True Triaxial Strength Research Articles

True Triaxial Stresses and the Brittle Fracture of Rock

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 Boker conducted conventional triaxial extension tests (σ 1=σ 2) on the same Carrara marble tested earlier in conventional triaxial compression by von Karman 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.

Brittle fracture in two crystalline rocks under true triaxial compressive stresses

Abstract We employed our new polyaxial cell to carry out true triaxial compression tests on dry (jacketed) rectangular prisms of two crystalline rocks, in which different magnitudes of the least and intermediate principal stresses σ 3 and σ 2 were maintained constant, and the maximum stress σ 1 was increased to its peak level in strain control. Both Westerly granite (Rhode Island, USA) and KTB amphibolite (Bohemian Massif, Germany) revealed similar mechanical behaviour, much of which is missed in conventional triaxial tests in which σ 2 = σ 3 . Compressive failure in both took the form of a main shear fracture, or fault, steeply dipping in the σ 3 direction. Compressive strength rose significantly with the magnitude of σ 2 , suggesting that the commonly used Mohr-type strength criteria, which ignore the σ 2 effect, predict only the lower limit of rock strength. The true triaxial strength criterion for each of the crystalline rocks can be expressed as the octahedral shear stress at failure as a function of the mean normal stress acting on the fault plane. We found that the onset of dilatancy increases considerably for higher σ 2 . Thus, σ 2 extends the elastic range for a given σ 3 and, hence, retards the onset of the failure process. The main fracture dip angle was found to increase as σ 2 rises, providing additional confirmation of the strengthening effect of σ 2 . SEM inspection of the micromechanics leading to specimen failure showed a multitude of stress-induced microcracks localized on both sides of the through-going fault. Here too the effect of σ 2 is noted, in that microcracks gradually align themselves with the σ 1 -σ 2 plane as the magnitude of σ 2 is raised.

True triaxial strength of the KTB amphibolite under borehole wall conditions and its use to estimate the maximum horizontal in situ stress

Estimation of the maximum horizontal in situ stress from logged borehole‐breakout dimensions in brittle elastic rocks requires knowledge of the true triaxial compressive strength of the medium. We employed our true triaxial loading apparatus to determine the strength criterion of the nearly impermeable amphibolite penetrated by the German Continental Deep Drilling Program (KTB) superdeep scientific hole at depths of 3200–7800 m. To better simulate borehole wall conditions, we left one pair of the prismatic specimens' faces unjacketed and in direct contact with the confining fluid. This testing variation brings about a fundamentally different failure mechanism from that in fully jacketed (dry) specimens. Brittle fracture occurs at or soon after dilatancy onset and results from the development of densely spaced extensile fractures subparallel and adjacent to one of the unjacketed faces. We infer that the confining fluid intrudes newly opened microcracks, which are predominantly subparallel to the unjacketed faces, and promotes their elongation into throughgoing fractures. For any given least principal stress, the compressive strength typically increases with the rise in the intermediate principal stress. The true triaxial strength criterion of the unjacketed amphibolite can be expressed as a linear relationship between the octahedral shear stress and the octahedral normal stress at failure. Employing this criterion together with all the other known data from the KTB hole, we recomputed the magnitude of the maximum horizontal in situ stress there. Our results show that it increases steadily with depth, with a relatively narrow band of uncertainty, confirming previous assessments of a strike‐slip stress regime.

True triaxial strength and deformability of the German Continental Deep Drilling Program (KTB) deep hole amphibolite

We designed and fabricated a true triaxial loading system and used it to determine deformational and strength characteristics of the amphibolite penetrated by the superdeep hole drilled in the Bohemian massif of southeastern Germany under the German Continental Deep Drilling Program (KTB). Amphibolite is found between 3200 and 7300 m and thus the dominant rock in this 9100‐m boring. Our loading system enables the application of three unequal principal stresses to a rectangular prismatic rock specimen. During a test we maintained the least principal (σ3) and the intermediate (σ2) stresses constant and increased the major principal stress (σ1) until brittle failure occurred, in the form of a fracture steeply dipping in the σ3 direction. Typically, for the same σ3 level the amphibolite compressive strength increased substantially with the magnitude of σ2, demonstrating the inadequacy of Mohr‐like failure criteria that ignore the effect of the intermediate principal stress on rock strength. We found that a general criterion for the amphibolite could be expressed in the form of a power function relating the octahedral shear stress at failure to the mean normal stress acting on the plane containing the fracture. With respect to deformation, we established that for the same σ3 the onset of dilatancy increases significantly with the magnitude of σ2. Thus the intermediate principal stress appears to extend the elastic range of the stress‐strain behavior for a given σ3 and hence to retard the onset of the failure process. Scanning electron microscopy observations of the failure process reveal that microcracks develop mainly parallel to σ2 direction, as the intermediate stress grows beyond σ3, localizing in close proximity of the eventual main fracture.

A new true triaxial cell for testing mechanical properties of rock, and its use to determine rock strength and deformability of Westerly granite

Abstract A new true triaxial cell has been designed, fabricated, calibrated, and successfully tested. Its main feature is very high loading capability in all three orthogonal directions, enabling the testing to failure of hard crystalline rocks subjected to large least and intermediate principal stresses. All three principal stresses applied to rectangular prismatic specimens, 19×19×38 mm in size, are servo controlled. The cell was used to conduct an extensive series of tests in Westerly granite. A new true triaxial strength criterion for the rock was obtained that takes into account the effect of the intermediate principal stress. This turns out to be so significant that it raises serious questions about the suitability of criteria such as those named after Mohr, Coulomb, Griffith, and others. Measurements of strain in all three principal directions revealed that the onset of dilatancy relative to the major principal stress at failure rises substantially as the intermediate principal stress increases. The true triaxial tests also demonstrate that for the same least horizontal stress the main fracture dip angle in Westerly granite increases as a function of the intermediate principal stress, suggesting a strengthening effect. Limited thin section and SEM study shows that microcrack propagation, crack localization, and main fracture characteristics are basically similar to those observed in common triaxial tests.

Results of true triaxial strength tests on rock salt

Knowledge of the thermomechanical properties of rock salt is important for the dimensioning of a permanent repository for radioactive wastes in a salt dome and for the necessary safety analysis, as well as for the design of mines and caverns. Therefore, research is conducted by the BGR on the creep and failure behavior of rock salt. Equations have been derived which describe strength and creep under various conditions. They are needed mainly for finite element model calculations. A true triaxial test rig for cubic samples has been used to conduct several test series on different types of rock salt. The effects of varying hydrostatic (mean) stress, load path (load geometry), and temperature on strength and residual strength are discussed. Strength is defined as the maximum octahedral shear stress in a test. A failure law in the sense of a conservative strength limit has been developed for a typical rock salt on the basis of an extended Drucker-Prager law and the experimental results. The law describes the influence of mean stress, load path, and temperature on strength and residual strength.

Results of true triaxial strength tests on rock salt

Results of true triaxial strength tests on rock salt