Rock masses without pre-existing macrocracks can usually be considered as granular materials with only microcracks.During the excavation of the tunnels, microcracks may nucleate, grow and propagate through the rock matrix; secondary microcracks may appear, and discontinuous and incompatible deformation of rock masses may occur. The classical continuum elastoplastic theory is not suitable for analyzing discontinuous and incompatible deformation of rock masses. Based on non-Euclidean model of the discontinuous and incompatible deformation of rock masses, the distribution of stresses in the surrounding rock masses in deep tunnels is fluctuant or wave-like. The stress concentration at the tips of microcracks located in vicinity of stress wave crest is comparatively large, which may lead to the unstable growth and coalescence of secondary microcracks, and consequently the occurrence of fractured zones. On the other hand, the stress concentration at the tips of microcracks located around stress wave trough is relatively small, which may lead to the arrest of microcracks, and thus the non-fractured zones. The alternate appearance of stress wave crest and trough thus may induce the alternate occurrence of fractured and non-fractured zones in deep rock masses. For brittle rocks, the dissipated energy of microcrack growth is small, but the elastic strain energy stored in rock masses may be larger than the dissipated energy growths of pre-existing microcracks and secondary microcracks. The sudden release of the residual elastic strain energy may lead to rockburst. Based on this understanding, the criteria of rockburst are established. Furthermore, the relationship between rockbursts and zonal disintegration in the surrounding rock masses around deep tunnels is studied. The influences of the in-situ stresses and the physico-mechanical parameters on the distribution of rockburst zones and the ejection velocity of rock fragments are investigated in detail.