{"id":292,"date":"2025-02-06T05:45:23","date_gmt":"2025-02-06T05:45:23","guid":{"rendered":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/chapter\/4-9-estimation-of-secondary-compression-settlement\/"},"modified":"2026-03-16T14:01:22","modified_gmt":"2026-03-16T14:01:22","slug":"4-9-estimation-of-secondary-compression-settlement","status":"publish","type":"chapter","link":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/chapter\/4-9-estimation-of-secondary-compression-settlement\/","title":{"raw":"4.9 Estimation of secondary compression settlement","rendered":"4.9 Estimation of secondary compression settlement"},"content":{"raw":"While delving into the mechanisms of soil creep is not within the scope of this Part, it is worth presenting the expression for estimating secondary compression or creep settlement <em>\u03c1<\/em><sub>sc<\/sub> at any time that stems from Hypothesis A i.e., that soil creep commences after soil excess pore pressures have dissipated (<a href=\"https:\/\/oercollective.caul.edu.au\/app\/uploads\/sites\/143\/2025\/02\/4.42-HR.png\">Figure 4.42<\/a>):\n\n<strong>(4.72)<\/strong> [latex]{\\rho _{sc}} = \\dfrac{{{C_\\alpha }}}{{1 + {e_c}}}{H_c}\\log \\left( {\\dfrac{{{t_{sc}}}}{{{{\\rm{t}}_c}}}} \\right)[\/latex]\n\nwhere <em>t<sub>sc<\/sub><\/em> is the time when secondary compression is sought, <em>t<\/em><sub>c<\/sub> is the time required for 90% consolidation to be completed, or the time required to reach <em>U<\/em> = 90% estimated from <a href=\"https:\/\/oercollective.caul.edu.au\/app\/uploads\/sites\/143\/2025\/02\/4.41-variation-of-average-degree-of-consolidation.png\">Figure 4.41<\/a>, according to the mentioned above. <em>e<sub>c<\/sub><\/em> and <em>H<sub>c<\/sub><\/em> in Eq. 4.72 are the void ratio and thickness of the soil layer at <em>U<\/em> = 90%, respectively, and these can be computed if we consider that:\n\n[caption id=\"attachment_291\" align=\"aligncenter\" width=\"500\"]<img class=\"wp-image-291 size-full\" src=\"https:\/\/libraryresources.nse.org.ng\/wp-content\/uploads\/sites\/9\/2025\/02\/4.42-HR-e1743559843644.png\" alt=\"Graph depicting the variation of the soil's void ratio with the logarithm of time. The inclination of the line at the secondary compression stage, when primary consolidation is completed, is defined as the coefficient Ca\" width=\"500\" height=\"429\"> Figure 4.42. Calculation of creep coefficient <em>C<sub>\u03b1<\/sub> <\/em>from oedometer tests.[\/caption]\n\n<strong>(4.73)<\/strong> [latex]\\dfrac{\\rho }{H} = \\dfrac{{\\Delta e}}{{1 + {e_0}}}[\/latex]\n\nwhere <em>e<\/em><sub>0<\/sub> is the initial void ratio of soil and \u0394<em>e<\/em> is the change in the soil void ratio that takes place during consolidation. In addition <em>C<\/em><sub>\u03b1<\/sub> is the creep coefficient, and is determined from oedometer tests (<a href=\"https:\/\/oercollective.caul.edu.au\/app\/uploads\/sites\/143\/2025\/02\/4.42-HR.png\">Figure 4.42<\/a>). The creep coefficient is related to the compression index <em>C<sub>c<\/sub><\/em>. In lack of soil-specific tests, one can consider that <em>C<\/em><sub>\u03b1<\/sub>\/<em>C<sub>c<\/sub><\/em> = 0.03 to 0.08 for clays and silts, and <em>C<\/em><sub>\u03b1<\/sub>\/<em>C<sub>c<\/sub><\/em> = 0.05 to 0.10 for organic soils (Mitchel and Soga, 2005).","rendered":"<p>While delving into the mechanisms of soil creep is not within the scope of this Part, it is worth presenting the expression for estimating secondary compression or creep settlement <em>\u03c1<\/em><sub>sc<\/sub> at any time that stems from Hypothesis A i.e., that soil creep commences after soil excess pore pressures have dissipated (<a href=\"https:\/\/oercollective.caul.edu.au\/app\/uploads\/sites\/143\/2025\/02\/4.42-HR.png\">Figure 4.42<\/a>):<\/p>\n<p><strong>(4.72)<\/strong> [latex]{\\rho _{sc}} = \\dfrac{{{C_\\alpha }}}{{1 + {e_c}}}{H_c}\\log \\left( {\\dfrac{{{t_{sc}}}}{{{{\\rm{t}}_c}}}} \\right)[\/latex]<\/p>\n<p>where <em>t<sub>sc<\/sub><\/em> is the time when secondary compression is sought, <em>t<\/em><sub>c<\/sub> is the time required for 90% consolidation to be completed, or the time required to reach <em>U<\/em> = 90% estimated from <a href=\"https:\/\/oercollective.caul.edu.au\/app\/uploads\/sites\/143\/2025\/02\/4.41-variation-of-average-degree-of-consolidation.png\">Figure 4.41<\/a>, according to the mentioned above. <em>e<sub>c<\/sub><\/em> and <em>H<sub>c<\/sub><\/em> in Eq. 4.72 are the void ratio and thickness of the soil layer at <em>U<\/em> = 90%, respectively, and these can be computed if we consider that:<\/p>\n<figure id=\"attachment_291\" aria-describedby=\"caption-attachment-291\" style=\"width: 500px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-291 size-full\" src=\"https:\/\/libraryresources.nse.org.ng\/wp-content\/uploads\/sites\/9\/2025\/02\/4.42-HR-e1743559843644.png\" alt=\"Graph depicting the variation of the soil's void ratio with the logarithm of time. The inclination of the line at the secondary compression stage, when primary consolidation is completed, is defined as the coefficient Ca\" width=\"500\" height=\"429\" srcset=\"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-content\/uploads\/sites\/9\/2025\/02\/4.42-HR-e1743559843644.png 500w, https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-content\/uploads\/sites\/9\/2025\/02\/4.42-HR-e1743559843644-300x257.png 300w, https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-content\/uploads\/sites\/9\/2025\/02\/4.42-HR-e1743559843644-65x56.png 65w, https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-content\/uploads\/sites\/9\/2025\/02\/4.42-HR-e1743559843644-225x193.png 225w, https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-content\/uploads\/sites\/9\/2025\/02\/4.42-HR-e1743559843644-350x300.png 350w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><figcaption id=\"caption-attachment-291\" class=\"wp-caption-text\">Figure 4.42. Calculation of creep coefficient <em>C<sub>\u03b1<\/sub> <\/em>from oedometer tests.<\/figcaption><\/figure>\n<p><strong>(4.73)<\/strong> [latex]\\dfrac{\\rho }{H} = \\dfrac{{\\Delta e}}{{1 + {e_0}}}[\/latex]<\/p>\n<p>where <em>e<\/em><sub>0<\/sub> is the initial void ratio of soil and \u0394<em>e<\/em> is the change in the soil void ratio that takes place during consolidation. In addition <em>C<\/em><sub>\u03b1<\/sub> is the creep coefficient, and is determined from oedometer tests (<a href=\"https:\/\/oercollective.caul.edu.au\/app\/uploads\/sites\/143\/2025\/02\/4.42-HR.png\">Figure 4.42<\/a>). The creep coefficient is related to the compression index <em>C<sub>c<\/sub><\/em>. In lack of soil-specific tests, one can consider that <em>C<\/em><sub>\u03b1<\/sub>\/<em>C<sub>c<\/sub><\/em> = 0.03 to 0.08 for clays and silts, and <em>C<\/em><sub>\u03b1<\/sub>\/<em>C<sub>c<\/sub><\/em> = 0.05 to 0.10 for organic soils (Mitchel and Soga, 2005).<\/p>\n","protected":false},"author":1,"menu_order":14,"template":"","meta":{"pb_show_title":"","pb_short_title":"4.9 Estimation of secondary compression settlement","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-292","chapter","type-chapter","status-publish","hentry"],"part":215,"_links":{"self":[{"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/pressbooks\/v2\/chapters\/292","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/wp\/v2\/users\/1"}],"version-history":[{"count":1,"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/pressbooks\/v2\/chapters\/292\/revisions"}],"predecessor-version":[{"id":293,"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/pressbooks\/v2\/chapters\/292\/revisions\/293"}],"part":[{"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/pressbooks\/v2\/parts\/215"}],"metadata":[{"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/pressbooks\/v2\/chapters\/292\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/wp\/v2\/media?parent=292"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/pressbooks\/v2\/chapter-type?post=292"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/wp\/v2\/contributor?post=292"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/wp\/v2\/license?post=292"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}