Steven Wojtal

Strain hardening and strain softening in fault zones from foreland thrusts

The movement of thrust sheets is accomplished, in part, by deforming the rocks adjacent to thrust faults. In foreland fold-and-thrust belts, emplacement generates an array of mesoscopic faults in a thick layer along the base of a sheet. Ductile deformation of rocks in the layer occurs by displacing fault-bounded blocks relative to one another in a kind of mesoscopic “grain boundary” sliding. Analyses of data from three southern Appalachian thrust sheets indicate that this block sliding is first accompanied by strain hardening, then by strain softening, and it is accommodated by intra-block fractures, small faults, and veins. The density of accommodation features increases near thrusts, and where these features become sufficiently numerous, a layer of cataclastic rocks forms along the thrust. We describe foliated cataclasites from two thrusts, the microstructures of which indicate that the cataclasites exhibited extreme ductility, interrupted occasionally by brittle processes. Deformation of the cataclasites was accompanied by strain softening. Strain softening deformation in fault arrays near thrusts is genetically related to strain softening deformation in cataclasites. During the formation of the cataclasite, rocks in the sheet are impelled to cross a strain energy “hump,” after which they deform at either higher rates or lower stresses.

Deformation within foreland thrust sheets by populations of minor faults

The dominant deformation mechanism within foreland thrust sheets is the displacement of blocks of weakly deformed rock on discrete, mineral-coated minor faults. In highly deformed layers at the bases of three Southern Appalachian foreland sheets, such minor faults are members of families or populations of consistently oriented structures. The deformation style is similar in all three sheets. Rock nearest each thrust was shortened in the direction of sheet transport and thickened by a family of faults oriented at low angles to the thrusts. Rock further above each thrust experienced only the first of these two deformation stages. Statistical analyses of fault populations from these three sheets demonstrate that their deformation is quantitatively as well as qualitatively similar. Deformation due to movement on minor faults is statistically homogeneous at the scale of an outcrop in one of these sheets; strain due to minor faults can be measured in that sheet. A strain profile across this sheet is similar to strain profiles across continuously deformed sheets from internal portions of mountain belts, suggesting that their responses to emplacement are similar.

Changes in fault displacement populations correlated to linkage between faults

In Carboniferous strata exposed at the western margin of the southern Appalachian (U.S.A.) fold—thrust belt, mesoscopic faults accommodated strains as the Cumberland Plateau thrust sheet moved ≤ 1 km WNW on a sub-horizontal detachment. These faults are confined to a layer ∼ 75 m thick above the detachment. In the upper part of this ∼ 75 m thick layer, a laterally persistent coal seam separates two stratigraphic units subjected to different amounts of sub-horizontal elongation. Distinct sets of mesoscopic faults that cut bedding at high angles and have normal offsets accommodate the strains in each unit. Below the coal seam, a sample line ∼ 500 m long intersects 504 faults. A plot of log N (size rank) vs log d (dip separation in mm) for these faults is linear, suggesting that a scaling law N = ad−c holds for this population. Least-squares regression gives c ≈ 0.8 and log10 a ≈ 3.1. Above the coal seam, a sample line ∼250 m long intersects 745 faults. A plot of log N vs log d for these faults has two distinct linear trends. Faults with separations ≤ 1.25 m yield a scaling law N = ad−c with c ≈ 0.5 and log10 a ≈ 2.9. Seventeen faults with separations d ≥ 1.25 m define a second linear segment N = a′ d−c′, with c′ ≈ 1.8 and log10 a′ ≈ 6.9. The break in slope at d ≈ 1.25 m corresponds to faults with heights of ∼30 m, roughly equal to the thickness of the faulted strata. Faults here with d ≤ 1.25 m and d ≥ 1.25 m, which exhibit different scaling characteristics, are, respectively, analogous to faults within and those that extend across the brittle crust in regional studies. Comparing the two displacement populations described here, small-offset faults make a proportionally smaller contribution to the total strain in the larger strain setting. This pattern, which is observed elsewhere, suggests that fault systems within individual layers exhibit different scaling characteristics at different stages in their history. This contribution argues that fault linkage is the key to such changes in fault scaling behavior; it is a mesoscopic to macroscopic structural change that alters the subsequent development of faults. Fault linkage, like fault size or sampling dimension, should be considered in examinations of fault scaling laws.

Measuring displacement gradients and strains in faulted rocks

In homogeneous deformations, spatial gradients of the displacement field are constant and related to strain parameters by straightforward algebraic relationships. Deformations which are inhomogeneous (displacement gradients values are not constant) when viewed at one scale may be statistically homogeneous (have approximately constant displacement gradients) when viewed at a smaller scale. From average values of the displacement gradients in a statistically homogeneous deformation, one can calculate bulk strains. Displacement diagrams provide a way to determine the displacements of material points at different positions within inhomogeneously deformed media. From these data, one may measure mean values of the displacement gradients for the deformation, and if the gradients are approximately constant, calculate bulk strains. This strain measurement technique yields reasonable strain values. Strain values from a natural fault array in the Tennessee Appalachians (U.S.A.) differ slightly from values reported earlier, but still conform with kinematic indicators in those deformed rocks.

Fault scaling laws and the temporal evolution of fault systems

Abstract Through an analysis of the temporal evolution of duplex fault systems, this contribution shows that it is unlikely that all faults in a deformed area will conform to a single frequency-size scaling relationship. The development of a duplex leads to different size—frequency relationships for the faults that compose the duplex and those confined to individual horses. The faults that compose the duplex define segments with relatively steep stopes on a log N (number of faults, i.e. frequency) vs log D (displacement magnitude, i.e. size) plot; faults within individual horses define segments with relatively shallow slopes on a log N vs log D plot. The distinction between these two types of faults in a duplex is akin to the distinction between large active faults, which cut the entire seismogenic layer, and small active faults, which do not extend across the seismogenic layer. If, as is often the case, the faults that compose a duplex do not extend across the seismogenic layer, the stepped nature of the resulting log N vs log D plot may make it particularly difficult to assess the contribution of these ‘small’ faults to regional deformation. Since duplex geometries result in part from anisotropies present in deforming rocks, the anisotropy present in nearly all crustal rocks will affect the size-frequency relationship observed for systems of faults. Different parts of a deforming rock mass are likely to have different initial anisotropies. Combining data on fault systems from markedly different portions of a deforming region may, then, obscure the unique characteristics of the size-frequency relationship in either area and may lead to inaccurate assessments of the relative contributions of ‘small’ and ‘large’ faults to regional fault-accommodated strains.

Displacement control of geologic structures

Structural geologists routinely undertake geological analyses, particularly studies of faulting, by assuming that applied stresses are the controlling parameters. An alternative view is the assumption that material velocities, incremental displacements, or total displacements are imposed on the system, with stresses then part of the material response to these imposed boundary conditions. In our view, taking velocities and displacements as independent variables in deformation and stresses as dependent variables requires fewer assumptions and is more consistent with the observed geology. # 1999 Elsevier Science Ltd. All rights reserved.

Partitioning of Deformation within Several External Thrust Zones of the Appalachian Orogen

Mesoscopic contractional and extensional faults dominate many external thrust zones. The fault arrays occur in the hanging walls of some thrusts and in the footwalls of others. In a thrust zone from the Little Mountains fold-thrust belt of New York state mesoscopic faults cut and offset a major thrust contact and involved rocks from the thrusts hanging wall and its footwall simultaneously. The Little Mountains exposure indicates that minor faults were active during thrust slip and are not early-formed features which were passively translated with the remainder of a sheet. When both contractional and extensional mesoscopic faults occur in thrust zones, foreland-dipping extensional faults overprint contractional faults. Contractional and extensional microfaults (with

One-dimensional models for plane and non-plane power-law flow in shortening and elongating thrust zones

R_{1} and R_{2}