Significance of flow rule for the passive earth pressure problem

Christoph Schmüdderich,Helmut F Schweiger,Franz Tschuchnigg

doi:10.1007/s11440-021-01193-x

Christoph Schmüdderich, Helmut F Schweiger + Show 1 more

Open Access

https://doi.org/10.1007/s11440-021-01193-x

Copy DOI

Abstract

Determination of earth pressures is one of the fundamental tasks in geotechnical engineering. Although many different methods have been utilized to present passive earth pressure coefficients, the influence of non-associated plasticity on the passive earth pressure problem has not been discussed intensively. In this study, finite-element limit analysis and displacement finite-element analysis are applied for frictional materials. Results are compared with selected data from literature in terms of passive earth pressure coefficients, shape of failure mechanism and robustness of the numerical simulation. The results of this study show that passive earth pressure coefficients determined with an associated flow rule are comparable to the Sokolovski solution. However, comparison with a non-associated flow rule reveals that passive earth pressure coefficients are significantly over predicted when following an associated flow rule. Moreover, this study reveals that computational costs for determination of passive earth pressure are considerably larger following a non-associated flow rule. Additionally, the study shows that numerical instabilities arise and failure surfaces become non-unique. It is shown that this problem may be overcome by applying the approach suggested by Davis (Soil Mech 341–354, 1968).

Highlights

For the design of retaining walls, gravity dams, cantilever walls or bridge abutments determination of earth pressures is a fundamental task
A more detailed analysis reveals that finite-element limit analysis (FELA) provides smaller Kph values than finite-element analysis (FEA) and even the upper bound (UB) solution is slightly smaller than FEA
An explanation for this observation can be given with respect to the adaptive mesh refinement which allows for more accurate approximation of the failure mechanism in FELA

Summary

Introduction

For the design of retaining walls (e.g. sheet pile, bored pile or diaphragm walls), gravity dams, cantilever walls or bridge abutments determination of earth pressures is a fundamental task. Since earth pressure coefficients are based on different theories and assumptions, it is highly recommended for practitioners to be familiar with the fundamental theories used to derive earth pressure coefficients. The passive earth pressure force Eph is calculated based on three terms which are related to soil weight c, effective cohesion c0 and surcharge q. For a purely frictional material and no surcharge applied to the backfill, determination of Eph can be reduced to Eq 1, with the height of the wall h and the passive earth pressure coefficient Kph

Objectives

Methods

Results

Conclusion