An integrated approach to soil structure, shrinkage, and cracking in   samples and layers
  A recent model showed how a clay shrinkage curve is step-by-step transformed into the shrinkage curve of an aggregated soil at any clay content if it is measured on samples so small that cracks do not occur at shrinkage. Such a shrinkage curve was called a reference curve. The present work generalizes this model to any soil sample size or layer thickness, i.e., to any crack contribution to the shrinkage curve. The approach is based on: (i) recently suggested features of an intra-aggregate structure; (ii) detailed accounting for the contributions to the soil volume and water content during shrinkage; and (iii) new concepts of lacunar factor, crack factor, and critical sample size. The following input parameters are needed for the prediction: (i) all parameters determining the basic dependence of the reference shrinkage curve; (ii) parameters determining the critical sample size (structural porosity and minimum and maximum aggregate size at maximum swelling); and (iii) initial sample size or layer thickness. A primary experimental validation of the new model concepts is conducted using the relevant available data on the shrinkage curves of four soils with different texture and structure that were obtained utilizing the samples of two essentially different sizes. The results show evidence in favor of the model. 
V. Y. Chertkov
physics.geo-ph cond-mat.soft