What, if Anything, Should the Structural Geologist Know about the Mechanics of Rock Deformation?
Raymond C. Fletcher, Pennsylvania State University
Much work in structural geology does not involve mechanics. An example is the determination of the complex structure of metamorphic rocks in New England, an area of limited outcrop, which has involved dozens of workers and 10s to 100s of structural geology person-years. Concepts of stress, strain or rheological behavior are not required. Another example is the construction of a balanced cross-section using the geometric methods of fault-bend and fault-propagation folding.
Concepts of stress, strain and rheological behavior, incompletely integrated into a complete mechanics, are of limited use in the formulation and answering of questions and problems in structural geology. Maybe they are distracting. Stress, without equations of stress equilibrium; strain, excluding kinematics; and results on deformation mechanisms, excluding specification of constitutive relations do not allow formulation of models (boundary-value problems). It seems pointless to introduce these concepts unless the development is brought to the point of modeling. Is the student motivated? I first encountered a BVP ~ 50 years ago, for flow of a viscous fluid between approaching, or separating, rigid plates, in Jaeger's: Elasticity, Fracture and Flow with Engineering and Geological Applications.
A question and procedure for answering it, which involves substantial knowledge of a complete mechanics, is embodied in Gilbert's study of laccoliths in the Henry Mountains. The "sketch," more a "mental construct" than an interpretative drawing, but which incorporates such drawings, starts with motivating observations: (i) the image of a laccolith lifting the super-incumbent rocks; and (ii) the increase in size of a laccolith with depth. He "sketched," in his imagination, a mechanical model that fit these observations. It is not appropriate to think of his model as "simple."
Questions concerning process, involving mechanics, often enter as after-thoughts. Gay (1968) presented a relation for the deformation of a viscous elliptical cylindrical inclusion embedded in a viscous host in plane flow. Bilby et al. (1975) showed that this result was incorrect. Treagus & Treagus (2001) used it to estimate the bulk strain of a polymict conglomerate and the relative viscosities of its components. Whatever Gay thought, his result is the exact result for a viscous sphere embedded in an incompressible viscous medium. As an example of the application of a complete mechanics, I discuss the mechanics of objects – lingula, crinoid ossicles and concretions - used to estimate strain in the central Appalachians. Several unanswered questions raised earlier by structural geologists are answered.