{"id":235,"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-single-confined-aquifer\/"},"modified":"2022-01-16T23:24:09","modified_gmt":"2022-01-16T23:24:09","slug":"pumping-from-a-single-confined-aquifer","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/chapter\/pumping-from-a-single-confined-aquifer\/","title":{"raw":"2.3 Pumping from a Single Confined Aquifer","rendered":"2.3 Pumping from a Single Confined Aquifer"},"content":{"raw":"
\r\n

Let \u0394z<\/em> be the piezometric decline in the confined aquifer (Figure\u00a014). Since the weight of the overlying soil column does not change, that is, \u03c3<\/em>c<\/em><\/sub> is constant, there is an equal, albeit of opposite sign, change in the effective intergranular stress and the pore pressure, that is, \u0394\u03c3<\/em>z<\/em><\/sub>\u00a0=\u00a0p<\/em>\u00a0=\u00a0\u03b3<\/em>\u0394z<\/em>. Computing \u03c3<\/em>c<\/em><\/sub> at the mid\u2011point of the aquifer as the sum of the stress \u03c3<\/em>c<\/em><\/sub>\u2032 at the bottom of the overlying aquitard plus the weight of aquifer column down to the mid\u2011point results in:<\/p>\r\n

\u03c3<\/em>c<\/em><\/sub> = \u03c3<\/em>c<\/em><\/sub>\u2032 + 0.5s<\/em>0<\/sub>[(1 - \u03d5<\/em>)\u03b3<\/em>\u2032 + \u03d5\u03b3<\/em>]<\/p>\r\n

thus, the intergranular stress is shown by Equation\u00a011.<\/a><\/p>\r\n\r\n\r\n\r\n\r\n
<\/td>\r\n\u03c3<\/em>z<\/em>0<\/sub> = \u03c3<\/em>c<\/em><\/sub>\u2032 + 0.5s<\/em>0<\/sub>[(1 - \u03d5<\/em>)\u03b3<\/em>\u2032 + \u03d5\u03b3<\/em>] - p<\/em><\/td>\r\n(11)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nwhere:\r\n\r\n\r\n\r\n\r\n
\u03c3<\/em>c<\/em><\/sub>\u2032<\/td>\r\n=<\/td>\r\ngeostatic stress at the bottom of the overlying impermeable layer (ML-1<\/sup>T-2<\/sup>)<\/td>\r\n<\/tr>\r\n
p<\/em><\/td>\r\n=<\/td>\r\npore pressure measured on the mid\u2011plane of the aquifer prior to the piezometric decline (ML-1<\/sup>T-2<\/sup>)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

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

Figure\u00a014<\/strong>\u00a0<\/strong>\u2011\u00a0<\/strong>Sketch of a pumped confined aquifer.<\/p>\r\n

Land subsidence is equal to the aquifer compaction as calculated by the use of a graph as shown in Figure\u00a012<\/a> and Equation\u00a03<\/a>. Again, if s<\/em>0<\/sub> is large, it can be split into sub\u2011intervals and \u03c3<\/em>z<\/em><\/sub>0<\/sub> computed for each sub\u2011interval (while \u0394\u03c3<\/em>z<\/em><\/sub> is the same for each sub\u2011interval).<\/p>\r\n

In summary, the compaction of a single confined aquifer amounts to (Equation\u00a012):<\/a><\/p>\r\n\r\n\r\n\r\n\r\n
<\/td>\r\n\u03b7<\/em> = s<\/em>0<\/sub>c<\/em>b<\/em><\/sub>\u0394\u03c3<\/em>z<\/em><\/sub><\/td>\r\n(12)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

with s<\/em>0<\/sub> the aquifer thickness, c<\/em>b<\/em><\/sub> is the uniaxial vertical soil compressibility, and \u0394\u03c3<\/em>z<\/em><\/sub> is the change in the effective intergranular stress.<\/p>\r\n\r\n<\/div>","rendered":"

\n

Let \u0394z<\/em> be the piezometric decline in the confined aquifer (Figure\u00a014). Since the weight of the overlying soil column does not change, that is, \u03c3<\/em>c<\/em><\/sub> is constant, there is an equal, albeit of opposite sign, change in the effective intergranular stress and the pore pressure, that is, \u0394\u03c3<\/em>z<\/em><\/sub>\u00a0=\u00a0p<\/em>\u00a0=\u00a0\u03b3<\/em>\u0394z<\/em>. Computing \u03c3<\/em>c<\/em><\/sub> at the mid\u2011point of the aquifer as the sum of the stress \u03c3<\/em>c<\/em><\/sub>\u2032 at the bottom of the overlying aquitard plus the weight of aquifer column down to the mid\u2011point results in:<\/p>\n

\u03c3<\/em>c<\/em><\/sub> = \u03c3<\/em>c<\/em><\/sub>\u2032 + 0.5s<\/em>0<\/sub>[(1 – \u03d5<\/em>)\u03b3<\/em>\u2032 + \u03d5\u03b3<\/em>]<\/p>\n

thus, the intergranular stress is shown by Equation\u00a011.<\/a><\/p>\n\n\n\n
<\/td>\n\u03c3<\/em>z<\/em>0<\/sub> = \u03c3<\/em>c<\/em><\/sub>\u2032 + 0.5s<\/em>0<\/sub>[(1 – \u03d5<\/em>)\u03b3<\/em>\u2032 + \u03d5\u03b3<\/em>] – p<\/em><\/td>\n(11)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

where:<\/p>\n\n\n\n\n
\u03c3<\/em>c<\/em><\/sub>\u2032<\/td>\n=<\/td>\ngeostatic stress at the bottom of the overlying impermeable layer (ML-1<\/sup>T-2<\/sup>)<\/td>\n<\/tr>\n
p<\/em><\/td>\n=<\/td>\npore pressure measured on the mid\u2011plane of the aquifer prior to the piezometric decline (ML-1<\/sup>T-2<\/sup>)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\"Sketch<\/p>\n

Figure\u00a014<\/strong>\u00a0<\/strong>\u2011\u00a0<\/strong>Sketch of a pumped confined aquifer.<\/p>\n

Land subsidence is equal to the aquifer compaction as calculated by the use of a graph as shown in Figure\u00a012<\/a> and Equation\u00a03<\/a>. Again, if s<\/em>0<\/sub> is large, it can be split into sub\u2011intervals and \u03c3<\/em>z<\/em><\/sub>0<\/sub> computed for each sub\u2011interval (while \u0394\u03c3<\/em>z<\/em><\/sub> is the same for each sub\u2011interval).<\/p>\n

In summary, the compaction of a single confined aquifer amounts to (Equation\u00a012):<\/a><\/p>\n\n\n\n
<\/td>\n\u03b7<\/em> = s<\/em>0<\/sub>c<\/em>b<\/em><\/sub>\u0394\u03c3<\/em>z<\/em><\/sub><\/td>\n(12)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

with s<\/em>0<\/sub> the aquifer thickness, c<\/em>b<\/em><\/sub> is the uniaxial vertical soil compressibility, and \u0394\u03c3<\/em>z<\/em><\/sub> is the change in the effective intergranular stress.<\/p>\n<\/div>\n","protected":false},"author":1,"menu_order":8,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-235","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\/235","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":9,"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/pressbooks\/v2\/chapters\/235\/revisions"}],"predecessor-version":[{"id":444,"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/pressbooks\/v2\/chapters\/235\/revisions\/444"}],"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\/235\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/wp\/v2\/media?parent=235"}],"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=235"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/wp\/v2\/contributor?post=235"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/land-subsidence-and-its-mitigation\/wp-json\/wp\/v2\/license?post=235"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}