{"id":275,"date":"2022-01-13T23:17:39","date_gmt":"2022-01-13T23:17:39","guid":{"rendered":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/chapter\/box-2-visualization-of-relationship-between-effective-stress-and-void-ratio\/"},"modified":"2022-01-17T00:04:34","modified_gmt":"2022-01-17T00:04:34","slug":"box-2-visualization-of-relationship-between-effective-stress-and-void-ratio","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/chapter\/box-2-visualization-of-relationship-between-effective-stress-and-void-ratio\/","title":{"raw":"Box\u00a02 Visualization of Relationship between Effective Stress and Void Ratio","rendered":"Box\u00a02 Visualization of Relationship between Effective Stress and Void Ratio"},"content":{"raw":"
\r\n

To visualize the relationship between compaction and void ratio presented in Figure\u00a02<\/a>, which is repeated here for the readers convenience, it is useful to view abstract version of Figure\u00a02<\/a>. In the abstract version (Figure\u00a0Box\u00a02\u20111) in which all solids are grouped with no pore space, and all pore space occupies the remainder of the volume, with example values are assigned, as illustrated in Figure\u00a0Box\u00a02\u20111. The total compaction \u03b7<\/em> of a layer as illustrated in Figure 2<\/a>, with initial thickness s<\/em>0<\/sub> and initial void ratio e<\/em>0<\/sub> is completely due to reduced pore space as reflected by Equation\u00a04 (repeated here for the readers convenience).<\/p>\r\n\r\n\r\n\r\n\r\n
<\/td>\r\n[latex]\\displaystyle \\eta =\\Delta z\\frac{\\Delta e}{1+e_{0}}[\/latex]<\/td>\r\n(repeat of Equation 4)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

\"Figure<\/p>\r\n

Repeat of Figure\u00a02 for the reader\u2019s convenience\u00a0<\/strong>\u2011\u00a0<\/strong>Soil compaction \u03b7<\/em> with a reduction of the porous space (grains are incompressible for all practical purposes).<\/p>\r\n

\"\u00a0Abstract<\/p>\r\n

Figure\u00a0Box\u00a02<\/strong>\u20111\u00a0<\/strong>\u2011<\/strong>\u00a0<\/strong>Abstract representation of the fine\u2011grained layer of Figure\u00a02 in which all solids are grouped with no pore space, all pore space occupies the remainder of the volume.<\/p>\r\n

\"Soil<\/p>\r\n

Figure\u00a0<\/strong>Box\u00a0<\/strong>2<\/strong>\u20112\u00a0<\/strong>\u2011\u00a0<\/strong>Soil compaction \u03b7<\/em> illustrated using the abstract example of the fine\u2011grained material shown in Figure\u00a0Box\u00a02\u20111 with example values assigned to the pertinent parameters.<\/p>\r\n

Calculation of the change in effective stress for a decline in the piezometric level from A to B at a point within an unconfined aquifer as shown in Figure\u00a013<\/a>, is illustrated in Figure\u00a0Box\u00a02\u20113 and Figure\u00a0Box\u00a02\u20114.<\/p>\r\n

\"Presentation<\/p>\r\n

Figure\u00a0Box\u00a02<\/strong>\u20113\u00a0<\/strong>\u2011<\/strong>\u00a0<\/strong>Presentation of Equations 8<\/a> and 9<\/a> in words.<\/p>\r\n

\"Worked<\/strong><\/p>\r\n

Figure\u00a0Box\u00a02<\/strong>\u20114\u00a0<\/strong>\u2011<\/strong>\u00a0<\/strong>Worked example of calculating effective stress.<\/p>\r\n

Return to where text linked to Box 2<\/span><\/a><\/p>\r\n\r\n<\/div>","rendered":"

\n

To visualize the relationship between compaction and void ratio presented in Figure\u00a02<\/a>, which is repeated here for the readers convenience, it is useful to view abstract version of Figure\u00a02<\/a>. In the abstract version (Figure\u00a0Box\u00a02\u20111) in which all solids are grouped with no pore space, and all pore space occupies the remainder of the volume, with example values are assigned, as illustrated in Figure\u00a0Box\u00a02\u20111. The total compaction \u03b7<\/em> of a layer as illustrated in Figure 2<\/a>, with initial thickness s<\/em>0<\/sub> and initial void ratio e<\/em>0<\/sub> is completely due to reduced pore space as reflected by Equation\u00a04 (repeated here for the readers convenience).<\/p>\n\n\n\n
<\/td>\n\"\displaystyle \eta =\Delta z\frac{\Delta e}{1+e_{0}}\"<\/td>\n(repeat of Equation 4)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\"Figure<\/p>\n

Repeat of Figure\u00a02 for the reader\u2019s convenience\u00a0<\/strong>\u2011\u00a0<\/strong>Soil compaction \u03b7<\/em> with a reduction of the porous space (grains are incompressible for all practical purposes).<\/p>\n

\"\u00a0Abstract<\/p>\n

Figure\u00a0Box\u00a02<\/strong>\u20111\u00a0<\/strong>\u2011<\/strong>\u00a0<\/strong>Abstract representation of the fine\u2011grained layer of Figure\u00a02 in which all solids are grouped with no pore space, all pore space occupies the remainder of the volume.<\/p>\n

\"Soil<\/p>\n

Figure\u00a0<\/strong>Box\u00a0<\/strong>2<\/strong>\u20112\u00a0<\/strong>\u2011\u00a0<\/strong>Soil compaction \u03b7<\/em> illustrated using the abstract example of the fine\u2011grained material shown in Figure\u00a0Box\u00a02\u20111 with example values assigned to the pertinent parameters.<\/p>\n

Calculation of the change in effective stress for a decline in the piezometric level from A to B at a point within an unconfined aquifer as shown in Figure\u00a013<\/a>, is illustrated in Figure\u00a0Box\u00a02\u20113 and Figure\u00a0Box\u00a02\u20114.<\/p>\n

\"Presentation<\/p>\n

Figure\u00a0Box\u00a02<\/strong>\u20113\u00a0<\/strong>\u2011<\/strong>\u00a0<\/strong>Presentation of Equations 8<\/a> and 9<\/a> in words.<\/p>\n

\"Worked<\/strong><\/p>\n

Figure\u00a0Box\u00a02<\/strong>\u20114\u00a0<\/strong>\u2011<\/strong>\u00a0<\/strong>Worked example of calculating effective stress.<\/p>\n

Return to where text linked to Box 2<\/span><\/a><\/p>\n<\/div>\n","protected":false},"author":1,"menu_order":30,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-275","chapter","type-chapter","status-publish","hentry"],"part":177,"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/pressbooks\/v2\/chapters\/275","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/wp\/v2\/users\/1"}],"version-history":[{"count":4,"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/pressbooks\/v2\/chapters\/275\/revisions"}],"predecessor-version":[{"id":451,"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/pressbooks\/v2\/chapters\/275\/revisions\/451"}],"part":[{"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/pressbooks\/v2\/parts\/177"}],"metadata":[{"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/pressbooks\/v2\/chapters\/275\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/wp\/v2\/media?parent=275"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/pressbooks\/v2\/chapter-type?post=275"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/wp\/v2\/contributor?post=275"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/wp\/v2\/license?post=275"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}