Transmission of vertical soil stress under agricultural tyres: Comparing measurements with simulations

• Accurate stress measurements are crucial when comparing measured with simulated stress.
• Upper stress model boundary condition has a huge impact on stress transmission.
• Stress transmission was according to elasticity theory for our experimental conditions.
• Layering affects stress transmission only when differences in stiffness are large.
• Better knowledge of (anisotropy of) mechanical properties of arable soil is needed.

The transmission of stress induced by agricultural machinery within an agricultural soil is typically modelled on the basis of the theory of stress transmission in elastic media, usually in the semi-empirical form that includes the “concentration factor” (v). The aim of this paper was to measure and simulate soil stress under defined loads. Stress in the soil profile at 0.3, 0.5 and 0.7 m depth was measured during wheeling at a water content close to field capacity on five soils (13–66% clay). Stress transmission was then simulated with a semi-analytical model, using vertical stress at 0.1 m depth estimated from tyre characteristics as the upper boundary condition, and v was obtained at minimum deviation between measurements and simulations. For the five soils, we obtained an average v of 3.5 (for stress transmitting from 0.1 to 0.7 m depth). This was only slightly different from v = 3 for which the elasticity theory-based classical solution of Boussinesq (1885) is satisfied. We noted that the estimated v was strongly dependent on (i) the reliability of stress measurements, and (ii) the upper stress boundary condition used for simulations. Finite element simulations indicated that the transmission of vertical stresses in a layered soil is not appreciably different from that seen in a homogeneous soil unless very high differences in soil stiffness are considered. Our results highlight the importance of accurate stress readings and realistic upper model boundary conditions, and suggest that the actual stress transmission could be well predicted according to the theory of elasticity for the conditions investigated.