An accurate description of the in-situ stress field in a rock mass is crucial in different areas of geo-engineering such as: underground excavations, hydrocarbon extraction, CO2 storage, hydraulic fracture etc. In this paper, a novel methodology to numerically generate the in-situ stress state within the Finite Elements framework is presented. It involves two steps: 1) an estimate of the stress components is given for integration point of the discretization, and 2) global equilibrium is verified and re-balancing nodal forces are applied if needed. While the second step is a closed procedure based only on statics, the estimate of the in-situ stress field can be done in different ways in order to incorporate all the information available of the rock mass. In this paper, more traditional approaches are discussed and a new procedure based on the Airy stress function is described, in order to generate a stress state proposal at each Gauss point of the domain. Finally, the performance of different approaches is illustrated with a reservoir example.


A rock mass or any geological material that is located at a certain depth is subjected to an in-situ stress field. This stress field is the result not only of the geometry and weight of the geologic structure but also of a non-trivial geologic history. This history may include complex phenomena such as deposition, compaction, erosion or tectonic events.

Gravitational stresses are induced by the weight of the overburden, and often the vertical (or z) axis is a principal stress direction, while the other two principal stresses are contained in the horizontal plane (xy). Tectonic stresses may be the result of the tectonic movements at local or regional scale. The residual stresses are produced by strain energy locked-in in the rock from previous processes such as burial, lithification, denudation, heating and cooling. According to Friedman, 1972 a fraction of these residual stresses persist even after the rock is freed from boundary loads. When the in-situ stresses at a site are measured using any of the techniques available, the stress measure obtained includes the contributions from all those origins combined.

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