There are several limitations to this technique. The first is that the finite element algorithm is linear elastic, while the cement paste should be treated as a viscoelastic material. However, at later ages, where durability questions are important, the cement paste is well-hydrated and not nearly as viscoelastic as at early ages [4], so that linear elasticity certainly becomes a better approximation. The second limitation is that the technique only considers stress analysis, and does not consider fracture mechanics, which is the correct theory of how cracks propagate [10]. The regions of maximum tensile stress will certainly tell where cracks will be important, but will not precisely define crack propagation.
A third limitation is the finite size of the samples, which is only partly overcome by using effective material boundary conditions. However, our electron microscope can image fairly large regions, so that this is only a limitation for crack patterns that are correlated over length scales longer than we can image at one time. Also, we could, if necessary, take carefully correlated mosaic images. Related to this are questions of boundary conditions, for example: How good is the approximation of zero displacement boundary conditions at the bottom of a pavement?
A fourth limitation is that while the cracks were formed in 3-D, we are studying them in 2-D. This limitation can only be overcome by developing 3-D images of damaged concretes, and applying the same technique in 3-D. The program thermal3d.f [ 5] exists, which handles 3-D images, and 3-D images of damaged concrete can be acquired using x-ray microtomography at resolutions that are sufficient to see the damage, though perhaps not all the cracks [11]. Acquisition of such images at the resolutions needed (several micrometers per pixel) are not routine, at present.
Even with all of these limitations, however, this technique should at least still give some qualitative insight into how different deterioration mechanisms can cause different crack patterns. The analytic stress patterns around simple isolated shapes can be used to predict crack patterns under different mechanical conditions [12]. When many randomly-shaped aggregates are present, however, a numerical method like that described herein becomes necessary. The finite element programs are documented and available [5, 7], and the image analysis methods necessary are standard tools included in most image analysis packages. This technique represents a first step beyond the usual empirical guessing at deterioration mechanisms from crack patterns, and as such, is a possible new diagnostic tool for concrete petrography.