{"id":1304,"date":"2026-05-12T21:47:26","date_gmt":"2026-05-12T21:47:26","guid":{"rendered":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/chapter\/compressibility-and-storage-parameters\/"},"modified":"2026-05-13T03:23:36","modified_gmt":"2026-05-13T03:23:36","slug":"compressibility-and-storage-parameters","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/chapter\/compressibility-and-storage-parameters\/","title":{"raw":"15.4 Compressibility and Storage Parameters","rendered":"15.4 Compressibility and Storage Parameters"},"content":{"raw":"
\r\n
\r\n\r\nWe have discussed stress; now let\u2019s talk about strain and the relationship between strain and stress. In any given material, a certain amount of stress will result in a certain amount of strain. The ratio of strain to stress is called the compressibility. In terms more specific to what we are discussing here, the compressibility is the amount of shortening or extension\u2014that is, the change in thickness of a layer\u2014that occurs due to a change in stress\u2014in this case, the change in stress associated with a change in pore fluid pressure. We can express this as Equation\u00a0(114)<\/span><\/a>.\r\n\r\n<\/div>\r\n<\/colgroup>\r\n\r\n\r\n
<\/th>\r\n[latex]\\alpha = \\frac{\\frac{\\mathrm{\\Delta}L}{L}}{\\mathrm{\\Delta}\\sigma'}[\/latex]<\/th>\r\n(114)<\/span><\/th>\r\n<\/tr>\r\n<\/thead>\r\n<\/table>\r\n
\r\n\r\nwhere (parameter dimensions are dark green font with mass as M, length as L, time as T):\r\n\r\n<\/div>\r\n<\/colgroup>\r\n\r\n\r\n\r\n\r\n\r\n
[latex]\\alpha[\/latex]<\/th>\r\n=<\/th>\r\ncompressibility (LT2<\/sup>M-1<\/sup>)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
[latex]\\frac{\\mathrm{\\Delta}L}{L}[\/latex]<\/td>\r\n=<\/td>\r\nthe change in length (thickness) over the total length (:)<\/td>\r\n<\/tr>\r\n
[latex]\\mathrm{\\Delta}\\sigma'[\/latex]<\/td>\r\n=<\/td>\r\nthe change in effective stress (ML-1<\/sup>T-2<\/sup>)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
\r\n\r\nCompressibility is just a simple coefficient relating strain to stress, and it can be applied in several ways. If we know the compressibility of a material\u2014for example, a clay confining layer\u2014we can calculate how much the layer will consolidate for a given change in head. To do that, we convert the change in head to a change in pressure, then multiply by the compressibility to calculate the change in length over the total length.\r\n\r\n<\/div>\r\n
\r\n\r\nThe specific storage is directly related to the compressibility of the aquifer by the following relationship shown in Equation\u00a0(115)<\/span><\/a>.\r\n\r\n<\/div>\r\n<\/colgroup>\r\n\r\n\r\n
<\/th>\r\n[latex]S_{s} = \\rho_{w}g\\ \\phi\\ (\\alpha + \\beta)[\/latex]<\/th>\r\n(115)<\/span><\/th>\r\n<\/tr>\r\n<\/thead>\r\n<\/table>\r\n
\r\n\r\nwhere (parameter dimensions are dark green font with mass as M, length as L, time as T):\r\n\r\n<\/div>\r\n<\/colgroup>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
[latex]S_{s}[\/latex]<\/th>\r\n=<\/th>\r\nspecific storage (L-1<\/sup>)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
[latex]\\rho_{w}[\/latex]<\/td>\r\n=<\/td>\r\ndensity of water (ML-3<\/sup>)<\/td>\r\n<\/tr>\r\n
[latex]g[\/latex]<\/td>\r\n=<\/td>\r\ngravitational acceleration (LT-2<\/sup>)<\/td>\r\n<\/tr>\r\n
[latex]\\alpha[\/latex]<\/td>\r\n=<\/td>\r\ncompressibility of the aquifer framework (M-1<\/sup>LT2<\/sup>)<\/td>\r\n<\/tr>\r\n
[latex]\\phi[\/latex]<\/td>\r\n=<\/td>\r\nporosity (:)<\/td>\r\n<\/tr>\r\n
[latex]\\beta[\/latex]<\/td>\r\n=<\/td>\r\ncompressibility of water (M-1<\/sup>LT2<\/sup>)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>","rendered":"
\n
\n

We have discussed stress; now let\u2019s talk about strain and the relationship between strain and stress. In any given material, a certain amount of stress will result in a certain amount of strain. The ratio of strain to stress is called the compressibility. In terms more specific to what we are discussing here, the compressibility is the amount of shortening or extension\u2014that is, the change in thickness of a layer\u2014that occurs due to a change in stress\u2014in this case, the change in stress associated with a change in pore fluid pressure. We can express this as Equation\u00a0(114)<\/span><\/a>.<\/p>\n<\/div>\n\n\n\n\n<\/colgroup>\n\n\n
<\/th>\n[latex]\\alpha = \\frac{\\frac{\\mathrm{\\Delta}L}{L}}{\\mathrm{\\Delta}\\sigma'}[\/latex]<\/th>\n(114)<\/span><\/th>\n<\/tr>\n<\/thead>\n<\/table>\n
\n

where (parameter dimensions are dark green font with mass as M, length as L, time as T):<\/p>\n<\/div>\n\n\n\n\n<\/colgroup>\n\n\n\n\n\n
[latex]\\alpha[\/latex]<\/th>\n=<\/th>\ncompressibility (LT2<\/sup>M-1<\/sup>)<\/th>\n<\/tr>\n<\/thead>\n
[latex]\\frac{\\mathrm{\\Delta}L}{L}[\/latex]<\/td>\n=<\/td>\nthe change in length (thickness) over the total length (:)<\/td>\n<\/tr>\n
[latex]\\mathrm{\\Delta}\\sigma'[\/latex]<\/td>\n=<\/td>\nthe change in effective stress (ML-1<\/sup>T-2<\/sup>)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

Compressibility is just a simple coefficient relating strain to stress, and it can be applied in several ways. If we know the compressibility of a material\u2014for example, a clay confining layer\u2014we can calculate how much the layer will consolidate for a given change in head. To do that, we convert the change in head to a change in pressure, then multiply by the compressibility to calculate the change in length over the total length.<\/p>\n<\/div>\n

\n

The specific storage is directly related to the compressibility of the aquifer by the following relationship shown in Equation\u00a0(115)<\/span><\/a>.<\/p>\n<\/div>\n\n\n\n\n<\/colgroup>\n\n\n
<\/th>\n[latex]S_{s} = \\rho_{w}g\\ \\phi\\ (\\alpha + \\beta)[\/latex]<\/th>\n(115)<\/span><\/th>\n<\/tr>\n<\/thead>\n<\/table>\n
\n

where (parameter dimensions are dark green font with mass as M, length as L, time as T):<\/p>\n<\/div>\n\n\n\n\n<\/colgroup>\n\n\n\n\n\n\n\n\n
[latex]S_{s}[\/latex]<\/th>\n=<\/th>\nspecific storage (L-1<\/sup>)<\/th>\n<\/tr>\n<\/thead>\n
[latex]\\rho_{w}[\/latex]<\/td>\n=<\/td>\ndensity of water (ML-3<\/sup>)<\/td>\n<\/tr>\n
[latex]g[\/latex]<\/td>\n=<\/td>\ngravitational acceleration (LT-2<\/sup>)<\/td>\n<\/tr>\n
[latex]\\alpha[\/latex]<\/td>\n=<\/td>\ncompressibility of the aquifer framework (M-1<\/sup>LT2<\/sup>)<\/td>\n<\/tr>\n
[latex]\\phi[\/latex]<\/td>\n=<\/td>\nporosity (:)<\/td>\n<\/tr>\n
[latex]\\beta[\/latex]<\/td>\n=<\/td>\ncompressibility of water (M-1<\/sup>LT2<\/sup>)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n","protected":false},"author":8,"menu_order":66,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1304","chapter","type-chapter","status-publish","hentry"],"part":1510,"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters\/1304","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/users\/8"}],"version-history":[{"count":2,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters\/1304\/revisions"}],"predecessor-version":[{"id":1771,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters\/1304\/revisions\/1771"}],"part":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/parts\/1510"}],"metadata":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters\/1304\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/media?parent=1304"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapter-type?post=1304"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/contributor?post=1304"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/license?post=1304"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}