Rigorous lower and upper bounds for the 3D passive earth pressure problem

Christoph Schmüdderich*, Franz Tschuchnigg, Torsten Wichtmann

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


With the advent of advanced numerical methods, the three-dimensional (3D) passive earth pressure problem has received increasing attention within the last two decades. However, narrow brackets for the exact solution obtained via lower and upper bound simulations have not been presented. In this study, finite-element limit analysis is utilised to determine rigorous bounds for the 3D passive earth pressure problem. A parametric study accounting for different wall geometries, friction angles and wall friction ratios is performed and results are presented in terms of lateral earth pressure coefficient, Kpγh. The results of the lower and upper bound analyses show that in all analysed cases, the exact solution is bracketed within a very narrow range. Furthermore, comparison with existing approaches reveals that, in general, a good agreement is achieved between the current results with data from literature. Furthermore, both lower and upper bound have been improved, especially for narrow geometries, large friction angles and large wall friction ratios.
Original languageEnglish
Pages (from-to)100-105
Number of pages6
JournalGéotechnique Letters
Issue number2
Publication statusPublished - 1 Jun 2020

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