基于k_w-θ_w关系的非饱和土水力梯度模型

The Unsaturated Soil Hydraulic Gradient Model Based on k_w-θ_w Relation

水力梯度计算是研究渗流问题的重要一环,对于非饱和土而言,含水率的变化使得渗透系数不再是常数,水力梯度计算更加困难.本文基于一维稳态流下连续性方程,结合具体的kw-θw关系,分别获得了基于Gardner模型、Davidson模型和Compbell模型的水力梯度模型.最后通过算例对不同的水力梯度模型进行对比分析.研究结果表明:基于Gardner模型的水力梯度模型为具有双拟合参数的幂函数,基于Davidson模型的水力梯度模型为具有单拟合参数的指数函数,基于Compbell模型的水力梯度模型为具有单拟合参数的幂函数.通过对Lakeland细砂水力梯度与含水量关系模拟计算表明,基于Gardner模型的水力梯度模型在计算细砂水力梯度上效果最佳,基于Davidson模型和Compbell模型的水力梯度模型由于均引入了饱和渗透系数和饱和体积含水率而具有更明确的物理意义.

The hydraulic gradient calculation is important to study the filtration problems. For unsaturated soil, the change of water content makes the permeability coefficient no longer constant, therefore, the calculation of hydraulic gradient becomes more difficult. Based on the continuity equation in one-dimensional steady flow, this paper combined the kw-θw relation to obtain the hydraulic gradient models based on Gardner model, Davidson model and Compbell model, respectively. Finally, the different hydraulic gradient models were compared and analyzed through analysis of examples. The results show that the hydraulic gradient model based on Gardner model is a power function with double fitting parameters; the hydraulic gradient model based on Davidson model is an exponential function with single fitting parameter; and the hydraulic gradient model based on Compbell model is a power function with single fitting parameters. The simulation results of the relationship between the hydraulic gradient and the water content of the lakeland fine sands show that the hydraulic gradient model based on Gardner model is the best in calculating the hydraulic gradient of fine sands, while the hydraulic gradient models based on Davidson model and Compbell model have more explicit physical meanings due to the introduction of the saturated permeability coefficient and the saturated volumetric water content.