{"id":104,"date":"2025-03-20T04:11:49","date_gmt":"2025-03-20T04:11:49","guid":{"rendered":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/chapter\/1-13-additional-problems\/"},"modified":"2026-03-16T13:53:56","modified_gmt":"2026-03-16T13:53:56","slug":"1-13-additional-problems","status":"publish","type":"chapter","link":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/chapter\/1-13-additional-problems\/","title":{"raw":"1.13 Additional problems","rendered":"1.13 Additional problems"},"content":{"raw":"

1.13.1<\/h2>\nFor the design of a cut slope (grey dashed line)<\/em>, 3 boreholes were drilled. The geological description of the encountered formations, their USCS classification and the SPT test results are provided below. Use the canvas to create a geotechnical model of the area to be introduced in the slope stability calculations, and propose the necessary parameters to be employed in the corresponding stability analyses.\n\n[caption id=\"attachment_103\" align=\"aligncenter\" width=\"800\"]\"Cross-section Additional Problem 1.13.1. Problem description and input parameters.[\/caption]\n\n \n\n[caption id=\"attachment_103\" align=\"aligncenter\" width=\"1024\"]\"Visual Additional Problem 1.13.1. Problem description and input parameters.[\/caption]\n

Answer:<\/h2>\nLayer I: Dense clayey sand (SC) \u03c6\u2032\u2248<\/em>34<\/em>\u00b0<\/em>,<\/em> \u03b3<\/em>=18 to 20 kN\/m3<\/sup><\/em>\n\nLayer II: Very dense clayey gravels, poorely graded (GC-GP) \u03c6\u2032\u2248<\/em>40<\/em>\u00b0<\/em> to 43<\/em>\u00b0<\/em>, <\/em>\u03b3<\/em>=18 to 20 kN\/m3<\/sup><\/em>\n\nLayer III: Fault zone: infinite strength for slope stability analyses<\/em>\n\nLayer IV: Slightly to moderately weathered limestone (Lm): infinite strength for slope stability analyses<\/em>\n\n
\n\n

1.13.2<\/h2>\nFor the design of the deep foundation of a tall building, two (2) sampling boreholes were drilled and two (2) CPT soundings were performed. Results of the geotechnical investigation revealed a (more-or-less) consistent geotechnical profile: a medium-to-stiff low plasticity (PI \u2248 20%) clay formation prevails, interrupted by a loose-to-medium silty-clayey sand layer. The bedrock, a sandstone formation is encountered at depths 12.0 to 16.0 m.\n\nUse the in situ <\/em>SPT and CPT test results, combined with the provided empirical relations\/charts, to determine the characteristic undrained shear strength (Su<\/sub><\/em>) of the clay layer and the effective friction angle of the sand layer (<\/em>\u03c6\u2032<\/em>). <\/em>Assume the bulk unit weight of the clay\/sand layers to be constant \u03b3<\/em> = 17 kN\/m3<\/sup>.\n\n[caption id=\"attachment_103\" align=\"aligncenter\" width=\"1024\"]\"The Additional Problem 1.13.2. Problem description and input parameters.[\/caption]\n\n[caption id=\"attachment_103\" align=\"aligncenter\" width=\"1024\"]\"The Additional Problem 1.13.2. Problem description and input parameters.[\/caption]\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Example 1.13.2.<\/strong> CPT1 and CPT2 test results<\/caption>\n
CPT1<\/th>\nCPT2<\/th>\n<\/tr>\n
Depth (m)<\/td>\nqt<\/sub>\/pa<\/sub><\/em><\/td>\nFR<\/sub><\/em> (%)<\/td>\nDepth (m)<\/td>\nqt<\/sub>\/pa<\/sub><\/em><\/td>\nFR<\/sub><\/em> (%)<\/td>\n<\/tr>\n
1<\/td>\n3.5<\/td>\n2.5<\/td>\n1<\/td>\n3<\/td>\n2.5<\/td>\n<\/tr>\n
2<\/td>\n4<\/td>\n1.3<\/td>\n2<\/td>\n5<\/td>\n0.8<\/td>\n<\/tr>\n
3<\/td>\n6<\/td>\n0.8<\/td>\n3<\/td>\n6.5<\/td>\n1<\/td>\n<\/tr>\n
4<\/td>\n5.5<\/td>\n1<\/td>\n4<\/td>\n9<\/td>\n1.5<\/td>\n<\/tr>\n
5<\/td>\n20<\/td>\n1<\/td>\n5<\/td>\n7<\/td>\n0.6<\/td>\n<\/tr>\n
6<\/td>\n11<\/td>\n0.6<\/td>\n6<\/td>\n4<\/td>\n4<\/td>\n<\/tr>\n
7<\/td>\n20<\/td>\n0.6<\/td>\n7<\/td>\n5.5<\/td>\n4.5<\/td>\n<\/tr>\n
8<\/td>\n17<\/td>\n0.5<\/td>\n8<\/td>\n6<\/td>\n2<\/td>\n<\/tr>\n
9<\/td>\n19<\/td>\n0.5<\/td>\n9<\/td>\n8<\/td>\n6<\/td>\n<\/tr>\n
10<\/td>\n5<\/td>\n3<\/td>\n10<\/td>\n9<\/td>\n3<\/td>\n<\/tr>\n
11<\/td>\n3<\/td>\n4.5<\/td>\n11<\/td>\n7.5<\/td>\n5<\/td>\n<\/tr>\n
12<\/td>\n11<\/td>\n2.5<\/td>\n<\/td>\n<\/tr>\n
13<\/td>\n10.5<\/td>\n6<\/td>\n<\/tr>\n
14<\/td>\n12<\/td>\n1.4<\/td>\n<\/tr>\n
15<\/td>\n13<\/td>\n2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Answer:<\/h2>\nClay layer: Su<\/sub> = 20 kPa for depth z<4m and Su<\/sub> = 20+2(z-6) kPa for depth z>6m<\/em>\n\nSand layer: <\/em>\u03c6\u2032 =<\/em>\u00a030<\/em>o<\/sup><\/em>","rendered":"

1.13.1<\/h2>\n

For the design of a cut slope (grey dashed line)<\/em>, 3 boreholes were drilled. The geological description of the encountered formations, their USCS classification and the SPT test results are provided below. Use the canvas to create a geotechnical model of the area to be introduced in the slope stability calculations, and propose the necessary parameters to be employed in the corresponding stability analyses.<\/p>\n

\"Cross-section
Additional Problem 1.13.1. Problem description and input parameters.<\/figcaption><\/figure>\n

 <\/p>\n

\"Visual
Additional Problem 1.13.1. Problem description and input parameters.<\/figcaption><\/figure>\n

Answer:<\/h2>\n

Layer I: Dense clayey sand (SC) \u03c6\u2032\u2248<\/em>34<\/em>\u00b0<\/em>,<\/em> \u03b3<\/em>=18 to 20 kN\/m3<\/sup><\/em><\/p>\n

Layer II: Very dense clayey gravels, poorely graded (GC-GP) \u03c6\u2032\u2248<\/em>40<\/em>\u00b0<\/em> to 43<\/em>\u00b0<\/em>, <\/em>\u03b3<\/em>=18 to 20 kN\/m3<\/sup><\/em><\/p>\n

Layer III: Fault zone: infinite strength for slope stability analyses<\/em><\/p>\n

Layer IV: Slightly to moderately weathered limestone (Lm): infinite strength for slope stability analyses<\/em><\/p>\n

\n

1.13.2<\/h2>\n

For the design of the deep foundation of a tall building, two (2) sampling boreholes were drilled and two (2) CPT soundings were performed. Results of the geotechnical investigation revealed a (more-or-less) consistent geotechnical profile: a medium-to-stiff low plasticity (PI \u2248 20%) clay formation prevails, interrupted by a loose-to-medium silty-clayey sand layer. The bedrock, a sandstone formation is encountered at depths 12.0 to 16.0 m.<\/p>\n

Use the in situ <\/em>SPT and CPT test results, combined with the provided empirical relations\/charts, to determine the characteristic undrained shear strength (Su<\/sub><\/em>) of the clay layer and the effective friction angle of the sand layer (<\/em>\u03c6\u2032<\/em>). <\/em>Assume the bulk unit weight of the clay\/sand layers to be constant \u03b3<\/em> = 17 kN\/m3<\/sup>.<\/p>\n

\"The
Additional Problem 1.13.2. Problem description and input parameters.<\/figcaption><\/figure>\n
\"The
Additional Problem 1.13.2. Problem description and input parameters.<\/figcaption><\/figure>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Example 1.13.2.<\/strong> CPT1 and CPT2 test results<\/caption>\n
CPT1<\/th>\nCPT2<\/th>\n<\/tr>\n
Depth (m)<\/td>\nqt<\/sub>\/pa<\/sub><\/em><\/td>\nFR<\/sub><\/em> (%)<\/td>\nDepth (m)<\/td>\nqt<\/sub>\/pa<\/sub><\/em><\/td>\nFR<\/sub><\/em> (%)<\/td>\n<\/tr>\n
1<\/td>\n3.5<\/td>\n2.5<\/td>\n1<\/td>\n3<\/td>\n2.5<\/td>\n<\/tr>\n
2<\/td>\n4<\/td>\n1.3<\/td>\n2<\/td>\n5<\/td>\n0.8<\/td>\n<\/tr>\n
3<\/td>\n6<\/td>\n0.8<\/td>\n3<\/td>\n6.5<\/td>\n1<\/td>\n<\/tr>\n
4<\/td>\n5.5<\/td>\n1<\/td>\n4<\/td>\n9<\/td>\n1.5<\/td>\n<\/tr>\n
5<\/td>\n20<\/td>\n1<\/td>\n5<\/td>\n7<\/td>\n0.6<\/td>\n<\/tr>\n
6<\/td>\n11<\/td>\n0.6<\/td>\n6<\/td>\n4<\/td>\n4<\/td>\n<\/tr>\n
7<\/td>\n20<\/td>\n0.6<\/td>\n7<\/td>\n5.5<\/td>\n4.5<\/td>\n<\/tr>\n
8<\/td>\n17<\/td>\n0.5<\/td>\n8<\/td>\n6<\/td>\n2<\/td>\n<\/tr>\n
9<\/td>\n19<\/td>\n0.5<\/td>\n9<\/td>\n8<\/td>\n6<\/td>\n<\/tr>\n
10<\/td>\n5<\/td>\n3<\/td>\n10<\/td>\n9<\/td>\n3<\/td>\n<\/tr>\n
11<\/td>\n3<\/td>\n4.5<\/td>\n11<\/td>\n7.5<\/td>\n5<\/td>\n<\/tr>\n
12<\/td>\n11<\/td>\n2.5<\/td>\n<\/td>\n<\/tr>\n
13<\/td>\n10.5<\/td>\n6<\/td>\n<\/tr>\n
14<\/td>\n12<\/td>\n1.4<\/td>\n<\/tr>\n
15<\/td>\n13<\/td>\n2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Answer:<\/h2>\n

Clay layer: Su<\/sub> = 20 kPa for depth z<4m and Su<\/sub> = 20+2(z-6) kPa for depth z>6m<\/em><\/p>\n

Sand layer: <\/em>\u03c6\u2032 =<\/em>\u00a030<\/em>o<\/sup><\/em><\/p>\n","protected":false},"author":1,"menu_order":14,"template":"","meta":{"pb_show_title":"","pb_short_title":"1.13 Additional problems","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-104","chapter","type-chapter","status-publish","hentry"],"part":24,"_links":{"self":[{"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/pressbooks\/v2\/chapters\/104","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\/104\/revisions"}],"predecessor-version":[{"id":105,"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/pressbooks\/v2\/chapters\/104\/revisions\/105"}],"part":[{"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/pressbooks\/v2\/parts\/24"}],"metadata":[{"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/pressbooks\/v2\/chapters\/104\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/wp\/v2\/media?parent=104"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/pressbooks\/v2\/chapter-type?post=104"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/wp\/v2\/contributor?post=104"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/libraryresources.nse.org.ng\/fundamentalsoffoundationengineering\/wp-json\/wp\/v2\/license?post=104"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}