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 gradient of total head (gradient of hydraulic head) in Dracy’s law written as:
where: |
| - | velocity of water flowing through pores |
n | porosity | ||
Kr | relative coefficient of permeability | ||
| permeability matrix storing coefficients of permeability of fully saturated soil kx, ky, which may be different along individual coordinate axes | ||
| gradient of total head |
Total head at a given point of region of flow is defined as a sum of the pressure head and vertical coordinate 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 by1 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 years - 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 - 10-6m/day.
b) Field measurements
Dwell or sink tests, measurement of filtration velocity of flow, for the range of k 106 - 1m/day.
c) Using empirical expressions
Suitable for non-cohesive soils, k 106 - 10m/day, they produce only guidance values - e.g. according Terzaghi:
where: | k | - | coefficient of permeability [cm/s] |
d10 | - | diameter of effective solid particle [cm] | |
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 | - | unit density of water | |
g | - | gravitational acceleration | |
av | - | coefficient of compressibility |