An Elastic Solution for Twin Circular Tunnels’ Stress in Hydrostatic Stress Field

In order to present an elastic solution for twin circular tunnels’ stress distribution in hydrostatic stress field, based on the complex variable theory and the superposition principle, the stress field of twin tunnels under static hydraulic pressure is decomposed into two parts: the original stress field and the secondary stress field. According to the symmetry of the structural form and the load distribution, the secondary stress filed can be simplifyed into a half-plane model. Therefore, the stress filed can be analyzed with the complex variable theory conveniently. Finally, the elastic solution of the twin tunnels under static hydraulic pressure is demonstrated by the superposition of the original stress field and the secondary stress field. In order to verify the analytical solution, a finite element model is adopted as the comparative test.. The result of the finite element simulation shows that the stress concentration at the middle rock wall is most obvious. And the stress concentration factor keeps increasing when the twin tunnels’ spacing distance and supporting pressure are decreasing. Besides, the maximum tangential stress appears at the tunnel boundary. The farther away from the tunnel’s boundary, the tangential stress gets lower. Furthermore, the supporting pressure leads to the increasing of radial stress and the decreasing of tangential stress. The analytical results are highly consistent with the numerical results with finite element method.