Computing maximum and minimum horizontal stresses in in-situ stress measurements

At present, for the measurements and applications of in-situ stress, people often use the two nearly horizontal principal stresses or their projections on horizontal surface to replace or estimate the maximum and minimum horizontal stresses. Generally, there are no considerable errors. But when the stress structure is special, this replacement or approximation will bring great errors, even harm to engineering practice. To argue for this fact, taking projection approximation as an example, the variations of azimuth and magnitude error with the stress shape factor <>R and the inclination of the principal stress axis and different magnitudes of the maximum and the minimum principal stresses in three different 3D stress states are discussed. Also, as examples, the errors of azimuth and magnitude are calculated using the in-situ stress measurement data. Theoretical analysis and examples demonstrate that there may be considerable errors in using the projections of two nearly horizontal principal stresses on horizontal plane to approximate the two horizontal stresses. It is suggested that in the study of horizontal stresses or physical quantities related to horizontal direction, the proposed method should be employed.