# Representative Values of Hydraulic Properties

by Glenn M. Duffield, President, HydroSOLVE, Inc.

Aquifer tests (**pumping tests**, **slug tests** and **constant-head tests**) are performed to estimate the **hydraulic properties** of aquifers and aquitards including horizontal and vertical hydraulic conductivity, storativity, specific yield and porosity.

The following sections present **representative hydraulic property values** reported in the literature. Use these values when no site-specific field testing results are available for your investigation or as a means of reality-checking the results of your own field tests.

## Hydraulic

Conductivity (K)

Hydraulic conductivity is a measure of a material's capacity to transmit water. It is defined as a constant of proportionality relating the specific discharge of a porous medium under a unit hydraulic gradient in Darcy's law:

$$\nu =-Ki$$where $\nu $ is specific discharge [L/T], $K$ is hydraulic conductivity [L/T] and $i$ is hydraulic gradient [dimensionless]. *Coefficient of permeability* is another term for hydraulic conductivity.

Note that hydraulic conductivity, which is a function of water viscosity and density, is in a strict sense a function of water temperature; however, given the small range of temperature variation encountered in most groundwater systems, the temperature dependence of hydraulic conductivity is often neglected.

Transmissivity is the rate of flow under a unit hydraulic gradient through a unit width of aquifer of given saturated thickness. The transmissivity of an aquifer is related to its hydraulic conductivity as follows:

$$T=Kb$$where $T$ is transmissivity [L^{2}/T] and $b$ is aquifer thickness [L].

The following tables show representative values of hydraulic conductivity for various unconsolidated sedimentary materials, sedimentary rocks and crystalline rocks (from Domenico and Schwartz 1990):

Unconsolidated Sedimentary Materials | |

Material | Hydraulic Conductivity (m/sec) |

Gravel | 3×10^{-4} to 3×10^{-2} |

Coarse sand | 9×10^{-7} to 6×10^{-3} |

Medium sand | 9×10^{-7} to 5×10^{-4} |

Fine sand | 2×10^{-7} to 2×10^{-4} |

Silt, loess | 1×10^{-9} to 2×10^{-5} |

Till | 1×10^{-12} to 2×10^{-6} |

Clay | 1×10^{-11} to 4.7×10^{-9} |

Unweathered marine clay | 8×10^{-13} to 2×10^{-9} |

Sedimentary Rocks | |

Rock Type | Hydraulic Conductivity (m/sec) |

Karst and reef limestone | 1×10^{-6} to 2×10^{-2} |

Limestone, dolomite | 1×10^{-9} to 6×10^{-6} |

Sandstone | 3×10^{-10} to 6×10^{-6} |

Siltstone | 1×10^{-11} to 1.4×10^{-8} |

Salt | 1×10^{-12} to 1×10^{-10} |

Anhydrite | 4×10^{-13} to 2×10^{-8} |

Shale | 1×10^{-13} to 2×10^{-9} |

Crystalline Rocks | |

Material | Hydraulic Conductivity (m/sec) |

Permeable basalt | 4×10^{-7} to 2×10^{-2} |

Fractured igneous and metamorphic rock | 8×10^{-9} to 3×10^{-4} |

Weathered granite | 3.3×10^{-6} to 5.2×10^{-5} |

Weathered gabbro | 5.5×10^{-7} to 3.8×10^{-6} |

Basalt | 2×10^{-11} to 4.2×10^{-7} |

Unfractured igneous and metamorphic rock | 3×10^{-14} to 2×10^{-10} |

To Convert |
Multiply By |
To Obtain |

m/sec | 100 | cm/sec |

m/sec | 2.12×10^{6} |
gal/day/ft^{2} |

m/sec | 3.2808 | ft/sec |

## Hydraulic Conductivity Anisotropy Ratio (Kz/Kr)

An **anisotropy ratio** relates hydraulic conductivities in different directions. For example, vertical-to-horizontal hydraulic conductivity anisotropy ratio is given by ${K}_{\text{z}}/{K}_{\text{r}}$ where ${K}_{\text{z}}$ is vertical hydraulic conductivity [L/T] and ${K}_{\text{r}}$ is radial (horizontal) hydraulic conductivity [L/T]. Anisotropy in a horizontal plane is given by ${K}_{\text{x}}/{K}_{\text{y}}$ where ${K}_{\text{x}}$ and ${K}_{\text{y}}$ are horizontal hydraulic conductivities in the x and y directions, respectively [L/T].

Todd (1980) reports values of ${K}_{\text{z}}/{K}_{\text{r}}$ ranging between 0.1 and 0.5 for alluvium and possibly as low as 0.01 when clay layers are present.

The following table shows representative values of horizontal and vertical hydraulic conductivities for selected rock types (from Domenico and Schwartz 1990):

Material | Horizontal Hydraulic Conductivity (m/sec) |
Vertical Hydraulic Conductivity (m/sec) |

Anhydrite | 10^{-14} to 10^{-12} |
10^{-15} to 10^{-13} |

Chalk | 10^{-10} to 10^{-8} |
5×10^{-11} to 5×10^{-9} |

Limestone, dolomite |
10^{-9} to 10^{-7} |
5×10^{-10} to 5×10^{-8} |

Sandstone | 5×10^{-13} to 10^{-10} |
2.5×10^{-13} to 5×10^{-11} |

Shale | 10^{-14} to 10^{-12} |
10^{-15} to 10^{-13} |

Salt | 10^{-14} |
10^{-14} |

## Storativity (S)

The storativity of a confined aquifer (or aquitard) is defined as the volume of water released from storage per unit surface area of a confined aquifer (or aquitard) per unit decline in hydraulic head. Storativity is also known by the terms *coefficient of storage* and *storage coefficient*.

In a confined aquifer (or aquitard), storativity is defined as

$$S={S}_{\text{s}}b$$where $S$ is storativity [dimensionless], ${S}_{\text{s}}$ is specific storage [L^{-1}] and $b$ is aquifer (or aquitard) thickness [L]. Specific storage is the volume of water that a unit volume of aquifer (or aquitard) releases from storage under a unit decline in head by the expansion of water and compression of the soil or rock skeleton.

Specific storage is related to the compressibilities of the aquifer (or aquitard) and water as follows:

$${S}_{\text{s}}=\rho g\left(\alpha +{n}_{\text{e}}\beta \right)$$where $\rho $ is mass density of water [M/L^{3}], $g$ is gravitational acceleration (= 9.8 m/sec^{2})
[L/T^{2}], $\alpha $ is aquifer (or aquitard) compressibility [T^{2}L/M], ${n}_{\text{e}}$ is effective porosity [dimensionless], and $\beta $ is compressibility of water (= 4.4×10^{-10} m sec^{2}/kg or Pa^{-1}) [T^{2}L/M].

In an unconfined aquifer (or aquitard), storativity is given by

$$S={S}_{\text{y}}+{S}_{\text{s}}b$$where ${S}_{\text{y}}$ is specific yield. Because ${S}_{\text{s}}b$ is typically small in comparison to ${S}_{\text{y}}$, storativity in an unconfined aquifer is often simply equated with specific yield.

The storativity of a confined aquifer, which varies with specific storage and aquifer thickness, typically ranges from 5×10^{-5} to 5×10^{-3} (Todd 1980); in unconfined aquifers, storativity ranges from 0.1 to 0.3 (Lohman 1972).

The following table provides representative values of specific storage for various geologic materials (Domenico and Mifflin [1965] as reported in Batu [1998]):

Material | Ss (ft^{-1}) |

Plastic clay | 7.8×10^{-4} to 6.2×10^{-3} |

Stiff clay | 3.9×10^{-4} to 7.8×10^{-4} |

Medium hard clay | 2.8×10^{-4} to 3.9×10^{-4} |

Loose sand | 1.5×10^{-4} to 3.1×10^{-4} |

Dense sand | 3.9×10^{-5} to 6.2×10^{-5} |

Dense sandy gravel | 1.5×10^{-5} to 3.1×10^{-5} |

Rock, fissured | 1×10^{-6} to 2.1×10^{-5} |

Rock, sound | < 1×10^{-6} |

To Convert | Divide By | To Obtain |

ft^{-1} |
0.3048 | m^{-1} |

Freeze and Cherry (1979) provided the following **compressibility** values for various aquifer materials:

Material | Compressibility, α
(m^{2}/N or Pa^{-1}) |

Clay | 10^{-8} to 10^{-6} |

Sand | 10^{-9} to 10^{-7} |

Gravel | 10^{-10} to 10^{-8} |

Jointed rock | 10^{-10} to 10^{-8} |

Sound rock | 10^{-11} to 10^{-9} |

Pa^{-1} = m^{2}/N = m sec^{2}/kg

**Example Calculations***Use compressibility data to estimate the storativity of a 35-ft thick confined sand aquifer (assume $\rho $ = 1000 kg/m*^{3}and ${n}_{\text{e}}$ = 0.3).$S={S}_{\text{s}}b=\rho g\left(\alpha +{n}_{\text{e}}\beta \right)b$ = (1000 kg/m

^{3})(9.8 m/sec^{2}) [10^{-8}m^{2}/N + (0.3) (4.4×10^{-10}m^{2}/N)](35 ft)(0.3048 m/ft) = 1.1×10^{-3}*How much does the expansion of water contribute to the total storativity in this example?*${S}_{\text{w}}=\rho g{n}_{\text{e}}\beta b$ = (1000 kg/m

^{3})(9.8 m/sec^{2})(0.3) (4.4×10^{-10}m^{2}/N)(35 ft)(0.3048 m/ft) = 1.4×10^{-}^{5}*Use specific storage data to estimate storativity for the same aquifer given in the preceding example.*$S={S}_{\text{s}}b$ = (5×10

^{-5}ft^{-1})(35 ft) = 1.8×10^{-3}

## Specific Yield (Sy)

Specific yield is defined as the volume of water released from storage by an unconfined aquifer per unit surface area of aquifer per unit decline of the water table.

Bear (1979) relates specific yield to total porosity as follows:

$$n={S}_{\text{y}}+{S}_{\text{r}}$$where $n$ is total porosity [dimensionless], ${S}_{\text{y}}$ is specific yield [dimensionless] and ${S}_{\text{r}}$ is specific retention [dimensionless], the amount of water retained by capillary forces during gravity drainage of an unconfined aquifer. Thus, specific yield, which is sometimes called *effective porosity*, is less than the total porosity of an unconfined aquifer (Bear 1979).

Heath (1983) reports the following values (in percent by volume) for porosity, specific yield and specific retention:

Material | Porosity (%) | Specific Yield (%) |
Specific Retention (%) |

Soil | 55 | 40 | 15 |

Clay | 50 | 2 | 48 |

Sand | 25 | 22 | 3 |

Gravel | 20 | 19 | 1 |

Limestone | 20 | 18 | 2 |

Sandstone (unconsolidated) | 11 | 6 | 5 |

Granite | 0.1 | 0.09 | 0.01 |

Basalt (young) | 11 | 8 | 3 |

The following table shows representative values of specific yield for various geologic materials (from Morris and Johnson 1967):

Material | Specific Yield (%) |

Gravel, coarse | 21 |

Gravel, medium | 24 |

Gravel, fine | 28 |

Sand, coarse | 30 |

Sand, medium | 32 |

Sand, fine | 33 |

Silt | 20 |

Clay | 6 |

Sandstone, fine grained | 21 |

Sandstone, medium grained | 27 |

Limestone | 14 |

Dune sand | 38 |

Loess | 18 |

Peat | 44 |

Schist | 26 |

Siltstone | 12 |

Till, predominantly silt | 6 |

Till, predominantly sand | 16 |

Till, predominantly gravel | 16 |

Tuff | 21 |

## Porosity (n)

Porosity is defined as the void space of a rock or unconsolidated material:

$$n={V}_{\text{v}}/{V}_{\text{t}}$$where $n$ is porosity [dimensionless], ${V}_{\text{v}}$ is void volume [L^{3}] and ${V}_{\text{t}}$ is total volume [L^{3}].

The following tables show representative porosity values for various unconsolidated sedimentary materials, sedimentary rocks and crystalline rocks (from Morris and Johnson 1967):

Unconsolidated Sedimentary Materials | |

Material | Porosity (%) |

Gravel, coarse | 24 - 37 |

Gravel, medium | 24 - 44 |

Gravel, fine | 25 - 39 |

Sand, coarse | 31 - 46 |

Sand, medium | 29 - 49 |

Sand, fine | 26 - 53 |

Silt | 34 - 61 |

Clay | 34 - 57 |

Sedimentary Rocks | |

Rock Type | Porosity (%) |

Sandstone | 14 - 49 |

Siltstone | 21 - 41 |

Claystone | 41 - 45 |

Shale | 1 - 10 |

Limestone | 7 - 56 |

Dolomite | 19 - 33 |

Crystalline Rocks | |

Rock Type | Porosity (%) |

Basalt | 3 - 35 |

Weathered granite | 34 - 57 |

Weathered gabbro | 42 - 45 |

* See also:* Argonne National Laboratory, Wolff (1982)