The weathering of stones due to dissolution

We hypothesize that the weathering of building stones can be attributed to surface dissolution processes. We assume that chemical interactions occur on grain boundaries and/or microcracks and that diffusion is the controlling process. A dissolution layer (rind) develops adjacent to the weathering surface. We quantify the extent of dissolution by introducing a damage variable f; f=0 for pristine rock, and when f=1 the rock disintegrates. We assume that the variations of the damage variable are given by the diffusion equation. We solve two problems. The first is for the structure of the transient dissolution boundary layer prior to surface disintegration. We find an incubation time t_i, before active weathering (disintegration) begins. The second is the solution for steady-state weathering with a constant weathering velocity v_w. Our results are entirely consistent with weathering studies on Carrara marble gravestones in the United Kingdom. Typical incubation times are t_i=20-30 years, and typical steady-state weathering velocities are v_w=5-50 μm year^-1.