The physical effects of an intra-aggregate structure on soil shrinkage

Clay and soil containing it have shrinkage curves that are qualitatively different in shape. The objective of this work is to qualitatively show with maximum simplicity, how a clay shrinkage curve turns into a soil shrinkage curve. Because of the crack volume the measured shrinkage curve is not the single-valued feature of a soil. We use a concept of the reference shrinkage curve that is only stipulated by soil shrinkage without cracking, single-valued, and qualitatively similar to an observed shrinkage curve. We also use new concepts of an intra-aggregate soil structure: (i) a rigid superficial layer of aggregates that loses water during shrinkage; and (ii) lacunar pores (micro-cracks) inside an intra-aggregate clay that change in volume during shrinkage. Then, through a series of consecutive steps, illustrating each step by a separate graphic presentation, we move from a clay shrinkage curve to a soil shrinkage curve with predicted qualitative features that coincide with those experimentally observed in numerous soil shrinkage publications. We thereby demonstrate the qualitative physical impact of the intra-aggregate structure on soil shrinkage.

💡 Research Summary

The paper tackles the long‑standing observation that the shrinkage curve of a pure clay differs markedly in shape from that of a clay‑bearing soil. The authors argue that measured soil shrinkage curves are not single‑valued because macroscopic cracks develop during drying, and they therefore introduce the concept of a “reference shrinkage curve” – a theoretical, single‑valued curve that represents soil shrinkage in the absence of inter‑aggregate cracking. This reference curve retains the qualitative features of observed curves and can be used to estimate the crack‑volume contribution.

The core of the work is a qualitative, structure‑based explanation of how a clay shrinkage curve transforms into a soil shrinkage curve. Two intra‑aggregate structural elements are proposed: (i) a thin, rigid superficial layer that loses water early in the drying process, and (ii) lacunar pores (micro‑cracks) within the intra‑aggregate clay matrix. Lacunar pores exist only when the clay content c is below a critical value c*; above c* they disappear. Their presence is quantified by a lacunar factor k (0 ≤ k ≤ 1), with k = 0 indicating no lacunar pores and k > 0 indicating their existence.

For a disaggregated clay the volumetric shrinkage V(w) (specific volume V as a function of gravimetric water content w) consists of two linear segments (the saturation line and the basic shrinkage line with slope = 1) and a “squared” segment (structural shrinkage). When lacunar pores are introduced, the intra‑aggregate matrix volume U(w) can be expressed in terms of V(w) and k. The key result is that the slope of U(w) in the basic shrinkage region becomes (1 − k)/ρ_w, i.e., it is reduced proportionally to the lacunar factor. Consequently, soils with lacunar pores shrink more slowly than pure clay. Moreover, because lacunar pores remain empty, the matrix never reaches the true saturation line (1/ρ_s + w/ρ_w); instead its endpoint lies on a pseudo‑saturation line of unit slope. This explains two characteristic differences between soil and clay shrinkage curves: (a) a reduced slope in the basic shrinkage region, and (b) the presence of a pseudo‑saturation line.

The superficial rigid layer adds a further modification. As it loses water before the intra‑aggregate matrix, it drives an early volume reduction that makes the structural shrinkage portion of the soil curve upward‑convex. This layer also controls the deformation of structural pores that eventually give rise to macroscopic cracks.

Combining these mechanisms, the authors reproduce the four hallmark features of observed soil shrinkage curves: (a) upward convexity in the structural shrinkage zone, (b) a slope less than unity that varies with water content, (c) a basic‑shrinkage slope that can range from zero to one depending on clay content, and (d) a maximum swelling point that lies on the pseudo‑saturation line rather than the true saturation line.

The paper presents each transformation step—clay → lacunar‑pore‑filled matrix → addition of the superficial layer → full soil—using separate schematic figures, emphasizing that the qualitative shift can be understood without complex calculations. This structure‑based, physically grounded approach offers a clear alternative to existing empirical models that fit shrinkage data with multi‑parameter equations, and it deepens our mechanistic understanding of how intra‑aggregate architecture governs soil shrinkage behavior.