南宁膨胀土的体积含水率-等效介电常数关系

体积含水率-介电常数关系是时域反射法（TDR）测量土体体积含水率的理论基础。通过对重塑的南宁膨胀土进行试验，选择经验公式法、边界法及理论模型法模拟其体积含水率-等效介电常数的变化规律。研究发现，南宁膨胀土的实测值落在Hashin-Shtrikman边界和Wiener边界以内，但Hashin-Shtrikman边界具有更小的范围；由于膨胀土的黏性较大，结合水存在显著的影响，Topp公式计算值偏高，但采用考虑三相组分含量的Looyenga公式可反映结合水的影响，从而得到更好的结果；理论模型法的Maxwell-Garnett模型和差分有效介质模型（DEM）需要考虑三相的构成，单独采用气相连续或水相连续的模拟结果均不理想，但如考虑土中水、气分布形态，采用饱和度作为权重函数对单相计算结果进行加权平均后可取得较好的效果。

Relationship between volumetric water content and effective dielectric permittivity of Nanning expansive soil

The relationship between volumetric water content of soils and their effective dielectric permittivity is the theoretical basis of time domain reflectometry (TDR) technique. In this study, effective dielectric permittivity of a reconstituted expansive soil sampled from Nanning is measured by time domain reflectometry at different volumetric water contents, and three approaches including empirical equation method, theoretical bound method and theoretical model, are used to simulate the variation of the effective dielectric permittivity. The measured values of dielectric permittivity are found to be located within bounds of the Hashin-Shtrikman and Wiener, but the range of the solutions from the Hashin-Shtrikman bound is narrower than the Wiener bound’s. The effective dielectric permittivity of Nanning expansive soil is overestimated by Topp’s empirical equation, since the bound water in the expansive soil leads to a lower effective dielectric permittivity. The effect of bound water can be considered in Looyenga empirical equation in which three phases are separated and better agreements between predictions and tested results are obtained. Theoretical models have advantage in conceptualizing the effects of internal structure, but for the Maxwell-Garnett model and differential effective medium model, the predicting results of taking liquid phase or gaseous phase as a continuous phase are not satisfactory, since the three- phase configuration is greatly changed during water content increasing. The performance of these two theoretical models can be improved if the saturation are introduced as dependent weight functions to incorporate the calculated results of liquid phase and gaseous phase.