Determination of the In Situ Stress in an Continuous Anisotropic Elastic Rock Mass Using Inverse Problem Techniques

"It is frequently necessary to excavate a tunnel for Civil Engineering purposes, or wells for petroleum exploitation, in laminated rock mass like schists or phyllites or in highly foliated gneisses. The determination of the pre-existing in situ stresses is essential, in order to assure the stability of these excavations. In most cases, the pre-existing triaxial stress field is arbitrary in relation to the tunnel or well axis. For these rock masses the concept of Generalised Plane Strain can be correctly utilized.There are closed form solutions for the calculation of stresses in anisotropic rock masses under Generalised Plane Strain conditions (Lehknitskii, 1981 and Hong , 1994). Based on these analytical solutions, established for the cases of Generalised Plane Strain, a synthetic problem will be formulated: the theoretical in situ stress tensor acting on this rock mass will be determined, with the aid of Bayesian Inverse Problem Techniques, as developed by de Mello Franco (2009). Additionally, the reliability of results obtained will be evaluated, in accordance with the research performed by this author. INTRODUCTIONThe Inverse Problem Technique, as developed in the paper, is based on the definitions and concepts obtained from the current literature and used for the solution of Inverse Problems, but the innovation to be presented is the utilisation of Bayesian Techniques and the determination of the reliability of the results obtained. This will be shown in a synthetic example where the determination of the in situ stress tensor, from strain measurements in a drill hole is supposedly performed. It is assumed that this drill has its axis arbitrarily placed in relation to the rock mass. Generalised Plane Strain conditions will hold for use with problem. The equations of Beltrami – Mitchel, in agreement to Lekhnitskii (1981) and Ong (1994), will be used in this synthetic case, for calculating strains, hypothetically measured in the hole before the final excavations. Finally a synthetic example for the determination of the in situ stress in a fully anisotropic rock mass, based on Bayesian Techniques and its reliability, developed in de Mello Franco (2009) is presented."