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
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 quadril...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2022-08-01
|
| Series: | Journal of Rock Mechanics and Geotechnical Engineering |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1674775522000476 |
| _version_ | 1811221384282505216 |
|---|---|
| author | H.C. Nguyen L. Nguyen-Son |
| author_facet | H.C. Nguyen L. Nguyen-Son |
| author_sort | H.C. Nguyen |
| collection | DOAJ |
| description | 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 elements 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. |
| first_indexed | 2024-04-12T07:58:21Z |
| format | Article |
| id | doaj.art-018eb05112e54605b275362ed9e649d1 |
| institution | Directory Open Access Journal |
| issn | 1674-7755 |
| language | English |
| last_indexed | 2024-04-12T07:58:21Z |
| publishDate | 2022-08-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Journal of Rock Mechanics and Geotechnical Engineering |
| spelling | doaj.art-018eb05112e54605b275362ed9e649d12022-12-22T03:41:25ZengElsevierJournal of Rock Mechanics and Geotechnical Engineering1674-77552022-08-0114412531265A stable CS-FEM for the static and seismic stability of a single square tunnel in the soil where the shear strength increases linearly with depthH.C. Nguyen0L. Nguyen-Son1Department of Civil and Environmental Engineering, Imperial College London, London, UK; Department of Civil Engineering and Industrial Design, University of Liverpool, Liverpool, UK; Corresponding author. Department of Civil and Environmental Engineering, Imperial College London, London, UK.Faculty of Civil Engineering, Ho Chi Minh City University of Technology (HUTECH), Ho Chi Minh City, Viet NamA 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 elements 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.http://www.sciencedirect.com/science/article/pii/S1674775522000476TunnelsStabilityLimit analysisCell-based smoothed finite element method (CS-FEM)Second-order cone programming (SOCP) |
| spellingShingle | 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 Journal of Rock Mechanics and Geotechnical Engineering Tunnels Stability Limit analysis Cell-based smoothed finite element method (CS-FEM) Second-order cone programming (SOCP) |
| title | 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 |
| title_full | 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 |
| title_fullStr | 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 |
| title_full_unstemmed | 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 |
| title_short | 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 |
| title_sort | 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 |
| topic | Tunnels Stability Limit analysis Cell-based smoothed finite element method (CS-FEM) Second-order cone programming (SOCP) |
| url | http://www.sciencedirect.com/science/article/pii/S1674775522000476 |
| work_keys_str_mv | AT hcnguyen astablecsfemforthestaticandseismicstabilityofasinglesquaretunnelinthesoilwheretheshearstrengthincreaseslinearlywithdepth AT lnguyenson astablecsfemforthestaticandseismicstabilityofasinglesquaretunnelinthesoilwheretheshearstrengthincreaseslinearlywithdepth AT hcnguyen stablecsfemforthestaticandseismicstabilityofasinglesquaretunnelinthesoilwheretheshearstrengthincreaseslinearlywithdepth AT lnguyenson stablecsfemforthestaticandseismicstabilityofasinglesquaretunnelinthesoilwheretheshearstrengthincreaseslinearlywithdepth |