained fluids as in a gas outburst. An unstable excavation is used here to mean a circular opening in which the tangential stress concentration is sufficient to cause the rock to deform inelastically or fail. As a result of this inelastic deformation, the damaged rock may fall into the open space, thereby changing either the size and, more commonly, the cross-sectional shape from that of a circle. Sometimes the damaged rock remains in place so the excavation more or less retains its original cross section. For the remainder of this chapter, instability will be used to imply that the ratio of rock stress to rock strength exceeds the elastic limit producing either a zone of degraded rock adjacent to the circular cross section or resulting in a substantial change in cross section of the originally circular borehole. Frequently, the cross sections of boreholes or tunnels are observed to elongate in the direction of the minimum principal stress as a result of preferred failure in orientations that produce a breakout. A puzzling consequence of this is that the elongated shape becomes stable, i.e., further degradation of the rock and further changes in the cross section cease, although the magnitudes of the stress concentrations at the edge of the elongated or breakout cross section must be

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Stability, Failure, and Measurements of Boreholes and Other Circular Openings greater than those around the circular cross section (Detournay and Roegiers, 1986). In this sense, the elongated cross section of a borehole breakout is very stable, more stable, in fact, than the original circular opening. Analyses of the evolution and stability of borehole breakouts by Zheng et al. (1989) showed that they result in elongation in the direction of the minimum principal stress with a pointed end. This cross section is in accord with most laboratory observations (e.g., Haimson and Herrick, 1986, 1989) and some field observations, although other field observations (Zoback et al., 1985) suggested that the breakouts are rounded rather than pointed. For pointed ends, Zheng et al. (1989) showed that the stress concentrations near the ends approach a state of hydrostatic stress, as for a notch or mathematical crack, and that it is the reduction in shear stress and the increase in mean stress ahead of the end that stabilize the breakout cross section. Closure Measurements The mechanical stability of the fractured rock adjacent to the opening can be inferred from measurements of the changes in the opening diameter and from wall scanning devices. For small-diameter boreholes, the simplest such measurement is a caliper log, which uses one to four or more spring-loaded arms to provide a depth profile of borehole enlargements. Intervals of incompetent or extensively fractured rock are often indicated by substantial borehole wall enlargements. Recent studies using an oriented caliper device, known as a dipmeter in the petroleum industry, demonstrated the effectiveness of oriented caliper logs in the interpretation of the extent and orientation of the fractures (Gough and Bell, 1981; Plumb and Hickman, 1985). For larger diameter openings that are physically accessible, closure measurements can be made manually. Additional stability information can be obtained by inserting multiple-point extensometers in small-diameter boreholes drilled perpendicular to the axis of the tunnel or shaft. These instruments measure differential displacements away from the opening surface, and are useful for determining instabilities caused by bedding planes, geologic anomalies, or induced fractures not visible on the surface.

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Stability, Failure, and Measurements of Boreholes and Other Circular Openings Geophysical Measurements Detailed investigations of fracturing and alteration adjacent to the borehole can be made using borehole wall scanning devices based on optical, ultrasonic, and electrical conductivity measurements. Downhole television cameras are viable for borehole use, and technology associated with downhole cameras is advancing rapidly (Hawkins et al., 1989). The use of optical systems is limited by the need for transparent borehole fluids, electronic signal requirements incompatible with a standard geophysical wireline, and difficulties in relating visual appearances to the mechanical properties of rocks. In spite of the problems, downhole cameras, coupled with modern image enhancement methods, provide a useful tool for borehole wall inspection. One of the most important tools for interpretation of the degradation in the wall rocks of boreholes is the acoustic televiewer. This device produces an image of the radial distance to the wall of the borehole and of the acoustic reflectivity of the borehole wall. Early televiewer applications were focused on determining the strike and dip of intersections between fractures and boreholes. Subsequent study of televiewer logs demonstrates that the pattern of fracture interconnections and the extent of hole enlargement and spalling in fracture zones can be interpreted from televiewer data. This kind of information is especially useful in fracture zones where a core may be missing or extensively fragmented. In recent years, acoustic reflection data from televiewer systems have been digitized, and modern image processing software has been used to construct composite images based on both the intensity of the reflection and the distance to the wall (Zoback et al., 1985; Morin et al., 1989). This approach provides a great deal of information about the state of wall rocks that can be related to the engineering properties of rocks. One of the most important approaches is the systematic comparison of the cores with the borehole wall images. The comparison provides insight into the effects of stress relief on the fracture aperture, mechanical spalling of the fracture faces, and erosion of the infilling minerals and alteration minerals. An alternate method of borehole wall imaging has recently been introduced by expanding the number of small electrodes on the pad of a conventional resistivity logging tool to more than 20, and then constructing an electrical conductivity image of a vertical strip of borehole wall (Ekstrom et al., 1987; Laubach et al., 1988; Paillet, 1991a and 1991b). This image is interpreted to be similar to the image of the televiewer, except that the log represents the pattern of electrical

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Stability, Failure, and Measurements of Boreholes and Other Circular Openings conductivity in the borehole wall. The response to fractures depends on the electrical conductivity of fluids filling the fractures. The method has provided considerable insight into the detailed structure (laminations, sedimentary fabric, etc.) of sedimentary rocks. Measurements using seismic or electrical methods are made to predict the conditions of the borehole wall failure as a function of the in-situ stresses and mechanical properties of the formation adjacent to the boreholes. Acoustic full-waveform logs are applied in the interpretation of the elastic moduli to estimate the shear strength and Poisson's ratio of the formations. The method is useful when the core sample recovery and processing eliminate soft or brittle lithologies, so the continuous mechanical property profiles constructed from acoustic logs can be used to generate the profiles of the mechanical properties with the depth (Paillet and Morin, 1988; Tarif et al., 1988). In such situations, the dynamic moduli inferred from the logs may not agree closely with those determined from the cores, but the relative distribution of the static moduli may be estimated from the dynamic moduli profile. Downhole borehole wall imaging devices produce images that are deliberately limited to the surface of the borehole wall. This surface has been subjected to various amounts of damage during drilling, and subsequent erosion by the circulation of drilling fluids. The much larger wavelengths produced by the source transducers in conventional acoustic logging equipment can be used to penetrate behind the drilling damaged annulus and disturbed stresses. This approach is most effective in small-diameter boreholes, where acoustic wavelengths are several times larger than the borehole radius, and the acoustic signals refracted along the borehole penetrate a number of radii into the wall. Recent attempts to use acoustic information of this type have been based on the so-called acoustic full-waveform log, in which the entire signal received at the acoustic logging receiver is digitally recorded at successive depth stations (Paillet and Cheng, 1991). A useful profile of the mechanical properties of wall rocks and the extent of mechanical disruption by fracturing is obtained by plotting successive waveforms at the some scale. Various versions of such plots are described in the literature as acoustic signature logs. In many situations, the extent of the observed disturbance to these waveforms can be taken as an indication of the size of the local departure from the background conditions in the wall rocks in situ (Paillet, 1985). Several authors have attempted to make this analysis more quantitative by computing various indices from these waveform data that may then be related to rock properties. The most frequently cited versions of such indices are based on the waveform amplitude

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Stability, Failure, and Measurements of Boreholes and Other Circular Openings associated with compressional and shear arrivals, or the coherence of wave energy in a window with respect to specified background (unfractured and unaltered) wave signals (Paillet, 1985; Paillet and Kim, 1987). In some cases, the potential for fluid influx and damage produced by rapid inflows can be as important as the mechanical properties of the borehole wall. One particular application of acoustic waveform logging has been in the correlation of the waveform amplitude and other properties with the borehole wall permeability in the fracture zones. Waveform amplitude is related to the fracture permeability through the transmission of a guided wave mode similar to the Stoneley interface mode known to propagate along plane interfaces between elastic solids and fluids. Effective measurement of the tube-wave transmission and reflections requires tuning of the borehole logging systems to particular situations to ensure that the tube-wave modes are present and their amplitude can be measured without interference from other wave modes. Calculations indicate that the tube-wave amplitudes can be related to the fracture permeability over distances ranging from one to five meters beyond the borehole wall (Paillet, 1985; Tang and Cheng, 1989). Larger scale indications of the fracture permeability for the most permeable fractures intersecting the borehole are obtained from another tube-wave phenomenon. In this technique, the tube waves are excited in the borehole when the seismic waves from the surface sources squeeze the pulses of fluid into the borehole at the intersection with permeable fractures (Hardin et al., 1987). The amplitude of these tube waves as a function of depth and source offset can be used to estimate the permeability and orientation of the fractures intersecting the boreholes. In-Situ Stress Conditions The introduction of a cylindrical borehole into otherwise homogeneous rocks produces a local stress concentration field that depends on the in-situ stresses and the manner in which the borehole deforms under the influence of those stresses. In recent years, there have been a number of attempts to model borehole deformation under the local concentration of in-situ stresses and to apply those models to the interpretation of the in-situ state of stress. In the case of relatively soft sedimentary rocks, such as siltstones and shales, the tangential stress is assumed to produce shear fractures of the wall rocks adjacent to the regions of the maximum concentra-

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Stability, Failure, and Measurements of Boreholes and Other Circular Openings tion, resulting in an elliptical borehole cross section (Gough and Bell, 1981). In this model, the major axis of the elliptical cross section is assumed to be parallel to the direction of the minor principal horizontal stress. In hard crystalline rocks, differential compressive stresses adjacent to the wall of the borehole produce extensile crack growth where the values of the tangential stress are greatest, resulting in local borehole wall failure (Zheng et al., 1989). Theoretical models demonstrate that in the case of a vertical borehole the orientation of the borehole wall breakouts measured in the borehole agree with the location of breakouts predicted by the shear failure theory (Zoback et al., 1985). In general, the ratio of maximum to minimum horizontal stresses required to generate the borehole wall failure decreases with the increasing difference between the lithostatic and hydrostatic pressures. According to this theory, the model also allows the size of the observed breakouts to be related to the magnitude of the stresses, and shear strength of the wall rocks. This assumes, however, that the failure mechanism is fully understood; a premise that has been later challenged (Roegiers and Detournay, 1988; Zheng et al., 1989). The primary application of the borehole wall breakout theory in rock mechanics has been the use of the data to infer the orientation of the compressive stress field. This method provides a very simple and inexpensive way to identify the stress conditions, because the stress orientation can be inferred from the azimuth of the wall breakouts (Morin et al., 1989). For example, the in-situ stress measurements by hydraulic fracturing and overcoring measurements are very scarce in southern New England, but several boreholes in eastern Connecticut and Massachusetts indicate that breakouts are consistently oriented on the north and south sides of the boreholes, corresponding to a nearly east-west orientation for the regional compressive stress field. In addition to providing in-situ stress measurements, the borehole wall breakout observations may provide detailed profiles of the relative distribution of magnitudes of the stresses within geological formations, and the disturbance and reorientation of in-situ stresses by fractures and faults. The analysis of the vertical distribution of the breakouts in the boreholes has the potential for augmenting microhydraulic fracturing and overcoring stress measurements in the same way that continuous geophysical logs are used to interpolate the results of laboratory measurements of the physical properties of core samples. Recent results confirm that the vertical extent of the breakouts within structural units where stresses are concentrated by regional structure coincide with the extent of abnormal stress indicated by core disking

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Stability, Failure, and Measurements of Boreholes and Other Circular Openings (Paillet and Kim, 1987). Breakout identification using televiewer and dipmeter logs is now being applied to the interpretation of the mechanical stability of the boreholes drilled in the ocean floor under the deep-sea drilling program (Morin et al., 1989). This application of geophysical logging appears to be an area where significant future progress in rock mechanics is likely to occur. However, considerable uncertainty remains in the interpretation of breakout observations especially when the borehole is not drilled parallel to a principal stress direction (Roegiers and Detournay, 1988). Laboratory and field data often show complex behavior (Ewy et al., 1988b; Ewy and Cook, 1989). Laboratory experiments reported earlier do show that an anisotropic state of stress applied to a testing block provides an anisotropic rupture of the borehole drilled in the block (Guenot, 1987). However, when the applied state of stress is isotropic, the rupture is mostly anisotropic probably because of inherent strength anisotropy. This means that an isolated breakout in a borehole cannot give the stress direction with confidence. The current practice is to deal with those breakouts in a statistical manner. In addition, the volume of the breakout appears to be dramatically influenced by the loading path, questioning the validity (or even the hope) to relate it to any stress difference magnitude. It also appears that the orientation of this breakout can rotate by 90 degrees. This may occur in a well while deepening, or in a series of wells located in another area of the field. This can be very local, for example, near the intersection with a fault (Shamir and Zoback, 1989), or only in a particular area of a fractured field (Guenot, 1989). Furthermore, cases have been reported where in a whole field the breakouts are oriented in the direction of the maximum stress orientation given by the regional trend (Morin et al., 1989). These apparently anomalous variations between the orientation of in-situ stress and breakout azimuth are believed to be related to secondary, nonlinear mechanisms. Finally, boreholes can be broken in both directions at the same level in the well. Morin et al. (1989) described the case of one of the deep-sea wells, located offshore Nicaragua, where there is a dual distribution of breakout directions. The first breakout is oriented in the direction perpendicular to the direction of the regional maximum stress and is regularly distributed in the borehole, with an intensity increasing with depth. The second breakout occurs at several levels in the well, and seems to be related with particular drilling phases, involving coupling processes.

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Stability, Failure, and Measurements of Boreholes and Other Circular Openings Civil and Mining Engineering In civil and mining engineering, many shafts and tunnels have circular, or approximately circular, cross sections. The diameters of these excavations usually fall in the range from 2 to 10 meters. Degradation of the rock adjacent to the walls of shafts and tunnels occurs when the values of the horizontal stresses in this rock approach the uniaxial compressive strength of the rock. The in-situ strength is usually significantly less than the uniaxial compressive strength of the same rock measured in the laboratory tests. In part, this may be a result of the well-known, but poorly understood, effects of the size on the strength and in part a result of the quality of the rock mass. Hoek and Brown (1980) proposed a nonlinear Mohr failure criterion with adjustable parameters “m” and “s” to account for the effects of size and quality on the rock strength. Methods for assessing the rock quality have been developed by Barton et al. (1974) the Norwegian Geotechnical Institute (NGI) and Bieniawski (1974) the Council for Scientific and Industrial Research (CSIR). In the hard rocks at high stresses, tunnels and shafts often fail by extensile crack growth parallel to the tunnel wall forming extensive thin slabs of broken rock. As in the case of borehole breakouts, successive slabs elongate the cross section of the excavation in the direction of the minimum stress in the rock. In hard rock under lower stress conditions, slabbing often occurs by subcritical crack growth without dynamic instability again leading to an elongated breakout cross section. Although the magnitudes of the tangential stress adjacent to the end of the elongated cross section are greater than those around the original cross section of the excavation, the elongated shape is more stable than that of the original cross section. However, especially in near horizontal tunnels where the maximum stress is vertical, the larger span of the elongated cross section exacerbates problems of roof stability, so it is often important to install artificial support to prevent rockfalls from the roof as well as attempt to stabilize the sidewalls against the breakout. Experience has shown that artificial support can greatly strengthen the shafts and tunnels against the breakout-type instability, although the support stresses are relatively small in magnitude. The most effective types of support are often rock bolts with wire mesh and shotcrete. The principal advantages of this support are that it can be placed very soon after excavation and that it generates support virtually immediately. Support of this kind seems to operate through two mechanisms one dynamic and the other kinematic. Dynamically, the support pressure tends to generate the negative Mode I stress

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Stability, Failure, and Measurements of Boreholes and Other Circular Openings intensity factors inhibiting the growth of long extensile cracks parallel to the excavation surface and to increase the Coulomb frictional resistance in the broken rock. Kinematically, the support stabilizes the slabs against buckling and prevents “loosening” of the zone of fractured rock around the excavation by keeping key blocks of rock in place. These dynamic and kinematic effects of support appear to be quite universal and are effective in both intact and “blocky” rocks over a wide range of strengths and hardnesses. In truly soft, plastic rock, it is sometimes necessary to install support immediately behind the face. Often this is accomplished with a continuous steel or concrete lining of preformed sections installed immediately behind a shield tunneling machine.

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