Axisymmetric Lower-Bound Limit Analysis Using Finite Elements and Second-Order Cone Programming

Tang, Chong; Toh, Kim-Chuan; Phoon, Kok‐Kwang

doi:10.1061/(asce)em.1943-7889.0000669

Cited by 53 publications

(22 citation statements)

References 29 publications

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“…Note that MOSEK is based on a highly robust and efficient primal‐dual interior‐point algorithm for large‐scale problems of continuous linear, quadratic, conic, and semidefinite programming. Previously, this optimizer has been successfully employed in FELA to solve various stability problems in geotechnical engineering . Readers are referred to the details of the numerical formulation of MOSEK and its usage in the manual of MOSEK and Andersen et al Standard default settings in the MOSEK optimizer are used in all LB calculations that are performed on a personal computer, Windows 10 operating‐based system, Intel Core I7‐4770 CPU@3.40 GHz and 32 GB memory.…”

Section: Resultsmentioning

confidence: 99%

“…Note that, since the equilibrium equations are satisfied at the centroid and not everywhere within the triangular element, the strict LB solution cannot be obtained from the present study. However, the previous studies by Khatri and Kumar and Tang et al indicated that there was no significant error on the LB solution associated with imposing the equilibrium equations at the centroid of the triangular element.…”

Section: D Axisymmetric Lb Felamentioning

confidence: 96%

“…The standard constraints of the LB requirements are summarized below here. Readers are referred to Tang et al and Khatri and Kumar for the details of coefficients associated with vectors and matrices of the standard constraints.…”

Section: D Axisymmetric Lb Felamentioning

confidence: 99%

“…It can be observed that the nonlinear term of r in Equation makes it not possible for the stress state to satisfy the equilibrium equations in every material point within triangular elements by enforcing these at their corner nodes. To derive the equilibrium constraints of triangular elements, this paper adopts the concept of enforcing the equilibrium equations at the centroid of the element as proposed by Khatri and Kumar and Tang et al Thus, the first set of the equilibrium constraint on the unknown nodal stress can be obtained by substituting Equation into Equation and imposing at the centroid of each element as

([], A_{italiceq}) ({}, σ) = ({}, B_{italiceq})

…”

Section: D Axisymmetric Lb Felamentioning

confidence: 99%

See 3 more Smart Citations

Undrained lower bound solutions for end bearing capacity of shallow circular piles in non‐homogeneous and anisotropic clays

Ukritchon

Keawsawasvong

2019

Num Anal Meth Geomechanics

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SUMMARY The undrained bearing capacity of shallow circular piles in non‐homogeneous and anisotropic clay is investigated by the lower bound (LB) finite element limit analysis (FELA) under two‐dimensional (2D) axisymmetric condition using second‐order cone programming, and the new solution of the problem is presented. Modified from the isotropic von Mises yield criterion, a cross‐anisotropic undrained strength criterion of clays under the axisymmetric state of stress requiring three input shear strengths in triaxial compression, direct simple shear, and triaxial extension is employed in the 2D axisymmetric LB FELA. Parametric studies on the effects of pile embedment ratio, dimensionless strength gradient, anisotropic strength ratio, and pile roughness are investigated extensively, while the predicted failure mechanisms associated with these parameters are discussed and compared. Numerical results of undrained end bearing capacity of shallow circular piles are summarized in the form of design tables that are useful for design practice and represent a new contribution to the field of pile capacity considering the combined effects of undrained strength non‐homogeneity and anisotropy.

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Section: Resultsmentioning

confidence: 99%

Section: D Axisymmetric Lb Felamentioning

confidence: 96%

Section: D Axisymmetric Lb Felamentioning

confidence: 99%

([], A_{italiceq}) ({}, σ) = ({}, B_{italiceq})

…”

Section: D Axisymmetric Lb Felamentioning

confidence: 99%

See 2 more Smart Citations

Undrained lower bound solutions for end bearing capacity of shallow circular piles in non‐homogeneous and anisotropic clays

Ukritchon

Keawsawasvong

2019

Num Anal Meth Geomechanics

View full text Add to dashboard Cite

show abstract

“…Recent trends in limit analysis (see for instance [33][34][35][36][37][38][39][40][41]) demonstrated that the utilization of LP in solving the typical linear optimization problem associated to the upper and lower bound problems of limit analysis is less effective than the application of robust non-linear programming routines (NLP), with the considerable advantage that the linearization of the material strength domain is avoided. This allowed a further improvement in the numerical efficiency of FE limit analysis programs.…”

Section: Introductionmentioning

confidence: 99%

Upper bound sequential linear programming mesh adaptation scheme for collapse analysis of masonry vaults

Milani

2015

Advances in Engineering Software

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Lower bound limit analysis of an anisotropic undrained strength criterion using second‐order cone programming

Ukritchon

Keawsawasvong

2018

Num Anal Meth Geomechanics

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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.

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Axisymmetric Lower-Bound Limit Analysis Using Finite Elements and Second-Order Cone Programming

Cited by 53 publications

References 29 publications

Undrained lower bound solutions for end bearing capacity of shallow circular piles in non‐homogeneous and anisotropic clays

Undrained lower bound solutions for end bearing capacity of shallow circular piles in non‐homogeneous and anisotropic clays

Upper bound sequential linear programming mesh adaptation scheme for collapse analysis of masonry vaults

Lower bound limit analysis of an anisotropic undrained strength criterion using second‐order cone programming

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