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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 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