## 6 The Extension Strain Criterion as a Macroscopic Rock Sample Failure Condition
### Discussion of the Results  
As can be noted, the extension strain \(\varepsilon_{\rm TC}\) values obtained in the UCS and Brazilian tests differ significantly. In the case of UCS, the value falls within the interval of \(\varepsilon_{\rm TC}=-0.003\div-0.004\), while the Brazilian test value range is \(\varepsilon_{\rm TC}=-0.002\div-0.003\). Considering the results of triaxial tests, the limiting value of the extension strain additionally depends on the confining pressure, i.e., it is pressure sensitive. This conclusion was also confirmed in a study by [PERSON] and [PERSON] [15]. However, it should be borne in mind that the extension strain criterion is dedicated to stress conditions corresponding to low confinement conditions. Therefore, its use may be limited to complex stress conditions up to a certain confining pressure \(p\). Deformations are constant up to a limit below \(p=10\) MPa, as was shown by [PERSON] et al. [30]. Figure 9: The extension strain criterion values (**a**) schematically based on the radial strain plots of the specimens in the UCS test or (**b**) resulting from the Brazilian, UCS, and triaxial compression tests. In addition to these remarks, it should be noted that the values obtained here are completely different from those for [PERSON]'s condition. Both conditions, although mathematically similar from the physical point of view, describe completely different phenomena. The Use of the Extension Strain Criterion to Evaluate the Fracture Initiation in a Sandstone Sample Subjected to Tension in the Brazilian Test  
The possibility of using the extension strain criterion to assess fracture initiation ([PERSON]'s condition) was presented with reference to the results of the Brazilian test. The results of DIC analysis were used for this purpose (Figure 10a-c). Since the Brazilian test was conducted in a servo-controlled testing machine under the control of constant horizontal displacements of the measuring base (Figure 1a), it was possible to determine the full pre- and post-failure path of the specimen (Figure 10d). Noteworthy are the extreme values of the extension strain \(\varepsilon_{\text{xx}}\) (positive values) and their location (Figure 10). At a low load level of about \(0.63\sigma_{\text{T}}\), in the central part of the disk in the direction of the load action, the highest values of these strains are concentrated around \(\varepsilon_{\text{xx}}=1\times 10^{-3}\). Considering the load level, they are relatively high and exceed the fracture initiation criterion as proposed by [PERSON] (Table 3). It can be assumed that in the case of the sandstone under analysis, even before the tensile strength of the specimen was reached, the fracture initiation process had already begun. This is also indicated by the non-linear characteristics of the specimens in the Brazilian test (Figure 2a). For the load corresponding to tensile strength \(\sigma_{\text{T}}\), the values of the determined deformations are higher than \(\varepsilon_{\text{xx}}=3.5\times 10^{-3}\). Their extremum is not located in the centre of the sample but shifted towards the loading platens (Figure 10b). The extremum of deformations at this level of loading exceeds the values of [PERSON]'s criterion by many times, as confirmed by the fact that the first cracks had already been observed before the maximum load was reached. In the post-acting load phase (Figure 10c), deformations are determined based on the macro fracture. Figure 10: Maps of the horizontal strain on the surface of a rock disk in the Brazilian test at three loading levels, i.e., (**a**) \(0.63\sigma_{\text{T}}\), (**b**) \(\sigma_{\text{T}}\), and (**c**) in the post-failure loading phase, and (**d**) characteristics of the Brazilian test. The Application of the Extension Strain Criterion to Evaluate the Microscopic Failure of a Rock Sample in the Simple Shear Test  
The possibility of using the extension strain criterion was also presented to evaluate the macroscopic failure of a sandstone sample subjected to simple shear.