REDUCING COMPUTATIONAL EFFORT IN SOLVING GEOMECHANICS PROBLEMS WITH UPPER BOUND FINITE ELEMENTS LIMIT ANALYSIS AND LINEAR OPTIMIZATION

This paper presents a simple technique for reducing the computational effort while solving any geotechnical stability problem by using the upper bound finite element limit analysis and linear optimization. In the proposed method, the problem domain is discretized into a number of different regions in which a particular order (number of sides) of the polygon is chosen to linearize the Mohr-Coulomb yield criterion. A greater order of the polygon needs to be selected only in that region wherein the rate of the plastic strains becomes higher. The computational effort required to solve the problem with this implementation reduces considerably. By using the proposed method, the bearing capacity has been computed for smooth and rough strip footings and the results are found to be quite satisfactory.

Lower-Bound Axisymmetric Formulation for Geomechanics Problems Using Nonlinear Optimization

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.

Mathematical and Numerical Modeling in Maritime Geomechanics

A theoretical and numerical framework to model the foundation of marine offshore structures is presented. The theoretical model is composed by a system of partial differential equations describing coupling between seabed solid skeleton and pore fluids (water, air, oil,…) combined with a system of ordinary differential equations describing the specific constitutive relation of the seabed soil skeleton. Once the theoretical model is described, the finite element numerical procedure to achieve an approximate solution of the governing equations is outlined. In order to validate the proposed theoretical and numerical framework the seaward tilt mechanism induced by the action of breaking waves over a vertical breakwater is numerically reproduced. The results numerically attained are in agreement with the main conclusions drawn from the literature associated with this failure mechanism