strain and stress analysis

strain and stress analysis Strain analysis is a subdiscipline of structural geology concerned with the measurement of the shape changes (strains) associated with geological deformation. Stress analysis (or palaeostress analysis) is a closely allied field devoted to the estimation of past stresses (palaeostresses) from observed rock strains.

The calculation of geological strain involves the comparison of the original and deformed shapes of objects (strain markers) enclosed within the rock. Examples of strain markers are fossils and the outlines of sedimentary particles. Most useful are objects with known original dimensions. For example, the original length of certain graptolites can be estimated by counting the thecae present. A measure of length change is the stretch; the ratio of new to old lengths. Such measurements commonly reveal that the value of stretch varies according to the direction of the marker being measured. This accords with the concept of the strain ellipsoid; a representation of the state of strain, which considers the final form adopted by an original sphere with unit radius. The results of strain analysis are usually expressed in terms of this ellipsoid, which can be completely described by six quantities: the stretches in the directions of the principal axes (S₁ = S₂ = S₃ (and three angles defining the orientation of those axes. Ooids, that is grains in limestones with near-spherical original shapes, are examples of strain markers which allow direct estimation of strain ellipsoid parameters, though even here the usual lack of information on sizes means that only ratios of the principal stretches (R_s) can be determined. Only where principal stretches are known can volumetric strain be assessed. A large number of different techniques, many of ingenious design, have been developed for the treatment of natural strain gauges. An example is provided by the deformed fossil brachiopods shown in Fig. 1, which record changes in the length of lines or the modification of angles.

The application of strain analysis is limited by the availability of suitable markers. Furthermore, to give meaningful results the determination of strain should be carried out on samples where the strain is constant in both magnitude and direction (homogeneous strain). In practice, however, heterogeneous strain is the rule, brought about by differences in mechanical properties between components of the rock, e.g. larger grains versus matrix, lithological changes between beds. In many instances, there may be a competence contrast between strain markers and the rock enclosing them, leading to biased estimates of the bulk strain of the rock. In addition, angular strain gauges lose their sensitivity at some of the high levels of strain commonly found in rocks (R_s greater than 20:1). Some structural features used for the computation of strain (e.g. mineral growths in the pressure shadows around porphyroclasts) are of secondary origin and therefore do not record the total or finite strain experienced by the rock.

In spite of these problems, strain has been estimated in a wide range of structural environments. Such analyses have provided invaluable information on displacements in deformed rocks (e.g. the amount, direction, and sense of motion within shear zones) and greater understanding of the significance of certain structures (e.g. slaty cleavage, arcuate fold belts). Results from strain analyses can also be used to reconstruct the pre-tectonic geometry (e.g. to compute original thicknesses of rock units in metamorphic regions, and thus to construct balanced cross-sections).

The derivation of palaeostresses poses an altogether more daunting task, because a concept equivalent to the finite strain ellipsoid does not exist for stress. Stress conditions during deformation are likely to have been transitory, changing in magnitude and direction with time. Attempts to estimate stresses in deformed rocks almost invariably entail the measurement of strains coupled with making assumptions about the stress–strain relationship for the rock materials involved. Fault-slip analysis, sometimes called striation analysis, interprets field data from fault orientations and slip directions in terms of a ‘bulk’ stress state for the rock volume containing the faults. These methods, which yield estimates for the orientation of the three principal stress axes (σ₁, σ₂, and σ₃) and a parameter expressing the ratio of the differences of the principal stress values, assume that fault slip directions measured from lineations on each fault plane are parallel to the direction of resolved shear stress on the plane of the fault. Similar methods of stress analysis have been applied to microscopic deformation features in crystals, e.g. deformation twins. The orientation of brittle structures such as tensile and shear fracture are used to infer stress orientations at the time of fracture formation. Tensile fractures are oriented normal to the least compressive stress axis, σ₃. Stylolites, irregular pillar-and-socket surfaces produced by a pressure solution deformation mechanism, are frequently used as stress direction indicators. The greatest compressive stress axis (σ₁) is assumed to be parallel to the columns. The magnitudes of principal stresses can be inferred from experimentally derived data on brittle strength of rocks. Unfortunately, this is complicated by the fact that rock strength (the principal stresses at failure) is a function of the fluid pressure in the rock pores. Stress magnitudes may be more reliably estimated from intracrystalline deformation structures, e.g. mechanical twinning.

Richard J. Lisle

Bibliography

Angelier, J. (1994) Fault slip analysis and palaeostressreconstruction. In Hancock, P. L. (ed) Continental deformation, pp. 53–100. Pergamon Press, Oxford.
Lisle, R. J. (1994) Palaeostrain analysis. In Hancock, P. L. (ed.) Continental deformation, pp. 28–42. Pergamon Press, Oxford.
Ramsay, J. G. and and Huber, M. I. (1983) The techniques of modern structural geology. Vol. 1: Strain analysis. Academic Press, London.