Dynamic Response of Unlined Circular Tunnels Subjected to Internal Explosion

Due to the development of urban areas, underground structures are increasingly needed. Therefore, not only it is likely to have two tunnels located close to each other, but also it happens frequently.Because of the complexity of realistic problems, closed form analytical solutions are not accessible for them. However, latest advances in computational techniques have made numerical approaches more practical for realistic problems. Boundary element method (BEM) is one of such approaches. This technique formulates the problem in terms of boundary values. The main advantage of BEM, especially in comparison with finite element and finite difference methods, is that the discretization is only applied to the boundary, thus reducing the volume of modeling and the number of unknown variables. Moreover, the radiation condition at infinity is exactly satisfied in this method which is very striking for wave propagation problems. First the formulation of boundary element method in the time domain is presented and then a parametric study on the dynamic response of unlined circular tunnels subjected to internal explosion is done. Depth of tunnels, vertical and horizontal distance between two tunnels, diameter of tunnels, and other parameters related to geometry are important factors which can affect displacements and stresses of tunnels under explosive loading. In the present study, effect of two parameters has been investigated: changing the depth of the tunnel that is subjected to internal explosion (case A) and changing the horizontal distance between two shallow tunnels subjected to explosion (case B). Radial displacements and circumferential stresses are the results obtained. Case A- Tunnel depth: The tunnel behavior in depth of H=50R is alike to behavior of same tunnel in infinite depth. Also, radial displacement in upper point of tunnel in depth of H=2R is about 2.7 times of the same tunnel in infinite depth. Circumferential stress in points placed on horizontal diameter of tunnel in depth of H=2R is about 1.8 times of the same tunnel in infinite depth. Case B- Tunnels distance: Two tunnels with horizontal distance of greater than L=50R don’t affect each other. When horizontal distance parameter of two tunnels is L=2.5R then the maximum normalized displacement of the side point of the loaded tunnel, is approximately 2.15 times of the same tunnels with distance of infinite. Also, when horizontal distance of two tunnels is L=2.5R, circumferential stress in lower point of the loaded tunnel, which is normalized with static stress, is approximately 1.2 times of the same tunnels with distance of infinite. Normalized results calculated here display the importance of the geometric parameters on the behavior of unlined tunnels subjected to internal explosion and provide suitable criteria for displacement design of shallow tunnels that are subjected to internal explosion. The accuracy of the present study for the computation of radial displacements and circumferential stresses is verified by solving several problems.