An energy-based model of soil fragmentation by tillage

Tillage greatly modifies soil structure, yet existing approaches to modelling tillage-induced soil structural change remain largely qualitative or over-simplified. Here, we present a quantitative, energy-based reformulation of the classical tillage equation that predicts soil fragmentation from the initial soil state and the applied energy. The new model partitions tillage energy into surface creation through fragmentation, displacement of existing soil fragments, and plastic deformation of the soil. Soil moisture and mechanical properties control the energy partitioning among these processes. As fragmentation progresses, an increasing proportion of tillage energy is dissipated through the displacement of existing fragments, whereas at elevated soil water contents energy is consumed by plastic deformation. Soil fragmentation resulting in the creation of new fragment surface area scales with the remaining energy. Literature-derived soil fragmentation data from drop-shatter tests and tillage experiments were used for model parameterisation. The model was subsequently evaluated against separate, independent literature datasets not used for parameterisation, covering tillage-induced soil fragmentation across a range of soil conditions. Illustrative applications demonstrate the model’s ability to capture (i) the texture-dependent soil workability range and (ii) the diminishing effectiveness of repeated tillage operations. We outline how the model-derived fragment surface area can be linked to fragment size distributions under simplifying assumptions. Assuming spherical fragment geometry and a Weibull distribution of fragment sizes allows an estimation of the tillage-induced pore size distribution. Altogether, our physically grounded model provides a basis for predicting tillage-induced soil structural change and can be incorporated into agroecosystem models. Further model refinement would benefit from datasets that jointly quantify tillage energy input, soil water status, as well as pre- and post-tillage soil structure and hydraulic properties, enabling a more mechanistic description of the transition from brittle fragmentation to plastic deformation.