表征干燥失水诱发膨胀土收缩-开裂-沉陷机理的数学模型

膨胀土因干燥失水引起的收缩、开裂和沉陷会使其水力与力学特性发生显著变化，从而对膨胀土地区水工建筑物的稳定性产生负面影响，因此有必要研究这三个物理过程的细观机理和宏观响应。为此，先建立团粒、裂隙和沉陷这三个区域分布的数学模型；再通过分析收缩-开裂-沉陷过程中理想土块与裂隙之间的几何关系，推得裂隙相对宽度的理论计算公式；最后，对安康膨胀土开展收缩-开裂-沉陷的室内试验，并结合已有文献所述室内和现场试验结果，验证了这三种区域的数学模型在采用同一组参数描述团粒孔隙率、裂隙率及其相对宽度、沉陷率变化规律时的有效性，并建立了膨胀土团粒孔隙率-含水率-基质吸力的关系。该组数学模型为定量描述膨胀土的体变特征和渗透特性提供了一种新方法。

A set of mathematical models for the evolutions of shrinkage-cracking-subsidence for expansive soils during drying

Expansive soils may shrink, crack and subside as they dry, causing a remarkable influence on their hydraulic and mechanical behaviors and leading to an adverse impact on the deformation and stability of hydraulic structure in the regions of expansive soils. Therefore, it is necessary to investigate the meso-scale mechanism and macro-scale response of these three physical processesIn response, a set of mathematical models were first proposed for the aggregate, crack, and subsidence domainsIn the process of all three, the geometrical relationship between ideal soil block and crack was then applied to derivation of the equation for relative crack width. Finally, using the same set of parameters, the set of mathematical models were validated against the published data (including the supplementary test of expansive soil in Ankang) for different expansive soils in the laboratory and field, for describing the evolution of aggregate porosity, crack ratio, relative crack width, subsidence ratio and the relation among aggregate porosity, water content and matric suction. This set of mathematical models provides a method to analyze volume change characteristic and hydraulic conductivity behavior of expansive soils.