{"id":244,"date":"2025-03-28T03:57:19","date_gmt":"2025-03-28T03:57:19","guid":{"rendered":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/chapter\/example-4-1-immediate-settlement-of-a-footing-resting-on-saturated-clay\/"},"modified":"2026-03-16T13:59:40","modified_gmt":"2026-03-16T13:59:40","slug":"example-4-1-immediate-settlement-of-a-footing-resting-on-saturated-clay","status":"publish","type":"chapter","link":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/chapter\/example-4-1-immediate-settlement-of-a-footing-resting-on-saturated-clay\/","title":{"raw":"Example 4.1","rendered":"Example 4.1"},"content":{"raw":"Estimate the immediate settlement of a square 4 m x 4 m footing resting on the surface of a deep homogeneous saturated clay layer, using the methodology described in Section 4.5.4. The working load under serviceability conditions is Qext <\/sub><\/em>= 3 MN, the embedment depth is Df <\/sub><\/em>= 2 m, and the undrained clay compressibility parameters are Eu <\/sub><\/em>= 10 MPa and vu <\/sub><\/em>= 0.50.\n\n[caption id=\"attachment_243\" align=\"aligncenter\" width=\"350\"]\"The Example 4.1. Problem description and input parameters.[\/caption]\n

Answer:<\/h2>\nThe area of the rectangular footing is equal to:\n\nAb<\/sub><\/em>=4m x 4m =16 m2<\/sup>\n\nAs the half-length of the rectangle side is L <\/em>= 4 m\/2 = 2 m, the factor Ab<\/sub>\/<\/em>4L2<\/sup><\/em> is equal to:\n\nAb<\/sub>\/<\/em>4L2 <\/sup><\/em>= 16\/(4x22<\/sup>) = 1\n\nInfluence factors \u03bc<\/em>s<\/sub> and \u03bc<\/em>emb<\/sub> accounting for the effect of shape and of footing embedment, respectively, are provided from Eqs. 4.13 and 4.14. As the thickness of the footing is small, the shear resistance that may be mobilised is negligible, thus the influence factor accounting for the effect of wall friction \u03bc<\/em>wall<\/sub> is taken conservatively equal \u03bc<\/em>wall<\/sub> <\/em>= 1.0.\n\n[latex]{\\mu _s} = 0.45{\\left( {\\dfrac{{{A_b}}}{{4{L^2}}}} \\right)^{ - 0.38}} = 0.45[\/latex]\n\n[latex]{\\mu _{emb}} = 1 - 0.04\\dfrac{{{D_f}}}{B}\\left[ {1 + \\dfrac{4}{3}\\left( {\\dfrac{{{A_b}}}{{4{L^2}}}} \\right)} \\right] = 1 - 0.04\\dfrac{2}{2}\\left[ {1 + \\dfrac{4}{3} \\times 1} \\right] = 0.906[\/latex]\n\nThe immediate settlement is therefore estimated from Eq. 4.12 as:\n\n[latex]{\\rho _e} = \\dfrac{{{Q_{ext}}}}{{{E_u}L}}\\left( {1 - \\nu _u^2} \\right){\\mu _s}{\\mu _{emb}}{\\mu _{wall}} = \\dfrac{{3{\\rm{MN}}}}{{10\\dfrac{{{\\rm{MN}}}}{{{{\\rm{m}}^{\\rm{2}}}}} \\times 2\\rm{m}}}\\left( {1 - {{0.5}^2}} \\right) \\times 1 \\times 0.906 \\times 0.45 = 0.046{\\rm{ m}}[\/latex]","rendered":"

Estimate the immediate settlement of a square 4 m x 4 m footing resting on the surface of a deep homogeneous saturated clay layer, using the methodology described in Section 4.5.4. The working load under serviceability conditions is Qext <\/sub><\/em>= 3 MN, the embedment depth is Df <\/sub><\/em>= 2 m, and the undrained clay compressibility parameters are Eu <\/sub><\/em>= 10 MPa and vu <\/sub><\/em>= 0.50.<\/p>\n

\"The
Example 4.1. Problem description and input parameters.<\/figcaption><\/figure>\n

Answer:<\/h2>\n

The area of the rectangular footing is equal to:<\/p>\n

Ab<\/sub><\/em>=4m x 4m =16 m2<\/sup><\/p>\n

As the half-length of the rectangle side is L <\/em>= 4 m\/2 = 2 m, the factor Ab<\/sub>\/<\/em>4L2<\/sup><\/em> is equal to:<\/p>\n

Ab<\/sub>\/<\/em>4L2 <\/sup><\/em>= 16\/(4×22<\/sup>) = 1<\/p>\n

Influence factors \u03bc<\/em>s<\/sub> and \u03bc<\/em>emb<\/sub> accounting for the effect of shape and of footing embedment, respectively, are provided from Eqs. 4.13 and 4.14. As the thickness of the footing is small, the shear resistance that may be mobilised is negligible, thus the influence factor accounting for the effect of wall friction \u03bc<\/em>wall<\/sub> is taken conservatively equal \u03bc<\/em>wall<\/sub> <\/em>= 1.0.<\/p>\n

[latex]{\\mu _s} = 0.45{\\left( {\\dfrac{{{A_b}}}{{4{L^2}}}} \\right)^{ - 0.38}} = 0.45[\/latex]<\/p>\n

[latex]{\\mu _{emb}} = 1 - 0.04\\dfrac{{{D_f}}}{B}\\left[ {1 + \\dfrac{4}{3}\\left( {\\dfrac{{{A_b}}}{{4{L^2}}}} \\right)} \\right] = 1 - 0.04\\dfrac{2}{2}\\left[ {1 + \\dfrac{4}{3} \\times 1} \\right] = 0.906[\/latex]<\/p>\n

The immediate settlement is therefore estimated from Eq. 4.12 as:<\/p>\n

[latex]{\\rho _e} = \\dfrac{{{Q_{ext}}}}{{{E_u}L}}\\left( {1 - \\nu _u^2} \\right){\\mu _s}{\\mu _{emb}}{\\mu _{wall}} = \\dfrac{{3{\\rm{MN}}}}{{10\\dfrac{{{\\rm{MN}}}}{{{{\\rm{m}}^{\\rm{2}}}}} \\times 2\\rm{m}}}\\left( {1 - {{0.5}^2}} \\right) \\times 1 \\times 0.906 \\times 0.45 = 0.046{\\rm{ m}}[\/latex]<\/p>\n","protected":false},"author":1,"menu_order":6,"template":"","meta":{"pb_show_title":"","pb_short_title":"Example 4.1","pb_subtitle":"Immediate settlement of a footing resting on saturated clay","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-244","chapter","type-chapter","status-publish","hentry"],"part":215,"_links":{"self":[{"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/pressbooks\/v2\/chapters\/244","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\/244\/revisions"}],"predecessor-version":[{"id":245,"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/pressbooks\/v2\/chapters\/244\/revisions\/245"}],"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\/244\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/wp\/v2\/media?parent=244"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/pressbooks\/v2\/chapter-type?post=244"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/wp\/v2\/contributor?post=244"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/wp\/v2\/license?post=244"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}