Keywords: codes of practice, design methods, numerical analysis, retaining walls.

The majority of current design approaches for embedded retaining walls involve idealization of the earth pressures applied to the wall, determination of the embedment depth for overall stability, the use of factors of safety to account for uncertainties, such as soil conditions, method of analysis or to limit both soil and wall movements to acceptable levels. Horizontal equilibrium is used to determine the anchor or prop forces and the structural theory to obtain moments and shear forces in the wall for the assumed earth pressure distributions and anchor/prop forces. The earth pressure distributions provide a realistic representation only at limiting conditions and they do not provide a realistic representation under working load conditions since the values of earth pressure coefficients derived from a variety of analytical methods are assumed to be independent of the mode of wall deformation.

In fact the use of a constant mobilization factor to reduce peak shear strengths of soils to the values mobilized within the soil at serviceability limit state fails to take into account the fact that the strain needed to mobilize peak stress varies with soil. Moreover, since the wall and soil deformation vary with depth the mobilization factor should also vary with depth depending upon the anticipated deformed shape of the wall in order to be compatible with the mobilized shear strength at the observed deformation. Hence, the use of a mobilization factor in BS8002 [1] introduces earth pressure at serviceability state for use at ultimate state. On the other hand, design according to the Eurocode 7 [2] is based on limit state methods but a mobilization factor is not specified. Instead partial factors are applied to characteristic loads, material properties as well as structural forces. Through these factors mobilized strengths are related to wall and soil deformation at serviceability and ultimate limit states.

Advanced numerical analyses do not suffer from the above shortcomings and have been used to assess the accuracy of the more approximate calculations. They use as input the at rest earth pressures, based on peak soil parameters to obtain a balance between earth pressure values and wall and soil deformation. A case study of a deep multi-propped excavation in layered soil is presented to compare prop loading, wall moment and displacement using advanced numerical analyses as well as limit equilibrium methods. Numerical analyses were performed using the finite difference program FLAC [3] and the finite element program PLAXIS [4] while analyses based on the codes of practice were performed using the ReWaRD [5] program.

The structural forces calculated by the numerical analyses are smaller than the values calculated by the limit equilibrium methods. The results of the limit equilibrium methods are not greatly dissimilar, with the Eurocode 7 providing the lower bound values. Greater inexactitudes are evident in the calculation of prop loads, with the limit equilibrium methods appearing to underestimate the load on the top prop. The empirical calculation of prop loads based on Terzaghi and Peck's [6] envelopes also fails to match the loads derived from the numerical analyses. Coincidence in displacement calculation is regarded as fortuitous.

1

British Standards Institution, "BS 8002 Code of Practice for Earth retaining structures", HMSO, 111pp, London, 1994.

2

Eurocode 7, "Eurocode 7: Geotechnical design-Part 1: General rules", Comité Européen de Normalisation, 126pp, Brussels, 1994.

3

FLAC (Fast Lagraning in Analysis of Continua), User manual, Itasca Consulting Group, Minneapolis, 1993.

4

PLAXIS, Finite Element Code for Soil and Rock Analysis, 7.2 Professional version, 1998.

5

ReWaRD, "Retaining wall design", User manual, Geocentrix Ltd, U.K. 2001.

6

K. Terzaghi & R.B. Peck, "Soil mechanics in engineering practice", 2nd edition, John Wiley, New York, 1967.

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