A numerical procedure using a stable cell-based smoothed finite element method(CS-FEM)is presented for estimation of stability of a square tunnel in the soil where the shear strength increases linearly with depth.The kinematically admissible displacement fields are approximated by uniform quadrilateral el-ements in conjunction with the strain smoothing technique,eliminating volumetric locking issues and the singularity associated with the Mohr-Coulomb model.First,a rich set of simulations was performed to compute the static stability of a square tunnel with different geometries and soil conditions.The presented results are in excellent agreement with the upper and lower bound solutions using the standard finite element method(FEM).The stability charts and tables are given for practical use in the tunnel design,along with a newly proposed formulation for predicting the undrained stability of a single square tunnel.Second,the seismic stability number was computed using the present numerical approach.Numerical results reveal that the seismic stability number reduces with an increasing value of the horizontal seismic acceleration(αh),for both cases of the weightless soil and the soil with unit weight.Third,the link between the static and seismic stability numbers is described using corrective factors that represent reductions in the tunnel stability due to seismic loadings.It is shown from the numerical results that the corrective factor becomes larger as the unit weight of soil mass increases;however,the degree of the reduction in seismic stability number tends to reduce for the case of the homogeneous soil.Furthermore,this advanced numerical procedure is straightforward to extend to three-dimensional(3D)limit analysis and is readily applicable for the calculation of the stability of tunnels in highly anisotropic and heterogeneous soils which are often encountered in practice.

H.C. Nguyen;L. Nguyen-Son

Department of Civil and Environmental Engineering,Imperial College London,London,UK;Department of Civil Engineering and Industrial Design,University of Liverpool,Liverpool,UK;Faculty of Civil Engineering,Ho Chi Minh City University of Technology(HUTECH),Ho Chi Minh City,Viet Nam

岩石力学与岩土工程学报（英文版）

[1]H.C. Nguyen;L. Nguyen-Son-.A stable CS-FEM for the static and seismic stability of a single square tunnel in the soil where the shear strength increases linearly with depth)[J].岩石力学与岩土工程学报（英文版）,2022(04):1253-1265

kinematically,weightless

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