基于独立分量分析的黏土欧拉数与物理力学指标关系研究

Study on the Relationship of Clay Euler Number with Physical and Mechanical Indexes Based on Independent Component Analysis

为了分析欧拉数与物理力学指标的关系,首先采用室内土工试验测定了不同黏土的孔隙比、黏聚力、内摩擦角,通过选择测试土块、确定放大倍率、图像处理和细观特征参数提取等4个步骤测试黏土欧拉数;然后基于独立分量分析(ICA)方法,利用Matlab编制计算程序,建立了黏土欧拉数与孔隙比、黏聚力和内摩擦角的关系式;最后对关系式进行验证.结果表明:欧拉数越大,联结带数目越多,颗粒接触较为紧密,凝结趋势较强,宏观上表现为孔隙比越小,强度指标越大;ICA方法能够对所获取的解混信号进行正交化和归一化处理,去除黏土物理力学指标间的多重共线性,关系式系数矩阵的条件数恒等于1,获取的待定系数值最稳定;回归方程相关系数为0.978 0,验证组试验值与计算值误差仅为0.67%.该关系式具有较高稳定性、相关性和准确性,有助于为准确预测欧拉数和分析细观结构特征提供条件.

In order to analyze the relationship between the Euler number and physical and mechanical indexes,the porosity ratio,cohesion and internal friction angle of different clays were measured by geotechnical laboratory tests.The Euler number of clays was measured by four steps:selecting test soil block,determining magnification,image processing,and extracting microscopical characteristic parameters.Then,based on the independent component analysis(ICA) method,the relationship between the Euler number of clay and the pore ratio,cohesion and internal friction angle was established by MATLAB.Finally,the relationship was verified.Results show that the larger the Euler number is the more the number of bonding zone is,and the closer the particle contact is the stronger the condensation trend is.Macroscopically,the smaller the pore ratio is the larger the strength index is.The ICA method can orthogonalize and normalize the obtained unmixed signals,and remove the multi-collinearity between the physical and mechanical indexes of clay.The condition number of the coefficient matrix of the relationship equation is constantly equal to 1,and the undetermined coefficient value is the most stable.The correlation coefficient of the regression equation is 0.9780,and the error between the test value and the calculated value of the validation group is only 0.67%.This formula has high stability,correlation and accuracy,which is helpful to accurately predict Euler number and analyze the meso-structural characteristics.