Predicted tyre–soil interface area and vertical stress distribution based on loading characteristics

The upper boundary condition for all models simulating stress patterns throughout the soil profile is the stress distribution at the tyre–soil interface. The so-called FRIDA model (Schjønning et al., 2008. Biosyst. Eng. 99, 119–133) treats the contact area as a superellipse and has been shown to accurately describe a range of observed vertical stress distributions. Previous research has indicated that such distributions may be predicted from tyre and loading characteristics. The objective of this study was to establish a stepwise calculation procedure enabling accurate predictions from readily available data. We used multiple regression to identify equations for predicting the FRIDA model parameters from measured loading characteristics including tyre carcass volume (VT), wheel load (FW), tyre deflection (L), and an expression of tyre inflation pressure (Kr) calculated as the natural logarithm of the actual to recommended inflation pressure ratio. We found that VT and Kr accounted for nearly all variation in the data with respect to the contact area. The contact area width was accurately described by a combination of tyre width and Kr, while the superellipse squareness parameter, n, diminished slightly with increasing Kr. Estimated values of the contact area length related to observed data with a standard deviation of about 0.06 m. A difference between traction and implement tyres called for separate prediction equations, especially for the contact area. The FRIDA parameters α and β, reflecting the tyre’s ability to distribute the stress in the driving direction and in the transversal direction, respectively, increased with increases in the relevant contact area dimension (length or width). The α-parameter was further affected by FW, while Kr and L added to model performance for the β-parameter. The prediction accuracy of our models was tested on an independent data set and through a range of case studies. We found satisfactory small root mean square errors and effectively no bias in the comparisons. Further studies are needed, though, to quantify effects of topsoil consistencies deviating from those tested in this study.