Keywords: anchor wall, finite element analysis, non-linear, lateral load, cohesionless soil.

Anchor walls are often light structural members placed vertically to withstand horizontal forces, most commonly as support for anchored sheetpile walls in permanent quayside situations or in temporary excavation work. A number of laboratory-based studies reported in the past (e.g. Ovesen [1], Ovesen and Stromann [2]), have provided information on the comparative performance of embedded anchor walls extending to ground level (full depth walls) with those of potentially more economic embedded walls with bases at the same depth as their full depth equivalent. This work resulted in various recommendations relating to the design of anchor walls of this type.

Research reported by Dickin and King [3] included numerical modelling of the behaviour of short vertical anchor walls in loose and dense cohesionless soil. The finite element analyses were carried out using a two dimensional finite element program SOSTV incorporating the variable elastic hyperbolic soil model proposed by Duncan and Chang [4] and Clough and Duncan [5]. Friction between the soil and the wall was modelled using `zero thickness' interface elements based on the work of Goodman et al. [6]. The study was directed towards the behaviour of 1m high anchor walls with embedment ratios up to 12 and examined the influence of embedment and soil packing on load-displacement response. Comparisons were also drawn with results from physical studies in tests on model anchor walls in the Liverpool University geotechnical centrifuge facility.

The purpose of the research reported herein was to broaden the scope of the finite element aspects of the earlier work and to include the behaviour of vertical walls embedded to their full depth. Hence to examine the comparative performances of full depth walls and short anchor walls extending to the same depth, and to investigate the previously published relationships between their resistances to lateral loading.

Two series of finite element studies were conducted investigating the lateral load response of both short anchor walls and full depth walls, one using triaxial parameters and the other using plane strain parameters determined previously for fine Erith sand, the material used in the centrifuge tests. It was found that for both loose and dense sand packings the failure resistances of 1m high anchor walls expressed in terms of a dimensionless breakout factor increase with embedment ratio to a critical value at a depth of about 7m. A slight decrease was observed for greater depths. On the other hand breakout factors for full depth walls were found to increase steadily for the entire range of depths investigated as might be expected, the greatest increase occurring in the range up to 7m. Moreover failure displacements were found to increase with embedment ratio but reduce with soil packing in good agreement with the earlier study. Comparisons between displacements for the two wall geometries also showed that the full depth wall experienced slightly higher displacements for the same horizontal load. This was perhaps unexpected and further investigation is in progress.

Comparisons with the experimentally-based reduction factors recommended by Ovesen relating the resistances of `strip' anchor walls and those of full depth walls, and the present theoretical work reveal similar values. The computed reduction factors were found to reduce steadily with embedment ratio and with soil unit weight, in agreement with Ovesen's findings. However his values are slightly more conservative than those from the finite element analyses and it is therefore possible that smaller reductions could be applied to the full depth wall values in designing `strip' anchor walls. Sensitivity analyses were also carried out to identify the influence of various soil and wall parameters used in the variable elastic analyses. It was concluded that, in addition to the geometric wall dimensions, soil unit weight and coefficient of lateral earth pressure at rest, in particular for K₀ values less than 0.4, significantly influence behaviour. Furthermore, as would be anticipated, the point of application of lateral load, whilst relatively insignificant for a short anchor wall, was much more important for its fully embedded equivalent.

1

Ovesen, N.K., "Anchor Slabs, Calculation Methods and Model Tests", Bulletin No.16, Danish Geotechnical Institute,Denmark,1964.

2

Ovesen, N.K., Stromann, H., "Design Method for Vertical Anchor Slabs in Sand", in "Proceedings Speciality Conference on Performance of Earth and Earth-Supported Structures", (1), USA, 1418-1500,1972.

3

Dickin, E.A., King, G.J.W., "Numerical Modelling of the Load-Displacement Behaviour of Anchor Walls",Computers and Structures,63(4),849-858,1997. doi:10.1016/S0045-7949(96)00066-1

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.

5

Clough, R.W., Duncan, J.M., "Finite Element Analysis of Retaining Wall Behaviour", Journal of Soil Mechanics and Foundations Division, ASCE,97,1657-1673,1971.

6

Goodman, R.E., Taylor, R.L., Brekke, T.L., "A Model for the Mechanics of Jointed Rock", Journal of Soil Mechanics and Foundations Division,ASCE, 94,637-659,1968.

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