{"id":236,"date":"2022-01-13T23:17:24","date_gmt":"2022-01-13T23:17:24","guid":{"rendered":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/chapter\/pumping-from-a-multiaquifer-system\/"},"modified":"2022-01-15T04:39:00","modified_gmt":"2022-01-15T04:39:00","slug":"pumping-from-a-multiaquifer-system","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/chapter\/pumping-from-a-multiaquifer-system\/","title":{"raw":"2.4 Pumping from a Multi\u2011aquifer System","rendered":"2.4 Pumping from a Multi\u2011aquifer System"},"content":{"raw":"
\r\n

Let\u2019s consider an example of a complex multi aquifer system composed by an unconfined and two confined aquifers (Figure\u00a015). Denote by \u0394z<\/em>1<\/sub>, \u0394z<\/em>2<\/sub>, and \u0394z<\/em>3<\/sub>, the piezometric decline in the three pervious formations, respectively. Land settlement \u03b7<\/em>1<\/sub> caused by the depressurization of the unconfined aquifer is computed as is described in Section\u00a02.2<\/a>. As far as the two confined aquifers are concerned, we have to take into account the decrease of the total geostatic stress equal to \u0394z<\/em>1<\/sub>\u03b3<\/em>(\u03d5<\/em>f<\/em><\/sub>\u00a0\u2011\u00a0\u03b8<\/em>w<\/em><\/sub>), with \u03d5<\/em>f<\/em><\/sub> the porosity of the water table aquifer. As a result, \u03c3<\/em>z<\/em><\/sub> increases for formations\u00a02 and 3 (Figure\u00a015), respectively:<\/p>\r\n

\u0394\u03c3<\/em>2<\/sub> = \u0394z<\/em>2<\/sub>\u03b3 \u2212 \u0394z<\/em>1<\/sub>\u03b3<\/em>(\u03d5<\/em>f<\/em><\/sub> \u2212 \u03b8<\/em>w<\/em><\/sub>)<\/p>\r\n

\u0394\u03c3<\/em>3<\/sub> = \u0394z<\/em>3<\/sub>\u03b3 \u2212 \u0394z<\/em>1<\/sub>\u03b3<\/em>(\u03d5<\/em>f<\/em><\/sub> \u2212 \u03b8<\/em>w<\/em><\/sub>)<\/p>\r\n

The compactions \u03b7<\/em>2<\/sub> and \u03b7<\/em>3<\/sub> of the confined aquifers are obtained from Equation\u00a04<\/a> and Figure\u00a012<\/a> where the representative effective stress prior to pumping is calculated by the use of formulae similar to Equation\u00a011<\/a>. The subsidence \u03b7<\/em> at the ground surface is then represented by Equation\u00a013.<\/a><\/p>\r\n\r\n\r\n\r\n\r\n
<\/td>\r\n\u03b7<\/em> = \u03b7<\/em>1<\/sub> + \u03b7<\/em>2<\/sub> + \u03b7<\/em>3<\/sub><\/td>\r\n(13)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

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

Figure\u00a0<\/strong>15<\/strong>\u00a0<\/strong>\u2011\u00a0<\/strong>Sketch of a pumped multi<\/span>\u2011<\/span>aquifer system<\/span>.<\/p>\r\n\r\n<\/div>","rendered":"

\n

Let\u2019s consider an example of a complex multi aquifer system composed by an unconfined and two confined aquifers (Figure\u00a015). Denote by \u0394z<\/em>1<\/sub>, \u0394z<\/em>2<\/sub>, and \u0394z<\/em>3<\/sub>, the piezometric decline in the three pervious formations, respectively. Land settlement \u03b7<\/em>1<\/sub> caused by the depressurization of the unconfined aquifer is computed as is described in Section\u00a02.2<\/a>. As far as the two confined aquifers are concerned, we have to take into account the decrease of the total geostatic stress equal to \u0394z<\/em>1<\/sub>\u03b3<\/em>(\u03d5<\/em>f<\/em><\/sub>\u00a0\u2011\u00a0\u03b8<\/em>w<\/em><\/sub>), with \u03d5<\/em>f<\/em><\/sub> the porosity of the water table aquifer. As a result, \u03c3<\/em>z<\/em><\/sub> increases for formations\u00a02 and 3 (Figure\u00a015), respectively:<\/p>\n

\u0394\u03c3<\/em>2<\/sub> = \u0394z<\/em>2<\/sub>\u03b3 \u2212 \u0394z<\/em>1<\/sub>\u03b3<\/em>(\u03d5<\/em>f<\/em><\/sub> \u2212 \u03b8<\/em>w<\/em><\/sub>)<\/p>\n

\u0394\u03c3<\/em>3<\/sub> = \u0394z<\/em>3<\/sub>\u03b3 \u2212 \u0394z<\/em>1<\/sub>\u03b3<\/em>(\u03d5<\/em>f<\/em><\/sub> \u2212 \u03b8<\/em>w<\/em><\/sub>)<\/p>\n

The compactions \u03b7<\/em>2<\/sub> and \u03b7<\/em>3<\/sub> of the confined aquifers are obtained from Equation\u00a04<\/a> and Figure\u00a012<\/a> where the representative effective stress prior to pumping is calculated by the use of formulae similar to Equation\u00a011<\/a>. The subsidence \u03b7<\/em> at the ground surface is then represented by Equation\u00a013.<\/a><\/p>\n\n\n\n
<\/td>\n\u03b7<\/em> = \u03b7<\/em>1<\/sub> + \u03b7<\/em>2<\/sub> + \u03b7<\/em>3<\/sub><\/td>\n(13)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\"Sketch<\/p>\n

Figure\u00a0<\/strong>15<\/strong>\u00a0<\/strong>\u2011\u00a0<\/strong>Sketch of a pumped multi<\/span>\u2011<\/span>aquifer system<\/span>.<\/p>\n<\/div>\n","protected":false},"author":1,"menu_order":9,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-236","chapter","type-chapter","status-publish","hentry"],"part":121,"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/pressbooks\/v2\/chapters\/236","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":3,"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/pressbooks\/v2\/chapters\/236\/revisions"}],"predecessor-version":[{"id":372,"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/pressbooks\/v2\/chapters\/236\/revisions\/372"}],"part":[{"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/pressbooks\/v2\/parts\/121"}],"metadata":[{"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/pressbooks\/v2\/chapters\/236\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/wp\/v2\/media?parent=236"}],"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=236"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/wp\/v2\/contributor?post=236"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/wp\/v2\/license?post=236"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}