Keywords: strip anchors, uplift response, finite element, non-linear analysis, centrifuge, sand.

Anchor plates are light structural members often employed to withstand uplift forces experienced, for example, by transmission towers, masts and structures subject to buoyancy. A number of conventional laboratory-based studies have been reviewed by Frydman and Shaham [1] and provide experimental evidence of the influence of geometry and depth of embedment on the uplift behaviour of anchor plates. A centrifuge study reported by Dickin [2] simulating the behaviour of 1m wide anchor plates also demonstrated the influence of anchor size. Anchor plates with a range of geometries and embedment ratios were investigated and empirical shape factors proposed. Comparisons were drawn with a number of limit state and finite element based design methods

The purpose of the research reported herein was to compare computations using PLAXIS with results from the centrifuge modelling programme. PLAXIS is a finite element package specially developed for the analysis of deformation and stability in geotechnical engineering projects (Brinkgreve and Vermeer [3]). An elasto-plastic hyperbolic model, the so-called Hardening Soil Model (HSM), was used for the non- linear sand behaviour in this study. When subjected to primary deviatoric loading, sandy soil shows a decreasing stiffness and simultaneously irreversible plastic strains develop. The observed relationship between the pressure and axial strain can be well approximated by a hyperbola as used in the variable elastic, hyperbolic model (Duncan and Chang [4]). The HSM, however, far supercedes the hyperbolic model and is capable of simulating nonlinear, inelastic, stress dependent material behaviour.

Limiting states of stress are described by means of the friction angle (), the cohesion () and the dilatancy angle () while the increase in soil stiffness with pressure is also accurately accounted for. While the initial stresses in soil may be generated using Jaky's formula for , other more realistic values may be specified. The analyses were carried out using a plane strain geometry model. During the automatic generation of the mesh, clusters are divided into 15-node triangular elements to provide accurate calculation of stresses and failure loads. The meshes were chosen to correspond with the prototype geometries in the centrifuge tests and were 16m wide with depths ranging from 2.64m to 8.64m for embedment ratios from 2 to 8 where is the depth of embedment and is the breadth (width) of the anchor. The prototype length of the strip anchors was taken as 8m as in the centrifuge tests.

PLAXIS incorporates a fully automatic mesh generation procedure, in which the geometry is divided into elements of the basic element type and compatible structural elements. The strip anchors were represented by a rigid beam element with soil interface parameters generated using an interaction coefficient , defined as the ratio of shear strength of soil structure interface to corresponding shear strength of soil. In order to obtain the most suitable mesh, computations using the five available levels of global coarseness for an anchor with a ratio of 7 were conducted and as a result the coarse mesh, a default setting, was found to be sufficiently accurate and was adopted throughout the study. The size and number of elements varied with the anchor embedment but this mesh contained 124 elements and 425 nodal points. Since the anchor and loading were symmetrical only one half of the geometry was analysed. PLAXIS generates full fixity at the base of the geometry and roller conditions at the vertical sides.Uplift loads were applied incrementally with incremental multipliers chosen as 1kN/m.

The load-displacement relationships from the PLAXIS analyses generally showed good agreement with observed behaviour in the pre-peak region for all anchor depths. Anchors with embedment ratios of 3 and 7, considered as typical examples of shallow and intermediate depth anchors, were given particular attention. The change in response in the soil above a strip anchor, which is dependent on its embedment, was also reflected in the displacement contours obtained from PLAXIS. It may be concluded that the pre-peak uplift behaviour of strip anchors can be sensibly modelled by the Hardening Soil Model available in PLAXIS although the post-peak softening phase observed in some physical model tests requires a more sophisticated soil model.

1

Frydman, S., Shaham, I., "Pullout Capacity of Slab Anchors in Sand", Canadian Geotechnical Journal, 26,385-400, 1989. doi:10.1139/t89-053

2

Dickin, E.A., "Uplift Behaviour of Horizontal Anchor Plates in Sand", Journal of Geotechnical Engineering Division, ASCE, 114, GT11, 1300-1317, 1988. doi:10.1061/(ASCE)0733-9410(1988)114:11(1300)

3

Brinkgreve, R.B.J, Vermeer, P.A., "Finite Element Code for Soil and Rock Analyses", A.A. Balkema, Rotterdam, Netherlands, 1998.

4

Duncan, J.M., Chang, C.Y., "Non-Linear Analysis of Stress and Strain in Soils", Journal of Soil Mechanics and Foundations Division, ASCE, 96, 1629-1653, 1970.

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