{"id":2248,"date":"2019-09-26T15:23:36","date_gmt":"2019-09-26T14:23:36","guid":{"rendered":"https:\/\/www.nickzom.org\/blog\/?p=2248"},"modified":"2024-03-09T08:53:34","modified_gmt":"2024-03-09T07:53:34","slug":"how-to-calculate-and-solve-for-mohr-coulomb-criterion-rock-mechanics","status":"publish","type":"post","link":"https:\/\/www.nickzom.org\/blog\/2019\/09\/26\/how-to-calculate-and-solve-for-mohr-coulomb-criterion-rock-mechanics\/","title":{"rendered":"How to Calculate and Solve for Mohr – Coulomb Criterion | Rock Mechanics"},"content":{"rendered":"

\"\"<\/p>\n

The image above represents mohr – coulomb criterion. To calculate mohr – coulomb criterion, three essential parameters are needed and these parameters are Cohesion (|\u03c4o<\/sub>), Co-efficient of Friction (\u03bc) <\/strong>and Normal Stress (\u03c3n<\/sub>).<\/strong><\/p>\n

The formula for calculating the mohr – coulomb criterion:<\/p>\n

|\u03c4| = \u03c4o<\/sub>\u00a0+ \u03bc\u03c3n<\/sub><\/p>\n

Where;<\/p>\n

|\u03c4 = Mohr – Coulomb Criterion
\n|\u03c4o<\/sub>\u00a0= Cohesion
\n\u03bc = Co-efficient of Friction
\n\u03c3n<\/sub>\u00a0= Normal Stress<\/p>\n

Let’s solve an example;
\nFind the mohr – coulomb criterion when the cohesion is 7, the co-efficient of friction is 30 and the normal stress is 28.<\/p>\n

This implies that;<\/p>\n

|\u03c4o<\/sub> = Cohesion = 7
\n\u03bc = Co-efficient of Friction = 30
\n\u03c3n<\/sub> = Normal Stress = 28<\/p>\n

|\u03c4| = \u03c4o<\/sub>\u00a0+ \u03bc\u03c3n<\/sub>
\n|\u03c4| = 7 + 30(28)
\nSo, |\u03c4| = 7 + 840
\n|\u03c4| = 847<\/p>\n

Therefore, the\u00a0mohr – coulomb criterion\u00a0<\/strong>is\u00a0847.<\/strong><\/p>\n

Calculating the Cohesion when the Mohr – Coulomb Criterion, the Co-efficient of Friction and the Normal Stress are Given<\/strong><\/h3>\n

|\u03c4o<\/sub> = |\u03c4|\u00a0 – \u03bc\u03c3n<\/sub><\/p>\n

Where;<\/p>\n

|\u03c4o<\/sub>\u00a0= Cohesion
\n|\u03c4 = Mohr – Coulomb Criterion
\n\u03bc = Co-efficient of Friction
\n\u03c3n<\/sub>\u00a0= Normal Stress<\/p>\n

Let’s solve an example;
\nFind the cohesion when the mohr – coulomb criterion is 44, the co-efficient of friction is 10 and the normal stress is 4.<\/p>\n

This implies that;<\/p>\n

|\u03c4 = Mohr – Coulomb Criterion = 44
\n\u03bc = Co-efficient of Friction = 10
\n\u03c3n<\/sub> = Normal Stress = 4<\/p>\n

|\u03c4o<\/sub> = |\u03c4|\u00a0 – \u03bc\u03c3n<\/sub>
\nSo, |\u03c4o<\/sub> = 44\u00a0 – 10(4)
\n|\u03c4o<\/sub> = 44\u00a0 – 40
\n|\u03c4o<\/sub> = 4<\/p>\n

Therefore, the\u00a0cohesion\u00a0<\/strong>is\u00a04.<\/strong><\/p>\n

Read more:\u00a0How to Calculate and Solve for Bulk Modulus of Elasticity (stress) | Rock Mechanics<\/a><\/p>\n

Calculating the Co-efficient of Friction when the Mohr – Coulomb Criterion, the Cohesion and the Normal Stress are Given<\/strong><\/h3>\n

\u03bc = |\u03c4| – |\u03c4o<\/sub><\/sup> \/ \u03c3n<\/sub><\/sub><\/p>\n

Where;<\/p>\n

\u03bc = Co-efficient of Friction
\n|\u03c4 = Mohr – Coulomb Criterion
\n|\u03c4o<\/sub>\u00a0= Cohesion
\n\u03c3n<\/sub>\u00a0= Normal Stress<\/p>\n

Let’s solve an example;
\nFind the co-efficient of friction when the cohesion is 10, the mohr – coulomb criterion is 24 and the normal stress is 12.<\/p>\n

This implies that;<\/p>\n

|\u03c4 = Mohr – Coulomb Criterion = 24
\n|\u03c4o<\/sub> = Cohesion = 10
\n\u03c3n<\/sub> = Normal Stress = 12<\/p>\n

\u03bc = |\u03c4| – |\u03c4o<\/sub><\/sup> \/ \u03c3n<\/sub><\/sub>
\nThen, \u03bc = 24 – 10<\/sup> \/ 12<\/sub>
\n\u03bc = 14<\/sup> \/ 12<\/sub>
\n\u03bc = 1.667<\/p>\n

Therefore, the\u00a0co-efficient of friction\u00a0<\/strong>is\u00a01.667.<\/strong><\/p>\n

Calculating the Normal Stress when the Mohr – Coulomb Criterion, the Co-efficient of Friction and the Cohesion are Given<\/strong><\/h3>\n

\u03c3n<\/sub> = |\u03c4| – |\u03c4o<\/sub><\/sup> \/ \u03bc<\/sub><\/p>\n

Where;<\/p>\n

\u03c3n<\/sub>\u00a0= Normal Stress
\n|\u03c4 = Mohr – Coulomb Criterion
\n|\u03c4o<\/sub>\u00a0= Cohesion
\n\u03bc = Co-efficient of Friction<\/p>\n

Let’s solve an example;
\nFind the normal stress when the mohr – coulomb criterion is 30, the cohesion is 14, and the co-efficient of friction is 5.<\/p>\n

This implies that;<\/p>\n

|\u03c4 = Mohr – Coulomb Criterion = 30
\n|\u03c4o<\/sub> = Cohesion = 14
\n\u03bc = Co-efficient of Friction = 5<\/p>\n

\u03c3n<\/sub> = |\u03c4| – |\u03c4o<\/sub><\/sup> \/ \u03bc<\/sub>
\nSo, \u03c3n<\/sub> = 30 – 14<\/sup> \/ 5<\/sub>
\n\u03c3n<\/sub> = 16<\/sup> \/ 5<\/sub>
\n\u03c3n<\/sub> = 3.2<\/p>\n

Therefore, the\u00a0normal stress\u00a0<\/strong>is\u00a03.2.<\/strong><\/p>\n

How to Calculate Mohr – Coulomb Criterion Using Nickzom Calculator<\/strong><\/h3>\n

Nickzom Calculator \u2013\u00a0The Calculator Encyclopedia<\/strong> is capable of calculating the mohr – coulomb criterion.<\/p>\n

To get the answer and workings of the mohr – coulomb criterion 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

\"\"<\/p>\n

Now, Click on\u00a0Rock Mechanics<\/strong>\u00a0<\/strong>under\u00a0Geology<\/strong><\/p>\n

\"\"<\/p>\n

Now, Click on\u00a0Mohr – Coulomb Criterion<\/strong>\u00a0under Rock Mechanics<\/strong><\/p>\n

\"How<\/p>\n

The screenshot below displays the page or activity to enter your values, to get the answer for the mohr – coulomb criterion according to the respective parameters which are the Cohesion (|\u03c4o<\/sub>), Co-efficient of Friction (\u03bc) <\/strong>and Normal Stress (\u03c3n<\/sub>).<\/strong><\/p>\n

\"How<\/p>\n

Now, enter the values appropriately and accordingly for the parameters as required by the Cohesion (|\u03c4o<\/sub>)<\/strong> is 7<\/strong>, Co-efficient of Friction (\u03bc)<\/strong> is 30 <\/strong>and Normal Stress (\u03c3n<\/sub>)<\/strong> is\u00a028<\/strong>.<\/strong><\/p>\n

\"How<\/p>\n

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

\"\"<\/p>\n

As\u00a0you can see from the screenshot above,\u00a0Nickzom Calculator<\/strong>\u2013 The Calculator Encyclopedia solves for the mohr – coulomb criterion and presents the formula, workings and steps too.<\/p>\n","protected":false},"excerpt":{"rendered":"The image above represents mohr – coulomb criterion. To calculate mohr – coulomb criterion, three essential parameters are…","protected":false},"author":5,"featured_media":13182,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_opengraph-title":"","_yoast_wpseo_opengraph-description":"","_yoast_wpseo_twitter-title":"","_yoast_wpseo_twitter-description":"","_lmt_disableupdate":"","_lmt_disable":"","_sitemap_exclude":false,"_sitemap_priority":"","_sitemap_frequency":"","_yoast_wpseo_focuskw_text_input":"","csco_display_header_overlay":false,"csco_singular_sidebar":"","csco_page_header_type":"","footnotes":"","_members_access_role":[],"_members_access_error":""},"categories":[48],"tags":[658,84,683,681,64,682,87,655,657],"class_list":["post-2248","post","type-post","status-publish","format-standard","has-post-thumbnail","category-geology","tag-add-on","tag-calculator-encyclopedia","tag-co-efficient-of-friction","tag-cohesion","tag-geology","tag-mohr-coulomb-criterion","tag-nickzom-calculator","tag-normal-stress","tag-rock-mechanics","cs-entry"],"yoast_head":"\nHow to Calculate and Solve for Mohr - Coulomb Criterion | Rock Mechanics<\/title>\n<meta name=\"description\" content=\"Learn the step by step guidelines, accurate workings, and formula on How to Calculate and Solve for Mohr - Coulomb Criterion | Rock Mechanics\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.nickzom.org\/blog\/2019\/09\/26\/how-to-calculate-and-solve-for-mohr-coulomb-criterion-rock-mechanics\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"How to Calculate and Solve for Mohr - Coulomb Criterion | Rock Mechanics\" \/>\n<meta property=\"og:description\" content=\"Learn the step by step guidelines, accurate workings, and formula on How to Calculate and Solve for Mohr - Coulomb Criterion | Rock Mechanics\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.nickzom.org\/blog\/2019\/09\/26\/how-to-calculate-and-solve-for-mohr-coulomb-criterion-rock-mechanics\/\" \/>\n<meta property=\"og:site_name\" content=\"Nickzom Academy\" \/>\n<meta property=\"article:published_time\" content=\"2019-09-26T14:23:36+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-03-09T07:53:34+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/09\/347e248d-56b5-4bce-aed9-c4f502d35ab4.jpeg\" \/>\n\t<meta property=\"og:image:width\" content=\"1024\" \/>\n\t<meta property=\"og:image:height\" content=\"1024\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Loveth Idoko\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Loveth Idoko\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/www.nickzom.org\\\/blog\\\/2019\\\/09\\\/26\\\/how-to-calculate-and-solve-for-mohr-coulomb-criterion-rock-mechanics\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/www.nickzom.org\\\/blog\\\/2019\\\/09\\\/26\\\/how-to-calculate-and-solve-for-mohr-coulomb-criterion-rock-mechanics\\\/\"},\"author\":{\"name\":\"Loveth Idoko\",\"@id\":\"https:\\\/\\\/www.nickzom.org\\\/blog\\\/#\\\/schema\\\/person\\\/c11f31e5522ed7e1ed0d78e7d9767042\"},\"headline\":\"How to Calculate and Solve for Mohr – Coulomb Criterion | Rock Mechanics\",\"datePublished\":\"2019-09-26T14:23:36+00:00\",\"dateModified\":\"2024-03-09T07:53:34+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/www.nickzom.org\\\/blog\\\/2019\\\/09\\\/26\\\/how-to-calculate-and-solve-for-mohr-coulomb-criterion-rock-mechanics\\\/\"},\"wordCount\":658,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\\\/\\\/www.nickzom.org\\\/blog\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/www.nickzom.org\\\/blog\\\/2019\\\/09\\\/26\\\/how-to-calculate-and-solve-for-mohr-coulomb-criterion-rock-mechanics\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/www.nickzom.org\\\/blog\\\/wp-content\\\/uploads\\\/2019\\\/09\\\/347e248d-56b5-4bce-aed9-c4f502d35ab4.jpeg\",\"keywords\":[\"add-on\",\"calculator encyclopedia\",\"co-efficient of friction\",\"cohesion\",\"geology\",\"mohr - 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