Dynamic response of twin closely-spaced circular tunnels to harmonic plane waves in a full space

An analytical solution for dynamic stress concentration of twin closely-spaced circular tunnels to plane P and SV waves in a full space is derived by the complex variable method in elastodynamics. Using the Helmholtz decomposition, the scattered wave fields by two circular cavities are expressed by wave function expansions. The complex variable method, the conformal transformation and the pertinent boundary conditions are jointly employed to develop an exact mathematical solution of the corresponding boundary value problem. The convergence of the present method is verified by the variation of the amplitude of the dynamic stress concentration factor of the cavities with the truncation of the series number. The influences of the space between two tunnels and the frequency of the incident waves on the dynamic stress concentration along the cavity walls are examined by the proposed solution. Numerical results show that they have considerable influence on the dynamic responses of the tunnel walls.

► An analytical solution for dynamic response of twin circular tunnels is derived.
► A conformal mapping function is introduced to formulate the boundary value problem.
► The convergence of the present method is verified.
► A parametric investigation is conducted.