Simplified internal variable gradient model for zonal disintegration of rocks in circular underground tunnels

As one of the typical nonlinear phenomena of deep level surrounding rock masses, zonal disintegration has captured many attentions of geotechnical engineers in the past years. On the basis of the internal variable theory, the closed-form analytical solutions to stress, strain and displacement fields near circular tunnels are obtained. The gradient-dependent solutions are compared with the results of the classical elasticity theory, and the effects of microstructures on the stresses and deformation fields are investigated as well. It is noted that the stress and deformation fields derived from the gradient model show remarkable quasi-periodicity and fluctuation, which is consistent with the in-situ observation in the surrounding rock masses, in view of the influences of microstructures on macro behaviors. The influence of microstructures is reflected by the internal length scale. When the length scale of microstructure is comparable to the radius of circular openings, the effect of microstructure is large; when the microstructural length is much smaller than the scale of openings, the effect of microstructure is negligible. Combined with Mohr-Coulomb failure criterion, the location and width of surrounding rock failure zone of circular tunnel are estimated. The results show that surrounding rock fracture zones of circular tunnel increases with the increase of initial in-situ stress, and the failure range expands outwards. At last, the applicability of the proposed model is verified by comparing the predictions of the gradient model with the results of the laboratory test. The proposed gradient model provides an effective theoretical approach to explain zonal disintegration.