{"id":543,"date":"2025-03-31T04:23:18","date_gmt":"2025-03-31T04:23:18","guid":{"rendered":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/chapter\/example-6-7-estimation-of-the-design-bearing-capacity-of-a-pile-group\/"},"modified":"2026-03-16T14:11:55","modified_gmt":"2026-03-16T14:11:55","slug":"example-6-7-estimation-of-the-design-bearing-capacity-of-a-pile-group","status":"publish","type":"chapter","link":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/chapter\/example-6-7-estimation-of-the-design-bearing-capacity-of-a-pile-group\/","title":{"raw":"Example 6.7","rendered":"Example 6.7"},"content":{"raw":"An offshore pole is going to be founded on a pile group consisting of 4 cylindrical piles, with the geometry shown in the figure below. Determine the short-term design bearing capacity of the pile group, according to AS 2159 provisions, For the specific project, assume a basic geotechnical strength reduction factor \u03c6<\/em>gb<\/sub> equal to \u03c6<\/em>gb <\/sub>= 0.60.\n\n[caption id=\"attachment_542\" align=\"aligncenter\" width=\"400\"]\"Schematic Example 6.7. Problem description and input parameters.[\/caption]\n

Answer:<\/h2>\nIn the Example 6.1<\/a> we have determined the ultimate geotechnical strength of each single pile with the \u03b1<\/em>-Method as:\n\n[latex]{Q_f} = {Q_{sf}} + {Q_b} = 1059{\\rm{ \\:kN}}[\/latex]\n\n1. Ultimate geotechnical strength of pile group considering efficiency, ng<\/sub><\/em>:\n\nAccording to FHWA (2006), pile group efficiency ng<\/sub><\/em> for cases where the pile cap is not in firm contact with the ground and s\/D <\/em>= 4 m\/1 m =4 (Eq. 6.88) is:\n\n[latex]{n_g} = 0.1\\left( {\\dfrac{s}{D}} \\right) + 0.4 = 0.8[\/latex]\n\nTherefore the ultimate geotechnical strength of pile group considering is (Eq. 6.87):\n\n[latex]{Q_{f,group}} = {n_g}\\left( {n{Q_f}} \\right) = 0.8 \\times 4 \\times 1059 = 3389{\\rm{ \\:kN}}[\/latex]\n\n2. Ultimate geotechnical strength of pile group for block-type failure:\n\nWe will apply Eq. 6.89, considering B <\/em>= 4 m and Z <\/em>= 4 m i.e., the dimensions of the pile group, not the pile cap (Figure 6.65b<\/a>). Also, as for the calculation of the skin friction resistance of a single pile, the first 1.5D<\/em> meters of the pile shaft will not contribute to the friction resistance:\n\n[latex]{Q_{f,group}} = {S_{u,ave}}\\left[ {2L\\left( {B + Z} \\right)} \\right] + {N_{cp}}{S_{u,b}}\\left( {BZ} \\right) = 40\\left[ {2\\left( {8 - 1.5} \\right)\\left( {4 + 4} \\right)} \\right] + 40 \\times 9 \\times \\left( {4 \\times 4} \\right) = 9920{\\rm{\\: kN}}[\/latex]\n\nObserve that the ultimate geotechnical strength for block-type failure is grossly larger than the ultimate geotechnical strength considering failure of individual piles, even when pile group efficiency ng<\/sub><\/em> < 1 is applied to the latter. This does not come as surprise: Block-type failure can, by definition, be critical only for very dense pile spacings, when the area of the pile group (B<\/em> \u00d7Z<\/em>) + 2(B<\/em> \u00d7L<\/em>)+ 2(Z<\/em> \u00d7L<\/em>) is smaller than the surface area of the individual piles.\n\n3. Design bearing capacity of pile group\n\nThe design bearing capacity \u03c6<\/em>gb<\/sub>Qf,group<\/sub><\/em> is:\n\n[latex]{\\varphi _{gb}}{Q_{f,group}} = 0.60 \\times 3389 = 2033{\\rm{ \\:kN}}[\/latex]","rendered":"

An offshore pole is going to be founded on a pile group consisting of 4 cylindrical piles, with the geometry shown in the figure below. Determine the short-term design bearing capacity of the pile group, according to AS 2159 provisions, For the specific project, assume a basic geotechnical strength reduction factor \u03c6<\/em>gb<\/sub> equal to \u03c6<\/em>gb <\/sub>= 0.60.<\/p>\n

\"Schematic
Example 6.7. Problem description and input parameters.<\/figcaption><\/figure>\n

Answer:<\/h2>\n

In the Example 6.1<\/a> we have determined the ultimate geotechnical strength of each single pile with the \u03b1<\/em>-Method as:<\/p>\n

[latex]{Q_f} = {Q_{sf}} + {Q_b} = 1059{\\rm{ \\:kN}}[\/latex]<\/p>\n

1. Ultimate geotechnical strength of pile group considering efficiency, ng<\/sub><\/em>:<\/p>\n

According to FHWA (2006), pile group efficiency ng<\/sub><\/em> for cases where the pile cap is not in firm contact with the ground and s\/D <\/em>= 4 m\/1 m =4 (Eq. 6.88) is:<\/p>\n

[latex]{n_g} = 0.1\\left( {\\dfrac{s}{D}} \\right) + 0.4 = 0.8[\/latex]<\/p>\n

Therefore the ultimate geotechnical strength of pile group considering is (Eq. 6.87):<\/p>\n

[latex]{Q_{f,group}} = {n_g}\\left( {n{Q_f}} \\right) = 0.8 \\times 4 \\times 1059 = 3389{\\rm{ \\:kN}}[\/latex]<\/p>\n

2. Ultimate geotechnical strength of pile group for block-type failure:<\/p>\n

We will apply Eq. 6.89, considering B <\/em>= 4 m and Z <\/em>= 4 m i.e., the dimensions of the pile group, not the pile cap (Figure 6.65b<\/a>). Also, as for the calculation of the skin friction resistance of a single pile, the first 1.5D<\/em> meters of the pile shaft will not contribute to the friction resistance:<\/p>\n

[latex]{Q_{f,group}} = {S_{u,ave}}\\left[ {2L\\left( {B + Z} \\right)} \\right] + {N_{cp}}{S_{u,b}}\\left( {BZ} \\right) = 40\\left[ {2\\left( {8 - 1.5} \\right)\\left( {4 + 4} \\right)} \\right] + 40 \\times 9 \\times \\left( {4 \\times 4} \\right) = 9920{\\rm{\\: kN}}[\/latex]<\/p>\n

Observe that the ultimate geotechnical strength for block-type failure is grossly larger than the ultimate geotechnical strength considering failure of individual piles, even when pile group efficiency ng<\/sub><\/em> < 1 is applied to the latter. This does not come as surprise: Block-type failure can, by definition, be critical only for very dense pile spacings, when the area of the pile group (B<\/em> \u00d7Z<\/em>) + 2(B<\/em> \u00d7L<\/em>)+ 2(Z<\/em> \u00d7L<\/em>) is smaller than the surface area of the individual piles.<\/p>\n

3. Design bearing capacity of pile group<\/p>\n

The design bearing capacity \u03c6<\/em>gb<\/sub>Qf,group<\/sub><\/em> is:<\/p>\n

[latex]{\\varphi _{gb}}{Q_{f,group}} = 0.60 \\times 3389 = 2033{\\rm{ \\:kN}}[\/latex]<\/p>\n","protected":false},"author":1,"menu_order":25,"template":"","meta":{"pb_show_title":"","pb_short_title":"Example 6.7","pb_subtitle":"Estimation of the design bearing capacity of a pile group","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-543","chapter","type-chapter","status-publish","hentry"],"part":421,"_links":{"self":[{"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/pressbooks\/v2\/chapters\/543","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\/543\/revisions"}],"predecessor-version":[{"id":544,"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/pressbooks\/v2\/chapters\/543\/revisions\/544"}],"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\/543\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/wp\/v2\/media?parent=543"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/pressbooks\/v2\/chapter-type?post=543"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/wp\/v2\/contributor?post=543"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/wp\/v2\/license?post=543"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}