Volumetric bands are associated with primarily volumetric strain localization. Dilation bands form in response to and generally perpendicular to the maximum remote extensional stress (Du Bernard et al., 2002). On the grain scale, deformation mainly involves the enlargement of pore space between, or through, the neighboring grains (Figure 1) and may have some lateral shift with respect to adjacent grains. In contrast, compaction bands form in response to, and generally perpendicular to, the maximum remote compressive stress. It is commonly assumed that they initiate with the collapse of pore or grain-scale flaws, and then propagate outward to form tabular inclusions of compacted material of a few centimeters thick and tens of meters in planar extent. Viewed in thin section (Figure 2), the boundaries of compaction bands can be delineated within the precision of a few grain size (Figure 2a). Judging from the overall continuity of the depositional bedding cut by the bands (Figure 2a), and absence of granular disaggregation despite grain fracturing, the volume change appears to have resulted from uniaxial compaction normal to the plane of the band.

Figure 1. Dilation bands and joints as distinct classes of opening-mode failure. (a) Dilation bands are characterized by large pores that apparently grow from initial pores by grain displacement over a zone of finite width. (b) In contrast to the conceptual diagram in (a), joints are characterized by two discrete surfaces that form by inter and transgranular fracturing with planar boundaries that move apart from each other. From Du Bernard et al (2002).

Figure 2. Compaction bands in the Aztec sandstone. (a) Mosaic of a compaction band at high angle to depositional bedding, which passes through the band with no apparent shear offset, change in direction, nor change in thickness. White grains are quartz, dark grains are mostly stained orthoclase, blue is epoxy-filled pore space. (b) Backscatter electron image (BEI) from just outside the compaction band. Light gray is quartz, off-white is orthoclase, dark gray is kaolinite, stark white is hematite, black is pore space. (c) BEI from inside the compaction band. Note the abrupt drop in porosity, pore size, and pore connectivity accommodated by intense damage to quartz grains. This damage as well as attendant grain interpenetration is predominantly due to pervasive microfracturing. Despite grain fracturing, granular disaggregation is absent. From Sternlof (2006).

Relatively high porosity, greater than 10 to 15 percent (Holcomb et al., 2007 and Aydin et al., 2006), appears to be necessary for the formation of compaction bands. In addition, the rock mineral composition and presence and content of cement appear to have a significant influence on compactive strain localization (Haimson and Lee, 2004).

Several laboratory investigations have produced compaction bands. Olsson (1999) and Olsson and Holcomb (2000) are among those who produced compaction bands and documented their transverse growth or thickening in experiments. Wong et al. (2001) have also produced discrete compaction bands in the laboratory. The associated stress-nominal strain curves have a saw-tooth appearance, with the local stress drops correlating with the formation of individual bands. In contrast to the wide compaction bands observed by Olsson and Olsson and Holcomb, the compaction bands in Wong's experiments are thin and interlayered with uncrushed material.

Different theoretical approaches have been taken to describe the formation or the nucleation and propagation of compaction bands. We have mentioned the Cap model under deformation bands. However, the longitudinal extension of bands to lengths of tens of meters requires propagation due to stress concentration at their tips (Sternlof et al., 2005; Katsman et al., 2006). A good summary of these models are given by Rudnicki (2007).