The Analysis of Variance.

The ability of elastic tissues to deform under physiological forces and to subsequently release stored energy to drive passive recoil is vital to the function of many dynamic tissues. Within vertebrates, elastic fibres allow arteries and lungs to expand and contract, thus controlling variations in blood pressure and returning the pulmonary system to a resting state. Elastic fibres are composite structures composed of a cross-linked elastin core and an outer layer of fibrillin microfibrils. These two components perform distinct roles; elastin stores energy and drives passive recoil, whilst fibrillin microfibrils direct elastogenesis, mediate cell signalling, maintain tissue homeostasis via TGFβ sequestration and potentially act to reinforce the elastic fibre. In many tissues reduced elasticity, as a result of compromised elastic fibre function, becomes increasingly prevalent with age and contributes significantly to the burden of human morbidity and mortality. This review considers how the unique molecular structure, tissue distribution and longevity of elastic fibres pre-disposes these abundant extracellular matrix structures to the accumulation of damage in ageing dermal, pulmonary and vascular tissues. As compromised elasticity is a common feature of ageing dynamic tissues, the development of strategies to prevent, limit or reverse this loss of function will play a key role in reducing age-related morbidity and mortality.

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Tissue elasticity and the ageing elastic fibre

In geomechanics, limit analysis provides a useful method for assessing the capacity of structures such as footings and retaining walls, and the stability of slopes and excavations. This paper presents a finite element implementation of the kinematic (or upper bound) theorem that is novel in two main respects. First, it is shown that conventional linear strain elements (6-node triangle, 10-node tetrahedron) are suitable for obtaining strict upper bounds even in the case of cohesive-frictional materials, provided that the element sides are straight (or the faces planar) such that the strain field varies as a simplex. This is important because until now, the only way to obtain rigorous upper bounds has been to use constant strain elements combined with a discontinuous displacement field. It is well known (and confirmed here) that the accuracy of the latter approach is highly dependent on the alignment of the discontinuities, such that it can perform poorly if an unstructured mesh is employed. Second, the optimization of the displacement field is formulated as a standard second-order cone programming (SOCP) problem. Using a state-of-the-art SOCP code developed by researchers in mathematical programming, very large example problems are solved with outstanding speed. The examples concern plane strain and the Mohr-Coulomb criterion, but the same approach can be used in 3D with the Drucker-Prager criterion, and can readily be extended to other yield criteria having a similar conic quadratic form.

Upper bound limit analysis using simplex strain elements and second-order cone programming

This paper presents a simple linear tetrahedron element that can be used in explicit dynamics applications involving nearly incompressible materials or incompressible materials modelled using a penalty formulation. The element prevents volumetric locking by defining nodal volumes and evaluating average nodal pressures in terms of these volumes. Two well-known examples relating to the impact of elasto–plastic bars are used to demonstrate the ability of the element to model large isochoric strains without locking. © 1998 John Wiley & Sons, Ltd.

A simple average nodal pressure tetrahedral element for incompressible and nearly incompressible dynamic explicit applications

Model studies on circular footing supported on geocell reinforced sand underlain by soft clay

Plane-strain, finite-element, and finite-difference computations of the bearing-capacity factor, Nγ, have been made for smooth and rough footings, for friction angles, ϕ, in the 30°–45° range, and dilation angles, ψ, in the 0 ≤ψ≤ϕ range. The finite-element analyses were based on a tangent stiffness approach. The commercially available code, fast Lagrangian analysis of continua (FLAC), was used for the finite-difference analyses. It was found that these methods may be used to obtain reliable Nγ values provided they are used cautiously. To obtain high-quality solutions, however, it is necessary to review the results critically, and, if necessary, alter the control parameters (e.g., mesh dimensions, number of calculation increments) being used. Computational difficulties were found to increase with increasing ϕ, and with increasing difference between ϕ and ψ, and the significant of these difficulties with regard to the use of the two computational techniques is discussed here. Curves relating Nγ to ϕ are pre...

Numerical studies of bearing-capacity factor Nγ

Numerical modelling of the accommodating lens.

Current practice for assessment of settlement damage to buildings due to tunnel construction usually starts with a procedure in which greenfield settlements are imposed on a structual model of the building. This process ignores the important interaction effects that the weight and stiffness of the building have on the settlements. This paper describes a three-dimensional finite element analysis in which the tunnel, the soil and a building are all treated in a single analysis. Example calculations are described, and these indicate that interaction between the building and the ground can have a significant effect on the extent of the predicted damage. The performance of the building is seen to be highly dependent on whether the settlements induce a sagging or hogging mode of deformation. The analyses are used to plot contours of soil surface settlement and also expected crack patterns within the building.

Modelling tunnelling-induced settlement of masonry buildings

The effectiveness of geogrid reinforcement, placed at the base of a layer of granular fill on the surface of soft clay, has been studied by small-scale model tests in the laboratory. In the tests, monotonic loading was applied by a rigid footing, under plane strain conditions, to the surface of reinforced and unreinforced systems, using a range of fill thicknesses and subgrade strengths. Continuous measurements were made of footing load and footing displacement, and deformations of the subgrade and of the geogrid reinforcement were measured from photographs. From these measurements the different mechanisms of failure in the unreinforced and reinforced system were established. Performance of reinforced systems was found to be superior even at small deformations, owing to the significant change in the pattern of shear forces acting on the surface of the clay, brought about by the presence of the reinforcement. Membrane action of the reinforcement only became significant at large deformations.A finite elemen...

Analytical and model studies of reinforcement of a layer of granular fill on a soft clay subgrade

A study has been carried out of the bearing capacity of sand layers overlying clay soils for the case where the thickness of the sand layer is comparable to the width of a rigid foundation placed on the soil surface. A review of previous work is given and a discussion is presented of the dimensionless groups that govern the behaviour of this type of foundation. A parametric study is carried out using both finite element and finite difference methods. This study is based on the use of soil parameters obtained from an assessment of the range of values that might be expected to be appropriate for full-scale structures. The results of the parametric study are used to illustrate the mechanics of the system and also to develop charts that may be used directly in design. In particular, the results illustrate that the shear strength of the clay has an important influence on the mechanisms of load spread within the fill. Resume : Lion a rOalisO une Otude sur la capacitO portante de couches de sable reposant sur des sols argileux pour le cas oo liOpaisseur de la couche de sable est comparable ‡ la largeur diune fondation rigide posOe sur la surface du sol. Lion prOsente une revue des travaux antOrieurs et une discussion sur les groupes sans dimension qui rOgissent le comportement de ce type de fondation. Une Otude paramOtrique est rOalisOe en utilisant les mOthodes tant des OlOments finis que des diffOrences finies. Cette Otude est fondOe sur liutilisation des paramtres de sols obtenus en partant de liOvaluation de la plage des valeurs que lion pourrait siattendre ‡ trouver dans des structures ‡ pleine Ochelle. Les rOsultats de liOtude paramOtrique ont OtO utilisOs pour illustrer le mOcanisme du systme et aussi pour dOvelopper des abaques qui peuvent Œtre utilisOes directement dans la conception. En particulier, les rOsultats illustrent que la rOsistance au cisaillement de liargile a une influence importante sur les mOcanismes de rOpartition de la charge ‡ liintOrieur du remblai. Mots clOs : capacitO portante, sols multicouches, analyse numOrique. (Traduit par la rOdaction)

Harvey J. Burd

Papers

Numerical studies of bearing-capacity factor Nγ

Numerical modelling of the accommodating lens.

Modelling tunnelling-induced settlement of masonry buildings

Analytical and model studies of reinforcement of a layer of granular fill on a soft clay subgrade

Bearing capacity of plane-strain footings on layered soils