The Influence of Seepage and Gravitational Loads on Elastoplastic Solution of Circular Tunnels


1 Department of Civil and Environmental Engineering, Amirkabir University of Technology, ‎ ‎ Tehran, Iran

2 Department of Civil Engineering, Tafresh University, Tafresh, Iran

3 Deaprtment of Civl Engineering, Tafresh University, Tafresh, Iran‎


In this paper, an elastoplastic model is proposed to analyze the circular tunnels below the groundwater table under axial-symmetric condition, considering the effects of seepage and gravitational loads. In the proposed method, the strain-softening behavior model and Hoek-Brown failure criterion are used. To evaluate the effect of gravitational loads and variations of pore pressure, the equations concerning different directions around the tunnel (crown, wall, and floor) are derived. Since, the derived differential equations do not have closed-form solution in the plastic zone, the numerical finite difference 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 varies 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 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 is demonstrated by a number of examples. The results well exhibited the effects of dilatancy angle and increment of elastic strain in the plastic zone. Based on the results obtained, ignoring the effects of gravitational loads and seepage will definitely produce computational errors.