Root growth in the field is often slowed by a combination of soil physical stresses, including mechanical impedance, water stress, and oxygen deficiency. The stresses operating may vary continually, depending on the location of the root in the soil profile, the prevailing soil water conditions, and the degree to which the soil has been compacted. The dynamics of root growth responses are considered in this paper, together with the cellular responses that underlie them. Certain root responses facilitate elongation in hard soil, for example, increased sloughing of border cells and exudation from the root cap decreases friction; and thickening of the root relieves stress in front of the root apex and decreases buckling. Whole root systems may also grow preferentially in loose versus dense soil, but this response depends on genotype and the spatial arrangement of loose and compact soil with respect to the main root axes. Decreased root elongation is often accompanied by a decrease in both cell flux and axial cell extension, and recent computer-based models are increasing our understanding of these processes. In the case of mechanical impedance, large changes in cell shape occur, giving rise to shorter fatter cells. There is still uncertainty about many aspects of this response, including the changes in cell walls that control axial versus radial extension, and the degree to which the epidermis, cortex, and stele control root elongation. Optical flow techniques enable tracking of root surfaces with time to yield estimates of two-dimensional velocity fields. It is demonstrated that these techniques can be applied successfully to time-lapse sequences of confocal microscope images of living roots, in order to determine velocity fields and strain rates of groups of cells. In combination with new molecular approaches this provides a promising way of investigating and modelling the mechanisms controlling growth perturbations in response to environmental stresses.

>The response of skirted offshore foundations to combined vertical (V), moment (M) and horizontal (H) loading has been studied using two-dimensional finite-element analysis and upper-bound plasticity analysis assuming the soil to be undrained. New information has been gained about the shape of the yield locus and the soil deformation mechanisms occurring at yield from the finite-element analysis. The shape of the yield locus was found to be similar to that predicted by previous workers in V—M and V— H space but differed significantly in M—H space. This behaviour is explained using upper-bound plasticity mechanisms suggested by the soil deformation mechanisms calculated in the finite element analysis. This procedure is then used to give a good approximation to the shape of the yield locus and thus may form the basis for future design methods. Additionally, a simplifying transformation is suggested for the yield locus in H—M space based on plasticity analysis, which allows use of simple mathematical expressions to form a design envelope. Nous 6tudions la réponse de fondations offshore à jupe à une combinaison de charge verticale (V), instantanée (M) et horizontale (H) en utilisant des analyses d'é1éments finis en deux dimensions et une analyse de plasticité de limite supérieure en supposant un sol non drainé. Nous drons de Panalyse d'é1éments finis de nouveaux renseignements sur la forme du lieu d'é1asticité limite et sur les mécanismes de déformation du sol qui se produisent à la limite é1astique. La forme du lieu se révèle comme similaire à celle présagée par les travaux précédents dans les espaces Vmdash;M et V—H mais considérablement différente dans Pespace M—H. Nous expliquons cc comportement en utilisant les mécanismes de plasticité de limite supérieure qui sont suggérés par les mécanismes de déformation du sol calcu1és dans 1'analyse d'é1éments finis. Cette procédure est alors utilisée pour donner une bonne approximation de la forme du lieu qui pourra ainsi former la base des futures méthodes de design. De plus, nous suggérons une transformation simplificatrice pour le lieu d'é1asticité limite dans Pespace H—M sur la base de 1'analyse de plasticité qui permet Putilisation d'expressions mathématiques simples pour former une enveloppe de design.

The response of skirted foundations to combined vertical, horizontal and moment loading is important for the design of offshore installations. The vertical skirts beneath the footing interact with the soil and increase the foundation capacity, compared with a surface footing. Previous researchers have assumed that the soil within the skirts remains rigid during undrained loading, but this assumption has not been investigated rigorously. A series of plane-strain finite element analyses has been conducted to investigate directly how the skirt geometry affects the undrained strip foundation capacity under combined horizontal–moment loading and the mechanisms occurring at failure. Conditions of both uniform and non-uniform undrained strength soil have been considered. The results show that deformation of the soil between external skirts can lead to significantly less foundation capacity than that of an equivalent solid embedded foundation. Hence the specific geometry of the foundation must be considered in design. In addition, the failure envelopes for skirted foundations with different embedment ratios differed significantly. This makes general recommendations for failure envelope shapes problematical. Finally, significant increases in foundation bearing capacity may be achieved by adding an intermediate skirt to the foundation, which results in a foundation capacity that is almost equal to that of a solid embedded foundation.

Finite element analysis has been used to investigate the interaction between anchor flukes and undrained soil at failure. The behaviour of a rectangular and a wedge-shaped anchor has been investigated when the anchors are subject to combined rotational and translational loadings similar to those experienced during anchor dragging. The results have been presented in terms of a plasticity framework to produce an associated plastic failure locus for combined loading conditions. It is seen that the wedge-shaped anchor has a different shaped failure locus and displacements at failure because of its asymmetrical shape, and this will affect drag anchor behaviour. A new design method is introduced that aims to predict drag anchor embedment trajectory and holding capacity through examination of the fluke–soil interaction. The yield loci and plastic potentials produced from consideration of fluke–soil interaction are used in the new design method to predict drag anchor kinematics. Results from the new analysis method are compared to empirically based methods, and it is seen that there is good agreement between results, even without further calibration from physical modelling. This suggests that the approach has promise, and with further refinement of the yield loci and better approximations to the complex anchor geometry, it may develop into a useful anchor design tool that allows for both the anchor geometry and the soil conditions explicitly.Key words: drag anchor capacity, undrained clays, numerical method.