Stability of Unsupported Vertical Circular Excavations
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 140, Issue 7
Abstract
A methodology has been presented for determining the stability of unsupported vertical cylindrical excavations by using an axisymmetric upper bound limit analysis approach in conjunction with finite elements and linear optimization. For the purpose of excavation design, stability numbers () have been generated for both (1) cohesive-frictional soils and (2) pure cohesive soils, with an additional provision accounting for linearly increasing cohesion with increasing depth by means of a nondimensional factor . The variation of with has been established for different values of and , where and refer to the height and radius of the cylindrical excavation. A number of useful observations have been gathered about the variation of the stability number and nodal velocity patterns as , , and change. The results of the analysis compare quite well with the different solutions reported in the literature.
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References
Bishop, A. W. (1966). “The strength of soils as engineering materials.” Geotechnique, 16(2), 91–130.
Bjerrum, L., and Eide, O. (1956). “Stability of strutted excavation in clay.” Geotechnique, 6(1), 32–47.
Bottero, A., Negre, R., Pastor, J., and Turgeman, S. (1980). “Finite element method and limit analysis theory for soil mechanics problem.” Comput. Methods Appl. Mech. Eng., 22(1), 131–149.
Britto, A., and Kusakabe, O. (1982). “Stability of unsupported axisymmetric excavations in soft clay.” Geotechnique, 32(3), 261–270.
Britto, A., and Kusakabe, O. (1983). “Stability of axisymmetric excavations in clays.” J. Geotech. Engrg., 666–681.
Cox, A. D., Eason, G., and Hopkins, H. G. (1961). “Axially symmetric plastic deformation in soils.” Philos. Trans. R. Soc. London, Ser. A, 254(1036), 1–45.
Griffiths, D. V., and Koutsabeloulis, N. (1985). “Finite element analysis of vertical excavations.” Comput. Geotech., 1(3), 221–235.
Haar, A., and von Kármán, Th. (1909). “Zur Theorie der Spannungszustände in plastischen und sandartigen Medien.” Nachr. Ges. Wiss. Göttingen, Math.-Phys. Kl., 204–218.
Houlsby, G. T., and Wroth, C. P. (1982). “Direct solution of plasticity problems in soils by the method of characteristics.” Proc., 4th Int. Conf. on Numerical Methods in Geomechanics, Edmonton, AB, Canada, 3, 1059–1071.
Khatri, V. N., and Kumar, J. (2010). “Stability of an unsupported vertical circular excavation in clays under undrained condition.” Comput. Geotech., 37(3), 419–424.
Kumar, J., and Chakraborty, D. (2012). “Stability numbers for an unsupported vertical circular excavation in soil.” Comput. Geotech., 39, 79–84.
Kumar, J., and Kouzer, K. (2007). “Effect of footing roughness on bearing capacity factor .” J. Geotech. Geoenviron. Eng., 502–511.
Lyamin, A. V., and Sloan, S. W. (2002). “Upper bound limit analysis using linear finite elements and non-linear programming.” Int. J. Numer. Anal. Methods Geomech., 26(2), 181–216.
MATLAB 7.8.0 (R2009a) [Computer software]. Natick, MA, MathWorks.
Pastor, F., Kondo, D., and Pastor, J. (2013). “3D-FEM formulations of limit analysis methods for porous pressure-sensitive materials.” Int. J. Numer. Methods Eng., 95(10), 847–870.
Pastor, F., Loute, E., and Pastor, J. (2009). “Limit analysis and convex programming: A decomposition approach of the kinematic mixed method.” Int. J. Numer. Methods Eng., 78(3), 254–274.
Pastor, J. (1981). “Analyse limite et stabilité des fouilles.” Proc., 10th Int. Conf. on Soil Mechanics and Foundation Engineering, Balkema, Rotterdam, Netherlands, 505–508.
Pastor, J., Thore, Ph., and Pastor, F. (2010). “Limit analysis and numerical modelling of spherically porous solids with Coulomb and Drucker Prager matrices.” J. Comput. Appl. Math., 234(7), 2162–2174.
Pastor, J., and Turgeman, S. (1982). “Limit analysis in axisymmetrical problems: Numerical determination of complete statical solutions.” Int. J. Mech. Sci., 24(2), 95–117.
Prater, E. G. (1977). “An examination of some theories of earth pressure on shaft linings.” Can. Geotech. J., 14(1), 91–106.
Sahoo, J. P., and Kumar, J. (2012). “Seismic stability of a long unsupported circular tunnel.” Comput. Geotech., 44, 109–115.
Shield, R. T. (1955). “On the plastic flow of metals under conditions of axial symmetry.” Proc. R. Soc. London, Ser. A, 233(1193), 267–287.
Sloan, S. W., and Kleeman, P. W. (1995). “Upper bound limit analysis using discontinuous velocity fields.” Comput. Methods Appl. Mech. Eng., 127(1–4), 293–314.
Turgeman, S., and Pastor, J. (1982). “Limit analysis: a linear formulation of the kinematic approach for axisymmetrical mechanic problems.” Int. J. Numer. Anal. Methods Geomech., 6(1), 109–128.
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Published In
Journal of Geotechnical and Geoenvironmental Engineering
Volume 140 • Issue 7 • July 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Sep 25, 2013
Accepted: Feb 19, 2014
Published online: Mar 21, 2014
Published in print: Jul 1, 2014
Discussion open until: Aug 21, 2014
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