I am reading through the documentation of the HM benchamrks and I found a mismatch between the specific storage defined in the pdf description (1.e-10 or 0), while in the input file the storage is defined for the fracture as S_f, where S_f = 1.e-12 . Can you comment on that?

Additionally, what is the p(x,t) function used to calculate the analytical response presented in the pdf?

After some struggling, I found that a semi-analytical solution can be found in

Wijesinghe, A. M. (1986). Similarity solution for coupled deformation and fluid flow in discrete fractures (No. UCRL-95316; CONF-860910-2). Lawrence Livermore National Lab., CA (USA).
(available here pag 349-358)

I provide a jupyter notebook to reproduce the Wijesinghe’s paper integration and results (without any warranty on its correctness) and to compute values for the p(x,t) function.