Significance of flow rule for the passive earth pressure problem

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 ).