Specific storage coefficient

In hydrogeology, the specific storage coefficient is a parameter of the subsurface and indicates how much water the soil can absorb or release.

definition

According to DIN 4049-3, the specific storage coefficient is the ratio of the volume of water released (or absorbed) to the total volume when the standpipe level changes by one meter. So it is ${\displaystyle S_{\text{sp}}}$

${\displaystyle S_{\text{sp}}={\frac {\Delta V_{W}}{V_{\text{ges}}\cdot \Delta h_{s}}}}$.

Here is

• ${\displaystyle S_{\text{sp}}}$ the specific storage coefficient in ${\displaystyle m^{-1}}$
• ${\displaystyle \Delta V_{W}}$the change in the volume of water in cubic meters ( ) ${\displaystyle m^{3}}$
• ${\displaystyle V_{\text{ges}}}$ the total volume in cubic meters
• ${\displaystyle \Delta h_{s}}$ the change in the standpipe height in meters

example

A water-soaked, cylindrical sample with a diameter of 10 cm and a height of 30 cm is given. If the sample is allowed to drain, it loses 0.3 liters of water. The volume of the sample is calculated based on the cylinder geometry

${\displaystyle V_{\text{ges}}=\pi \cdot r^{2}\cdot h\approx 2{,}36\cdot 10^{-3}m^{3}}$

with and . The volume of water released is ${\displaystyle r=0{,}05m}$ ${\displaystyle h=0{,}3m}$

${\displaystyle \Delta V_{W}=0{,}3l=3\cdot 10^{-4}m^{3}}$.

Since the sample is drained, this corresponds to the fall of the standpipe level below the level of the sample and thus a change in the standpipe level of

${\displaystyle \Delta h_{s}=0{,}3m}$.

The specific storage coefficient is thus calculated

${\displaystyle S_{\text{sp}}\approx {\frac {3\cdot 10^{-4}m^{3}}{2{,}36\cdot 10^{-3}m^{3}\cdot 0{,}3m}}\approx 0{,}424m^{-1}}$

Determination with different groundwater conditions

Confined groundwater

In the case of confined groundwater, the storage coefficient is determined

${\displaystyle S_{\text{sp}}=\rho _{W}\cdot g\left(\chi _{\text{Fe}}+n_{p}\cdot \chi _{\text{W}}\right)}$

Here is

• ${\displaystyle \rho _{W}}$the density of the water in kilograms per cubic meter (approx. ) ${\displaystyle 1000kg/m^{3}}$
• ${\displaystyle g}$the acceleration due to gravity in meters per second squared (approx. ) ${\displaystyle 9{,}81m/s^{2}}$
• ${\displaystyle \chi _{\text{Fe}}}$the compressibility of the porous medium in square meters per Newton
• ${\displaystyle n_{p}}$the dimensionless pore fraction
• ${\displaystyle \chi _{\text{W}}}$ the compressibility of the water in square meters per Newton

Free groundwater

With free groundwater, the storage coefficient is determined

${\displaystyle S_{\text{sp}}=\rho _{W}\cdot g\left((1-n_{p})\chi _{\text{Fe}}+n_{p}\cdot \chi _{\text{W}}\right)}$

Here is

• ${\displaystyle \rho _{W}}$the density of the water in kilograms per cubic meter (approx. ) ${\displaystyle 1000kg/m^{3}}$
• ${\displaystyle g}$the acceleration due to gravity in meters per second squared (approx. ) ${\displaystyle 9{,}81m/s^{2}}$
• ${\displaystyle \chi _{\text{Fe}}}$the compressibility of the porous medium in square meters per Newton
• ${\displaystyle n_{p}}$the dimensionless pore fraction
• ${\displaystyle \chi _{\text{W}}}$ the compressibility of the water in square meters per Newton

Individual evidence

1. ^ Bernward Hölting, Wilhelm Georg Coldewey: Hydrogeology . Introduction to General and Applied Hydrogeology. 8th edition. Springer-Verlag, Berlin / Heidelberg 2013, ISBN 978-3-8274-2353-5 , pp. 36-37 , doi : 10.1007 / 978-3-8274-2354-2 .