  In a porous rock, the spatial distribution of the pore space induces a strong
heterogeneity in fluid flow rates and in the stress distribution in the rock
mass. If the rock microstructure evolves through time, for example by
dissolution, fluid flow and stress will evolve accordingly. Here, we consider a
core sample of porous limestone that has undergone several steps of
dissolution. Based on 3D X-ray tomography scans, we calculate numerically the
coupled system of fluid flow in the pore space and stress in the solid. We
determine how the flow field affects the stress distribution both at the pore
wall surface and in the bulk of the solid matrix. We show that, during
dissolution, the heterogeneous stress evolves in a self-similar manner as the
porosity is increased. Conversely, the fluid velocity shows a stretched
exponential distribution. The scalings of these common master distributions
offer a unified description of the porosity evolution, pore flow, and the
heterogeneity in stress for a rock with evolving microstructure. Moreover, the
probability density functions of stress invariants (mechanical pressure or von
Mises stress) display heavy tails towards large stresses. If these results can
be extended to other kinds of rocks, they provide an additional explanation of
the sensitivity to failure of porous rocks under slight changes of stress.
