A new gradient elasticity model is employed to discuss strain gradient effects and its ability in predicting size effects on an elastic rock mass with microstructure, around an axisymmetric borehole under internal pressure and remote isotropic compressive stress. The constitutive equation of the model involves the Laplacian of the strain tensor multiplied by the gradient coefficient. The formulated boundary value problem is solved analytically to derive stress, strain, and displacement distributions and discuss respective gradient effects on the mechanical behavior of the rock mass and the corresponding borehole stability. The paper concludes with the employment of the Rankine failure criterion to investigate size effects on the stress concentration factor at the perimeter of the borehole, and the comparison with another gradient elasticity model which involves the Laplacian of the hydrostatic part of the strain tensor.
Nowadays, the demands of technology are very high for the thorough study of the mechanical behavior of materials. Although generalized theories of classical elasticity had been proposed in the 1960s they did not apply extensively to engineering problems because they provided a large number of phenomenological constants and the technology of that time did not require a detailed study of the effect of microstructure on elastic behavior and the corresponding stress analysis. The size effects (i.e. the strength of the specimen depends on its size), which related to the material microstructure and cannot be predicted by classical elasticity (CE), require the use of a generalized theory (or a non-local theory) such as gradient elasticity (GE) which introduces higher-order strain (or stress) gradients in the constitutive law. The GE can adequately describe the effect of the microstructure on the macro scale [1-4]. Since deformation is always non-uniform at the microstructural level, the influence of strain gradients in the macroscopic material behavior becomes increasingly important as the dimensions of the specimen decrease down to the micro and nanoscale. This, in turn, results in phenomena that usually are not observed in the macroscale including size-dependent strength and stress-strain responses. The size effects relate to the question of the transferability of mechanical test results of geometrically similar scaled-down structural models to the full-scale structures using similitude laws. They also concern about the validity of small-scale laboratory-type test results and their use as a basis for the computational modeling of large-scale components [5].