@MISC{Timoshenko51theoryof, author = {S P Timoshenko and J N Goodier}, title = {Theory of Elasticity,}, year = {1951} }
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Abstract
ABSTRACT The knowledge of the in-situ stress field in rock masses is in general of crucial importance in various areas of geo-engineering, such as mining or civil underground excavations, hydrocarbon extraction, CO2 storage, hydraulic fracture operations, etc. In the context of the Finite Element Method, the in-situ stress conditions should be incorporated in the analysis following the generation of the FE mesh and prior to the consideration of the actions due to the engineering design The method described in this paper involves basically two steps. In the first one a first estimate of the stress state at each Gauss point is proposed, and in a second one global equilibrium is verified and rebalanced nodal forces are applied as needed. While the re-equilibration step is a closed procedure based only on statics, the first estimate of the stress state can be done in a variety of ways to incorporate all the information available, aside of course from the most basic method consisting of using vertical stresses due to gravity and horizontal due to K 0 . In this paper, the various options available are discussed and compared, and one new alternative procedure is developed based on Airy stress function REFERENCES [1] E. T. Brown and E. Hoek, "Trends in relationships between measured in-situ stresses and depth,"