Experiments in which borehole breakouts were produced in different rocks have revealed three major mechanisms of rock fracturing. In all tests a true triaxial stress condition was applied to cubical rock specimens. Then a central vertical borehole was drilled, which induced borehole-breakout failure, depending on the magnitudes of the far-field stresses. In crystalline granite intra- and trans-granular dilatant microcracking subparallel to the borehole wall and to the direction of the maximum horizontal stress σH preceded the development of breakout failure, resulting in 'V'-shaped failed zones along the σh spring line. In well-consolidated sandstone breakout failure took a similar 'V' final shape. However, microcracks preceding failure were mainly intergranular, and only occasionally intragranular. In a less consolidated but still competent sandstone, failure did occur at the same locations as with the other rock types but, surprisingly, the final breakout shape was a narrow linear fracture perpendicular to σH direction. The mechanism of this failure mode appears to be largely matrix non-dilatational disintegration leading to grain disaggregation.

Editor’s Note The present Special Issue of the ARMA e-Newsletter is dedicated to Discrete Fracture Network Modeling in Rock Mechanics, the use of which has become an important tool in hydrocarbon extraction applications, as well as in mining and civil works design. Eight leading practitioners of DFN modeling accepted our invitation and submitted articles in the form of technical notes or case histories. They will be published in two volumes, one in this newsletter, and the other in the upcoming Spring issue. ARMA member, Dr. Paul La Pointe, played a major role in securing the contributions you are invited to read. In addition to submitting a co-authored article, he also composed the Preface to this Special Issue. Bezalel Haimson

A series of laboratory drilling experiments were conducted on two arkosic sandstones (Tenino and Tablerock) under polyaxial far-field stress conditions (σ h  ≠ σ H  ≠ σ v ). V-shaped breakouts, aligned with the σ h direction and revealing stress-dependent dimensions (width and length), were observed in the sandstones. The microscale damage pattern leading to the breakouts, however, is different between the two, which is attributed to the difference in their cementation. The dominant micromechanism in Tenino sandstone is intergranular microcracking occurring in clay minerals filling the spaces between clastic grains. On the other hand, intra- and transgranular microcracking taking place in the grain itself prevails in Tablerock sandstone. To capture the grain-scale damage and reproduce the failure localization observed around the borehole in the laboratory, we used a discrete element (DE) model in which a grain breakage algorithm was implemented. The microparameters needed in the numerical model were calibrated by running material tests and comparing the macroscopic responses of the model to the ones measured in the laboratory. It is shown that DE modeling is capable of simulating the microscale damage of the rock and replicating the localized damage zone observed in the laboratory. In addition, the numerically induced breakout width is determined at a very early stage of the damage localization and is not altered for the rest of the failure process.

In the last 10 years, hydrofracturing has emerged as the most important technique for measuring stress in the earth's crust. Laboratory confirmation of the predicted hydrofracture orientation and of the theoretical stress-hydrofracturing pressure relationships, combined with very encouraging initial testing in oil fields, led to our first major scientific measurement, at Rangely, Colorado. The success of this test as part of an earthquake control experiment led to a number of additional hydrofracturings throughout the United States. To date, such tests have been conducted in nearly 20 states from California to South Carolina and from Idaho to Louisiana, within a depth range of 30–5100m. A pattern of principal stress direction and magnitude profile is beginning to emerge. It appears that throughout the United States all three principal stresses are compressive, with the major horizontal principal compression typically oriented in the north-eastern quadrant. Near the San Andreas fault the direction of the major horizontal principal stress is N15°E, in accord with the fault strike-slip characteristic. In the Sierra Nevada Mountains it becomes N25°E, gradually rotating to N35°E–N45°E in Nevada, and averaging N60°E east of the Rockies. At shallow depths (0–600m), both horizontal principal compressions are often larger than the vertical, notably in the Midwest and the Appalachians. At greater depths the predominant stress regime throughout the United States is one in which the vertical component is intermediate in magnitude. Only toward the lower end of the range of depths tested does the vertical component appear to approach the magnitude of the largest horizontal compressive stress. Linear regressions of all the hydrofracturing stress results throughout the United States with respect to depth yield high correlation coefficients and the following relationships: σHmin = 20 + 0.16D, σHmax = 75 + 0.24D, and σV = 0.25D, where σHmin, σHmax and σV are the least horizontal, largest horizontal, and vertical compressive stresses, respectively, measured in bars, and D is depth in meters (limited to 0–5000m). We compare hydrofracturing results with known overcoring stress measurements and with focal mechanism solutions.

► Two series of true triaxial tests conducted on the SAFOD granodiorite . ► In both tests rock strength increases with raising σ 2 for a given σ 3 . But unjacketed rock strength is 50% lower than jacketed one for the same σ 2 and σ 3 . ► Jacketed sample failed typically by forming a through-going shear fracture . But unjacketed sample failed by forming extensile cracks parallel to the σ 3 faces.

We conducted true triaxial compression tests on rectangular prismatic specimens (19×19×38 mm) of siltstone core extracted from a depth of 1252 m, some 140 m below the borehole intersection with the Chelungpu Fault, Taiwan. Experiments consisted of four series of tests in each of which σ3 was kept constant and σ2 was varied from test to test. The major principal stress (σ1), aligned with the long vertical side of the specimen, was raised at constant strain rate until a through-going, steeply dipping fault was initiated. As in igneous and metamorphic rocks previously tested, σ1 required to bring about faulting rose as σ2 was set at increasing levels above σ3. This observation reflects the significant contribution of σ2 to the compressive strength, and raises doubt about the suitability of the Mohr-Coulomb criterion. Rather, a strength criterion in terms of the invariants octahedral shear stress (τoct) as a function of mean stress (σoct) provides a good fit to the experimental data. In all tests fault strike was aligned with σ2 direction. The angle (or dip) θ of the fault was also strongly affected by σ2. For constant σ3 the angle rose with σ2, again departing from the Mohr-Coulomb criterion, which predicts a fault angle independent of the intermediate principal stress.

Wellbore instability often leads to failure in the form of breakouts, which are a major concern in the petroleum industry because they interfere with production and facilitate unwanted sanding. We report on two sets of experiments in which a high-porosity quartz sandstone was subjected to conditions inducing breakouts around boreholes. As in other quartz-rich sandstones, breakouts are not “dog eared” but rather tabular, long and very narrow. They resemble compaction bands that have been partially emptied. The apparent creation of compaction bands initiated by the borehole stress concentration constitutes an added concern, since such bands have diminished porosity and can impede the free flow of fluids through the sandstone.

This paper reviews the efforts made in the last 100 years to characterize the effect of the intermediate principal stress σ 2 on brittle fracture of rocks, and on their strength criteria. The most common theories of failure in geomechanics, such as those of Coulomb, and Mohr, disregard σ 2 and are typically based on triaxial testing of cylindrical rock samples subjected to equal minimum and intermediate principal stresses (σ 3=σ 2). However, as early as 1915 Böker conducted conventional triaxial extension tests (σ 1=σ 2) on the same Carrara marble tested earlier in conventional triaxial compression by von Kármán that showed a different strength behavior. Efforts to incorporate the effect of σ 2 on rock strength continued in the second half of the last century through the work of Nadai, Drucker and Prager, Murrell, Handin, Wiebols and Cook, and others. In 1971 Mogi designed a high-capacity true triaxial testing machine, and was the first to obtain complete true triaxial strength criteria for several rocks based on experimental data. Following his pioneering work, several other laboratories developed equipment and conducted true triaxial tests revealing the extent of σ 2 effect on rock strength (e.g., Takahashi and Koide, Michelis, Smart, Wawersik). Testing equipment emulating Mogi's but considerably more compact was developed at the University of Wisconsin and used for true triaxial testing of some very strong crystalline rocks. Test results revealed three distinct compressive failure mechanisms, depending on loading mode and rock type: shear faulting resulting from extensile microcrack localization, multiple splitting along the σ 1 axis, and nondilatant shear failure. The true triaxial strength criterion for the KTB amphibolite derived from such tests was used in conjunction with logged breakout dimensions to estimate the maximum horizontal in situ stress in the KTB ultra deep scientific hole.

To reveal details of stress perturbations associated with faults and fractures, we investigated the faults and large fractures accompanied by stress-induced borehole breakouts or drilling-induced tensile fractures in hole B of the Taiwan Chelungpu-fault Drilling Project (TCDP). Then, we determined the relationship between the faults and fractures and stress orientation changes. We identified faults and fractures from electrical images of the borehole wall obtained by downhole logging but also from photographs and descriptions of retrieved core samples, and measured the variations in the principal horizontal stress orientation ascertained from borehole breakouts observed on the electrical images in the vicinity of the faults and fractures. Identification of geological structures (faults, fractures, and lithologic boundaries) by electrical images only is difficult and may sometimes yield incorrect results. In a novel approach, therefore, we used both the electrical images and core photographs to identify geological structures. We found four patterns of stress orientation change, or no change, in the vicinity of faults and fractures in TCDP hole B: (i) abrupt (discontinuous) rotation in the vicinity of faults or fractures; (ii) gradual rotation; (iii) suppression of breakouts at faults, fractures, or lithologic boundaries; and (iv) no change in the stress orientation. We recognized stress fluctuations, that is, heterogeneous mesoscale (≥10cm) stress distributions with respect to both stress orientation and magnitude. In addition, we found that stress state changes occurred frequently in the vicinity of faults, fractures, and lithologic boundaries.