Modeling the stress state around a borehole, a tunnel or other underground excavations and using it to verify the failure criteria is one of the main challenging goals of geomechanics and geotechnics. This tool provides a solution to a very basic problem of a vertical well located in an isotropic elastic formation subjected to a farfield vertical stress σV and maximum and minimum horizontal stresses, σHmax and σhmin, respectively. The borehole wall is assumed to be impermeable (due to a perfect cake) and Terzaghi's effective stress is considered (Biot's coefficient equal to 1). The plane strain condition on the horizontal plane is assumed. Analytical solutions to that problem was derived by Kirsch (1898) which are also annexed in many petrophysical handbooks (e.g. Fjaer et al., 2008; Sayers, 2010, Cui et al., 1997).
Fjaer, E., Horsrud, P., Raaen, A. M., Risnes, R., & Holt, R. M. (1992). Petroleum related rock mechanics (Vol. 33). Elsevier.
Sayers, C. M. (2010). Geophysics under stress: Geomechanical applications of seismic and borehole acoustic waves. Society of Exploration Geophysicists and European Association of Geoscientists and Engineers.
Cui, L., Cheng, A. H., & Abousleiman, Y. (1997). Poroelastic solution for an inclined borehole. Journal of applied mechanics, 64(1), 32-38.
Kirsch, E. G. (1898). Die Theorie der Elastizit t und die Bed rfnisse der Festigkeitslehre. Zeitshrift des Vereines deutscher Ingenieure, 42, 797-807.