This paper presents an elastic analytical solution to a circular tunnel with releasing slots at high stress areas near the hole by using a conformal mapping method and the complex variable theory. Compared to the original stress distribution around the circular hole, the releasing effect on elastic stresses is evaluated. After grooving slots, low stress area is generated where the high stress concentration is located. This is agreeable with what was predicted by the finite difference FLAC2D. Besides, displacements are obtained along the periphery of the released hole and are in accordance with those of FLAC2D. In addition to the intersection of the mapping contour, the influences of the sampling points distribution, series number in mapping function, and slot shape are discussed. It is inevitable that the mapping accuracies for the slot and the circle cannot be satisfied at the same time The mapping effect on the circle has to be considered primarily since the stress distribution around the circle is much more significant than the tunnel stability. The analytical solution can be available and fast method of estimating the releasing effect of the application on the tunnel without rock parameters.
Discussion: Elastic solutions for a deep circular tunnel
