Tectonic regimes and stress

Principal Stress Regimes and Types of Stress
The concept of plate tectonics offers a useful framework for structural geological analysis on all relevant scales in petroleum geology, from regional in the exploration stage, to local in the reservoir evaluation and production stages. This is natural, because the principal geological stress systems are ruled by processes in the deep earth like mantle convection and lithosphere subduction, the secondary effects of which are manifested at the base of the lithosphere and along plate margins. Based on these concepts, the basic dynamics of the lithosphere can be quantified, which is a prerequisite for the evaluation and calculation of the state of stress at any point. As seen in the perspective of the petroleum structural geologist, understanding and quantifying the stress situation at the plate margins is a prerequisite for understanding the state of stress in any basin system and in any reservoir. We term principal stresses originated at plate margins far-field or contemporary stresses. The stress situation in a basin or a reservoir may be a sum of several far-field stresses combined with a local stress, which may be related to burial, erosion, geothermal gradients, topography, basement relief and structural inhomogeneities in the substratum. In other words, the plate tectonic framework provides a basic and general concept on which any structural geological analysis of a sedimentary basin rests, but it must be supplied with information on the local stress system that is superimposed on it. In the context of the far-field plate tectonic stress, we distinguish between the plate boundary and the intra-plate component. The plate boundary stress is subdivided into three basic plate margin settings, namely constructive boundaries where adjoining plates are moving away from each other and new crust is formed by magmatic activity, destructive boundaries where lithosphere is consumed by subduction or obduction, and conservative boundaries where plates are moving past each other in a strike-slip sense and where lithosphere is neither created nor consumed. It is important to note that plate boundaries have been generated and destroyed throughout large parts of the history of our planet, so that many may be preserved inside the present plates and hence do not coincide with present continent/ocean margins.The three basic types of plate margin coincide with the three principal stress configurations, namely the tensional, the compressional and the strike-slip regimes. To describe these regimes, we rely on the concept of principal stress configurations and their definition in the context of the principal axes of stress.
Tectonic stress

Tectonic Stress in the Earth's Lithosphere

In addition to stresses generated at tectonic plate contacts, several other processes contribute to the generation of stresses. We may, for example, have residual stress, which is inherited from previous deformation, where a rock body may have become bent with the elastic stress component remaining unreleased, and thermal stress which is related to expansion of rocks during heating or contraction during cooling and stress related to local gravitational gradients. Accordingly, the total stress consists of several components:

Total stress = reference stress + residual stress + thermal stress + tectonic stress 
Where the reference stress refers to the stress inside the plate, devoid of plate tectonic stresses, and thus the

Tectonic stress = contemporary stress + local stress. 
We will not go further into the analysis of residual and thermal stress here, but concentrate on stress generated by primary interactions at plate margins or forces derived thereof. Taking in to consideration the reference stress conditions, one can describe the stress situations for the three principal conditions of deformation, namely extension, contraction and strike-slip. This was done by Anderson in two influential works in 1934 and 1951, in which the framework for all modern tectonic and structural geological analysis is defined. Anderson used the vertical lithostatic stress (σv) as a reference: (where ρ is the specific weight, g is the constant of gravity and z is the height of the rock column). This applies for the three principal stress conditions because σv can be considered similar for one rock type for a constant h, assuming that the burial history has been similar. Thereby the three principal stress systems can be defined, each corresponding to a regime of deformation:

  • σv > σ H > σ h; extension
  • σH > σ v > σ h; strike-slip
  • σH > σ h > σ v; contraction
where σH and σh are the maximum and minimum horizontal stresses, respectively. By using σv as a reference, further calculations become dependent on the reference system applied. In the contractional regime there will be a tectonic component σt in addition to the reference stress, so that the greatest (horizontal) stress is: 

σH = ρgz+σ*t

Assuming uni-axial stress, which implies that the reference stress is a function of the elastic properties of the rock, and ignoring the thermal expansion, we can describe the stress as: 
σH = [υ/1− υ] ρgz + σt where υ is Young’s modulus. Because (υ/1− υ) < 0, the tectonic stress is σt > σ*t . Accordingly, the reference stress condition selected also influences the calculated total tectonic stress as long as the buried rock is compressive. For a non-compressive rock (υ =0.5), lithostatic and uni-axial reference systems are equal.

Deformation Mechanisms and Analogue Models

Our daily contact with the physical world tells us that materials deform in many ways, depending on the type of material and its physical state. Thus, a liquid reacts to outer stress very differently from a piece of rock, and one type of rock like chalk has very different physical properties as compared to another like granite. Furthermore, one material may change its mechanical properties dramatically by change of temperature and pressure. These contrasts are founded on processes occurring on the scales of the grains (in a rock), the molecule and the atom. These processes and their associated meso- and macroscopic physical expressions names like brittle, elastic, plastic, viscous and ductile, and sometimes combinations like elastico-plastic. Unfortunately, these terms are not always used in a consequent manner and are therefore liable to cause confusion when taken out of context or not precisely defined. This particularly concerns the term "brittle", because it is used in a double sense, namely as a deformation mechanism and a deformation style. When applied in the context of deformation mechanisms, brittle deformation implies that existing bonds are physically broken between mineral grains, or that fracturing of the individual grains themselves takes place. As a consequence, the rock loses its cohesion and (potentially) physically falls apart. In contrast, the plastic deformation mechanism implies that deformation takes place by the transfer of dislocations on the atomic scale. This means that the mineral can change its shape without loss of cohesion. Generally, plastic deformation occurs at higher p,T-conditions than those accompanying brittle deformation. Concerning deformation style, the term brittle is used about localised strain, like that associated with jointing and faulting, and particularly in cases when the rock loses its cohesion and where the deformation occurs at lower p,T-conditions (though not necessarily so). The ductile deformation style characterises strain which is distributed over a wider area, as commonly observed in connection with folding and meso- and mega-scale shear-zones. A ductile style of deformation is predominant at high p,T-conditions, but may also occur under very low p,T-conditions, if it involves weak materials like sand and clay. In such cases, however, displacement takes place along grain boundaries or along borders between rock bodies and not by dislocation creep or other atomic-scale mechanisms that characterise the plastic deformation mechanism.
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