This study aims at deriving a closed-form solution of the effective stress state and pore pressure fields around a horizontal wellbore drilled in an anisotropic low permeable rock. As the rock is low permeable and the drilling rate is relatively fast, the undrained condition is thus reasonably assumed. A fully coupled hydro-mechanical problem under the undrained condition is shown to be equivalent to a purely mechanical one. The elastic fields of the latter one, including displacement, stress, and strain, around an elliptical-shaped borehole are derived by using the complex potential approach. Then, the elastic solution of the equivalent mechanical problem allows deriving the pore-elastic field of the considered hydro-mechanical problem. The presence of the pore pressure field solution exhibits the drilling-induced the over pore pressure and the depression around the borehole. This phenomenon was observed in situ when excavating the depth tunnel as reported in the literature. The comparison between the closed-form solution and the FEM solution is made to show the accuracy of the mathematical development. Parametric analysis is also done to study the effect of the anisotropic ratio (ratio of horizontal and vertical Young's moduli) on the occurrence of over pore pressure and of depression. The presence of the poro-elastic closed-form solution derived in this study is very helpful for the borehole stability or the hydraulic fracturing design, in particular the probabilistic design.
