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In-situ stress characterization and applications (view source)
Revision as of 16:15, 28 April 2022
, 16:15, 28 April 2022→2-D Mohar Circle
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 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, H., 2016) [4.0]]]
===3-D Mohr Circle===
===3-D Mohr Circle===