Probabilistic stability assessment using adaptive limit analysis and random fields

For deterministic scenarios, adaptive finite element limit analysis has been successfully employed to achieve tight bounds on the ultimate load of a geotechnical structure in a much more efficient manner than a dense uniform mesh. However, no probabilistic studies have so far considered finite element limit analysis with adaptive remeshing. Therefore, this research explores the benefits of combining adaptive mesh refinement with finite element limit analysis for probabilistic applications. The outcomes indicate that in order to achieve tight bounds on probabilistic results (such as the probability of failure), the ultimate load in each individual simulation (e.g. factor of safety or bearing capacity) has to be estimated with a very high level of accuracy and this can be achieved more economically using adaptive mesh refinement. The benefits, assessed here for undrained conditions, are expected to be much more pronounced in the case of frictional soils and complex geometries.     

Lower bound limit analysis using finite elements and linear programming

This paper describes a technique for computing lower bound limit loads in soil mechanics under conditions of plane strain. In order to invoke the lower bound theorem of classical plasticity theory, a perfectly plastic soil model is assumed, which may be either purely cohesive or cohesive-frictional, together with an associated flow rule. Using a suitable linear approximation of the yield surface, the procedure computes a statically admissible stress field via finite elements and linear programming. The stress field is modelled using linear 3-noded traingles and statically admissible stress discontinuities may occur at the edges of each triangle. Imposition of the stress-boundary, equilibrium and yield conditions leads to an expression for the collapse load which is maximized subject to a set of linear constraints on the nodal stresses. Since all of the requirements for a statically admissible solution are satisfied exactly (except for small round-off errors in the optimization computations), the solution obtained is a strict lower bound on the true collapse load and is therefore ‘safe’. A major drawback of the technique, as first described by Lysmer,¹ is the large amount of computer time required to solve the linear programming problem. This paper shows that this limitation may be avoided by using an active set algorithm, rather than the traditional simplex or revised simplex strategies, to solve the resulting optimization problem. This is due to the nature of the constraint matrix, which is always very sparse and typically has many more rows that columns. It also proved that the procedure can, without modification, be used to derive strict lower bounds for a purely cohesive soil which has increasing strength with depth. This important class of problem is difficult to tackle using conventional methods. A number of examples are given to illustrate the effectiveness of the procedure.     

Intensity measurements of chromospheric fine structures in Lyman-α

The intensity of the sun was measured in the Lyman- emission line with 2.5 arc-seconds of resolution. The experiment was flown in an Aerobee-150 rocket on April 28, 1966. It contained a Cassegrain telescope with a pinhole aperture placed at the focus followed by a gas-gain ionization chamber whose spectral response was 1050 Å to 1350 Å.An isophote map 1.5 by 3 arc-minutes in size made from a composite of 90 linear scans shows an enhanced region and adjacent to it a prominent dark lane 20 arc-seconds wide. The measured intensity ratio of these two regions is nine. Bright features between 6 and 20 arc-seconds in size showed typical peak intensities of 20% greater than the surrounding chromosphere. The smallest features observed were 2.5 arc-seconds in size. A direct measurement of the absolute intensity at 1216 Å gave a value of 5.9 × 10⁴ erg cm^–2 s^–1 sterad^–1 in the quiet chromosphere.Based on observations made by the author at the E. O. Hulburt Center for Space Research (supported jointly by the Office of Naval Research and the National Science Foundation) at the Naval Research Laboratory.