Lower-Bound Finite Elements Limit Analysis for Hoek-Brown Materials Using Semidefinite Programming
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VIEW THE REPLYPublication: Journal of Engineering Mechanics
Volume 143, Issue 9
Abstract
The lower-bound finite elements limit analysis in combination with semidefinite programming (SDP) has been used to solve stability problems involving a modified Hoek-Brown (HB) yield criterion with the exponent . In order to demonstrate the applicability of the proposed computational approach, bearing capacities of strip and circular foundations on rock mass have been determined. The results have been given in the form of nondimensional bearing capacity factors as a function of different material input parameters. By comparing the results obtained from the present analysis with that reported in literature, it is noted that the proposed approach remains quite accurate and is highly efficient to deal with any large-scale optimization problem. The method does not require any kind of the smoothing of the yield surface and it can even be implemented to deal with any three-dimensional problem as well.
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References
Alizadeh, F. (1995). “Interior point methods in semidefinite programming with applications to combinational optimization.” SIAM J. Optim., 5(1), 13–51.
Andersen, E. D., Roos, C., and Terlaky, T. (2003). “On implementing a primal-dual interior-point method for conic quadratic optimization.” Math. Program., 95(2), 249–277.
Chakraborty, D., and Kumar, J. (2014). “Solving axisymmetric stability problems by using upper bound finite elements, limit analysis, and linear optimization.” J. Eng. Mech., 06014004.
Chakraborty, M., and Kumar, J. (2015). “Bearing capacity of circular footings over rock mass by using axisymmetric quasi lower bound finite element limit analysis.” Comput. Geotech., 70, 138–149.
Clausen, J. (2013). “Bearing capacity of circular footings on a Hoek-Brown material.” Int. J. Rock Mech. Min. Sci., 57, 34–41.
Clausen, J., and Damkilde, L. (2008). “An exact implementation of the Hoek-Brown criterion for elasto-plastic finite element calculations.” Int. J. Rock Mech. Min. Sci., 45(6), 831–847.
Hoek, E., and Brown, E. T. (1980). “Empirical strength criterion for rock masses.” J. Geotech. Eng. Div., 106(GT9), 1013–1035.
Hoek, E., and Brown, E. T. (1988). “The Hoek–Brown failure criterion—A 1988 update.” Rock Engineering for Under-Ground Excavations, Proc., 15th Canadian Rock Mech. Symp., Univ. of Toronto, Toronto, 31–38.
Hoek, E., and Brown, E. T. (1997). “Practical estimates of rock mass strength.” Int. J. Rock Mech. Min. Sci., 34(8), 1165–1186.
Hoek, E., Carranza-Torres, C., and Corkum, B. (2002). “Hoek–Brown failure criterion—2002 edition.” Proc., 5th North American Rock Mechanics Symp. and the 17th Tunnelling Association of Canada Conf.: NARMS-TAC, Toronto.
Krabbenhoft, K., and Damkilde, L. (2003). “A general non-linear optimization algorithm for lower bound limit analysis.” Int. J. Numer. Methods Eng., 56(2), 165–184.
Krabbenhoft, K., Lyamin, A. V., and Sloan, S. W. (2007). “Formulation and solution of some plasticity problems as conic programs.” Int. J. Solids Struct., 44(5), 1533–1549.
Krabbenhoft, K., Lyamin, A. V., and Sloan, S. W. (2008). “Three dimensional Mohr-Column limit analysis using semidefinite programming.” Commun. Numer. Methods Eng., 24(11), 1107–1119.
Kumar, J., and Chakraborty, M. (2014). “Upper-bound axisymmetric limit analysis using the Mohr-Coulomb yield criterion, finite elements, and linear optimization.” J. Eng. Mech., 06014012.
Kumar, J., and Khatri, V. N. (2011). “Bearing capacity factors of circular foundations for a general soil using lower bound finite elements limit analysis.” Int. J. Numer. Anal. Methods Geomech., 35(3), 393–405.
Li, A. J., Merifield, R. S., and Lyamin, A. V. (2008). “Stability charts for rock slopes based on the Hoek-Brown failure criterion.” Int. J. Rock. Mech. Min. Sci., 45(5), 689–700.
Lyamin, A. V., and Sloan, S. W. (2002). “Lower bound limit analysis using non-linear programming.” Int. J. Numer. Methods Eng., 55(5), 573–611.
Lyamin, A. V., Yu, H. S., Sloan, S. W., and Hossain, M. Z. (1998). “Lower bound limit analysis for jointed rocks using the Hoek-Brown yield criteria.” Austr. Geomech. J., 33(1), 46–62.
Makrodimopoulos, A., and Martin, C. M. (2006). “Lower bound limit analysis of cohesive frictional materials using second-order cone programming.” Int. J. Numer. Methods Eng., 66(4), 604–634.
Makrodimopoulos, A., and Martin, C. M. (2007). “Upper bound limit analysis using simplex strain elements and second-order cone programming.” Int. J. Numer. Anal. Methods Geomech., 31(6), 835–865.
Martin, C. M., and Makrodimopoulos, A. (2008). “Finite element limit analysis of Mohr-Coulomb material in 3D using semidefinite programming.” J. Eng. Mech., 339–347.
MATLAB [Computer software]. MathWorks, Natick, MA.
Merifield, R. S., Lyamin, A. V., and Sloan, S. W. (2006). “Limit analysis solutions for the bearing capacity of rock masses using the generalized Hoek-Brown yield criterion.” Int. J. Rock. Mech. Min. Sci., 43(6), 920–937.
MOSEK ApS version 8.0 [Computer software]. MOSEK, Copenhagen, Denmark.
Nesterov, Y. E., and Nemirovskii, A. S. (1994). Interior-point polynomial algorithms in convex programming, SIAM, Philadelphia.
Nesterov, Y. E., and Todd, M. J. (1998). “Primal-dual interior-point methods for self-scaled cones.” SIAM J. Optim., 8(2), 324–364.
Sloan, S. W. (1988). “Lower bound limit analysis using finite elements and linear programming.” Int. J. Numer. Anal. Methods Geomech., 12(1), 61–77.
Tang, C., Toh, K., and Phoon, K. (2014). “Axisymmetric lower-bound limit analysis using finite elements and second order cone programming (SOCP).” J. Eng. Mech., 268–278.
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©2017 American Society of Civil Engineers.
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Received: Sep 12, 2016
Accepted: Feb 28, 2017
Published online: May 29, 2017
Published in print: Sep 1, 2017
Discussion open until: Oct 29, 2017
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