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Lower bound limit analysis of an anisotropic undrained strength criterion using second‐order cone programming
Author(s) -
Ukritchon Boonchai,
Keawsawasvong Suraparb
Publication year - 2018
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.2781
Subject(s) - classification of discontinuities , mathematics , limit analysis , second order cone programming , stress field , discretization , upper and lower bounds , finite element method , stress (linguistics) , mathematical analysis , anisotropy , interpolation (computer graphics) , geometry , structural engineering , engineering , physics , convex optimization , quantum mechanics , regular polygon , telecommunications , linguistics , philosophy , frame (networking)
Summary In this paper, the formulation of the lower bound limit analysis of an anisotropic undrained strength criterion using second‐order cone programming is described. The finite element concept was used to discretize the soil mass into 3‐noded triangular elements. The stress field was modeled using a linear interpolation within the elements while stress discontinuities were permitted to occur at the shared edges of adjacent elements. An elliptical yield criterion was adopted to model the anisotropic undrained strength of the clay. A statically admissible stress field was defined by enforcing the equilibrium equations within all triangular elements and along all shared edges of adjacent elements, stress boundary conditions, and no stress violation of the anisotropic strength envelope cast in the form of a conic quadratic constraint. The lower bound solution of the proposed formulation was solved by second‐order cone programming. The proposed formulation of the anisotropic undrained strength criterion was validated through comparison of the model's predictions with the known exact solutions of strip footings, and was applied to solve undrained stability of a shallow unlined square tunnel. Computational performance between the proposed approach of second‐order cone programming and linear programming was examined and discussed.