描述土体级配分布的级配方程及其适用性

Gradation equation for describing gradation distribution of soil and its applicability

对Weibull模型公式进行变形和演化,得到一个用于定量表示连续级配分布的级配方程,该级配方程可以表示双曲线、近似直线、反S形曲线3种典型级配分布形态。对粉土、黏土、砂土、粗粒土的级配分布进行拟合,拟合结果均良好。从粒径的分布范围考虑,用理论推导的方法,对级配参数的取值范围进行了详细的研究。将实际拟合结果和理论推导结果相结合,得到最终的级配参数范围:c为0.001~1.5,n为0.065~4.8。将新级配方程与Talbot分形级配方程、吴二鲁单参数级配方程进行对比分析,发现Talbot分形级配方程不能反映反S形级配分布,单参数级配方程不能反映颗粒均匀的窄级配分布,而新级配方程对以上不同级配分布均拟合良好,因此新级配方程具有更广泛的适用性。另外,对级配参数在剔除法、相似级配法、等量替代法、混合法下的演变进行了推导,实现了对缩尺前后级配分布的定量表示。

By deforming and evolving the Weibull model formula,a gradation equation for quantitatively representing the continuous gradation distribution is obtained.The gradation equation can express three typical gradation distribution forms of hyperbola,approximate straight line and reversed S-shaped curve.The gradation distribution of silt,clay,sand,and coarse-grained soil is fitted,and the fitting results are all good.Considering the distribution range of the particle size,the value range of the gradation parameter is studied in detail with the method of theoretical deduction.By combining the actual fitting results with the theoretical derivation results,the final grading parameter range is obtained:c is 0.001-1.5,n is 0.065-4.8.Comparing the new gradation equation with Talbot fractal gradation equation and Wu Er-lu’s single-parameter gradation equation,it is found that the Talbot fractal gradation equation cannot reflect the reversed S-shaped gradation distribution,and the single-parameter gradation equation cannot reflect the uniform and narrow gradation distribution of particles,and the proposed gradation equation fits the above different gradation distributions well.The proposed gradation equation has wider applicability.In addition,the evolution of gradation parameters under the elimination method,similar gradation method,equivalent substitution method,and hybrid method is derived,and the quantitative expression of the gradation distribution before and after scaling is realized.