黏土微结构参数的相关分析和主成分分析
Correlation analysis and principal component analysis on microstructure parameters of clay
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摘要: 将统计学中的相关分析和主成分分析方法引入到对土微结构参数的研究之中,并给出了具体分析方法。从而不仅可以消除不同微结构参数在反映土体内部机理方面存在的"部分信息重复"现象,而且可以大大降低微结构参数的维数。根据对累积贡献率的要求不同,可以用不同数目的主成分近似表达所有微结构参数携带的大部分信息,这使得微结构参数的广泛应用成为可能。降维得到的主成分指标,可以用来建立本构方程、强度准则等土力学关系,以反映土微结构特征与宏观力学现象之间的固有联系;并可以利用建立的关系研究土微结构再造过程。对由64幅SEM照片组成的黏土样本进行的域微结构分析表明,微结构参数之间存在明显的"信息重复"现象,2个主成分就可以反映6个原始微结构参数95.28%的信息,从而达到了降维目的。Abstract: The techniques of correlation analysis and principal component analysis are introduced into the field of microstructural study.The means of correlation analysis and principal component analysis on the parameters of soil microstructure are put forward successively.These means can be utilized to eliminate the superposition messages obtained from different parameters of microstructure and to reduce the dimension of parameter matrix for microstructure markedly.The minority representative principal components can approximately synthesize the overall meaning of microstructure according to the desired value of accumulative contribution,which makes possible the extensive use of microstructural theory in soil mechanics.The deduced principal components can be used to establish constitutive equations,strength criteria and other theories in soil mechanics to mirror relationships between microstructure and macroscopic mechanical variables.Studies on a swatch composed by 64 clay SEM photos display that the message superposition is clear and severe among microstructural parameters.The first and the second principal components deduced,whose accumulative contribution is 95.28%,can exhibit almost all messages expressed by the 6 original microstructure parameters.The proposed method can be employed to establish the principal components for any kind of soil even it is illustrated by the given clay samples.