Changes

Stress is often represented by the Greek letter sigma (σ) and can be defined as the force applied over an area. When the force acts perpendicular to a plane, the stress is called a Normal Stress (σn), whereas when the force acts parallel to a plane, the stress is called a Horizontal Stress (σs). Generally, the stress acting on a plane is oblique which means it is neither parallel nor at a right angle to that plane. Therefore, the stress vector is resolved into normal and shear components that are aligned with the three cartesian axes: x, y and z. Since the shear stress component is generally not aligned with these axes, it needs to be resolved further into two components (see [[:File:GeoWikiWriteOff2021-Tayyib-Figure3.png|Figure 3]]).  

Stress is often represented by the Greek letter sigma (σ) and can be defined as the force applied over an area. When the force acts perpendicular to a plane, the stress is called a Normal Stress (σn), whereas when the force acts parallel to a plane, the stress is called a Horizontal Stress (σs). Generally, the stress acting on a plane is oblique which means it is neither parallel nor at a right angle to that plane. Therefore, the stress vector is resolved into normal and shear components that are aligned with the three cartesian axes: x, y and z. Since the shear stress component is generally not aligned with these axes, it needs to be resolved further into two components (see [[:File:GeoWikiWriteOff2021-Tayyib-Figure3.png|Figure 3]]).  

These components act on each visible face of an infinitesimal cube used to represent a point within a rock mass. This results in a total of nine stress components that can be organized in a 3x3 matrix, called the stress tensor (see [[:File:GeoWikiWriteOff2021-Tayyib-Figure4.png|Figure 4]]). Assuming the rock is at rest, the stresses of equal magnitudes and opposite directions will cancel out each other and prevent the cube from rotating. There is a special orientation in space where all shear stresses equal to zero and only three normal compressive components exist, called principle stresses (see Figure 5). The three principle stresses are the vertical stress (σV), the maximum horizontal stress (σH), and the minimum horizontal stress (σh).  

These components act on each visible face of an infinitesimal cube used to represent a point within a rock mass. This results in a total of nine stress components that can be organized in a 3x3 matrix, called the stress tensor (see [[:File:GeoWikiWriteOff2021-Tayyib-Figure4.png|Figure 4]]). Assuming the rock is at rest, the stresses of equal magnitudes and opposite directions will cancel out each other and prevent the cube from rotating. There is a special orientation in space where all shear stresses equal to zero and only three normal compressive components exist, called principle stresses (see [[:File:GeoWikiWriteOff2021-Tayyib-Figure5.png|Figure 5]]). The three principle stresses are the vertical stress (σV), the maximum horizontal stress (σH), and the minimum horizontal stress (σh).  

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File:GeoWikiWriteOff2021-Tayyib-Figure3.png|{{Figure number|3}}Illustration of resolving an oblique stress vector into normal and shear components.

File:GeoWikiWriteOff2021-Tayyib-Figure3.png|{{Figure number|3}}Illustration of resolving an oblique stress vector into normal and shear components.

===3-D Mohr Circle===

===3-D Mohr Circle===

Mohar diagram can also represent the state of stress in three dimensions. The state of stress is presented as three circles which connect the three principle stresses in one Mohar diagram (see figure 7). The three principle stresses are plotted in the horizontal axis. The center of each circle is calculated as follow:

Mohar diagram can also represent the state of stress in three dimensions. The state of stress is presented as three circles which connect the three principle stresses in one Mohar diagram (see [[:File:GeoWikiWriteOff2021-Tayyib-Figure7.png|Figure 7]]). The three principle stresses are plotted in the horizontal axis. The center of each circle is calculated as follow:

::<math>C1 = \frac{1}{2}(\sigma_1 + \sigma_2) </math>

::<math>C1 = \frac{1}{2}(\sigma_1 + \sigma_2) </math>

::<math>C2 = \frac{1}{2}(\sigma_1 + \sigma_3) </math>

::<math>C2 = \frac{1}{2}(\sigma_1 + \sigma_3) </math>

Determination methods of in-situ stresses can be classified into three categories as shown in [[:File:GeoWikiWriteOff2021-Tayyib-Figure8.png|Figure 8]]. The loading method involves disturbing the in-situ stress condition in the rock such as pumping high pressure fluid into the formation to create fractures. The relief method involves isolating the rock sample partially or completely from the surrounding rocks and observe the natural rock response to the in-situ stress. Other methods can be used to deduce the in-situ stress in the rock such as geological and geophysical method. Since stress cannot be measured directly, the methods rely on the measurements of any change in rock volume or shape (Strain). Figure 9 shows the integration of the different methods in one workflow to infer the in-situ stress state.

Determination methods of in-situ stresses can be classified into three categories as shown in [[:File:GeoWikiWriteOff2021-Tayyib-Figure8.png|Figure 8]]. The loading method involves disturbing the in-situ stress condition in the rock such as pumping high pressure fluid into the formation to create fractures. The relief method involves isolating the rock sample partially or completely from the surrounding rocks and observe the natural rock response to the in-situ stress. Other methods can be used to deduce the in-situ stress in the rock such as geological and geophysical method. Since stress cannot be measured directly, the methods rely on the measurements of any change in rock volume or shape (Strain). Figure 9 shows the integration of the different methods in one workflow to infer the in-situ stress state.

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GeoWikiWriteOff2021-Tayyib-Figure8.png|{{Figure number|8}}Summary of the stress determination methods. (modified from Heidbach et al. [5.0], 2016, and Moawietz et al. [6], 2020)   

GeoWikiWriteOff2021-Tayyib-Figure8.png|{{Figure number|8}}Summary of the stress determination methods. (modified from Heidbach et al.<ref name=Heidbachetal>Heidbach, O., A. Barth, B. Müller, J. Reinecker, O. Stephansson, M. Tingay, and A. Zang, 2016, WSM quality ranking scheme, database description and analysis guidelines for stress indicator: World Stress Map Technical Report 16-01</ref> and Moawietz et al. [6], 2020)   

GeoWikiWriteOff2021-Tayyib-Figure9.png|{{Figure number|9}}Workflow of the integrated approach for in-situ stress determination (from Hudson et al, 2003, as cited in Zhang<ref name=Zhang />).

GeoWikiWriteOff2021-Tayyib-Figure9.png|{{Figure number|9}}Workflow of the integrated approach for in-situ stress determination (from Hudson et al, 2003, as cited in Zhang<ref name=Zhang />).

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The shape of the hole is identified using four-arm caliper tools or well imaging tools (see Figure 20). These tools are used during the drilling of the well for petroleum exploration and production. The four caliper arms push against the wall as they move along the wellbore, recording the shape of the hole, from which the orientation of the horizontal stresses can be inferred.

The shape of the hole is identified using four-arm caliper tools or well imaging tools (see Figure 20). These tools are used during the drilling of the well for petroleum exploration and production. The four caliper arms push against the wall as they move along the wellbore, recording the shape of the hole, from which the orientation of the horizontal stresses can be inferred.

[[File:GeoWikiWriteOff2021-Tayyib-Figure20.png|framed|center|{{Figure number|20}}(a) Four-arm Caliper tool used to identify the shape of the well. (b) Well imaging tool used to detect breakouts. (from Heidbach et al., 2016) [5.1]]]

[[File:GeoWikiWriteOff2021-Tayyib-Figure20.png|framed|center|{{Figure number|20}}(a) Four-arm Caliper tool used to identify the shape of the well. (b) Well imaging tool used to detect breakouts. (from Heidbach et al.<ref name=Heidbachetal />).

==Applications of In-situ Stress==

==Applications of In-situ Stress==

5.0 5.1 Heidbach, O., Barth, A., Müller, B., Reinecker, J., Stephansson, O., Tingay, M., Zang, A, 2016, WSM quality ranking scheme, database description and analysis guidelines for stress indicator. World Stress Map Technical Report 16-01: GFZ German Research Centre for Geosciences. DOI: http://doi.org/10.2312/wsm.2016.001

6 Morawietz, S., Heidbach, O., Reiter, K. et al., 2020, An open-access stress magnitude database for Germany and adjacent regions. Geotherm Energy doi:https://doi.org/10.1186/s40517-020-00178-5

6 Morawietz, S., Heidbach, O., Reiter, K. et al., 2020, An open-access stress magnitude database for Germany and adjacent regions. Geotherm Energy doi:https://doi.org/10.1186/s40517-020-00178-5