Skip to main content
Research article - Peer-reviewed, 2022

Simulation of soil stress under plate sinkage loading: A comparison of finite element and discrete element methods

Bahrami, Mostafa; Naderi-Boldaji, Mojtaba; Ghanbarian, Davoud; Keller, Thomas


Stress propagation in soil under vehicular traffic can be simulated either analytically based on the laws of continuum mechanics or numerically using finite element (FEM) and discrete element methods (DEM). Soil stress measured by a stress probe may differ from the "true" stress (i.e. the stress without the probe), as probes under- or over-estimate soil stress. No instrument has yet been developed to enable true stress measurement, while simulated stress can only be validated by comparing with measured stress. Hence, it is important to model the interaction of soil with a load cell probe to understand the difference between "with probe" and "without probe" soil stress. This study aimed at modelling the interaction of a load cell stress probe and soil under circular surface loading (i.e. by plate sinkage test) using FEM and DEM to understand the differences of the two methods, and to address whether arable soil is a continuum or a discrete media with regard to stress propagation. Simulated stress was compared with experimental stress (i.e. the stress measured by the probe). Experimental stress measurements were made in a clay loam soil at a gravimetric water content of 11% (corresponding to 0.5 PL, the lower plastic limit) and bulk densities of 1000 and 1150 kg m−3 corresponding to loose to slightly compacted soil, respectively. The load cell probe was installed at 0.15 m depth within a soil column, and varying surface loads were applied by a circular plate. The measured stress as a function of applied load was compared with simulated stress using either FEM or DEM. Simulations underestimated the measured stress, with an RMSE of 22.8 kPa for DEM and 40.1 kPa for FEM. The difference in soil stress between simulations with and without a probe were small for DEM, but significant for FEM. For FEM simulations, embedding a stress probe into the soil resulted in an overestimation of the “true” stress by 94% for the soil and boundary conditions tested. For DEM, the average overestimation was only 11%. Differences between FEM and DEM simulations with and without a probe were discussed and attributed to the sponge effect in FEM, and to differences in stress distribution at the soil-loading plate interface caused by the arching effect. Simulations showed that increasing the ratio of probe housing diameter to sensing surface decreased the stress overestimation for both DEM and FEM methods. More research is needed to address how stress propagation and the stress readings by a sensor probe are influenced in continuum and granular media, and how soil stress should be best modelled (as a continuum or granular material) depending on soil properties and characteristics.


Soil stress; Continuum mechanics; Granular matter; Stress transducer; Numerical simulations; Boussinesq stress

Published in

Soil and Tillage Research
2022, volume: 223, article number: 105463

Authors' information

Bahrami, Mostafa
Shahrekord University
Naderi-Boldaji, Mojtaba
Shahrekord University
Ghanbarian, Davoud
Univ Art
Swedish University of Agricultural Sciences, Department of Soil and Environment

UKÄ Subject classification

Applied Mechanics
Soil Science

Publication Identifiers


URI (permanent link to this page)