MK模型的拟合方程和预测方程在土-水特征曲线中的应用及参数敏感性分析

Fitted and predicted equations of MK model for soil-water characteristic curve and their parametric analysis

土-水特征曲线可以预测非饱和土的各种性质(如:非饱和渗透系数、剪应力和热学性能等)。但测量土-水特征曲线耗时久且花费昂贵。为了解决这一问题,目前,很多研究都致力于从基本的岩土工程性质预测土-水特征曲线。基于此,以MK(Modified Kovács)模型的2种形式(拟合方程和预测方程)为土-水特征曲线模型,以Matlab编程语言中的cftool为拟合工具,以西宁黄土、粉砂土、红黏土和冰碛土4种细粒土为研究对象,对比拟合方程和预测方程描述细粒土土-水特征曲线的效果和差异,分析MK模型中黏附饱和度S_a=1解ψ_c的变化规律,提出了基于MK模型的饱和度进行参数敏感性分析的计算公式。结果表明:拟合曲线和预测曲线在描述4类典型细粒土土-水特征曲线时均具有较好的效果,但拟合曲线整体上优于预测曲线;土壤质地和黏粒含量影响ψ_c值;饱和度对拟合参数a的敏感性较大,对拟合参数m的敏感性较小。

Soil-water characteristic curves（SWCCs） can be used to predict the properties of unsaturated soils, including unsaturated permeability coefficient, shear strength and thermal property. However, the measurement of SWCCs is time-consuming and expensive. To solve this problem, considerable research efforts have been made to developing the procedures to directly estimate the SWCCs from basic geotechnical properties. Two types of MK models（fitted equations and prediction equations） are used for the SWCCs models, and the cftool in the scientific programming language Matlab is applied to fit the MK models, based on which four types of soils are analyzed, i.e. Xining loess, silty sand, red silty clay, moraine soil. The effects and differences of fitting equations and prediction equations are compared with regard to their capability of describing SWCCs of fine-grained soils. A calculation formulation is developed for parametric analysis based on MK model. It is shown that both the fitted equations and predicted equations of MK model perform well in describing SWCCs of the 4 types of fine-grained soils, though the former is better than the latter; it is also shown that soil texture and clay content influence ψc. The sensitivity analysis shows that the degree of saturation is more sensitive to parameter a than to parameter m.