聚类分析和因子分析在黄土湿陷性评价中的应用

影响黄土湿陷性等级的因子之间存在着相关性,针对这一问题,利用聚类分析和因子分析理论研究了因子之间的相关性,并建立了分析模型。选用天然重度、干重度、孔隙比、含水率、塑性指数5项指标作为评价因子,以湿陷系数作为评价指标,通过聚类分析和因子分析表明黄土的天然重度、干重度、孔隙比对黄土湿陷性等级影响具有共性,可归为一类因子;含水率和塑性指数分别为一类,这样就将相关的原始因子转换为相互独立的因子。将聚类分析和因子分析引入黄土湿陷性系数等级评价中,不仅保留了原始因子的信息,而且还消除了多重共线性的影响,减小了误差,提高了分析结果的准确性。工程实例分析表明,提出的分析模型与实际工程相吻合,具有重要的工程实际意义。

Application of cluster analysis and factor analysis to evaluation of loess collapsibility

To study the relevance existing in the factors which influence the collapsibility of loess, an analytical model is established by using the cluster analysis and factor analysis. The natural specific gravity, dry bulk density, void ratio, moisture and plasticity index are chosen as the evaluation factors; and the collapsible index of loess is selected as the evaluation index. It is shown that the natural specific gravity, dry bulk density and void ratio can be considered as the same class of factors due to their same contribution to the collapsibility of loess. In addition, the moisture and the plasticity are considered as an independent class respectively, which makes the relevant origin factors independent. The cluster analysis and factor analysis are used to evaluate the collapsible level of loess, not only retains the information of origin factors, but also eliminates the influence caused by the multicollinearity; thus makes the analytical results more accurate. Finally, it is demonstrated through an engineering example that the calculation results by the presented model have good agreement with the practical results; and it is significant in engineering practice.