Irrigation Engineering and water Resources

1. Agricultural Land Drainage
Lecture # 20
Hydraulic conductivity
Dr. Abdul Latif Qureshi
Professor, USPCAS-W, MUET, Jamshoro
alqureshi.uspcasw@faculty.muet.edu.pk
U.S.-Pakistan Centers for Advanced
Studies in Water (USPCAS-W)
Partnering Universities:

2. Learning Objectives
At the end of the lecture, students will be
able:
 To define the permeability/hydraulic
conductivity.
 To explain factors affecting the permeability
and discuss the correlation of soil particles
with permeability.
 To calculate the Hydraulic Conductivity
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3. PERMEABILITY
Factors effecting permeability?
Definition:
 The property of porous material
which permits the seepage of
water through its interconnecting
voids/ pore space and. Such
type of material is called
permeable material.
 In most of practical flow
problems in soil mechanics the
flow is laminar.
Factors effecting
permeability? 8/12/2022
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4. PERMEABILITY
Factors effecting permeability?
1. Grain size;
2. Property of soil;
3. Voids ratio of the soil;
4. Adsorbed water in clayey
soil
5. Saturated arrangement of
the soil particles; and
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5. Porosity
 Ratio of pore volume to total volume of a soil or
rock.
Mathematically,
Porosity (η) is the ratio of openings (voids) to the
total volume of a soil.
η = (Vt-Vs) / Vt = Vv / Vt
Vt= total volume of the soil or rock
Vs= volume of solids in the sample
Vv= volume of openings (voids)
Expressed as percentage.
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6. Graphical Illustration of Porosity
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7. Open Porosity or
Effective Porosity
 Ratio of accessible
pore volume to total
volume.
 Porosity determines
the amount of water
that a given volume
of soil or rock can
contain.
Well-
sorted
sediments
Poorly-
sorted
sediments
Reduction of
porosity by
cementation
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8. Hydraulic Conductivity
 The volume of water that will move in unit time under
a unit hydraulic gradient through a unit area of a
porous medium, which is at right angles to the
direction of flow.
 Hydraulic conductivity is a function of not only the
porous medium through which the fluid moves, but of
the fluid itself.
 Commonly, in the fields of groundwater hydrology
and hydrogeology, the two terms are used
interchangeably.
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9. 8/12/2022
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10. Determination of coefficient of
Permeability/Hydraulic conductivity (K)
 Laboratory methods:
1) Constant head method; and
2) Falling head method (is not be discussed here)
 Field methods:
Different methods will be discussed
(Here, Auger hole method is discussed here)
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11. Constant Head Method
Fig. 2 shows the apparatus arrangement
Discharge through soil sample (Q) can be
described as,
Q = V/T ……………………….…..(i)
Where, V is the volume of water passing
through soil sample in time T
According to the Darcy’s law,
Q = K i A = K x (H/L) x A ………(ii)
Equating eqns. (i) and (ii),
K*H*A / L = V/T = Volume / Time
After re-arranging it turn to:
A
H
T
L
V
K 
Where, V= Volume, T = Time, L = Length of soil specimen,
H = Difference in head (water levels)
A = Cross-sectional area of the soil sample
Volume
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12. Determination of Hydraulic Conductivity
(Field method)
 Auger hole method: (Hooghoudt, 1936)
 Related K to the rate of rise of water level in a bailed out
auger hole (K ~ dh/dt),
 Auger hole to a depth well below the water table and deep
into the layer to be measured,
 Allow water level to rise till equilibrium (10-15 min) in
permeable soils, and days in poorly permeable soils,
 Bailing or pumping water out of the hole to lower the water
level in the hole,
 Flow enters the hole due to the created hydraulic gradient,
 Record the rising of water level in the hole over an
appropriate time period (20 sec),
 Perform readings of rising water level before 25% of the
water removed from the hole has been replaced to assure
a near steady state water table level outside of the hole.
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13. CALCULATION
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14. 8/12/2022
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15. Example: Calculation of K…….
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16. Example: calculation of K
H/r = 80/4 =20
S/H = 40/80 = 0.5
h = (h0+hn)/2
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17. Example: calculation of K cont’d
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(hi-hi-1) h = (ho+hn)/2
= (42.8+37.2)/2
= 40 cm
ℎ
𝐻
=
40
80
=
1
2
=0.5
Dr. A. L. Qureshi

18. Example: Calculation of K cont’d
H/r = 20
S/H = 0.5
0.5
h
H

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Δh = ho-hn
=42.8-37.2
= 5.6 cm
𝑲 = 𝑪
𝜟𝒉
𝜟𝒕
= 6.6
𝟓.𝟔
𝟏𝟎𝟎
= 0.37 m/day
Dr. A. L. Qureshi

19. Determination of average hydraulic conductivity
for the flow parallel to different layers
 Figure 3 (The Physical model) is self
explanatory
 Uniform flow through different layers
 Hydraulic gradient is uniform for all the
layers, therefore the Darcy equation
dh/dx can be replaced by H/L
Where, H is the difference of the
hydraulic heads between given two
points and L is the distance between
these points.
The cross-sectional area of flow , A = Dt* B
where, Dt is the total thickness of the soil layers and B is its
width; is spatially unvaried.
In the given case, the total flow rate is equal to the sum of all
the flow rates passing through separate layers.
i.e. Qt = Q1 + Q2 + Q3 ……………………………. (4)
Fig. 3: Steady flow parallel to soil layers
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20.  According to Darcy’s law, The total discharge can be
determined by:
Qt = Dt B H/L (m3/day)
 Similarly, for separate layer it is found that
Q1 = K1 D1 B H/L;
Q2 = K2 D2 B H/L;
Q3 = K3 D3 B H/L
 Therefore, from equation (4), we have
Dt B H/L = K1 D1 B H/L + K2 D2 B H/L + K3 D3 B H/L or
Dt = K1D1 + K2D2 + K3D3
or = (K1D1 + K2D2 + K3D3 )/ Dt ………………….(5)
Where, is average hydraulic conductivity
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21. Flow perpendicular to different soil layers
 Flow through different soil layers,
perpendicular to the direction of the
flow (Fig.4). It is seen from this fig.
that:
Ht = H1 +H2 + H3 …….(6)
 The total hydraulic gradient is Ht/Dt,
where Dt is the total thickness of the
soil layers.
 If the cross-sectional area of flow is:
A = L x B
where L is the height end B is the
width of the soil layers, then the law
of Darcy gives,
Figure 4: Steady flow perpendicular
to soil layers
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22. or
K
D
K
D
K
D
K
Dt
3
3
2
2
1
1



)
7
.(
..........
..........
3
3
2
2
1
1











K
D
K
D
K
D
D
K t
Where, is average hydraulic conductivity
Similarly, for separate layer it is found that:
Putting these values of Ht, H1, H2 and H3 in equation
(6) after rearranging
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23. Learning Objectives
At the end of the lecture, students will be
able to:
 Describe the permeability/hydraulic
conductivity and factors affecting the
permeability.
 Calculate the Hydraulic Conductivity
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24. Thanks
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25. Permeability Apparatus
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Dr. A. L. Qureshi