基于双分形级配模型参数的粗粒土渗透系数计算公式

Formula for permeability coefficient of coarse-grained soil based on parameters of two-dimensional fractal gradation model

粗粒土在自然界中分布广泛且在工程中应用普遍。渗透性是粗粒土的重要性质,对于同种粗粒土,因颗粒级配与孔隙特征几乎决定其渗透性,原则上其渗透系数应该可基于颗粒级配和孔隙特征参量计算得到。采用基于分形理论建立的双分形级配模型对粗粒土的连续级配、间断级配进行定量描述,以确定该级配模型的适用性并获得级配模型参数。在此基础上,基于双分形级配模型参数和Kozeny-Carman公式构造出包含级配参量及孔隙率的渗透系数计算公式。在论述了计算公式中各项物理意义后,基于现有文献的实测数据验证该计算公式的有效性。结果表明,双分形级配模型能准确唯一地定量描述粗粒土的颗粒级配;建立的含颗粒级配参量和孔隙率的粗粒土渗透系数计算公式是合理的,该公式适用于计算连续和间断级配粗粒土的渗透系数。

The coarse-grained soil is widely distributed in nature and used in engineering.The permeability is one of its key properties,and for the same type of coarse-grained soil,its permeability is almost determined by the grain-size distribution and the pore characteristics.In principle,its permeability coefficient can be calculated based on the grain-size distribution and the pore characteristic parameters.The two-dimensional fractal gradation model based on the fractal theory is used to quantitatively describe the continuous gradation and gap gradation of the coarse-grained soil so as to determine the applicability of the gradation model and obtain its parameters.Then,based on the parameters of the two-dimensional fractal gradation model and the Kozeny-Carman formula,a formula for calculating the permeability coefficient including grain-size distribution parameters and the porosity is established.After discussing the physical meaning of each item in the formula,the validation of the formula is verified by using the measured data in the existing researches.The results show that the two-dimensional gradation model can accurately and uniquely describe the grain size distribution of the coarse-grained soil.The established formula for calculating the permeability coefficient of the coarse-grained soil including grain-size distribution parameters and the porosity is reasonable,and it is suitable for calculating the permeability coefficient of continuously graded and gap-graded coarse-grained soil.