Comparing pseudo-analytical solutions with 2D and 3D numerical simulations of soil stress induced by agricultural field traffic

Soil compaction models basically consist of pseudo-analytical and numerical models. The accuracy of these models still require studies of concentration factor assignment, and two-dimensional plane strain or three-dimensional soil domain geometry. The aim of this study was to perform pseudo-analytical analysis using different Fröhlich's (3, 4, 5 or 6) concentration factors, and compare the results of vertical stress with plane strain (2D) and three-dimensional (3D) soil domain numerical simulations using the finite element method. Results revealed that pseudo-analytical and 3D numerical models showed to be similar for the propagation of vertical stress. The use of a concentration factor equal to 6 overestimated propagation stress by approximately 150 kPa at soil surface in comparison to Boussinesq's solution. Additionally, the equivalence between the pseudo-analytical and 3D numerical simulations was achieved for a Fröhlich's concentration factor equal to 3. The 2D plane strain analysis overestimated (∼100 kPa) the stress propagation, inducing vertical stress bulbs superposition between tyres of a same axle, concentrating and propagating the stress to soil depths so far beyond the level that was observed for the pseudo-analytical or 3D numerical models. Our results suggest that assigning a concentration factor for simulations of stress transmission induced by field tyres in agricultural arable soils with pseudo-analytical models using Fröhlich's solution could be unnecessary. The stress under these conditions could be described by Boussinesq's solution. From a practical point of view, numerical simulations with 2D plane strain approach could cause some inconsistency in the interpretation of the stress field.