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This paper presents a rigorous lowerbound solution for the bearing capacity of soft clays under embankments. The analysis is carried out by using a numerical technique that is based on the lowerbound theorem and finite elements. It is found that the lowerbound solution obtained in this paper agrees well with the upperbound solutions obtained from Hill and/or Prandtl failure mechanisms. The lowerbound solution for the vertical stresses that a soft foundation can support in combination with a surface shear stress (or shear force) can be used to obtain a safe design for the critical heights of both unreinforced and reinforced embankments by following an iterative procedure similar to that described by Michalowski in 1992. The usual assumption of a uniform shear stress mobilization underneath the embankment is shown to be conservative as it leads to a slightly lower value of the vertical bearing capacity.

This paper addresses elastic analysis based on 2D finite element models for metallic hollowsphere structures. In the first part, the influence of microporosity on the elastic behaviour of sintered metallic hollow sphere wall material is investigated. Youngs modulus of the metallic hollow sphere wall material is found to linearly decrease with increasing microporosity ranging up to about 45. In the second part, elastic parameters for metallic syntactic foams MSF consisting of thin or thick walled hollow spheres, and for epoxy containing spherical pores are studied. Data obtained from finite element models are compared with theoretical predictions based on the rule of mixtures developed elsewhere and found to be in good agreement with each other for MSF but not for porous epoxy. The shear modulus of MSF with thinwalled hollow spheres was found to increase with increasing volume fraction of matrix whereas that of MSF with thick walled hollow spheres was found to decrease. Specific Youngs modulus of MSF with thinwalled hollow spheres was also found to increase with increasing foam density whereas that of MSF with thick walled hollow spheres was found to decrease. Poissons ratio obtained was relatively low for porous epoxy matrix material but high for MSF with thin or thickwalled hollow spheres.Dieser Artikel beschäftigt sich mit der elastischen FiniteElementeAnalyse zweidimensionaler Modelle von Hohlkugelstrukturen. Im ersten Teil der Arbeit wird der Einfluss von Mikroporosität auf das elastische Verhalten der gesinterten Hohlkugelschale untersucht. Es wurde beobachtet, dass der Elastizitätsmodul des gesinterten Materials linear mit steigender Porosität abnimmt. Der zweite Teil der Arbeit befasst sich mit Hohlkugelstrukturen bestehend aus Hohlkugeln und Epoxidmatrix verschiedener Wandstärken t: dickwandige Hohlkugeln, dünnwandige Hohlkugeln und dem Grenzfallt→ 0 kugelförmige Einschlüsse ohne Hohlkugelschale. Die Ergebnisse der FiniteElementeAnalyse wurden mit analytischen Modellen verglichen und mit Ausnahme der kugelförmigen Einschlüsse eine gute Übereinstimmung erzielt. Der Schubmodul dünnwandiger Hohlkugelstrukturen nimmt mit zunehmendem Volumenanteil der Epoxidmatrix zu, der Schubmodul von dickwandigen Hohlkugelstrukturen jedoch ab. Die ermittelten Querkontraktionszahlen sind für den Fall kugelförmiger Einschlüsse t→ 0 vergleichsweise niedrig. Deutlich höhere Ergebnisse wurden für dünn und dickwandige Hohlkugelstrukturen erzielt.

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.

A new method for computing rigorous upper bounds on the limit loads for one‐, two‐ and three‐dimensional continua is described. The formulation is based on linear finite elements, permits kinematically admissible velocity discontinuities at all interelement boundaries, and furnishes a kinematically admissible velocity field by solving a non‐linear programming problem. In the latter, the objective function corresponds to the dissipated power (which is minimized) and the unknowns are subject to linear equality constraints as well as linear and non‐linear inequality constraints.

Soil anchors are commonly used as foundation systems for structures requiring uplift resistance, such as transmission towers, or for structures requiring lateral resistance, such as sheet pile walls. To date, the design of these anchors has been largely based on empiricism. This paper applies numerical limit analysis to rigorously evaluate the stability of vertical and horizontal strip anchors in undrained clay. Rigorous bounds on the ultimate pull–out capacity are obtained by using two numerical procedures that are based on finite element formulations of the upper and lower bound theorems of limit analysis. These formulations follow standard procedure by assuming a rigid perfectly plastic clay model with a Tresca yield criterion, and generate large linear programming problems. By obtaining both upper and lower bound estimates of the pull–out capacity, the true pull–out resistance can be bracketed from above and below. Results are presented in the familiar form of break–out factors based on various soil strength profiles and geometries, and are compared with existing numerical and empirical solutions.

Abstract:  In this paper, some practical aspects of the finite element implementation of critical state models are discussed. Improved automatic algorithms for stress integration and load and time stepping are presented. The implementation of two generalized critical state soil models, with one described first in this paper and the other recently published elsewhere, is discussed. The robustness and correctness of the proposed numerical algorithms are illustrated through both coupled and uncoupled analyses of geotechnical problems.

This paper applies numerical limit analysis to evaluate the undrained bearing capacity of a rigid surface footing resting on a two-layer clay deposit. Rigorous bounds on the ultimate bearing capacity are obtained by employing finite elements in conjunction with the upper and lower bound limit theorems of classical plasticity. Both methods assume a perfectly plastic soil model with a Tresca yield criterion and generate large linear programming problems. The solution to the lower bound linear programming problem is obtained by modelling a statically admissible stress field, whereas the upper bound problem is solved through modelling a kinematically admissible velocity field. Results from the limit theorems typically bracket the true collapse load to within approximately 12%, and have been presented in the form of bearing capacity factors based on various layer properties and geometries. A comparison is made between existing limit analysis, empirical and semi-empirical solutions. This indicates that the latter can overestimate or underestimate the bearing capacity by as much as 20% for certain problem geometries. Dans cet exposé, nous servons d'analyses limites numériques pour évaluer la capacité porteuse non drainée d'une assise à surface rigide reposant dur un dépöt argileux à deux couches. On obtient des limites rigoureuses pour la capacité porteuse ultime en employant des é1éments finis en conjonction avec les théorèmes de limite à borne supérieure et inférieure de la plasdcité classique. Les deux méthodes supposent un modéle de sol parfaitement plastique avec un critère d'élasdcité Tresca et entraïnent de gros problèmes de programmation linéaire. On obtient la solution au problème de programmation linéaire de limite inférieure en faisant la maquette d'un champ de contrainte admissible en statistique tandis que le problème de limite supérieure est résolu par la mise en maquette d'un champ de vélocité admissible en cinétique. De manière typique, les résultats de théorèmes limites cernent dans une marge d'environ 12% la vraie charge d'affaissement et sont présentés sous forme de facteurs de capacité porteuse basés sur les propriétés et géométries des diverses couches. Nous comparons les analyses limites existantes, les solutions empiriques et les solutions semiempiriques. Cette comparaison indique que ces dernières peuvent surévaluer ou sousestimer de 20% la capacité porteuse dans le cas de certaines géométries à problème.

This paper examines the stability of a purely cohesive layer resting on a trapdoor. Although this problem has been studied for a number of years and is of considerable interest for analysing the stability of tunnels and mine workings, its exact collapse load is unknown. Rigorous bounds on the load needed to support the trapdoor against active failure are derived using two numerical techniques which employ finite elements in conjunction with the limit theorems of classical plasticity. Both of the methods assume a perfectly plastic soil model with a Tresca yield criterion and lead to large linear programming problems. The solution to the lower bound linear programming problem defines a statically admissible stress field whereas the solution to the upper bound linear programming problem defines a kinematically admissible velocity field. The upper and lower bounds derived from the numerical methods typically bracket the exact collapse load to within ten per cent over the range of trapdoor geometries considered, and are substantially tighter than existing analytical bounds. They are shown to agree well with the collapse loads that are predicted from a traditional dis-placment type of finite element analysis. L'article examine la stabilité d'une couche purement cohérente reposant sur une trappe. Bien qu'on étudie depuis quelques années ce problème de grande importance pour analyser la stabilité des travaux miniers, la charge de rupture reste encore inconnue. Des limites strictes sur le chargement nécessaire pour la rupture active au droit de la trappe contre la rupture active sont derivées à l'aide de deux techniques numériques qui emploient des éléments finis conjointement avec les théorèmes limites de la plasticité classique. Les deux méthodes admettent un modèle de sol parfaitement plastique avec un critère d'ecoulement de Tresca et conduisent à des problemes considérables en ce qui concerne la préparation de programmes linéaires. La solution du problème de la préparation des programmes linéaires à la limite inférieure définit un champ de contrainte statiquement admissible, tandis que la solution de ce problème à la limite supérieure définit un champ de vitesse cinématiquement admissible. De façon typique, les limites supérieure et inférieure dérivées à partir des méthodes numériques se situent au voisinage du chargement de rupture précis à moins de dix pour cent près pour la gamme considérée de géometries de trappe et elles sont essentiellement plus précises que les limites analytiques à present acceptées. L'article démontre qu'elles s'accordent bien avec les chargements de rupture prédits à partir d'une analyse à elements finis traditionnelle basée sur le déplacement.