关键词: 岭回归, 多重共线性, 初始地应力场, 反演, 岩体

Abstract: To make the initial geo-stress field of rock masses obtained by the inversion analysis more realistic, three conditions are proposed, which are the initial geo-stress field of rock masses should be superposed by compressive stress fields, the tectonic load of boundary obtained by the inversion analysis should not be too large, and the constituent of stress fields obtained by the inversion analysis should be consistent with the constituents of the stresses field measured by the in-situ test. Based on the theory of multiple linear regression, in the inversion analysis of the initial geo-stress field of rock masses, the reason leads to negative, too large and insignificant regression coefficient is uncovered firstly. It is the multicollinearity between independent variables that may lead to negative, excessive and insignificant regression coefficient when the least square method is adopted to obtain the regression coefficients. Then, two sources of multicollinearity are given. The one is that a narrow range of measured in-situ stresses can lead to multicollinearity among independent variables. The other one is that using multiple equations to express the initial geo-stress field of rock masses which commonly leads to nearly completely multicollinearity between independent variables. Finally, some methods for detecting and avoiding multicollinearity are proposed, and applied in the inversion analysis of the initial geo-stress field of rock masses for the Banzhulin tunnel. Based on the results of this inversion analysis, it is found that ridge regression can replace the least square method to solve regression coefficients effectively if independent variables suffer from the multicollinearty.

Key words: ridge regression, multicollinearity, initial geo-stress field, inversion, rock mass