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 tunnelsbelow a groundwater table under axial-symmetric conditions, considering the eects ofseepage and gravitational loads. in the proposed method, the strain-softening behaviormodel and hoek-brown failure criterion are used. to evaluate the eect of gravitationalloads and variations of pore pressure, the equations concerning dierent directions aroundthe tunnel (crown, wall and oor) are derived. since the derived dierential equations donot have a closed-form solution in the plastic zone, the numerical nite dierence methodis applied. considering the strain-softening behavior of the rock mass, the problem in theplastic zone is solved through a stepwise method, where the strength parameters of therock 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 theelastoplastic boundary to tunnel boundary values. furthermore, the closed-form analyticalsolutions are obtained for the elastic zone. the accuracy and application of the proposedmethod are demonstrated by a number of examples. the results well exhibit the eectsof dilatancy angle and increment of elastic strain in the plastic zone. based on the resultsobtained, ignoring the eects of gravitational loads and seepage will denitely producecomputational errors.