Shajiang black soil (Vertisol) has a high shrinkage capacity and contains many calcareous concretions (CC). We assume the volume of CC to be rigid during wetting and drying cycles. Thus, the soil containing CC may have different shrinkage behavior from that of fine soils (without CC). We aimed to quantify the effects of CC content and size on soil shrinkage behavior, as well as to develop a model to characterize the relationship among the void ratio (e), moisture ratio (υ), and solid volume of CC (Csv) in Shajiang black soil. Four different sizes (2–5, 5–10, 10–20 and, 20–30 mm) of the CC at a rate of 10% on mass, and four different contents (0, 5%, 10%, and 20% on mass) of 5–10 mm CCs were mixed into the fine soils to prepare the CC-soil mixtures. Our results showed that the increasing CC content significantly reduced the saturated void ratio (e_s), coefficient of linear extensibility (COLE), and shrinkage index of all pores except the medium pores (P < 0.05), but the CC size did not. The shrinkage curves of the CC–soil mixtures were proportional to that of the fine soil, which was modified by the portion of CC volume in the CC–soil mixtures. We proposed a new numerical equation based on Peng and Horn shrinkage model (2005) to illustrate the relationship among e– υ –Csv. The shrinkage curve of the CC–soil mixture was predicted well (R² = 0.95–0.98) by the new model based on that of fine soil and the CC volume modification. However, the proposed model underestimated the volume change for the dry side of the shrinkage curve, in which the swelling and shrinkage of fine soil matrix among CCs were partially concealed. Our work demonstrates that the CC in the Shajiang black soil does not change soil shrinkage behavior except the modification of void ratio, and thus its shrinkage curve can be estimated from that of the non-CC soil. It can be concluded that this study provides a useful model for estimating the shrinkage behavior of soils containing rigid coarse inclusions.

沙江黑土（Vertisol）具有很高的收缩能力，并含有许多钙质结核（CC）。我们假设 CC 的体积在润湿和干燥循环期间是刚性的。因此，含有 CC 的土壤可能具有与细土（不含 CC）不同的收缩行为。我们旨在量化 CC 含量和尺寸对土壤收缩行为的影响，并建立一个模型来描述孔隙比 ( e )、水分比 (υ) 和 CC 固体体积 ( C ) 之间的关系。sv) 在沙江黑土中。四种不同尺寸（2-5、5-10、10-20 和 20-30 毫米）的 CC，质量百分比为 10%，四种不同含量（0、5%、10% 和 20%）将 5-10 mm CCs 混合到细土中以制备 CC-土壤混合物。结果表明，CC含量的增加显着降低了除中孔以外的所有孔隙的饱和孔隙比（e _s）、线性延伸系数（COLE）和收缩指数（P  < 0.05），但CC尺寸没有显着降低。CC-土混合物的收缩曲线与细土的收缩曲线成正比，细土由CC-土混合物中CC体积的比例修正。我们基于 Peng 和 Horn 收缩模​​型 (2005) 提出了一个新的数值方程来说明它们之间的关系e – υ – C sv。 基于细土和CC体积修正的新模型很好地预测了CC-土壤混合物的收缩曲线（R ^{2 = 0.95-0.98）。}然而，所提出的模型低估了收缩曲线干侧的体积变化，其中CCs之间细土基质的膨胀和收缩被部分掩盖。我们的工作表明沙江黑土中的CC除了改变孔隙比外不会改变土壤的收缩行为，因此可以根据非CC土壤的收缩曲线来估计其收缩曲线。可以得出结论，这项研究为估计含有刚性粗夹杂物的土壤的收缩行为提供了一个有用的模型。