{"id":577,"date":"2025-03-13T03:29:25","date_gmt":"2025-03-13T03:29:25","guid":{"rendered":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/chapter\/6-21-consolidation-settlement-of-pile-groups\/"},"modified":"2026-03-16T14:13:40","modified_gmt":"2026-03-16T14:13:40","slug":"6-21-consolidation-settlement-of-pile-groups","status":"publish","type":"chapter","link":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/chapter\/6-21-consolidation-settlement-of-pile-groups\/","title":{"raw":"6.21 Consolidation settlement of pile groups","rendered":"6.21 Consolidation settlement of pile groups"},"content":{"raw":"When a pile group consisting of friction piles is embedded in, or rests above a soft clay layer, it may transfer compressible stresses to the subsoil below the pile toe sufficient to cause substantial consolidation settlement, that must be added to the group settlement calculated using the methods described in <a href=\"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/chapter\/6-20-immediate-settlement-of-pile-groups\/\">Chapter 6.20<\/a>.\n\nA simplified procedure to estimate this settlement is based on the assumption that the total serviceability load transferred by the pile group <em>Q<sub>w,group<\/sub><\/em> is acting at a depth equal to (2\/3)<em>L<\/em>\u00a0 below the pile cap (<a href=\"https:\/\/oercollective.caul.edu.au\/app\/uploads\/sites\/143\/2025\/03\/6.79-hr.png\">Figure 6.79<\/a>), and is distributed in the underlying soil following a 2:1 stress distribution (Das 2007, Budhu 2011).\n\n[caption id=\"attachment_576\" align=\"aligncenter\" width=\"500\"]<img class=\"wp-image-576 size-full\" src=\"https:\/\/libraryresources.nse.org.ng\/wp-content\/uploads\/sites\/9\/2025\/03\/6.79-corrected-typo-e1747025987161.png\" alt=\"Schematic of a floating pile group consisting of four friction piles embedded in saturated clay. The distance between the centre of the piles in the longitudinal direction is B and the distance between the centre of the piles in the transverse direction is Z. The piles are connected with a pile cap, on which an axial compressive force Qw,group is applied. The length of the piles is L. At distance H from the pile toe an incompressible layer is found. The vertical stress applied at depth 2L\/3 from the head of the piles is \u0394\u03c3z = Qw,group\/(ZB). At depth z + 2L\/3 from the ground surface the vertical stress is reduced to \u0394\u03c3z = Qw,group\/[(Z+z)(B+z)], following a 2:1 distribution.\" width=\"500\" height=\"760\"> Figure 6.79. Additional stress distribution for the estimation of the consolidation settlement of a pile group.[\/caption]Under this assumption, the increase in the vertical stress in the clay layer is calculated as (see also <a href=\"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/chapter\/3-6-stresses-in-the-soil-due-to-a-rectangular-pressure\/\">Chapter 3.6<\/a>):\n\n<strong>(6.102)<\/strong> [latex]\\Delta {\\sigma _z} = \\dfrac{{{Q_{w,group}}}}{{\\left( {Z + z} \\right)\\left( {B + z} \\right)}}[\/latex]\n\nwhere <em>Z <\/em>and <em>B<\/em> are the dimensions of the pile group, depicted in <a href=\"https:\/\/oercollective.caul.edu.au\/app\/uploads\/sites\/143\/2025\/03\/6.79-hr.png\">Figure 6.79<\/a>, and <em>z<\/em> is measured from the level where the total load is assumed to act (at 2\/3<em>L<\/em> from the surface).\n\nFollowing the estimation of the distribution of \u0394<em>\u03c3<\/em><sub>z<\/sub> with depth along the compressible layer of thickness <em>H<\/em>+(1\/3)<em>L<\/em> (<a href=\"https:\/\/oercollective.caul.edu.au\/app\/uploads\/sites\/143\/2025\/03\/6.79-hr.png\">Figure 6.79<\/a>) we can estimate its consolidation settlement using the 1D (or 2D if the thickness of the compressible layer is comparable to the pile cap dimensions) linear or non-linear consolidation methods described in Part 4. Note that settlement of the soil layers above a depth equal to (2\/3)<em>L<\/em> are not considered.","rendered":"<p>When a pile group consisting of friction piles is embedded in, or rests above a soft clay layer, it may transfer compressible stresses to the subsoil below the pile toe sufficient to cause substantial consolidation settlement, that must be added to the group settlement calculated using the methods described in <a href=\"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/chapter\/6-20-immediate-settlement-of-pile-groups\/\">Chapter 6.20<\/a>.<\/p>\n<p>A simplified procedure to estimate this settlement is based on the assumption that the total serviceability load transferred by the pile group <em>Q<sub>w,group<\/sub><\/em> is acting at a depth equal to (2\/3)<em>L<\/em>\u00a0 below the pile cap (<a href=\"https:\/\/oercollective.caul.edu.au\/app\/uploads\/sites\/143\/2025\/03\/6.79-hr.png\">Figure 6.79<\/a>), and is distributed in the underlying soil following a 2:1 stress distribution (Das 2007, Budhu 2011).<\/p>\n<figure id=\"attachment_576\" aria-describedby=\"caption-attachment-576\" style=\"width: 500px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-576 size-full\" src=\"https:\/\/libraryresources.nse.org.ng\/wp-content\/uploads\/sites\/9\/2025\/03\/6.79-corrected-typo-e1747025987161.png\" alt=\"Schematic of a floating pile group consisting of four friction piles embedded in saturated clay. The distance between the centre of the piles in the longitudinal direction is B and the distance between the centre of the piles in the transverse direction is Z. The piles are connected with a pile cap, on which an axial compressive force Qw,group is applied. The length of the piles is L. At distance H from the pile toe an incompressible layer is found. The vertical stress applied at depth 2L\/3 from the head of the piles is \u0394\u03c3z = Qw,group\/(ZB). At depth z + 2L\/3 from the ground surface the vertical stress is reduced to \u0394\u03c3z = Qw,group\/[(Z+z)(B+z)], following a 2:1 distribution.\" width=\"500\" height=\"760\" srcset=\"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-content\/uploads\/sites\/9\/2025\/03\/6.79-corrected-typo-e1747025987161.png 500w, https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-content\/uploads\/sites\/9\/2025\/03\/6.79-corrected-typo-e1747025987161-197x300.png 197w, https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-content\/uploads\/sites\/9\/2025\/03\/6.79-corrected-typo-e1747025987161-65x99.png 65w, https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-content\/uploads\/sites\/9\/2025\/03\/6.79-corrected-typo-e1747025987161-225x342.png 225w, https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-content\/uploads\/sites\/9\/2025\/03\/6.79-corrected-typo-e1747025987161-350x532.png 350w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><figcaption id=\"caption-attachment-576\" class=\"wp-caption-text\">Figure 6.79. Additional stress distribution for the estimation of the consolidation settlement of a pile group.<\/figcaption><\/figure>\n<p>Under this assumption, the increase in the vertical stress in the clay layer is calculated as (see also <a href=\"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/chapter\/3-6-stresses-in-the-soil-due-to-a-rectangular-pressure\/\">Chapter 3.6<\/a>):<\/p>\n<p><strong>(6.102)<\/strong> [latex]\\Delta {\\sigma _z} = \\dfrac{{{Q_{w,group}}}}{{\\left( {Z + z} \\right)\\left( {B + z} \\right)}}[\/latex]<\/p>\n<p>where <em>Z <\/em>and <em>B<\/em> are the dimensions of the pile group, depicted in <a href=\"https:\/\/oercollective.caul.edu.au\/app\/uploads\/sites\/143\/2025\/03\/6.79-hr.png\">Figure 6.79<\/a>, and <em>z<\/em> is measured from the level where the total load is assumed to act (at 2\/3<em>L<\/em> from the surface).<\/p>\n<p>Following the estimation of the distribution of \u0394<em>\u03c3<\/em><sub>z<\/sub> with depth along the compressible layer of thickness <em>H<\/em>+(1\/3)<em>L<\/em> (<a href=\"https:\/\/oercollective.caul.edu.au\/app\/uploads\/sites\/143\/2025\/03\/6.79-hr.png\">Figure 6.79<\/a>) we can estimate its consolidation settlement using the 1D (or 2D if the thickness of the compressible layer is comparable to the pile cap dimensions) linear or non-linear consolidation methods described in Part 4. Note that settlement of the soil layers above a depth equal to (2\/3)<em>L<\/em> are not considered.<\/p>\n","protected":false},"author":1,"menu_order":31,"template":"","meta":{"pb_show_title":"","pb_short_title":"6.21 Consolidation settlement of pile groups","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-577","chapter","type-chapter","status-publish","hentry"],"part":421,"_links":{"self":[{"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/pressbooks\/v2\/chapters\/577","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\/577\/revisions"}],"predecessor-version":[{"id":578,"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/pressbooks\/v2\/chapters\/577\/revisions\/578"}],"part":[{"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/pressbooks\/v2\/parts\/421"}],"metadata":[{"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/pressbooks\/v2\/chapters\/577\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/wp\/v2\/media?parent=577"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/pressbooks\/v2\/chapter-type?post=577"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/wp\/v2\/contributor?post=577"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/wp\/v2\/license?post=577"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}