非贯通裂纹岩石压缩试验及非线性回归分析

Compression Test of Intermittent Crack Under Uniaxial and Nonlinear Regression

采用岩石力学伺服试验机,对非贯通预制裂纹大理岩进行了单轴压缩试验;利用简单相关系数和偏相关系数,基于试验结果对裂纹间距、裂纹长度、裂纹数目、裂纹倾角等因素与试验岩样抗压强度之间的相关性以及各影响因素之间的相关性进行了对比分析.结果表明:非贯通预制裂纹岩石的各个影响因素之间相互交叉影响,互为因果,存在较为严重的多重相关性;偏相关系数能更为合理、准确地反映出影响参数之间的相互关系,可以作为定量描述多重相关性的尺度.针对非贯通裂纹岩石的各个影响因素之间的多重相关性,采用偏最小二乘法对影响参数进行主成分的提取,使得相互影响的因素转变为相互之间不相关的主成分,并分析解释了所提取的主成分.采用多项式对普通偏最小二乘法回归进行了改进,得到了一种不仅能有效克服参数之间的多重相关性,而且可以进行偏最小二乘非线性回归分析的方法;基于提取的各主成分,对非贯通裂纹岩石各个影响因素与单轴抗压强度进行了偏最小二乘非线性回归分析,得到了较为精确的回归预测结果.

Uniaxial compression tests were carried out for marble with intermittent pre-existing cracks by using the rock mechanics servo-controlled testing system. Based on the experimental results, the correlations among crack distance, crack length, crack number, crack angle and compressive strength were analyzed. The result shows that these factors of pre-existing cracks rock affect each Other and have a significan multiple correlation among them. Partial correlation coefficient can accurately reflect the interdependence of influencing factors and suit to be a dimension for quantitatively describing multiple correlations. In order to avoid the hazard of multiple correlations, principal components were extracted using the partial least-squares method, making those factors affecting each become in-correlate principal components. At the same time, extracted principal components were analyzed. A new algorithm is put forward by combining the polynomial with the partial least-squares method. The new method can not only avoid the hazard of multiple correlations but also carry out the nonlinear regression analysis. Throughout this method, the interdependences among all kinds of influencing factors of pre-existing cracks rock were regressed. The result shows that the nonlinear regression model of rock accords well with the measured values.