## 1 Introduction  
For brittle materials such as rock, tension failure is one of the most significant failure modes [1]. In a complex stress field of underground mining or geotechnical practice, tension damage/failure in rock masses is easily triggered and dominant because: (1) The tensile strength (\(\sigma_{t}\)) of rocks is much lower than their compressive strength, and (2) joints and fractures of rock mass can offer little resistance to tensile stress [2]. After an excavation is taken underground, tension failure and its induced fractures will occur in surrounding rock masses near the opening [3; 4; 5; 6; 7; 8]. The initiated fractures will develop/propagate and bring weakening effects on the rock masses under the effect of time and constant stress disturbance (development of entry or shaft, mining activities, etc.). As it is well established that the Young's modulus of a rock mass is directly related to the fracture or joint intensity [9; 10; 11; 12; 13], the aforementioned fracture development can be described as a Young's modulus degradation process in the view of an equivalent material method in continuum mechanics. The macroscopic mechanical behaviors of intact and jointed rocks have been widely investigated, most of which has been focused on the material behaviors in compression [14; 15; 16]. However, unlike metals or other materials, rocks are generally bi-modularity materials with different Young's moduli and Poisson's ratios in compression and tension. Previous studies done by direct tension tests showedthat the Young's modulus in tension (\(E_{t}\)) was always no larger than the compressive Young's modulus (\(E_{c}\)) [17; 18; 19; 20; 21]. [PERSON] et al. [17] conducted direct tension tests on different kinds of rocks, and the results showed that the ratio of \(E_{t}\)/\(E_{c}\) was 1/9 for Barre sandstone and 0.5 for Barre granite. [PERSON] and [PERSON] [20] acquired the ratios to be 0.5, 1.0, 0.7, and 0.3-0.4 for four different rocks from cyclic loading uniaxial tension and compression tests. Similar results were obtained by [PERSON] et al. [22] with an originally developed loading frame for direct tension. It has been addressed by researchers that the improper assumption that \(E_{t}\) equals to \(E_{c}\) may lead to errors in calculating stress distributions around underground openings by means of analytical or numerical analysis, as well as in determining the tensile strength of rocks with Brazilian tests [18; 20; 22; 23]. To date, it is still quite challenging to conduct direct uniaxial tension tests on intact rock specimens in laboratories due to the difficulties in avoiding: 1) Unfavorable stress concentration over the grip and 2) bending moments due to the non-coaxial gripping and curvature of the specimen. Various attempts have been made in this regard. [PERSON] and [PERSON] [20] conducted their tests on rock samples with a special hollow cylinder geometry. [PERSON] and [PERSON] [24] glued the rock samples directly to the loading platen to carry out direct tension tests. [PERSON] and [PERSON] [25] developed a direct tension apparatus with hard steel tension jaws to ensure the connection between samples and the apparatus and that the applied load is pure tension. [PERSON] and [PERSON] [26] developed a compression-to-tension load converter to determine the tensile strength and Young's modulus from dog-bone-shaped specimens. As described above, the Young's modulus estimation for jointed rocks and rock masses is essential for stability analysis. However, rock specimens with joints or fractures are difficult to be prepared, and simplifications have to be made with rock-like materials (such as gypsum) or simple notches. Furthermore, the uniaxial tension tests rely on specially made, non-universal apparatuses. In recent years, numerical and computational resources have taken significant leaps forward, and numerical methods have become strong and efficient research tools by overcoming the limitations in laboratory and physical tests.