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Coefficient of permeability
Ability of porous body (soils, rocks) to transport water of given properties (e.g. ground water) is denoted as seepage. The amount of water flowing through a certain area can be represented by the coefficient of permeability. The coefficient of permeability represents the slope of a linear dependence of water flow velocity on the hydraulic gradient (gradient of hydraulic head) in Dracy’s law written as:
| where: | vs | - | velocity of water flowing through pores |
| n | - | porosity | |
| Kr | - | relative coefficient of permeability | |
| Ksat | - | Permeability matrix storing coefficients of permeability of fully saturated soil kx , ky , which may be different along individual coordinate axes | |
| h | - | hydraulic head |
Hydraulic head at a given point of region of flow is defined a sum of vertical coordinate and pressure head and as such it determines the height of water in piezometer at a given point:
| where: | γw | - | the weight of water |
Example values of coefficients of permeability for various soils (Myslivec)
| Type of soil |
Coefficient of permeability k
[m/day] |
Motion of water particle by 1 cm for hydraulic gradient i=1 per time |
| Soft sand | 102 - 10 | 6 s – 10 min |
| Clayey sand | 10-1 - 10-2 | 100 min – 18 hrs |
| Loess loam | 10-2 - 10-4 | 18 hrs – 70 days |
| Loam | 10-4 - 10-5 | 70 days – 2 years |
| Clayey soil | 10-5 - 10-6 | 2 years – 20 years |
| Clay | 10-6 - 10-7 | 20 -200 years |
There are several ways for determining the coefficient of permeability k. They grouped as follows:
a) Laboratory measurements
Several types are available for the range of k 104 - 10-6 m/day.
b) Field measurements
Dwell or sink tests, measurement of filtration velocity of flow, for the range of k 106 - 1 m/day.
c) Using empirical expressions
Suitable for non-cohesive soils, k 106 - 10 m/day, they produce only guidance values – e.g. according Terzaghi:
| where: | d10 | - | diameter of effective solid particle |
| e | - | void ratio |
d) By calculation from time dependent consolidation process
One must know the coefficient of consolidation cv and consolidation curve (semi-logarithmic dependence of deformation on time). This is only an indirect determination from the expression:
| where: | e0 | - | initial void ratio |
| cv | - | coefficient of consolidation | |
| ρw | - | bulk density of water | |
| g | - | gravitational acceleration | |
| av | - | coefficient of compressibility |
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