Incorporation of water content in the Weibull model for soil aggregate

strength

Brittle failure is the desired mode of failure in most tillage operations as it results in an overall loosening of the soil. Mechanistic/phenomenological models based on the probalistic Weibull “weakest link” theory have been applied to model brittle fracture of air-dry soil aggregates. The objective of this study was to develop and evaluate a Weibull model for brittle fracture of aggregates that takes into account differences in water content. In addition, we wanted to investigate the influence of water content on the rupture energy-aggregate size relationship. Aggregate strength data were analyzed for a sandy loam (Oxyaquic Agriudoll). Samples were taken from two field experiments in which a compaction treatment was compared with an uncompacted reference treatment. Rupture energy was determined on aggregates adjusted to –10, –30, –100, –350 kPa matric potential and on air-dry aggregates (–166 MPa). The relationship between the Weibull parameter α (i.e. characteristic strength) and relative water content (= water content / water content in an air-dry state) could be modeled by a power law function. For the Weibull parameter β (i.e. the spread of rupture energies around α) there was no clear dependence on water content. A proposed modified Weibull model that takes account of the effect of water content described the pooled data very well (0.82 ≤ R² ≤ 0.94 and 0.94 ≤ R² ≤ 0.97, respectively for the two experiments). Water content displayed a different effect on the size-scaling factor D. The D factor increased with increasing water content for one of the experiments, whereas no significant correlation was found for the other. An increase in D with increasing water content may be related to the expected shift in mode of failure from brittle to ductile.