RI 8414 Least Squares Calculation of Horizontal Stresses From More Than Three Diametral Deformations in Vertical Boreholes

The borehole deformation gage and overcoring techniques developed by the Bureau of Mines form one of the primary methods of determining in situ rock stress. This report describes a least squares method of calculating the average rock stress components in the horizontal plane from more than three diametral deformation measurements in a vertical borehole. This least squares analysis provides a means of determining the multiple correlation coefficient, the variance, and the scatter for a set of deformation measurements. From this information, confidence limits can be calculated for the secondary horizontal principal stresses and their directions. The material presented in this report can be used as a guide to the development of least squares solutions for stress measurement techniques other than the borehole deformation method. Since the statistical information that results from the least squares method is extremely useful in the interpretation of results, it is recommended that a least squares analysis be used on stress measurement data whenever possible.