Mechanical properties and progressive failure characteristics of sandstone containing elliptical and square openings subjected to biaxial stress

Two kinds of common tunnel shapes, i.e. elliptical opening and square opening were selected for biaxial compression tests, and the influences of two kinds of opening shapes on the mechanical properties, failure characteristics and failure modes of sandstone were compared and analyzed. The complex variable theory and mapping functions were used to obtain the analytical stress solution around elliptical and square openings. The results show that the stability of the specimen containing an elliptical opening was better than that of the specimen containing a square opening under the same lateral stress. Compared with the elliptical opening, the local damage was formed earlier in the square opening which might be caused by a higher stress concentration around the square opening. The stress distributions around openings were influenced by the opening shape and lateral stress coefficient. The top and bottom of square opening were more prone to tensile fracture, and the distribution range of tensile was larger than that of elliptical opening. When the opening failed, the intensity of square opening failure was weaker than that of elliptical opening. On the basis of the average frequency value and the rise angle value, the failure mode of specimen containing elliptical or square opening was distinguished. It was found that the mixed tension and shear failure dominated the failure of specimens with different opening shapes, and the number of shear cracks in the specimen containing a square opening was greater than that in the specimen containing an elliptical opening. The above method of judging failure mode by acoustic emission signals was well verified by the CT images of damaged specimens.

Solutions for Non-Newtonian Flow Into Elliptical Openings

A semi-analytical solution for plane velocity fields describing steady-state incompressible flow of nonlinearly viscous fluid into an elliptical opening is presented. The flow is driven by hydrostatic pressure applied at infinity. The solution is obtained by minimizing the rate of energy dissipation on a sufficiently flexible incompressible velocity field in elliptical coordinates. The medium is described by a power creep law and solutions are obtained for a range of exponents and ellipse eccentricites. The obtained solutions compare favorably with results of finite element analysis.