This study focuses on the stress and displacement of a circular opening that is excavated in a strain-softening rock mass under hydraulic-mechanical coupling.It follows the generalized Hoek-Brown(H-B) failure criterion.Moreover,an improved numerical method and stepwise procedure are proposed.This method considers the deterioration of the strength,deformation,and dilation angle.It also incorporates the hydraulic-mechanical coupling and the variation of elastic strain in the plastic region.Several examples are conducted to demonstrate the validity and accuracy of the proposed solution through MATLAB programming and FLAC software.Parametric studies are also conducted to highlight the influence of hydraulic–mechanical coupling on stress and displacement.Results show that in this case,stress confinement is lower and tunnel convergences are higher than the corresponding stresses and displacements obtained when those factors are not considered.The displacement and plastic radius are also larger than those obtained when hydraulic-mechanical coupling is not considered.
Abstract.Similarity solution is investigated for the synchronous grouting of shield tunnel under the vertical non-axisymmetric displacement boundary condition in the paper.The synchronous grouting process of shield tunnel was simplified as the cylindrical expansion problem,which was based on the mechanism between the slurry and stratum of the synchronous grouting.The stress harmonic function on the horizontal and vertical ground surfaces is improved.Based on the virtual image technique,stress function solutions and Boussinesq’s solution,elastic solution under the vertical non-axisymmetric displacement boundary condition on the vertical surface was proposed for synchronous grouting problems of shield tunnel.In addition,the maximum grouting pressure was also obtained to control the vertical displacement of horizontal ground surface.The validity of the proposed approach was proved by the numerical method.It can be known fromthe parameter analysis that larger vertical displacement of the horizontal ground surface was induced by smaller tunnel depth,smaller tunnel excavation radius,shorter limb distance,larger expansion pressure and smaller elastic modulus of soils.
The out-of-plane stress is sometimes the major or intermediate principal stress in a circular tunnel opening.The influences of the outof-plane stress and axial strain are often neglected in the stability analyses of tunnel excavation,which can induce significant errors in the determination of surrounding rock deformations.In this paper,the use of a simple approach is proposed to solve the quasi-plane-strain problem of circular tunneling considering the effect of the out-of-plane stress,which is deformation-dependent and influenced by the in situ stress.As the intermediate principal stress is deformation-dependent,to obtain the numerical solution of the intermediate principal stress,the quasi-plane-strain problem is defined based on assumptions that the initial axial total strain is a nonzero constant(e0)and that the axial plastic strain is nonzero.With the numerical solution for the plastic strain,obtained using the plastic potential functions based on the three-dimensional failure criteria,the formula for the intermediate principal stress can be derived using Hooke’s law.The proposed approach can be utilized to obtain the numerical solution for the intermediate principal stress,which is deformationdependent,and the numerical results can be simplified as the solution presented by Pan and Brown.The proposed approach can also be used to obtain the solution for the strain softening of the surrounding rock.To verify its validity and accuracy,the results obtained using the proposed approach are compared with the solution of Pan and Brown.In addition,parametric studies are performed to address the influences of the out-of-plane stress on the stress and displacement in the circular tunnel.
Large amount of groundwater discharging from tunnel is likely to cause destruction of the ecological environment in the vicinity of the tunnel, thus an appropriate drainage criterion should be established to balance the tunnel construction and groundwater.To assess the related problems, an limiting drainage standard ranging from 0.5 to 2.0 m3/(m·d) was suggested for mountain tunnels based on survey and comparative analysis. After that, for the purpose of verifying the rationality of the standard, a calculated formula for dewatering funnel volume caused by drainage was deduced on the basis of the groundwater dynamics and experience method.Furthermore, the equation about the relationship between water discharge and drawdown of groundwater table was presented. The permeability coefficient, specific yield and groundwater table value were introduced, and then combined with the above equation, the drawdown of groundwater table under the proposed limiting drainage criterion was calculated. It is shown that the proposed drainage standard can reach the purpose of protecting ecological environment under the following two conditions. One is the permeability coefficient ranges from 10-4 to 10-5 m/s and the specific yield ranges from 0.1 to 0.001. The other is the permeability coefficient varies from 10-6 to 10-8 m/s and the specific yield varies from 0.1 to 0.01. In addition, a majority of common geotechnical layers are involved in the above ranges. Thus, the proposed limiting drainage standard which ranges from 0.5 to 2.0 m3/(m·d) for mountain tunnel is reasonable.
