The mechanical paradox of large overthrusts
The mechanical paradox of large overthrusts originates with a fallacious assumption in the conceptual model upon which mechanical analyses of overthrust faulting have been based. The notion that the maximum width of a sheet of rock that may be displaced along an overthrust fault can be determined by using the Mohr-Coulomb failure criterion to compare the strength of the rocks with the stress required to overcome the total frictional resistance to slip (and the total cohesion or adhesion?) over the entire fault surface tacitly assumes that slip is initiated, and occurs, simultaneously over the entire fault surface. This unstated and untenable assumption, which is incompatible with what is known about real faults, is the real explanation for the "mechanical paradox." A realistic model for overthrust faulting must be compatible with the nature of real overthrust faults, and particularly with the way in which displacements, including earthquake displacements, occur on real faults. Most large overthrusts are discrete shear surfaces within a coherent mass of rock that is physically continuous around their ends. Total displacement clearly varies from place to place over these discrete shear surfaces and, moreover, must be the cumulative result of many relatively small incremental displacements that also varied from place to place over the finite part of the fault surface on which they occurred. Each increment began as a local shear failure and propagated along the fault as a "smeared-out" (Somigliana) dislocation at a velocity that was small considering the time required for propagation over the total area of the fault. During any individual displacement "event," whether a megathrust earthquake or a creep event, only a small part of the fault surface was in relative motion at any one time. Fault displacements may appear to occur simultaneously across laboratory specimens that are very small relative to the velocity of propagation of displacement because the transit time is so short. When the linear scale is expanded over six orders of magnitude to encompass an entire surface of a large overthrust fault, however, the transit time is much longer because the velocity of propagation is very small relative to the area of the fault surface, and the displacement clearly involves only a very small part of the fault surface at any one time. The shape and size of overthrust faults result from the propagation of dislocations, and this process is controlled by the strength heterogeneity and anisotropy of the rock mass as well as by variations in the regional stress field, but not by the frictional resistance to sliding integrated over the entire fault surface.