The structures considered are far simpler than that of a three-dimensional polycrystalline rock. They are simplified versions of the natural structures modeled. The physical and chemical behavior is simplified from what might occur in nature. The simplifications allow me to carry out an analysis of the process by elementary means. If warranted, especially to interpret a good set of field data, a refined model might be formulated and treated by a more laborious analytical or numerical approach (for example, see Kenkmann and Dresen, 1998). The structures treated are not as complex and varied as those in Win’s experiments with deforming and recrystallizing polycrystals; yet they have a resemblance to them. In this respect, I have approached the next step, to understand the underlying physics and chemistry of processes in a polycrystalline rock and the evolution of its fabric.

Although it is conventional to speak of "pressure shadows" (Etchecopar and Malavielle, 1987), a reviewer has pointed out two problems with this usage. First, what one observes is a mineral segregation; the stress inhomogeneity is no longer present. Second, the magnitude of the stress inhomogeneity operative when the mineral segregation formed is, as the present results show, proportionately reduced the more prominently developed the segregation, for comparable bulk strain. When there is no segregation, because of sluggishness of transport or kinetics, all other things being equal, the pressure shadow has maximal magnitude. A third problem, as with the term "pressure-solution," is that the pressure, or negative of the mean stress, is not always the stress quantity whose gradient drives the transport. In the present case, that quantity is the local interfacial normal stress.

The same reviewer also pointed out that the present formulation involves the somewhat paradoxical choice of concentrating dissolution, transport, and precipitation at the boundaries of objects – boudins, porphyroblasts, and folded layers – the dimensions of which are several orders of magnitude larger than the grain scale. It would seem more plausible that such processes, because of scale dependence – especially in diffusive transport, would operate much more efficiently at the grain scale, and, thus, that in most cases the transport of material at a much larger scale would be "short-circuited." This idea has also occurred to me and to others. Observations are generally in support of transport at the larger scale, as in the present models. Of course, in the case of boudin separation, there is no alternative. The same issue also enters in "pressure-solution", in which discrete solution seams (or stylolites) dominate over any pervasive grain-scale process. The suggestion is that large, continuous surfaces behave differently from grain interfaces. As the reviewer suggested, this may have substantial importance in treating all types of transport in rock. Clearly, interconnected cracks will dominate in fluid flow if the grain-scale permeability is sufficiently low. In diffusive transport, intergranular surfaces may be substantially tighter than larger surfaces. Equivalent diffusive transport lengths for two surfaces with effective "gaps" of d₁ and d₂ will have the ratio

As with solution seams, it may also be that these larger surfaces are crack-like in their behavior.

NSF Grant EAR 95-26983 to L. B. Goodwin and R. C. Fletcher supported this research. Reviews by Ron Vernon and an anonymous reviewer were helpful.