Lower-Bound Axisymmetric Formulation for Geomechanics Problems Using Nonlinear Optimization

Chakraborty, Manash and Kumar, Jyant (2015) Lower-Bound Axisymmetric Formulation for Geomechanics Problems Using Nonlinear Optimization. In: INTERNATIONAL JOURNAL OF GEOMECHANICS, 15 (5).

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Abstract

A lower-bound limit analysis formulation, by using two-dimensional finite elements, the three-dimensional Mohr-Coulomb yield criterion, and nonlinear optimization, has been given to deal with an axisymmetric geomechanics stability problem. The optimization was performed using an interior point method based on the logarithmic barrier function. The yield surface was smoothened (1) by removing the tip singularity at the apex of the pyramid in the meridian plane and (2) by eliminating the stress discontinuities at the corners of the yield hexagon in the pi-plane. The circumferential stress (sigma(theta)) need not be assumed. With the proposed methodology, for a circular footing, the bearing-capacity factors N-c, N-q, and N-gamma for different values of phi have been computed. For phi = 0, the variation of N-c with changes in the factor m, which accounts for a linear increase of cohesion with depth, has been evaluated. Failure patterns for a few cases have also been drawn. The results from the formulation provide a good match with the solutions available from the literature. (C) 2014 American Society of Civil Engineers.

Item Type:	Journal Article
Publication:	INTERNATIONAL JOURNAL OF GEOMECHANICS
Publisher:	ASCE-AMER SOC CIVIL ENGINEERS
Additional Information:	Copy right for this article belongs to the ASCE-AMER SOC CIVIL ENGINEERS, 1801 ALEXANDER BELL DR, RESTON, VA 20191-4400 USA
Keywords:	Axisymmetric; Bearing capacity; Limit analysis; Lower-bound solution; Nonlinear optimization; Plasticity
Department/Centre:	Division of Mechanical Sciences > Civil Engineering
Date Deposited:	30 Oct 2015 07:10
Last Modified:	30 Oct 2015 07:10
URI:	http://eprints.iisc.ac.in/id/eprint/52589

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