Incorporation of Water Content in the Weibull Model for Soil Aggregate Strength

Abstract

Tillage impacts many components and functions of the soil ecosystem. Thus, the prediction of soil structures produced by tillage may be regarded as a major objective in soil science. Brittle fracture is the desired mode of failure in most tillage operations. Mechanistic or phenomenological models based on the probabilistic Weibull “weakest link” theory are commonly applied to model brittle fracture of air-dry aggregates. The overall objective of this study was to develop a Weibull model to describe the strength of different-sized soil aggregates across a wide range of water contents. Rupture energy data were obtained for aggregates sampled in three field experiments. These included two soil compaction experiments (Bygholm I and II, sandy loam) and a long-term tillage and fertilization experiment (Maury, silt loam). Aggregates were subjected to a crushing test after having been adjusted to matric potentials ranging from −10 kPa to −163 MPa (air dry). Water content strongly affected the characteristic rupture energy (Weibull α parameter), and this relationship was successfully modeled with a power law function. In contrast, water content had little or no effect on the spread of aggregate strengths (Weibull β parameter). Based on these results, we proposed a three-parameter Weibull brittle fracture model for the tested sandy loam and silt loam soils that takes account of the effect of water content for a single aggregate size fraction. This model, in which only α depends on water content, explained on average 89% of the total variation in rupture energy. Further research is needed to fully investigate the influence of water content on the rupture energy of different-sized aggregates.