# Failure in Confined Brazilian Tests on Sandstone
## 1 Introduction  
In the confined tension region, also referred to as the confined extension region, the minimum principal stress (\(\sigma_{3}\)) is tensile (taken as negative here) and the maximum principal stress (\(\sigma_{1}\)) is compressive (positive) (Figure 1). Strength of rocks in the confined tension region has only infrequently been measured and is not well understood [1, 2, 3, 4, 5]. In this region, as \(\sigma_{3}\) becomes increasingly tensile (negative), the failure mechanism transitions from frictional to purely tensile in the direct or uniaxial tension test. There are many important applications where the rock behavior in the confined tension region is of interest. Failures such as borehole breakouts and spalling and rockbursts can occur under confined tension stress states [6]. Interpretation of some natural fractures suggests they may form from confined tension stress conditions [1]. The extent of damage zones surrounding excavations is significantly affected by the tensile strength derived from tests conducted under confined tension conditions [7]. In addition, fluid pressure induced fracture, e.g., hydrofracturing, can occur under confined tension stress conditions. Strength criteria that include the confined tension region are required for the design and evaluation of structures of rock. The most common strength criteria used for rock, such as Mohr-Coulomb and Hoek-Brown, are developed from tests under compressive stress states. These criteria reflect the frictional processes from which the rock derives its strength under compressive stresses and are characterized by a positive correlation between the maximum (\(\sigma_{1}\)) and minimum principal stresses (\(\sigma_{3}\)); that is, \(\sigma_{1}\) increases with increasing \(\sigma_{3}\)[3]. When these criteria are extrapolated into the confined tension region, they generally do not successfully represent the strength under these stress conditions [2, 3, 4, 6]. A common approach is to extend the criterion into the confined tension region until a threshold stresscondition is reached beyond which the strength is set equal to the tensile strength of the rock. This is the tension cut-off approach [3; 8; 9]. In Figure 2, strength data from two sets of confined extension tests are presented. The figure also includes the strength data from other tests (unconfined compression, triaxial compression and direct tension), and the fitting of the Hoek-Brown criterion to these data. The figure illustrates that strength criteria developed from tests under compressive stresses do not successfully represent the strength in the confined tension region [2; 3; 4; 6]. Further, as illustrated in Figure 2b, the tension cut-off does not describe the strength data that have a \(\sigma_{3}\) less than the cut-off value as observed in some data obtained in the confined tension region. Finally, the data in the figures also reveal that the strength in biaxial compression obtained from confined extension tests and the strength from uniaxial compression can be substantially different [4]. It is obvious that the strength developed in the confined tension region is an important and unresolved issue. Strength data in the confined tension region are limited. The Brazilian tensile strength (BTS) test is the most common test in the confined tension region [4; 7]. However, BTS tests only follow one stress path (\(\sigma_{3}=-1/3\sigma_{1}\), \(\sigma_{2}=0\) at the sample center) and therefore cannot be used solely to characterize the confined tension region. Strength data in the confined tension region under a range of stress conditions can be generated from triaxial extension tests on dog bone samples at different confining pressures [1; 3; 10; 11; 12]. The samples are subjected to a compressive hydrostatic stress state from a confining pressure and axial force. The confining pressure is kept constant while gradually reducing the axial force, which eventually induces a tensile axial stress in the sample.