Changes

===2-D Mohar Circle===

===2-D Mohar Circle===

The horizontal and the vertical axes represent the normal and the shear stress respectively (see [[:File:GeoWikiWriteOff2021-Tayyib-Figure6.png|Figure 6]]). The difference between the maximum principle stress (σ1) and the minimum principle stress (σ3) is called the differential stress and it represents the radius of the Mohr circle. The center of Mohr circle for any given two principal stresses is calculated as follow:

The horizontal and the vertical axes represent the normal and the shear stress respectively (see [[:File:GeoWikiWriteOff2021-Tayyib-Figure6.png|Figure 6]]). The difference between the maximum principle stress (σ1) and the minimum principle stress (σ3) is called the differential stress and it represents the radius of the Mohr circle. The center of Mohr circle for any given two principal stresses is calculated as follow:

The coordinate (σn, σs) = (((σ1 + σ3))/2 , 0)  

The coordinate (σn, σs) = (((σ1 + σ3))/2 , 0)  

The maximum shear stress is given by the circle’s radius R:

The maximum shear stress is given by the circle’s radius R:

R= ½ (σ1 - σ3)

:R= ½ (σ1 - σ3)

[[File:GeoWikiWriteOff2021-Tayyib-Figure6.png|framed|center|{{Figure number|6}}Mohr Circle is used in two dimensions. The x and y coordinates give the normal and shear stresses that are acting on a plane of arbitrary orientation. (from Fossen, H., 2016) [4.0]]]

[[File:GeoWikiWriteOff2021-Tayyib-Figure6.png|framed|center|{{Figure number|6}}Mohr Circle is used in two dimensions. The x and y coordinates give the normal and shear stresses that are acting on a plane of arbitrary orientation. (from Fossen<ref name=Fossen>Fossen, H., 2016, Structural geology: Cambridge, U.K., Cambridge University Press, 524 p.</ref>)

===3-D Mohr Circle===

===3-D Mohr Circle===

===In-situ Stress from Historical Data===

===In-situ Stress from Historical Data===

Databases of topographical and tectonic information can be used to determine the principal stress directions. The World Stress Map is an online database that compiles in-situ stress measurements and present the maximum horizontal stresses on the world map (see [[:File:GeoWikiWriteOff2021-Tayyib-Figure10.png|Figure 10]]).

Databases of topographical and tectonic information can be used to determine the principal stress directions. The World Stress Map is an online database that compiles in-situ stress measurements and present the maximum horizontal stresses on the world map (see [[:File:GeoWikiWriteOff2021-Tayyib-Figure10.png|Figure 10]]).

[[File:GeoWikiWriteOff2021-Tayyib-Figure10.png|framed|center|{{Figure number|10}}World Stress Map provides a better understanding of the in-situ stresses around the world (from Fossen, H., 2016) [4.1]]]

[[File:GeoWikiWriteOff2021-Tayyib-Figure10.png|framed|center|{{Figure number|10}}World Stress Map provides a better understanding of the in-situ stresses around the world (from Fossen<ref name=Fossen />).

===In-situ Stress from Field Investigations===

===In-situ Stress from Field Investigations===

Geologic structures at the surface, that were created by tectonic processes, can give a reliable indication of the principle stress orientations. Geological structures such as the volcanic vent alignment and active vertical fractures are formed perpendicular to the minimum horizontal stress and parallel to the maximum horizontal stress (see Figure 18).  

Geologic structures at the surface, that were created by tectonic processes, can give a reliable indication of the principle stress orientations. Geological structures such as the volcanic vent alignment and active vertical fractures are formed perpendicular to the minimum horizontal stress and parallel to the maximum horizontal stress (see Figure 18).  

<gallery mode=packed heights=300px style=centered>

<gallery mode=packed heights=300px style=centered>

GeoWikiWriteOff2021-Tayyib-Figure18a.png|Figure 18(a) Volcanic vent alignment (from Fossen, H., 2016) [4.2]

GeoWikiWriteOff2021-Tayyib-Figure18a.png|Figure 18(a) Volcanic vent alignment (from Fossen<ref name=Fossen />).

GeoWikiWriteOff2021-Tayyib-Figure18b.png|Figure 18(b) Active vertical fracture. (from Fossen, H., 2016) [4.2]

GeoWikiWriteOff2021-Tayyib-Figure18b.png|Figure 18(b) Active vertical fracture (from Fossen<ref name=Fossen />).

</gallery>

</gallery>

====Geophysical Method (Borehole Breakouts)====

====Geophysical Method (Borehole Breakouts)====

Borehole breakout is the breaking zone of the wellbore’s wall, causing the hole to have an irregular elongated shape, from which the orientation of the horizontal stresses can be inferred. The breaking of fragments is assumed to occur parallel to the minimum horizontal stress and perpendicular to the maximum horizontal stress (see Figure 19).

Borehole breakout is the breaking zone of the wellbore’s wall, causing the hole to have an irregular elongated shape, from which the orientation of the horizontal stresses can be inferred. The breaking of fragments is assumed to occur parallel to the minimum horizontal stress and perpendicular to the maximum horizontal stress (see Figure 19).

[[File:GeoWikiWriteOff2021-Tayyib-Figure19.png|framed|center|{{Figure number|19}}Breaking of rock fragments gives information about the orientation of the horizontal stresses. (from Fossen, H., 2016) [4.3]]] 

[[File:GeoWikiWriteOff2021-Tayyib-Figure19.png|framed|center|{{Figure number|19}}Breaking of rock fragments gives information about the orientation of the horizontal stresses (from Fossen<ref name=Fossen />).

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.

4.0 4.1 4.2 4.3 Fossen, H., 2016, Structural geology. Cambridge, United Kingdom: Cambridge University Press.

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

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