THE CONCEPTS OF TIME DEPENDANT STRAIN AND OF CONTINUA IN THE ANALYSIS OF GEOLOGIC STRUCTURES

The evolution of a geologic structure may involve the deformation of a continuous body, a discontinuous (i.e., faulted) body, and/or a body to which mass has been added or removed. This papers comments on the treatment of time dependent strain and the concept of continua for the simplest situation, a continuous body.

It is difficult to track time dependant strain even in a continuous 2D analytical mathematical model because the equations quickly become complex. A simpler approach is to envision a deforming body as a collection of points that move within a fixed reference frame. As the points move, the strains within an area circumscribed by various, closest four point sets can be calculated using analytical geometry and transformation constants. The method is a numerical graphical procedure, best done on a computer. Several theoretical concepts emerge from such an analysis: spatial variation of strain, strain rate, and rate of change of strain rate. Strains observed during deformation may be based on comparison with the original configuration of the body or with a prior configuration of the deforming body.

The paths of movement of points as the body deforms can vary and are perceived according to an analyst’s insight, taking into account strain indicators if any. The least amount of mechanical work done in bringing about deformation is another criterion that may prove useful. In this paper, we show an example from the Appalachians in which an intermediate state of deformation is defined by the onset of observed strains preserved in the final state.

The problem with a continuum is as follows: considering the size of geologists and the size and complexities of structures, it is impossible to analyze for all details. It is essential, therefore, to realize that one must define a continuum of size and character appropriate to the objective of the analysis.