To investigate the failure behaviour of the stress concentration areas of deeply buried hard rock tunnels, model tests under uniaxial and biaxial loading conditions and a single-free-face true triaxial compression (TTC) test were carried out on Beishan granite. The failure forms of the specimens under the above three loading conditions are different: under the first loading condition, the model specimen was prone to tensile fracturing at the tensile stress concentration the at top and bottom of the hole, which is similar to splitting along a road tunnel; under the second loading condition, the sidewall of the model specimen was progressively damaged and ultimately formed breakout notches, which is similar to spalling failure in deep engineering; under the third loading condition, the prismatic specimen underwent a slight strain burst. Since the failure of the specimen under the latter two loading conditions was induced by compressive stress concentrations, the reasons for the difference in the failure behaviours of the specimens in these two types of tests were discussed. It was found that the intrinsic potential energy (Wbk) of the rock determines the failure form of the specimen. For rock model tests with lateral stress, rock with a high Wbk fails by strain bursting, and rock with a low Wbk fails by spalling. However, for intact rock specimens under single-free-face TTC, a low Wbk can induce strain bursts. The outcome of this research could be applied to rock failure behaviour analysis around underground excavations in deep hard rock engineering.