#### Description

Mogi’s (1971) seminal article on a new testing machine for conducting true triaxial experiments in rock included the first set of test results showing that failure (in the form of s1, peak) is a function of not only s3, but also of s2. However, Mogi’s pioneering work went seemingly unnoticed by the rock mechanics community. Some 30 years later, Haimson and colleagues (2000–2014) fabricated a similar loading system and employed it to determine true triaxial deformability and failure criteria in several crystalline and clastic rocks. The most important discovery enabled by true triaxial measurements was the effect of the intermediate principal stress s2, for given s3, on failure level s1, peak (it is at its lowest when s2 = s3), on fault-normal direction (always aligned with that of s3), on fault angle ? (? rises, as s2 increases, by up to 20° in crystalline rocks and up to 10° in clastics), and on deformability (the onset of dilatancy rises with s2). Haimson and Rudnicki (2010) complemented true triaxial experimental data on TCDP siltstone with results of shear band localization theory applied to fault angles observed for axisymmetric compression (Lode angle T = +30°) and deviatoric pure shear (T = 0°), to infer properties of the inelastic constitutive behavior. They employed these properties to predict ? for other Lode angles used during the experiments, yielding acceptable agreement with actual observations. The results were used to predict the angle variation for constant mean normal stress with increase in Lode angle, and for constant Lode angle with increasing mean normal stress. More recently, Ma et al. (2014) reported true triaxial experimental results in porous sandstones in which failure stress conditions and failure-plane angles were recorded and analyzed. The observed effect of s2 on both s1, peak and failure-plane angles was compared with Rudnicki (2013) theory. It was found that the theoretical predictions of failure-related s1, peak for given s3 replicated reasonably well actual test data, except for the two extreme magnitudes of s2, where predictions underestimated experimental data. With respect to failure-plane angles, Rudnicki’s theoretical prediction replicated the general rise of the experimentally observed ? with s2 for a given s3, as well as the diminished rise at high s3 magnitudes. The reasonable qualitative agreement between the predicted and the observed failure-plane angles demonstrated not only the applicability, but also the limitations of Rudnicki’s (2013) theory.

#### Recommended Citation

Haimson, B.
(2014).
True triaxial failure characteristics in rocks from granite to sandstone: experimental results and theoretical predictions – a review.
In A. Bajaj, P. Zavattieri, M. Koslowski, & T. Siegmund (Eds.).
*
Proceedings of the Society of Engineering Science 51st Annual Technical Meeting, October 1-3, 2014
*,
West Lafayette: Purdue University Libraries Scholarly Publishing Services, 2014.
https://docs.lib.purdue.edu/ses2014/honors/rudnicki/4

True triaxial failure characteristics in rocks from granite to sandstone: experimental results and theoretical predictions – a review

Mogi’s (1971) seminal article on a new testing machine for conducting true triaxial experiments in rock included the first set of test results showing that failure (in the form of s1, peak) is a function of not only s3, but also of s2. However, Mogi’s pioneering work went seemingly unnoticed by the rock mechanics community. Some 30 years later, Haimson and colleagues (2000–2014) fabricated a similar loading system and employed it to determine true triaxial deformability and failure criteria in several crystalline and clastic rocks. The most important discovery enabled by true triaxial measurements was the effect of the intermediate principal stress s2, for given s3, on failure level s1, peak (it is at its lowest when s2 = s3), on fault-normal direction (always aligned with that of s3), on fault angle ? (? rises, as s2 increases, by up to 20° in crystalline rocks and up to 10° in clastics), and on deformability (the onset of dilatancy rises with s2). Haimson and Rudnicki (2010) complemented true triaxial experimental data on TCDP siltstone with results of shear band localization theory applied to fault angles observed for axisymmetric compression (Lode angle T = +30°) and deviatoric pure shear (T = 0°), to infer properties of the inelastic constitutive behavior. They employed these properties to predict ? for other Lode angles used during the experiments, yielding acceptable agreement with actual observations. The results were used to predict the angle variation for constant mean normal stress with increase in Lode angle, and for constant Lode angle with increasing mean normal stress. More recently, Ma et al. (2014) reported true triaxial experimental results in porous sandstones in which failure stress conditions and failure-plane angles were recorded and analyzed. The observed effect of s2 on both s1, peak and failure-plane angles was compared with Rudnicki (2013) theory. It was found that the theoretical predictions of failure-related s1, peak for given s3 replicated reasonably well actual test data, except for the two extreme magnitudes of s2, where predictions underestimated experimental data. With respect to failure-plane angles, Rudnicki’s theoretical prediction replicated the general rise of the experimentally observed ? with s2 for a given s3, as well as the diminished rise at high s3 magnitudes. The reasonable qualitative agreement between the predicted and the observed failure-plane angles demonstrated not only the applicability, but also the limitations of Rudnicki’s (2013) theory.