确定土的最大干密度和最优含水率的Cauchy分布拟合法

The Cauchy Distribution Fitting Method for Determining the Maximum Dry Density and Optimal Moisture Content of Soil

为避免人工图解法确定最大干密度和最优含水率任意性大和常规多项式拟合法二次求解繁琐的缺陷,提出一个基于Cauchy分布拟合室内土工击实试验数据的方法。将非标准双截尾Cauchy分布密度函数用于描述土的含水率和干密度关系,从而建立确定土的最大干密度和最优含水率的拟合模型,并采用Excel规划求解工具求解模型。结果表明:Cauchy分布拟合法可以避免人为作图导致的任意性问题,使结果更加客观有效;相较于常用的多项式拟合法,Cauchy分布拟合法可在确定Cauchy分布模型待定系数的同时获得最大干密度和最优含水率,高效便捷。

In order to avoid the defects of serious arbitrariness in determining the maximum dry density and the optimal moisture content with the manual graphical method and the cumbersome quadratic solution with the conventional polynomial fitting method,this paper proposed a method of fitting indoor geotechnical compaction test data based on Cauchy distribution,which employed the non-standard double truncated Cauchy distribution density function to describe the relationship between the moisture content and the dry density of soil,thereby establishing a fitting model to determine the maximum dry density and the optimal moisture content of soil,and then the model was solved by the Excel programming tool.The results showed that the Cauchy distribution fitting method can avoid the arbitrary problem caused by human factors,rendering the results more objective and effective.Compared with the commonly used polynomial fitting method,the Cauchy distribution fitting method can obtain the maximum dry density and the optimal water content while determining the undetermined coefficients,in an efficient and convenient manner.