Compaction zones in ash-flow tuffs result from differential compaction of ash after emplacement. Ash compacts largely by viscous deformation, and the rate of compaction is therefore governed in part by the viscosity of the glass shards. Because viscosity depends largely on temperature, the geometry of compaction zonation will indicate the conditions that governed the cooling history of the ash-flow sheet. These conditions include the emplacement temperature and initial dimensions of the sheet and the heat flux across the boundaries of the sheet. In addition, the degree of compaction decrease at the boundaries of individual ash flows in compound cooling units depends in part on the length of the time interval between successive ash flows.
In order to investigate the relative effects of different initial and boundary conditions on the geometry of compaction zonation, a model of the compaction process is used to calculate compaction profiles for a variety of assumed conditions. The incremental rate of compaction is assumed to be one-dimensional and linearly related to the applied stress, that is, (see pdf for equation) where β is defined as the compaction coefficient of ash. For a given composition of ash, the compaction coefficient depends on temperature, volatile (water) pressure, and porosity; the compaction coefficient of rhyolitic ash may be derived as a function of these variables from the experimental compaction rates reported by Friedman and others (1963). Temperatures in cooling ash-flow sheets are calculated for a variety of conditions by an analytic solution of the transient heat-flow equation. Compaction profiles of idealized sheets are then constructed by calculating compaction increments (Δξ) for uniform time increments (Δt) at various positions within the sheets.
Within the limits of the assumptions implicit in the model, the following conclusions are drawn from the compaction profiles calculated for rhyolitic ash-flow sheets.
The relative position of maximum compaction in vertical profiles is nearly independent of emplacement temperature and initial thickness and occurs at about 40 percent of the compacted thickness above the base of the profile.
Both the degree of maximum compaction and the width of the compaction profile at one-half maximum compaction are sensitive indicators of the emplacement temperature.
The minimum temperature required for incipient compaction is estimated to range from about 625°C for sheets initially 10 m thick to about 575°C for sheets initially 40 m thick.
The compaction zonation of an ash-flow sheet does not vary significantly with lithic differences in the solid substrate, and the compaction zonation is partly governed by lateral heat flow only within a few meters of the margins of the sheet. However, the degree of compaction is drastically reduced in the lower portions of sheets emplaced in shallow bodies of water.
Observable decrease of the degree of compaction may develop at the boundaries of successive ash flows that are separated by time intervals as small as one or two days; the intervening cooling interval must be in excess of several months for successive ash flows to cool and compact independently.