## 1 Introduction  
The extension strain criterion condition first appeared in a publication by [PERSON] [1], according to whom the initiation of the rock fracture process can be predicted by tracking extension strains under appropriate stress conditions. As [PERSON] pointed out, while this condition depends on the rock type for the occurrence of crack initiation, the state of stress--low confinement in the vicinity of excavations in the rock--is also very important. It should be noted that this condition is dedicated to strong and brittle rocks. The criterion has been used repeatedly to evaluate crack initiation in tunnel walls in strong rocks [2; 3; 4] and to describe the excavation damage zone and the Aspo pillar stability [5]. The extension strain criterion can explain the reason why rock spalling begins in the tunnel wall when the compressive stress in the wall reaches approximately 0.4 times the uniaxial compressive strength (UCS) of the rock [3]. This phenomenon in tunnels has been observed and recorded numerous times [3; 6; 7; 8; 9; 10]. It should be noted that spalling phenomena are specific, as the conditions for their occurrence are unique, and the rupture process is local. The extension strain criterion has also been used to analyse the stability of large-diameter boreholes in radioactive waste disposal sites, [11] wellbore stability [12], as well as to explain slabbing phenomena in strong pillars, the thighs of underground galleries, and colluviums [9], or ultimately to explain natural vertical fractures in mountain peaks [6]. Since the extension strain criterion, as given by [PERSON], mainly refers to the fracture process, when identifying it, various authors generally use tensile or uniaxial compression tests where the phenomena of cracking or axial splitting are dominant and visible even before the limiting strength is reached. In identifying this condition, one can also find attempts at inverse analyses [5] or calibration on in situ observations and measurements [13]. However, the extension strain criterion has also been treated as a classical strength condition [14; 15; 16], describing the macroscopic failure of rock samples under saline stress conditions. Then, tensile, uniaxial and triaxial compression tests, and extreme extension strain values corresponding to the strength limit of rock samples are used to determine this condition. In summary, two forms of the extension strain criterion can be noted, the first being applied to describe the initiation of the fracture process locally, i.e., at the micro level, as suggested by [PERSON] [1], and the second serving as a failure criterion at the macroscopic level of the rock sample. Therefore, the experimental identification of the condition is based on various experiments that produce different results. The identification method proposed by [PERSON] is based on uniaxial compression tests and on tracking transverse deformation in rock samples. The crack initiation threshold has been studied by many researchers and determined by other methods, such as crack volumetric strain [17; 18] or Poisson's ratio [18]. Nevertheless, the first method to determine the threshold corresponding to the initiation of micro-cracking was proposed by [PERSON] [19] who recommended volumetric strain analysis in rocks. Tensile tests of rock samples are another very popular method for identifying crack initiation conditions. There are multiple methods of testing rocks under tensile conditions [20] yielding different results [21]. Depending on the rock type, the lowest values are obtained from the direct tension test, while the Brazilian test provides higher values. Due to its simplicity, the latter constitutes the most popular rock tension test. The methodology for conducting the Brazilian test is very important because different results are obtained with different loading patterns [20]. Although several Brazilian loading schemes are recommended, depending on the rock type, various failure mechanisms of specimens and tensile strength values can occur.