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| '''Specific storage''' (S<sub>s</sub>), '''storativity''' (S), '''specific yield''' (S<sub>y</sub>) and '''specific capacity''' are physical properties that characterize the capacity of an [[aquifer]] to release [[groundwater]]. They are sometimes referred to as "storage properties". In the field of [[hydrogeology]], these properties are often determined using some combination of field tests (e.g., [[aquifer test]]s) and laboratory tests on aquifer material samples.
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| ==Specific storage==
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| The '''specific storage''' is the amount of water that a portion of an [[aquifer]] releases from storage, per unit mass or volume of aquifer, per unit change in hydraulic head, while remaining fully saturated.
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| '''Mass specific storage''' is the mass of water that an [[aquifer]] releases from storage, per mass of aquifer, per unit decline in hydraulic head:
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| :<math>(S_s)_m = \frac{1}{m_a}\frac{dm_w}{dh}</math>
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| where
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| :<math>(S_s)_m</math> is the mass specific storage ([L<sup>-1</sup>]);
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| :<math>m_a</math> is the mass of that portion of the aquifer from which the water is released ([M]);
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| :<math>dm_w</math> is the mass of water released from storage ([M]); and
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| :<math>dh</math> is the decline in [[hydraulic head]] ([L]).
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| '''Volumetric specific storage''' (or '''volume specific storage''') is the volume of water that an [[aquifer]] releases from storage, per volume of aquifer, per unit decline in hydraulic head (Freeze and Cherry, 1979):
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| :<math>S_s = \frac{1}{V_a}\frac{dV_w}{dh} = \frac{1}{V_a}\frac{dV_w}{dp}\frac{dp}{dh}= \frac{1}{V_a}\frac{dV_w}{dp}\gamma_w</math>
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| where
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| :<math>S_s</math> is the volumetric specific storage ([L<sup>-1</sup>]);
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| :<math>V_a</math> is the bulk volume of that portion of the aquifer from which the water is released ([L<sup>3</sup>]);
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| :<math>dV_w</math> is the volume of water released from storage ([L<sup>3</sup>]);
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| :<math>dp</math> is the decline in [[pressure]]([[newton (unit)|N]]•m<sup>-2</sup> or [ML<sup>-1</sup>T<sup>-2</sup>]) ;
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| :<math>dh</math> is the decline in [[hydraulic head]] ([L]) and
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| :<math>\gamma_w</math> is the [[specific weight]] of water ([[newton (unit)|N]]•m<sup>-3</sup> or [ML<sup>-2</sup>T<sup>-2</sup>]).
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| In [[hydrogeology]], '''volumetric specific storage''' is much more commonly encountered than '''mass specific storage'''. Consequently, the term '''specific storage''' generally refers to '''volumetric specific storage'''.
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| In terms of measurable physical properties, specific storage can be expressed as
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| :<math>S_s = \gamma_w (\beta_p + n \cdot \beta_w)</math>
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| where
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| :<math>\gamma_w</math> is the [[specific weight]] of water ([[newton (unit)|N]]•m<sup>-3</sup> or [ML<sup>-2</sup>T<sup>-2</sup>])
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| :<math>n</math> is the [[porosity]] of the material (dimensionless ratio between 0 and 1)
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| :<math>\beta_p</math> is the [[compressibility]] of the bulk aquifer material (m<sup>2</sup>N<sup>-1</sup> or [LM<sup>-1</sup>T<sup>2</sup>]), and
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| :<math>\beta_w</math> is the compressibility of water (m<sup>2</sup>N<sup>-1</sup> or [LM<sup>-1</sup>T<sup>2</sup>])
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| The compressibility terms relate a given change in stress to a change in volume (a strain). These two terms can be defined as:
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| :<math>\beta_p = -\frac{dV_t}{d\sigma_e}\frac{1}{V_t}</math>
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| :<math>\beta_w = -\frac{dV_w}{dp}\frac{1}{V_w}</math>
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| where
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| :<math>\sigma_e</math> is the [[effective stress]] (N/m<sup>2</sup> or [MLT<sup>-2</sup>/L<sup>2</sup>])
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| These equations relate a change in total or water volume (<math>V_t</math> or <math>V_w</math>) per change in applied stress (effective stress — <math>\sigma_e</math> or pore pressure — <math>p</math>) per unit volume. The compressibilities (and therefore also S<sub>s</sub>) can be estimated from laboratory consolidation tests (in an apparatus called a consolidometer), using the consolidation theory of [[soil mechanics]] (developed by [[Karl Terzaghi]]).
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| ==Storativity==
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| '''Storativity''' or the '''storage coefficient''' is the [[volume]] of water released from storage per unit decline in [[hydraulic head]] in the aquifer, per unit [[area]] of the aquifer, or:
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| :<math>S = \frac{dV_w}{dh}\frac{1}{A} </math> | |
| Storativity is the vertically integrated specific storage value for a confined aquifer or aquitard. For a confined homogeneous aquifer or aquitard they are simply related by:
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| :<math>S=S_s b \,</math>
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| where <math>b</math> is the thickness of aquifer. Storativity is a dimensionless quantity, and ranges between 0 and the effective [[porosity]] of the aquifer; although for confined aquifers, this number is usually much less than 0.01.
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| The storativity or storage coefficient of an unconfined aquifer is approximately equal to the specific yield, <math>S_y</math>, since the release from specific storage, <math>S_s</math> is typically orders of magnitude less.
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| ==Specific yield==
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| {| class="wikitable" align="right"
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| |+Values of specific yield, from Johnson (1967)
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| |-
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| !rowspan=2| Material
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| !colspan=3| Specific Yield (%)
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| |-
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| ! min !! avg !! max
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| |-
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| |colspan=4 align="center"| ''Unconsolidated deposits''
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| |-
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| | Clay || 0 || 2 || 5
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| |-
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| | Sandy clay (mud) || 3 || 7 || 12
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| |-
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| | Silt || 3 || 18 || 19
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| |-
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| | Fine sand || 10 || 21 || 28
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| |-
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| | Medium sand || 15 || 26 || 32
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| |-
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| | Coarse sand || 20 || 27 || 35
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| |-
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| | Gravelly sand || 20 || 25 || 35
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| |-
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| | Fine gravel || 21 || 25 || 35
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| |-
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| | Medium gravel || 13 || 23 || 26
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| |-
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| | Coarse gravel || 12 || 22 || 26
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| |-
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| |colspan=4 align="center"| ''Consolidated deposits''
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| |-
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| | Fine-grained sandstone || || 21 ||
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| |-
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| | Medium-grained sandstone || || 27 ||
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| |-
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| | Limestone || || 14 ||
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| |-
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| | Schist || || 26 ||
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| |-
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| | Siltstone || || 12 ||
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| |-
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| | Tuff || || 21 ||
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| |-
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| |colspan=4 align="center"| ''Other deposits''
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| |-
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| | Dune sand || || 38 ||
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| |-
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| | Loess || || 18 ||
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| |-
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| | Peat || || 44 ||
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| |-
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| | Till, predominantly silt || || 6 ||
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| |-
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| | Till, predominantly sand || || 16 ||
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| |-
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| | Till, predominantly gravel || || 16 ||
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| |}
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| '''Specific yield''', also known as the drainable porosity, is a ratio, less than or equal to the [[effective porosity]], indicating the volumetric fraction of the bulk [[aquifer]] volume that a given aquifer will yield when all the water is allowed to drain out of it under the forces of gravity:
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| :<math>S_y = \frac{V_{wd}}{V_T}</math>
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| where
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| :<math>V_{wd}</math> is the volume of water drained, and
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| :<math>V_T</math> is the total rock or material volume
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| It is primarily used for unconfined aquifers, since the elastic storage component, <math>S_s</math>, is relatively small and usually has an insignificant contribution. Specific yield can be close to effective porosity, but there are several subtle things which make this value more complicated than it seems. Some water always remains in the formation, even after drainage; it clings to the grains of sand and clay in the formation. Also, the value of specific yield may not be fully realized for a very long time, due to complications caused by unsaturated flow.
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| {{-}}
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| ==See also==
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| * [[Aquifer test]]
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| * [[Soil mechanics]]
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| * [[Groundwater flow equation]] describes how these terms are used in the context of solving groundwater flow problems
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| ==References==
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| * Freeze, R.A. and J.A. Cherry. 1979. ''Groundwater''. Prentice-Hall, Inc. Englewood Cliffs, NJ. 604 p.
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| * Johnson, A.I. 1967. ''Specific yield — compilation of specific yields for various materials''. U.S. Geological Survey Water Supply Paper 1662-D. 74 p.
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| * Morris, D.A. and A.I. Johnson. 1967. ''Summary of hydrologic and physical properties of rock and soil materials as analyzed by the Hydrologic Laboratory of the U.S. Geological Survey 1948-1960''. U.S. Geological Survey Water Supply Paper 1839-D. 42 p.
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| {{Aquiferproperties}}
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| {{Geotechnical engineering|state=collapsed}}
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| [[Category:Hydrology]]
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| [[Category:Aquifers]]
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| [[Category:Water]]
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| [[Category:Soil mechanics]]
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