Rock mass generally exhibits time-dependent rheological properties, while the changes in pore water pressure induced by seepage flow have a significant effect on the time-dependent effective stress field of rheological rock mass. After certain simplification of the force field problem of a twin tunnel of arbitrary size and arrangement in a viscoelastic rock body under the influence of seepage, the complex function method, the Schwartz alternation method, and the elastic-viscoelastic correspondence principle were used to achieve an analytical solution of the problem of weakly coupled fluid-solid coupling, and the solution was given. In terms of mechanical mechanism, the solution reflected the surface force effect and flow effect of seepage on the force field. The analytical results were consistent with the numerical results and field measurements, which verified the correctness of the model. The analytical model provided a means to validate the numerical model, and also provided a quick analysis and determination method for the time-related stability problems of multi-tunnels in water-rich areas during the excavation and operation phases. Based on the analytical model, the effects of tunnel clearances and coefficients of viscosity on stress and displacement over time were analyzed. The results show that: Even considering the steady-state seepage condition, the effective stress of the rock masses increases over time. For cases with the same viscosity properties, the convergence rate of stresses is faster than displacements. In addition, the existence of seepage flow can significantly increase the interactions between twin tunnels. Specifically, the difference in stress compared to the single tunnel value is less than 10% when the pillar width is greater than 6.6 times the tunnel radius, however, it is 4 times for purely mechanical problems.
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