{"id":2194,"date":"2019-09-26T12:11:02","date_gmt":"2019-09-26T11:11:02","guid":{"rendered":"https:\/\/www.nickzom.org\/blog\/?p=2194"},"modified":"2024-03-09T08:40:58","modified_gmt":"2024-03-09T07:40:58","slug":"how-to-calculate-and-solve-for-horizontal-strain-rock-mechanics","status":"publish","type":"post","link":"https:\/\/www.nickzom.org\/blog\/2019\/09\/26\/how-to-calculate-and-solve-for-horizontal-strain-rock-mechanics\/","title":{"rendered":"How to Calculate and Solve for Horizontal Strain | Rock Mechanics"},"content":{"rendered":"

\"\"<\/p>\n

The image above represents horizontal strain. To calculate the horizontal strain, five essential parameters are needed, and these parameters are Principal Horizontal Stress Component 1 (\u03c3H1<\/sub>), Principal Horizontal Stress Component 2 (\u03c3H2<\/sub>), Poisson’s Ratio (v), <\/strong>Vertical Stress (\u03c3v<\/sub>) <\/strong>and Young’s Modulus (E).<\/strong><\/p>\n

The formula for calculating the horizontal strain:<\/p>\n

\u03b5H<\/sub>\u00a0=\u00a0(\u03c3H1<\/sub>\u00a0– v\u03c3H2<\/sub>\u00a0– v\u03c3v<\/sub>)<\/sup>\u00a0\/\u00a0E<\/sub><\/p>\n

Where:<\/p>\n

\u03b5H<\/sub>\u00a0= Horizontal Strain
\n\u03c3H1<\/sub>\u00a0= Principal Horizontal Stress Component 1
\n\u03c3H2<\/sub>\u00a0= Principal Horizontal Stress Component 2
\nv = Poisson’s Ratio
\n\u03c3v<\/sub>\u00a0= Vertical Stress
\nE = Young’s Modulus<\/p>\n

So, let’s solve an example;
\nFind the horizontal strain when the principal horizontal stress component 1 is 7, the principal horizontal component 2 is 9, the Poisson’s ratio is 11, the vertical stress is 21 and then young’s modulus is 27.<\/p>\n

Hence, this implies that;<\/p>\n

\u03c3H1<\/sub> = Principal Horizontal Stress Component 1 = 7
\n\u03c3H2<\/sub> = Principal Horizontal Stress Component 2 = 9
\nv = Poisson’s Ratio = 11
\n\u03c3v<\/sub> = Vertical Stress = 21
\nE = Young’s Modulus = 27<\/p>\n

\u03b5H<\/sub>\u00a0=\u00a0(\u03c3H1<\/sub>\u00a0– v\u03c3H2<\/sub>\u00a0– v\u03c3v<\/sub>)<\/sup>\u00a0\/\u00a0E<\/sub>
\n\u03b5H<\/sub>\u00a0=\u00a0(7 – 11(9) – 11(21))<\/sup>\u00a0\/\u00a027<\/sub>
\nSo, \u03b5H<\/sub>\u00a0=\u00a0(7 – 99 – 231)<\/sup>\u00a0\/\u00a027<\/sub>
\n\u03b5H<\/sub>\u00a0=\u00a0-323<\/sup>\u00a0\/\u00a027<\/sub>
\n\u03b5H<\/sub>\u00a0= -11.96<\/p>\n

Therefore, the\u00a0horizontal strain\u00a0<\/strong>is\u00a0-11.96.<\/strong><\/p>\n

Calculating the Principal Horizontal Stress Component 1 when the Horizontal Stress, Principal Horizontal Stress Component 2, Poisson’s Ratio, Vertical Stress and Young’s Modulus are Given<\/strong><\/h3>\n

\u03c3H1<\/sub> = (\u03b5H<\/sub> x E) + v\u03c3H2<\/sub> + v\u03c3v<\/sub><\/p>\n

Where;<\/p>\n

\u03c3H1<\/sub>\u00a0= Principal Horizontal Stress Component 1
\n\u03b5H<\/sub>\u00a0= Horizontal Strain
\n\u03c3H2<\/sub>\u00a0= Principal Horizontal Stress Component 2
\nv = Poisson’s Ratio
\n\u03c3v<\/sub>\u00a0= Vertical Stress
\nE = Young’s Modulus<\/p>\n

So, let’s solve an example;
\nFind the principal horizontal stress component 1 when the horizontal strain is 22, the principal horizontal component 2 is 10, the Poisson’s ratio is 7, the vertical stress is 12 and then young’s modulus is 3.<\/p>\n

Hence, this implies that;<\/p>\n

\u03b5H<\/sub> = Horizontal Strain = 22
\n\u03c3H2<\/sub> = Principal Horizontal Stress Component 2 = 10
\nv = Poisson’s Ratio = 7
\n\u03c3v<\/sub> = Vertical Stress = 12
\nE = Young’s Modulus = 3<\/p>\n

\u03c3H1<\/sub> = (\u03b5H<\/sub> x E) + v\u03c3H2<\/sub> + v\u03c3v<\/sub>
\n\u03c3H1<\/sub> = (22 x 3) + 7(10) + 7(12)
\nThat is, \u03c3H1<\/sub> = 66 + 70 + 84
\n\u03c3H1<\/sub> = 220<\/p>\n

Therefore, the\u00a0principal horizontal stress component 1\u00a0<\/strong>is\u00a0220.<\/strong><\/p>\n

Calculating the Principal Horizontal Stress Component 2 when the Horizontal Stress, Principal Horizontal Stress Component 1, Poisson’s Ratio, Vertical Stress and Young’s Modulus are Given<\/strong><\/h3>\n

\u03c3H2<\/sub> = -((\u03b5H<\/sub> x E) – \u03c3H1<\/sub> + v\u03c3v<\/sub><\/sup> \/ v<\/sub>)<\/p>\n

Where;<\/p>\n

\u03c3H2<\/sub>\u00a0= Principal Horizontal Stress Component 2
\n\u03b5H<\/sub>\u00a0= Horizontal Strain
\n\u03c3H1<\/sub>\u00a0= Principal Horizontal Stress Component 1
\nv = Poisson’s Ratio
\n\u03c3v<\/sub>\u00a0= Vertical Stress
\nAnd then, E = Young’s Modulus<\/p>\n

So, let’s solve an example;
\nFind the principal horizontal stress component 2 when the horizontal strain is 28, the principal horizontal component 1 is 14, the Poisson’s ratio is 5, the vertical stress is 17 and then young’s modulus is 7.<\/p>\n

Hence, this implies that;<\/p>\n

\u03b5H<\/sub> = Horizontal Strain =28
\n\u03c3H1<\/sub> = Principal Horizontal Stress Component 1 = 14
\nv = Poisson’s Ratio = 5
\n\u03c3v<\/sub> = Vertical Stress = 17
\nAnd then, E = Young’s Modulus = 7<\/p>\n

\u03c3H2<\/sub> = -((\u03b5H<\/sub> x E) – \u03c3H1<\/sub> + v\u03c3v<\/sub><\/sup> \/ v<\/sub>)
\n\u03c3H2<\/sub> = -((28 x 7) – 14 + 5(17)<\/sup> \/ 5<\/sub>)
\nThen, \u03c3H2<\/sub> = -(196 – 14 + 85<\/sup> \/ 5<\/sub>)
\n\u03c3H2<\/sub> = -(182 + 85<\/sup> \/ 5<\/sub>)
\n\u03c3H2<\/sub> = -(267<\/sup> \/ 5<\/sub>)
\nSo, \u03c3H2<\/sub> = -(53.4)
\n\u03c3H2<\/sub> = -53.4<\/p>\n

Therefore, the principal horizontal stress component 2 <\/strong>is -53.4.<\/strong><\/p>\n

Read more:\u00a0How to Calculate and Solve for Lateral Strain | Rock Mechanics<\/a><\/p>\n

Calculating the Poisson’s Ratio when the Horizontal Stress, Principal Horizontal Stress Component 1, Principal Horizontal Stress Component 2, Vertical Stress and Young’s Modulus are Given<\/strong><\/h3>\n

v = \u03c3H1<\/sub> – (\u03b5H<\/sub> x E)<\/sup> \/ \u03c3H1<\/sub> + \u03c3H2<\/sub><\/sub><\/p>\n

Where:<\/p>\n

v = Poisson’s Ratio
\n\u03b5H<\/sub>\u00a0= Horizontal Strain
\n\u03c3H1<\/sub>\u00a0= Principal Horizontal Stress Component 1
\n\u03c3H2<\/sub>\u00a0= Principal Horizontal Stress Component 2
\n\u03c3v<\/sub>\u00a0= Vertical Stress
\nAnd then, E = Young’s Modulus<\/p>\n

So, let’s solve an example;
\nFind the Poisson’s ratio when the principal horizontal stress component 1 is 2, the principal horizontal component 2 is 4, the horizontal strain is 19, the vertical stress is 26 and then young’s modulus is 12.<\/p>\n

Hence, this implies that;<\/p>\n

\u03b5H<\/sub> = Horizontal Strain = 19
\n\u03c3H1<\/sub> = Principal Horizontal Stress Component 1 = 2
\n\u03c3H2<\/sub> = Principal Horizontal Stress Component 2 = 4
\n\u03c3v<\/sub> = Vertical Stress = 26
\nE = Young’s Modulus = 12<\/p>\n

So, v = \u03c3H1<\/sub> – (\u03b5H<\/sub> x E)<\/sup> \/ \u03c3H1<\/sub> + \u03c3H2<\/sub><\/sub>
\nv = 2 – (19 x 12)<\/sup> \/ 2 + 4<\/sub>
\nThat is, v = 2 – 228<\/sup> \/ 6<\/sub>
\nv = -226<\/sup> \/ 6<\/sub>
\nv = -37.6<\/p>\n

Therefore, the\u00a0Poisson’s ratio\u00a0<\/strong>is\u00a0-37.6.<\/strong><\/p>\n

Calculating the Vertical Stress when the Horizontal Stress, Principal Horizontal Stress Component 1, Principal Horizontal Stress Component 2, Poisson’s Ratio and Young’s Modulus are Given<\/strong><\/h4>\n

\u03c3v<\/sub> = -((\u03b5H<\/sub> x E) – \u03c3H1<\/sub> + v\u03c3H2<\/sub><\/sup> \/ v<\/sub>)<\/p>\n

Where:<\/p>\n

\u03c3v<\/sub>\u00a0= Vertical Stress
\n\u03b5H<\/sub>\u00a0= Horizontal Strain
\nAnd then, \u03c3H1<\/sub>\u00a0= Principal Horizontal Stress Component 1
\n\u03c3H2<\/sub>\u00a0= Principal Horizontal Stress Component 2
\nv = Poisson’s Ratio
\nE = Young’s Modulus<\/p>\n

So, let’s solve an example;
\nFind the vertical stress when the horizontal strain is 27, the principal horizontal stress component 1 is 12, the principal horizontal component 2 is 9, the Poisson’s ratio is 24 and then young’s modulus is 8.<\/p>\n

Hence, this implies that;<\/p>\n

\u03b5H<\/sub> = Horizontal Strain = 27
\n\u03c3H1<\/sub> = Principal Horizontal Stress Component 1 = 12
\n\u03c3H2<\/sub> = Principal Horizontal Stress Component 2 = 9
\nv = Poisson’s Ratio = 24
\nE = Young’s Modulus = 8<\/p>\n

\u03c3v<\/sub> = -((\u03b5H<\/sub> x E) – \u03c3H1<\/sub> + v\u03c3H2<\/sub><\/sup> \/ v<\/sub>)
\n\u03c3v<\/sub> = -((27 x 8) – 12 + 8(9)<\/sup> \/ 24<\/sub>)
\nThen, \u03c3v<\/sub> = -(216 – 12 + 72<\/sup> \/ 24<\/sub>)
\n\u03c3v<\/sub> = -(204 + 72<\/sup> \/ 24<\/sub>)
\n\u03c3v<\/sub> = -(276<\/sup> \/ 24<\/sub>)
\nSo, \u03c3v<\/sub> = -(11.5)
\n\u03c3v<\/sub> = -11.5<\/p>\n

Therefore, the\u00a0vertical stress\u00a0<\/strong>is\u00a0-11.5.<\/strong><\/p>\n

Calculating the Young’s Modulus when the Horizontal Stress, Principal Horizontal Stress Component 1, Principal Horizontal Stress Component 2, Poisson’s Ratio and Vertical Stress are Given<\/strong><\/h3>\n

E = (\u03c3H1<\/sub> – v\u03c3H2<\/sub> – v\u03c3v<\/sub>)<\/sup> \/ \u03b5H<\/sub><\/sub><\/p>\n

Where:<\/p>\n

E = Young’s Modulus
\n\u03b5H<\/sub>\u00a0= Horizontal Strain
\nAnd then, \u03c3H1<\/sub>\u00a0= Principal Horizontal Stress Component 1
\n\u03c3H2<\/sub>\u00a0= Principal Horizontal Stress Component 2
\nv = Poisson’s Ratio
\n\u03c3v<\/sub> = Vertical Stress<\/p>\n

So, let’s solve an example;
\nFind the young’s modulus when the horizontal strain is 44, principal horizontal stress component 1 is 28, the principal horizontal component 2 is 5, the Poisson’s ratio is 4 and then the vertical stress is 3.<\/p>\n

Hence, this implies that;<\/p>\n

\u03b5H<\/sub> = Horizontal Strain = 44
\n\u03c3H1<\/sub> = Principal Horizontal Stress Component 1 = 28
\nAnd then, \u03c3H2<\/sub> = Principal Horizontal Stress Component 2 = 5
\nv = Poisson’s Ratio = 4
\n\u03c3v<\/sub> = Vertical Stress = 3<\/p>\n

E = (\u03c3H1<\/sub> – v\u03c3H2<\/sub> – v\u03c3v<\/sub>)<\/sup> \/ \u03b5H<\/sub><\/sub>
\nE = (28 – 4(5) – 4(3))<\/sup> \/ 44<\/sub>
\nSo, E = (28 – 20 – 12)<\/sup> \/ 44<\/sub>
\nE = (8 – 12)<\/sup> \/ 44<\/sub>
\nThen, E = (-4)<\/sup> \/ 44<\/sub>
\nE = -0.09<\/p>\n

Therefore, the\u00a0young’s modulus\u00a0<\/strong>is\u00a0-0.09.<\/strong><\/p>\n

How to Calculate and Solve for Horizontal Strain Using the Nickzom Calculator<\/strong><\/h3>\n

Nickzom Calculator \u2013\u00a0The Calculator Encyclopedia<\/strong> is capable of calculating the horizontal strain.<\/p>\n

To get the answer and workings of the horizontal strain using the Nickzom Calculator \u2013 The Calculator Encyclopedia.\u00a0<\/strong>First, you need to obtain the app.<\/p>\n

You can get this app via any of these means:<\/p>\n

Web<\/strong>\u00a0\u2013\u00a0https:\/\/www.nickzom.org\/calculator-plus<\/a><\/p>\n

To get access to the\u00a0professional\u00a0<\/strong>version via web, you need to\u00a0register<\/strong>\u00a0and\u00a0subscribe\u00a0<\/strong>for\u00a0NGN 1,500\u00a0<\/strong>per\u00a0annum<\/strong>\u00a0to have utter access to all functionalities.
\nYou can also try the\u00a0demo\u00a0<\/strong>version via\u00a0https:\/\/www.nickzom.org\/calculator<\/a><\/p>\n

Android (Paid)<\/strong>\u00a0\u2013\u00a0https:\/\/play.google.com\/store\/apps\/details?id=org.nickzom.nickzomcalculator<\/a>
\nAndroid (Free)<\/strong>\u00a0\u2013\u00a0https:\/\/play.google.com\/store\/apps\/details?id=com.nickzom.nickzomcalculator<\/a>
\nApple (Paid)<\/strong>\u00a0\u2013\u00a0https:\/\/itunes.apple.com\/us\/app\/nickzom-calculator\/id1331162702?mt=8<\/a>
\nOnce, you have obtained the calculator encyclopedia app, proceed to the\u00a0Calculator Map,\u00a0<\/strong>then click on\u00a0Geology<\/strong>\u00a0<\/strong>under\u00a0Add-on.<\/strong><\/p>\n

\"How<\/p>\n

Then, Click on Rock Mechanics<\/strong>\u00a0<\/strong>under\u00a0Geology<\/strong><\/p>\n

\"\"<\/p>\n

Then, Click on Horizontal<\/strong>\u00a0<\/strong>Strain\u00a0<\/strong>under\u00a0Rock Mechanics<\/strong><\/p>\n

\"\"<\/p>\n

So, the screenshot below displays the page or activity to enter your values, to get the answer for the horizontal strain according to the respective parameters which are the Principal Horizontal Stress Component 1 (\u03c3H1<\/sub>), Principal Horizontal Stress Component 2 (\u03c3H2<\/sub>), Poisson’s Ratio (v), <\/strong>Vertical Stress (\u03c3v<\/sub>) <\/strong>and Young’s Modulus (E).<\/strong><\/p>\n

\"How<\/p>\n

Then, enter the values appropriately and accordingly for the parameters as required by the Principal Horizontal Stress Component 1 (\u03c3H1<\/sub>)<\/strong> is 7<\/strong>, Principal Horizontal Stress Component 2 (\u03c3H2<\/sub>)<\/strong> is 9<\/strong>, Poisson’s Ratio (v)<\/strong> is 11<\/strong>, Vertical Stress (\u03c3v<\/sub>) <\/strong>is 21 <\/strong>and Young’s Modulus (E)<\/strong> is 27<\/strong>.<\/p>\n

\"\"<\/p>\n

Finally, Click on Calculate<\/p>\n

\"How\"\"<\/p>\n

As\u00a0you can see from the screenshot above,\u00a0Nickzom Calculator<\/strong>\u2013 The Calculator Encyclopedia can calculate the horizontal strain and present the formula, workings, and steps.<\/p>\n","protected":false},"excerpt":{"rendered":"The image above represents horizontal strain. To calculate the horizontal strain, five essential parameters are needed, and these…","protected":false},"author":5,"featured_media":13169,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Calculate Horizontal Strain","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn the steps, workings, and formula on How to Calculate and Solve for Horizontal Strain | Rock 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