The theory of poroelasticity is nowdays a widely accepted framework to study interactions between fluid flow and solids deformation in porous media. On the basis of Terzaghi's work in 1923 where the deformation of the porous media was primarily cause by reageremnts of the porous voids, Biot (1941) generalized the theory of consolidations of porous media to three dimensions where not only the compressibility of the media is introduced but also the compressibility of the filling fluid.
For further reference please refer to Cheng, A. H. D. (2016), Verruijt, A. (2013) or Wang, H. F. (2017). Here, you will find the analytical solution to typical poroelasticity problems as well as numerical solutions coded on MOOSE's PorousFlow module (https://www.mooseframework.org/modules/porous_flow/). Feel free to colaborate and expand this database.
Biot, M. A. (1941). General theory of three‐dimensional consolidation. Journal of applied physics, 12(2), 155-164.
Cheng, A. H. D. (2016). Poroelasticity (Vol. 27). Cham, Switzerland: Springer International Publishing.
Terzaghi, K. (1943). Stress conditions for failure in soils. Theoretical Soil Mechanics; John Wiley and Sons: New York, NY, USA, 7-11.
Verruijt, A. (2013). Theory and problems of poroelasticity. Delft University of Technology, 71.
Wang, H. F. (2017). Theory of linear poroelasticity with applications to geomechanics and hydrogeology. Princeton University Press.