{"id":3556,"date":"2024-09-05T18:42:22","date_gmt":"2024-09-05T13:12:22","guid":{"rendered":"https:\/\/study.madeeasy.in\/?p=3556"},"modified":"2025-08-13T13:17:48","modified_gmt":"2025-08-13T07:47:48","slug":"compression-ratios","status":"publish","type":"post","link":"https:\/\/www.madeeasy.in\/study\/ce\/soil-mechanics-foundation-engineering\/compression-ratios","title":{"rendered":"Compression Ratios"},"content":{"rendered":"<p style=\"text-align: justify;\">The relative compression during initial compressibility, primary consolidation and secondary consolidations are defined by the following three ratios:<\/p>\n<p style=\"text-align: justify;\"><strong>(i) Initial Compression Ratio (r<sub>i<\/sub>):<\/strong><\/p>\n<ul style=\"text-align: justify;\">\n<li>Let R<sub>o<\/sub> be zero dial gauge reading and R<sub>c<\/sub> be the corrected reading.<\/li>\n<li>Also let R<sub>100<\/sub> be the dial gauge reading after primary consolidation and R<sub>f<\/sub> be the final dial gauge reading.<\/li>\n<li>The difference between R<sub>o<\/sub> and R<sub>c<\/sub> is known as initial compression and difference between R<sub>o<\/sub> and R<sub>f<\/sub> is known as total compression.<br \/>\nInitial compression (ri) = Initial compression \/ Total compression = Ro -Rc \/ Ro -Rf<\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><strong>(ii) Primary Compression Ratio (r<sub>p<\/sub>)<\/strong><\/p>\n<p style=\"text-align: justify;\">Primary Compression Ratio (r<sub>p<\/sub>) = Primary compression \/ Total compression = Rc -R100 \/ Ro -Rf<\/p>\n<p style=\"text-align: justify;\"><strong>(iii) Secondary Compression Ratio (r<sub>s<\/sub>)<\/strong><\/p>\n<p style=\"text-align: justify;\">Secondary compression ratio (r<sub>p<\/sub>) = Secondary compression \/ Total compression = R100 &#8211; Rf\/ Ro -Rf<\/p>\n<h2 style=\"text-align: justify;\"><strong>Immediate Settlement (S<sub>i<\/sub>)<\/strong><\/h2>\n<ul style=\"text-align: justify;\">\n<li>It occurs almost immediately after the load is imposed, as a result to distortion of the solid without any volume change.<\/li>\n<li>It is due to compression, expulsion of pore air, elastic deformation of solids and squeezing of water.<\/li>\n<\/ul>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_79_1 ez-toc-wrap-left counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.madeeasy.in\/study\/ce\/soil-mechanics-foundation-engineering\/compression-ratios\/#For-Cohesionless-Soils\" >For Cohesionless Soils<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.madeeasy.in\/study\/ce\/soil-mechanics-foundation-engineering\/compression-ratios\/#For-Cohesive-Soils\" >For Cohesive Soils<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.madeeasy.in\/study\/ce\/soil-mechanics-foundation-engineering\/compression-ratios\/#Consolidation-Settlement-Scon\" >Consolidation Settlement (Scon.)<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.madeeasy.in\/study\/ce\/soil-mechanics-foundation-engineering\/compression-ratios\/#i-Computation-of-Settlement-due-to-Primary-Consolidation\" >(i) Computation of Settlement due to Primary Consolidation:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.madeeasy.in\/study\/ce\/soil-mechanics-foundation-engineering\/compression-ratios\/#ii-Settlement-due-to-Secondary-Settlement\" >(ii) Settlement due to Secondary Settlement<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.madeeasy.in\/study\/ce\/soil-mechanics-foundation-engineering\/compression-ratios\/#VERTICAL-SAND-DRAINS\" >VERTICAL SAND DRAINS<\/a><\/li><\/ul><\/nav><\/div>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"For-Cohesionless-Soils\"><\/span>For Cohesionless Soils<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3557 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/09\/cohesionless-soils.jpg\" alt=\"Cohesionless Soils\" width=\"652\" height=\"170\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/09\/cohesionless-soils.jpg 652w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/09\/cohesionless-soils-300x78.jpg 300w\" sizes=\"auto, (max-width: 652px) 100vw, 652px\" \/><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"For-Cohesive-Soils\"><\/span>For Cohesive Soils<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul style=\"text-align: justify;\">\n<li>In case of saturated clays, immediate settlement is insignificant. However, small elastic settlement below the corners may occur due to elastic deformation to molecules and squeezing of water.<\/li>\n<li>The immediate elastic deformation below the corner of a rectangular base foundation is given by<\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3558 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/09\/cohesive-soils.jpg\" alt=\"Cohesive Soils\" width=\"614\" height=\"245\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/09\/cohesive-soils.jpg 614w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/09\/cohesive-soils-300x120.jpg 300w\" sizes=\"auto, (max-width: 614px) 100vw, 614px\" \/><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Consolidation-Settlement-Scon\"><\/span>Consolidation Settlement (S<sub>con.<\/sub>)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">The total consolidation settlement of soil can be further divided into two parts.<\/p>\n<p style=\"text-align: justify;\">(i) Settlement due to primary consolidation (S<sub>C<\/sub>)<br \/>\n(ii) Settlement due to secondary consolidation (S<sub>S<\/sub>)<\/p>\n<p style=\"text-align: justify;\">The total consolidation settlement and the time of consolidation in clays is much greater than that of sand. Hence clays are more compressible than sand.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3559 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/09\/consolidation-settlement.jpg\" alt=\"Consolidation Settlement\" width=\"299\" height=\"181\" \/><\/p>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"i-Computation-of-Settlement-due-to-Primary-Consolidation\"><\/span>(i) Computation of Settlement due to Primary Consolidation:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul style=\"text-align: justify;\">\n<li>It occurs due to expulsion of pore water from a loaded saturated soil mass.<\/li>\n<li>In primary consolidation, the rate of flow is controlled by pore pressure, the permeability and the compressibility of the soil.<\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3560 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/09\/primary-consolidation.jpg\" alt=\"Primary Consolidation\" width=\"481\" height=\"300\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/09\/primary-consolidation.jpg 481w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/09\/primary-consolidation-300x187.jpg 300w\" sizes=\"auto, (max-width: 481px) 100vw, 481px\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Method-1:<\/strong><\/p>\n<p style=\"text-align: justify;\">If \u2206e is change in void ratio due to increase in effective stress on soil layer, as per change in void ratio method,<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3561 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/09\/void-ratio-1.jpg\" alt=\"Void Ratio\" width=\"415\" height=\"142\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/09\/void-ratio-1.jpg 415w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/09\/void-ratio-1-300x103.jpg 300w\" sizes=\"auto, (max-width: 415px) 100vw, 415px\" \/><\/p>\n<p style=\"text-align: justify;\">This method is suitable for both over consolidated and normally consolidated soils.<\/p>\n<p style=\"text-align: justify;\"><strong>Method-2: When a<sub>v<\/sub> is known<\/strong><\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3562 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/09\/stress.jpg\" alt=\"Stress\" width=\"732\" height=\"222\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/09\/stress.jpg 732w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/09\/stress-300x91.jpg 300w\" sizes=\"auto, (max-width: 732px) 100vw, 732px\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Method-3: When Coeff. of Compressibility (m<sub>v<\/sub> ) is known<\/strong><\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3563 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/09\/compressibility.jpg\" alt=\"Compressibility\" width=\"754\" height=\"407\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/09\/compressibility.jpg 754w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/09\/compressibility-300x162.jpg 300w\" sizes=\"auto, (max-width: 754px) 100vw, 754px\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Method-4: When C<sub>c<\/sub> is known<\/strong><\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3564 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/09\/initial-effective.jpg\" alt=\"Initial Effective\" width=\"734\" height=\"253\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/09\/initial-effective.jpg 734w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/09\/initial-effective-300x103.jpg 300w\" sizes=\"auto, (max-width: 734px) 100vw, 734px\" \/><\/p>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"ii-Settlement-due-to-Secondary-Settlement\"><\/span><strong>(ii) Settlement due to Secondary Settlement<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul style=\"text-align: justify;\">\n<li>It is due to plastic readjustment of solids. It occurs at very slow rate and is negligible in granular soils.<\/li>\n<li>The secondary settlement, after time \u2018t\u2019 from the completion of primary settlement is given by<\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3565 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/09\/settlement.jpg\" alt=\"Settlement\" width=\"674\" height=\"308\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/09\/settlement.jpg 674w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/09\/settlement-300x137.jpg 300w\" sizes=\"auto, (max-width: 674px) 100vw, 674px\" \/><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"VERTICAL-SAND-DRAINS\"><\/span>VERTICAL SAND DRAINS<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul style=\"text-align: justify;\">\n<li>The slow consolidation process of clays, and silts may be accelerated by installing vertical sand drains which aids in the expulsion of pore water from the soil at a faster rate. This speeds up the rate of consolidation accelerates the rate of settlement whereas magnitude of settlement is unaffected.<\/li>\n<li>Sand drains are most widely used when an embankment is to be constructed over a highly compressible clay layer. Sand drains are also used to drain and to control landslides.<\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-3566 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/09\/impermeable-stratum.jpg\" alt=\"Impermeable Stratum \" width=\"495\" height=\"317\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/09\/impermeable-stratum.jpg 495w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/09\/impermeable-stratum-300x192.jpg 300w\" sizes=\"auto, (max-width: 495px) 100vw, 495px\" \/><\/p>\n<ul>\n<li style=\"text-align: justify;\">The main objective of providing sand drains is to reduce the drainage path and hence to accelerate the consolidation process. Consolidation is then mainly due to horizontal radial drainage which results in faster dissipation of excess pore water pressure.<\/li>\n<li style=\"text-align: justify;\">Sand drains are installed by driving a casing through the clay layer and making boreholes. These drains are placed in either a square or a triangular pattern.<\/li>\n<\/ul>\n<p style=\"text-align: center;\"><a class=\"btn btn-danger\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/ce\/soil-mechanics-foundation-engineering\/preconsolidation-pressure\/\" target=\"_blank\" rel=\"noopener\">&lt;&lt; Previous<\/a> | <a class=\"btn btn-success\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/ce\/soil-mechanics-foundation-engineering\/shear-strength\/\" target=\"_blank\" rel=\"noopener\"> Next &gt;&gt;<\/a><br \/>\n<strong> Must Read: <\/strong> <a href=\"https:\/\/study.madeeasy.in\/ce\/soil-mechanics-and-foundation-engineering\/\" target=\"_blank\" rel=\"noopener\"><strong>Soil Mechanics and Foundation Engineering<\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The relative compression during initial compressibility, primary consolidation and secondary consolidations are defined by the following three ratios: (i) Initial<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[957,2],"tags":[998,997,996],"class_list":["post-3556","post","type-post","status-publish","format-standard","hentry","category-soil-mechanics-foundation-engineering","category-ce","tag-cohesionless-soils","tag-cohesive-soils","tag-consolidation-settlement"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/3556","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/comments?post=3556"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/3556\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=3556"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=3556"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=3556"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}