The influence of seepage and gravitational loads on elastoplastic solution of circular tunnels

In this paper, an elastoplastic model is proposed to analyze the circular tunnels below a groundwater table under axial-symmetric conditions, considering the eects of seepage and gravitational loads. In the proposed method, the strain-softening behavior model and Hoek-Brown failure criterion are used. To evaluate the eect of gravitational loads and variations of pore pressure, the equations concerning dierent directions around the tunnel (crown, wall and oor) are derived. Since the derived dierential equations do not have a closed-form solution in the plastic zone, the numerical nite dierence method is applied. Considering the strain-softening behavior of the rock mass, the problem in the plastic zone is solved through a stepwise method, where the strength parameters of the rock mass vary, step-by-step, from their maximum values to the constant values. Besides, the stresses, strains, and deformations of the rock mass also vary step-by-step from the elastoplastic boundary to tunnel boundary values. Furthermore, the closed-form analytical solutions are obtained for the elastic zone. The accuracy and application of the proposed method are demonstrated by a number of examples. The results well exhibit the eects of dilatancy angle and increment of elastic strain in the plastic zone. Based on the results obtained, ignoring the eects of gravitational loads and seepage will denitely produce computational errors.