Analysis of 4-component borehole strain observation based on strain invariant

We offered 5 groups of formulas to compute strain invariant of 4-component borehole strain stations in China and the United States with Mohr's circle model in this paper. 5 groups of the principal strain and its directions of 25 stations are computed and analyzed with the methods of correlation and regression. The result shows that strain invariant changes smoothly in 1-2 years after installation; the principal strain and the principal direction are becoming more and more equal to each other; the correlation coefficient and regression coefficient between 5 groups of maximum and minimum principal strain is close to 1. These showed that borehole strainmeter data objectively record the real strain. However, 5 groups of directions of principal strain are very different, the reason for this phenomenon is that the maximum root mean square errors of principal strain obtained by error propagation theorem are limited, but maximum root mean square errors of its directions are unlimited. Finally, some factors that affect the borehole strain variable consistency are given. The result shows that the borehole strain observation technology has made important progress after half a century of practice, but there are still some technical problems to be solved because of its special difficulties.