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In-situ stress is the natural pre-existing stress confined in the rock before it is drilled, excavated or affected by outside influences. The in-situ stresses originate in the earth crust due to different factors, mainly the weight of the overlaying rock layers and tectonic movements (see [[:File:GeoWikiWriteOff2021-Tayyib-Figure1.png|Figure 1]]). The other factors are summarized in [[:File:GeoWikiWriteOff2021-Tayyib-Figure2.png|Figure 2]]. The in-situ stress can vary within one rock mass from one location to another due to varying rock properties. It is important to determine the magnitude and direction of in-situ stresses before doing underground work or designing underground structures, see [[:File:GeoWikiWriteOff2021-Tayyib-Table1.png|Table 1]] for their different applications. In-situ stress characterization is the science of estimating the stress magnitudes and determining the orientation of three principle stresses: maximum horizontal stress, minimum horizontal stress, and vertical stress.

In-situ stress is the natural pre-existing stress confined in the rock before it is drilled, excavated or affected by outside influences. The in-situ stresses originate in the earth crust due to different factors, mainly the weight of the overlaying rock layers and tectonic movements ([[:File:GeoWikiWriteOff2021-Tayyib-Figure1.png|Figure 1]]). The other factors are summarized in [[:File:GeoWikiWriteOff2021-Tayyib-Figure2.png|Figure 2]]. The in-situ stress can vary within one rock mass from one location to another due to varying rock properties. It is important to determine the magnitude and direction of in-situ stresses before doing underground work or designing underground structures, see [[:File:GeoWikiWriteOff2021-Tayyib-Table1.png|Table 1]] for their different applications. In-situ stress characterization is the science of estimating the stress magnitudes and determining the orientation of three principle stresses: maximum horizontal stress, minimum horizontal stress, and vertical stress.

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File:GeoWikiWriteOff2021-Tayyib-Figure1.png|{{Figure number|1}}Movement of the tectonic plate (Earth’s outer shell: Crust & Lithospheric Mantle) generate in-situ stress (from Duarte & Schellart<ref>Duarte, J., C., and W. P. Schellart, 2016, Introduction to plate boundaries and natural hazards, ''in'' J. C. Duarte and W. P. Schellart, eds., Plate boundaries and natural hazards: AGU Geophysical Monograph Series 219, p. 1-10.</ref>).

File:GeoWikiWriteOff2021-Tayyib-Figure1.png|{{Figure number|1}}Movement of the tectonic plate (Earth’s outer shell: Crust & Lithospheric Mantle) generate in-situ stress (from Duarte & Schellart<ref>Duarte, J., C., and W. P. Schellart, 2016, Introduction to plate boundaries and natural hazards, ''in'' J. C. Duarte and W. P. Schellart, eds., Plate boundaries and natural hazards: AGU Geophysical Monograph Series 219, p. 1-10.</ref>).

 

 

==Notation of Stress==

==Notation of Stress==

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 ([[: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 [[: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).  

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 ([[: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 ([[: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.

Mohr circle is a graphical way of representing the state of stress in a solid body. It is used to graphically construct the normal and shear stresses acting on a plane of arbitrary orientation (θ) through a point in the formation. All possible combinations of shear and normal stresses fall inside the Mohr circle and it can be used in two or three dimensions.  

Mohr circle is a graphical way of representing the state of stress in a solid body. It is used to graphically construct the normal and shear stresses acting on a plane of arbitrary orientation (θ) through a point in the formation. All possible combinations of shear and normal stresses fall inside the Mohr circle and it can be used in two or three dimensions.  

===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 follows:

The horizontal and the vertical axes represent the normal and the shear stress respectively ([[: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 follows:

::<math>\text{The coordinate }(\sigma_n, \sigma_s) = \frac{\sigma_1 + \sigma_3}{2 , 0}</math>

::<math>\text{The coordinate }(\sigma_n, \sigma_s) = \frac{\sigma_1 + \sigma_3}{2 , 0}</math>

===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 [[: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:

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 ([[: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>

===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 ([[: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<ref name=Fossen />).]]

[[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 />).]]

====Hydraulic Testing of Pre-existing Fracture (HTPF)====

====Hydraulic Testing of Pre-existing Fracture (HTPF)====

Hydraulic Testing of Pre-existing Fracture is similar to the conventional fracking. However, no fractures are created by the HTPF method. It is used to reopen a pre-existing fracture in the formation (see [[:File:GeoWikiWriteOff2021-Tayyib-Figure12.png|Figure 12]]). HTPF method requires the knowledge of the exact orientation and location of the pre-existing fractures before pumping fluid into the formation. HTPF can determine the normal stress acting perpendicular to the pre-existing fractures, which is equal to the shut-in pressure.

Hydraulic Testing of Pre-existing Fracture is similar to the conventional fracking. However, no fractures are created by the HTPF method. It is used to reopen a pre-existing fracture in the formation ([[:File:GeoWikiWriteOff2021-Tayyib-Figure12.png|Figure 12]]). HTPF method requires the knowledge of the exact orientation and location of the pre-existing fractures before pumping fluid into the formation. HTPF can determine the normal stress acting perpendicular to the pre-existing fractures, which is equal to the shut-in pressure.

[[File:GeoWikiWriteOff2021-Tayyib-Figure12.png|center|framed|{{Figure number|12}}Hydraulic Testing of Pre-existing Fractures. (from Gaines, et al. 2012 as cited in Lin et al.<ref>Lin, H., J. Oh, H. Masoumi, I. Canbulat, C. Zhang, and L. Dou, 2018, [https://ro.uow.edu.au/coal/690 A review of in situ stress measurement techniques], ''in'' N. Aziz, and B. Kininmonth, eds: Proceedings of the 2018 Coal Operators' Conference, February 18-20, 2018, Wollongong, Australia.</ref>)]]

[[File:GeoWikiWriteOff2021-Tayyib-Figure12.png|center|framed|{{Figure number|12}}Hydraulic Testing of Pre-existing Fractures. (from Gaines, et al. 2012 as cited in Lin et al.<ref>Lin, H., J. Oh, H. Masoumi, I. Canbulat, C. Zhang, and L. Dou, 2018, [https://ro.uow.edu.au/coal/690 A review of in situ stress measurement techniques], ''in'' N. Aziz, and B. Kininmonth, eds: Proceedings of the 2018 Coal Operators' Conference, February 18-20, 2018, Wollongong, Australia.</ref>)]]

Cores are cylindrical rock samples that are collected during or after well drilling. They are sent to the laboratory for further testing. The Anelastic Strain Recovery (ASR) is a method used to determine the in-situ stresses and their orientation from cores by measuring the strain over time.

Cores are cylindrical rock samples that are collected during or after well drilling. They are sent to the laboratory for further testing. The Anelastic Strain Recovery (ASR) is a method used to determine the in-situ stresses and their orientation from cores by measuring the strain over time.

The core is placed in a container filled with silicon and the strain is monitored (see [[:File:GeoWikiWriteOff2021-Tayyib-Figure17.png|Figure 17]]). The change in the core dimension is related to the microcracks creation in the rock when in-situ stress is relieved. The alignment of these micro fractures depends on the direction of the principal stresses. When the stress is relieved, the core tends to expand most in the maximum stress relief direction, and least in the minimum stress relief direction. The volume of the microcracks is proportional to the values of the in-situ stresses.  

The core is placed in a container filled with silicon and the strain is monitored ([[:File:GeoWikiWriteOff2021-Tayyib-Figure17.png|Figure 17]]). The change in the core dimension is related to the microcracks creation in the rock when in-situ stress is relieved. The alignment of these micro fractures depends on the direction of the principal stresses. When the stress is relieved, the core tends to expand most in the maximum stress relief direction, and least in the minimum stress relief direction. The volume of the microcracks is proportional to the values of the in-situ stresses.  

[[File:GeoWikiWriteOff2021-Tayyib-Figure17.png|center|framed|{{Figure number|17}}Anelastic Strain Recovery Apparatus (ASR; from Lin et al.<ref>Lin, W., E. Yeh, H. Ito, T. Hirono, W. Soh, C. Wang, K. Ma, J. Hung, and S. Song, 2007, Preliminary results of stress measurement using drill cores of TCDP hole-A: An application of anelastic strain recovery method to three-dimensional in-situ stress determination: Terrestrial, Atmospheric and Oceanic Sciences, v. 18, p. 379-393.</ref>]]

[[File:GeoWikiWriteOff2021-Tayyib-Figure17.png|center|framed|{{Figure number|17}}Anelastic Strain Recovery Apparatus (ASR; from Lin et al.<ref>Lin, W., E. Yeh, H. Ito, T. Hirono, W. Soh, C. Wang, K. Ma, J. Hung, and S. Song, 2007, Preliminary results of stress measurement using drill cores of TCDP hole-A: An application of anelastic strain recovery method to three-dimensional in-situ stress determination: Terrestrial, Atmospheric and Oceanic Sciences, v. 18, p. 379-393.</ref>]]

====Geological Method (Geologic Structure)====

====Geological Method (Geologic Structure)====

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 ([[:GeoWikiWriteOff2021-Tayyib-Figure18a.png|Figure 18a]], [[:GeoWikiWriteOff2021-Tayyib-Figure18b.png|b]]).  

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

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

====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 [[:File:GeoWikiWriteOff2021-Tayyib-Figure19.png|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 ([[:File:GeoWikiWriteOff2021-Tayyib-Figure19.png|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<ref name=Fossen />).]]

[[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 ([[:File:GeoWikiWriteOff2021-Tayyib-Figure20.png|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.<ref name=Heidbachetal />).]]

[[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 />).]]