非饱和土双应力变量广义土水特征曲线理论模型构建

土水特征曲线(soil-water characteristic curve,SWCC)方程是非饱和土力学中最重要的土性表征手段之一。该文评价当前经典的SWCC方程,指出其未具有包容复杂因素的能力,具有灵活性的优点但却同时具有对试验数据量依赖性高的缺点,不能处理多孔隙尺度集群土体固-液-气共同运动及作用的水力-力学耦合效应问题。建立双应力变量广义SWCC概念图示并定义相对体积含水比,基于Fredlund双应力变量理论及van Genuchten土-水表征方程,构建考虑土体变形及多孔隙分布形态的双应力状态变量的广义SWCC方程。相较于2个参数的Brooks等的方程、3个参数的van Genuchten方程以及4个参数的Fredlund等的方程,广义SWCC方程仅3个参数,其中2个参数在双对数坐标系的"相对体积含水比-吸力"平面中进行最小二乘法线性拟合得到,仅1个参数需非线性最小二乘法拟合得到。该模型可利用不同应力状态下的至少3个土水试验数据点,绘制出1条具有适宜精度的单峰SWCC;方程考虑了多峰孔隙概率密度函数分布及土体变形因素,实现了从应力历史推广到应力状态的广义情况,为定量描述不同孔隙结构土体双应力状态下的持水特性、渗透特性和强度特性提供了一条途径。

Establishment of generalized soil-water characteristic curve theoretical model considering two stress state variables for unsaturated soils

Abstract: As one of the fundamental soil-water modeling equations, soil water characteristic curve (SWCC) is widely employed to study soil-water retention, permeability, strength characteristics in the fields of agricultural engineering, environmental engineering, geotechnical engineering, etc. In this study, we evaluated the current classic SWCC equations and propose a generalized SWCC model. By summarizing the current models, we found that the current model considered only a single or two influential factors, the forms of the current equations were complex, they were sensitive to experimental data and the fitness accuracy was highly dependent on the numbers of the experimental points. And most of them couldn''t deal with the conditions of multimodal probability pore-size density function and hydro-mechanical coupling effects for the solid-liquid-gas materials in soil. Based on Fredlund et al''s two stress variables theory and van Genuchten''s soil-water characteristic equation, the concept of generalized SWCC was defined. Three characteristic suction zones included boundary-effect zone, transition zone and residual zone of unsaturation. We defined the generalized SWCC as spatial curves reflecting relationship between matric suction and soil water content under the condition affected by multiple factors such as pore structure, stress history and stress state. The relative volumetric water ratio was proposed. The stress history was expressed with initial void ratio and the stress state was described with void ratio. Thus, the relative volumetric water ratio was defined as a ratio of water content-related function and initial volume. Relative fluctuate volumetric water content was defined as the difference of volumetric water content and residual volumetric water content. Based on the relative fluctuate volumetric water content, the relative volumetric water ratio was expressed as the other form. Then, the figure of net normal stress-logarithm of matric suction-logarithm of relative volumetric water ratio corresponding to the characteristic suction zones was plotted. A good linear relationship (r>0.90, P<0.05) was found among the net normal stress, logarithm of matric suction and logarithm of relative volumetric water ratio. Thus, the generalized two stress state bimodal SWCC model was derived, which considered the multimodal probability pore-size density distribution function and soil deformation. Compared with the 2-parameter Brooks et al''s equation, 3-parameter van Genuchten equation as well as the 4-parameter Fredlund et al''s equation, the proposed generalized SWCC only had 3 parameters, 2 of which could be obtained by least-square linear fitting method in the plane of log-log coordinate system of relative volumetric water ratio versus matric suction and only one of which would be achieved by the nonlinear least-square fitting method. The model fitness needs at least 3 experimental points. The model provides with a new way to predict the soil-water retention, permeability, strength of the soil quantitatively in an easier and timesaving process.