This paper describes a new formulation, based on linear finite elements and non-linear programming, for computing rigorous lower bounds in 1, 2 and 3 dimensions. The resulting optimization problem is typically very large and highly sparse and is solved using a fast quasi-Newton method whose iteration count is largely independent of the mesh refinement. For two-dimensional applications, the new formulation is shown to be vastly superior to an equivalent formulation that is based on a linearized yield surface and linear programming. Although it has been developed primarily for geotechnical applications, the method can be used for a wide range of plasticity problems including those with inhomogeneous materials, complex loading, and complicated geometry. Copyright © 2002 John Wiley & Sons, Ltd.

Lower bound limit analysis using non-linear programming

Contrary to what has recently been assumed in modeling the proposed deforming bed mechanism for the rapid motion of Antarctic ice streams, the rheology of water saturated till is probably highly nonlinear, according to information from soil mechanics and preliminary experiments on till from the base of Ice Stream B. The equivalent flow law exponent n is probably as high as ∼100, and the nonlinearities of the shear stress and effective pressure dependences are closely linked. The high nonlinearity has important consequences for the deforming bed mechanism. A flow system operating by this mechanism can be unstable as a result of feedback from the generation of basal water by shear heating of basal till. The short-term feedback effect is analyzed for a perturbation in a model ice stream in which the basal meltwater is transported through a distributed system of narrow gap-conduits at the ice-till interface. Although the analysis is approximate and some of the system parameters are poorly known, the results suggest that the deforming bed mechanism is unstable for n > ∼ 20. The apparent lack of such an instability in the currently active ice streams implies that their motion is controlled not by the deforming bed mechanism but by some other as yet unidentified mechanism.

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Rheological nonlinearity and flow instability in the deforming bed mechanism of ice stream motion

Why study glaciers? some basic concepts mass balance flow of a crystalline material the velocity field in a glacier temperature distribution in polar ice sheets the coupling between a glacier and its bed water flow in and under glaciers - geomorphic implications stress and deformation stress and velocity distribution in an idealized glacier applications of stress and deformation principles to classical problems response of glaciers to changes in mass balance problems

Principles of glacier mechanics

Bearing capacity of circular foundations on soft clay of strength increasing with depth

Due to the effect of structure, Bangkok clay is stable in a metastable state. Its void ratio, e, is the summation of the void ratio sustained by the intrinsic fabric, eR, and the additional void ra...

Akio Nakase

Papers

Influence of strain rate on undrained shear characteristics of k0-consolidated cohesive soils

Undrained Shear Strength Anisotropy of Normally Consolidated Cohesive Soils

An upper bound calculation on bearing capacity of a circular footing on a non-homogeneous clay.

Undrained Shear Strength of Remoulded Marine Clays

Bearing capacity of rectangular footings on clays of strength increasing linearly with depth