Complete presentation on determination of hydraulic conductivity and also drainable porosity with diagrams and formulas.

1. Presentation on
Determination of hydraulic
conductivity
1
4/16/2018

2.  Hydraulic conductivity is the ratio of velocity
to hydraulic gradient indicating permeability of
porous media.
 Symbolically represented as K, that describes
the ease with which a fluid (usually water) can
move through pore spaces or fractures.
 It depends on the permeability of the
material, the degree of saturation, and on
the density and viscosity of the fluid.
 Saturated hydraulic conductivity Ksat,
describes water movement through saturated
media.
Hydraulic conductivity:
2
4/16/2018
Hydraulic conductivity in non saturated soil is called capillary conductivity.
In which ‘Ks’ is hydraulic conductivity of saturating soil and ‘KI’ is soil intrinsic permeability or natural conductivity.

3. The definition of the hydraulic conductivity follows from the Darcy’s Law –Darcy's flow velocity for laminar flow
is defined as the quantity of fluid flow along the hydraulic gradient per unit cross sectional area.
There fore, V = KI
1. In the saturated flow conditions and according to the Darcy’s Law, the flow velocity v can be expressed as
V= K (dh/dx)
2. where x is distance in the direction of groundwater flow, h is hydraulic head.
Generalized table with the ranges of K-values for certain soil texture are :-
Texture Hydraulic conductivity (m/day)
Gravelly coarse sand 10 – 50
Medium sand 1 – 5
Sandy loam, fine sand 1 – 3
Loam, clay loam, clay (well structured) 0.5 – 2
Very fine sandy loam 0.2 – 0.5
Clay loam, clay (poorly structured) 0.002 – 0.2
Dense clay (no cracks, pores) < 0.002
3

4. Methods of Hydraulic Conductivity Determination
Hydraulic conductivity determination
methods
Hydraulic
methods
Correlation
methods
Field methods Laboratory methods (soil
samples)
Large scale Small scale
- Pumping test
- Parallel drains
method
BELOW WATER TABLE
-Auger hole
- Piezometer
ABOVE WATER TABLE
-Guelph
-Double ring
-Inverse auger hole
-Constant head
-Falling head
-Pore size distribution
-Grain size distribution
-Soil texture
-Soil mapping unit
4
4/16/2018

5. Hydraulic methods (in the field )
Small scale(Below water table)
Auger hole method:
 Measurement of saturated hydraulic conductivity at a locality with available groundwater level in measured layer is
best operated by using the auger hole method.
 This method is quick and easy and does not demand any expensive equipment. Moreover, natural water from the
place being measured is used for the experiment.
 A hole is made to a certain depth below the groundwater table. The water table in the hole is lowered with a bailer
and then the rate of rise of the water table is measured.
 From the geometry of the auger hole, the value of hydraulic conductivity can be calculated .
 In the finer textured soils, the pressure required for the initial augering causes a thin, dense seal to form on the sides
of the hole.
 This seal is hard to remove with a hole scratcher. But the removal of seal is essential to obtain reliable data from the
test.
5
4/16/2018
Auger hole method
Piezometer

6. Drilling of the hole
 The hole is bored into the soil to a certain
depth below the groundwater (GW) level
 The depth where the GW level is reached for
the first time is registered
 Observe the changes in soil characteristics
(color, water saturation, etc.)
 Wait until the equilibrium with the
surrounding GW is reached (until the GW level
keeps constant), the stable GW level is
measured
 Ground water is removed manually by using a
bailer or pumped out from the hole
 Final GW level after removal is registered
6
4/16/2018
Measurement procedure
1) Drilling of the hole
2) Removal of the water from the hole
3) Measurement of the rate of the rise
4) Computation of the hydraulic conductivity from the measurement data

7.  Use of float gauge with a measuring
tape or electrical device.
 The observations are most often
made at regular time intervals.
About 10 readings are recommended
The Durango and Orchard type augers
are suitable for most soils, but the
Dutch type auger is preferable for some
of the high clay cohesive soils. Samples
from Durango are less distributed than
those from the other two types, thus
permitting a more reliable evaluation
of soil structure.
Dutch or open
type Orchard type Durango
Types of hand soil augers
7
4/16/2018

8. Observed parameters in field
H – stable GW level [m]
y0 – GW level difference from stable GW
after its removal, at the beginning of the
rise rate measurement [m]
yn – GW level difference from stable GW
at the end of the rise rate measurement
[m]
y – GW level during the rise rate
measurement [m]
r – borehole radius [m]
8
4/16/2018
The equation for direct calculation of hydraulic conductivity K,
where y1 , y2 are measured water levels in a hole at the corresponding times t1 , t2

9. Piezometer Methods
 The piezometer test measures the horizontal hydraulic conductivity of individual soil layers below a water table.
 This test is preferred over the auger hole test when the soil layers to be tested are less than 18 inches thick and
individual layers below the water table are to be tested.
 This test also provides reliable hydraulic conductivity data for any soil layer below the water table.
Non-perforated pipe is placed into the hole
under the water level, leaving only a small
cavity at the bottom. This means that water
can only flows through this cavity. The
water table in the hole is decreased with a
bailer then the rate of rise of the water
table is measured. From this water recharge
and from the geometry of the cavity, can be
calculated the value of hydraulic
conductivity.
9
4/16/2018
Piezometer
Soil surface
Water table2R
Y2
Y1
d
2a
z
L
∆y in ∆t
cavity

10.  This field method can be used for measuring the hydraulic conductivity of layers at relatively great depth or of
separate soil layers.
 Piezometer method is not used in practice very often. This method serves for estimation of impact of soils
heterogeneity and also for differentiation of horizontal and vertical components.
Disadvantages:
The value of hydraulic conductivity represents only the direct surrounding of the small cavity.
10
4/16/2018

11. 4/16/2018
11
Guelph permeameter method
 The Guelph Permeameter is an easy to use instrument to quickly and accurately measure in-situ hydraulic conductivity.
 Accurate evaluation of soil hydraulic conductivity, soil sorptivity, and matrix flux potential can be made in all types of
soils.
 The equipment can be transported, assembled, and operated easily by one person.
 Measurements can be made in 1/2 to 2 hours, depending on soil type, and require only about 2.5 liters of water.
 The Guelph Permeameter comes as a complete Kit consisting of the permeameter, field tripod, borehole auger, borehole
preparation and cleanup tools, collapsible water container, and vacuum test hand pump, all in a durable carrying
case.
Above
water
table
Guelph
method
Double
ring
Inverse
auger
hole

12. 4/16/2018
12
Measurements can be made in the range of 15 to 75 cm below the soil surface.
The method involves measuring the steady-state rate of water recharge into unsaturated soil from a cylindrical well hole,
in which a constant depth (head) of water is maintained.
is the saturated hydraulic
conductivity (cm/s)
a is bore hole radius (cm)
H1is the first head of water
established in borehole (cm)
C1 is the shape factor
Inserting Guelph permeameter into tripod stand

13.  This procedure is very well known and is
used very often, when the groundwater table is
absent.
 The unsaturated soils two concentric
infiltrometer rings are placed at the certain
depth, where the infiltration properties
(hydraulic conductivity) will be measured.
 The soil bellow and around the rings is
saturated by infiltration.
 The rings are then filled the water and the
rate of fall of the levels in both outer and inner
ring is measured.
Double ring infiltrometer method
13
4/16/2018

14.  The procedure is repeated.
 The water level in the outer ring being
constant and is kept approximately at the
same level as is the water table in inner ring.
 The role of the outer ring is to minimize
horizontal flow below the inner ring.
 The results are almost vertical flow path
below the inner ring, where the data are
measured.
 This process is known as cumulative
infiltration by ponding.
14
4/16/2018

15. Disadvantages:
 Results depend on actual moisture content of the soil (sorptivity); only values for the top layer (measured layer) can be
found.
 Boundary effects may cause errors. The rings are then refilled by water, the water level in outer ring is kept constant,
and the rate of fall in the inner ring being recorded.
 It means, that in inner ring is recorded certain infiltrated height of water (e.g. 5,0 mm) and at the same time is recorded
continued time.
 In inner ring is always refilled amount of water, which represented recorder infiltrated height (at this case 5.0 mm).
15
4/16/2018
Where ‘K’ is the saturated hydraulic conductivity and ‘A’ is the parameter

16. The inversed auger hole method,
described in French literature as the
Porchet method, consists of boring a
hole to a given depth, filling it with
water, and measuring the rate of fall of
the water level.
A hole is augered to a certain depth
well above the groundwater table.
 Water is flowed into the dry hole, and
then the rate of lowering of the water
table is measured.
The advantage of this method over the
infiltrometer method lies in the
difference between digging soil pits and
making auger holes.

Inversed Auger-Hole Method
16
4/16/2018

17.  Moreover, by gradually deepening the auger hole and filling it with water over the corresponding depth, the
hydraulic conductivity of successive layers can be measured in the same hole.
 From this rate of decreasing and from the geometry of the borehole, is calculated the value of hydraulic
conductivity.
 Common procedure in field surveys for surface or subsurface drainage design, if groundwater table is not present.
17
4/16/2018
Hydraulic conductivity by inverted auger hole method
In which,
K = hydraulic conductivity (cm/sec)
r = hole radius (cm)
hn = Depth of water level inside the hole (cm)
tn = End time (sec)
to = Start time (sec)

18. 4/16/2018
18
Large-scale field methods are designed for determining hydraulic conductivity below the water table (i.e., K of the
saturated zone).
The methods available for large-scale K determination are of two types :
(a) the method that uses pumping from wells (known as ‘pumping test’)
(b) the method that uses pumping or gravity flow from horizontal drains (‘parallel drains method’).
The pumping test is the standard and most accurate method for determining ‘hydraulic conductivity’ and ‘storage
coefficient’ of saturated zones (aquifers).
Large scale field methods
Pumping test
Parallel drains

19. 4/16/2018
19
Using the parallel drains method,
 hydraulic conductivity (K) can be determined from the functioning of drains in experimental fields, pilot areas, or on
existing drains and thus this method is very suitable for drainage.
 This method uses observations on drain discharges and corresponding elevations of the water table in the soil at some
distance from the drains.
 From these observed data, the value of K can be calculated using a drainage formula (either steadystate or unsteady
state formula) appropriate for the conditions under which the drains are functioning.
 The advantage of largescale determination is that the flow paths of the groundwater and the natural irregularities of
the K values along these paths are automatically taken into account in the overall K value found by the method.

20.  The water head at one of the sides of the
sample decreases with time.
 A high initial water head is desirable for low
hydraulic conductivities.
 The calculation of the hydraulic conductivity
from the velocity of total flux through the
sample can be somewhat complicated, because
the head difference is not constant.
 This laboratory method is suitable especially
for layers with a low hydraulic conductivity, in
horizontal or vertical direction.
Disadvantages:
Small sample area means the high possibility of
a large random error.
Falling-Head Method
20
4/16/2018

21. 4/16/2018
21
L y x
L
H
L
 
 
• L is length through the soil
• y is the height of ponded water
• x is the height of water required to lower the gradient so that y can be
maintained.
• Note: if the gradient is 1 then Ks = q as per Darcy’s Law.

22.  The constant-head permeameter is a suitable
method to determine the saturated hydraulic
conductivity (Ks).
 However, for highly permeable soils,
resistances to flow in tubing systems of
conventional constant-head permeameters may
result in an underestimation of Ks.
 A constant difference in head is created over
an undisturbed soil sample in a Kopecky steel
ring.
 At certain times, the volume of water that has
flowed through the sample is measured.
 From this discharge, the size of the soil
sample, and from the difference of head, can be
calculated the value of hydraulic conductivity.
Constant-Head Method
22
4/16/2018

23. Advantages
 Laboratory method is good tool to measure hydraulic conductivity of a certain layer in horizontal or in vertical direction.
Disadvantages
 The measured value is valid for the relatively small soil sample area only, so there may be a large error. This laboratory
method is not suitable for samples with extremely high or with very low hydraulic conductivity. 2
3
4/16/2018
K
aL
A t t
H
H
s 













( )
log
2 1
2
1
• a is the cross-sectional area of the burette
• A is the cross-sectional area of the soil column
• t2 – t1 is the time required for the head to drop from H1 to H2.

24. Correlation Methods
Correlation methods are based on predetermined relationships between an easily determined soil property
 Texture,
 Poresize Distribution,
 Grainsize Distribution,
 Soil Mapping Unit
 A variety of empirical formulae are available which relate K with content of sand, silt and clay; K with grain diameter
(mean or effective grain diameter); K with graindiameter and porosity; K with grainsize distribution; and K with soil series
and they can be used in the absence of field or laboratory values of hydraulic conductivity.
 For example, Smedema and Rycroft (1983) provided a generalized table with ranges of Kvalues for certain soil textures.
However, such tables should be handled with care.
 Smedema and Rycroft (1983) warn that: “Soils with identical texture may have quite different Kvalues due to
differences in structure and some heavy clay soils have welldeveloped structures and much higher Kvalues than those
indicated in the table”.
24
4/16/2018

25. 4/16/2018
25
Sl. No. Soil Texture
Range of K
(m/day)
1 Gravelly coarse sand 10–50
2 Medium sand 1–5
3 Sandy loam, fine sand 1–3
4
Loam, clay loam, clay (well
structured) 0.5– 2
5 Very fine sandy loam 0.2– 0.5
Values of K by soil texture (Smedema and Rycroft, 1983)

26. 4/16/2018
26
 Of the various empirical formulae, the Hazen formula is a simple relationship between the hydraulic conductivity
and the effective grain diameter, and it is often used for the estimation of hydraulic conductivity from grainsize
distribution data.
It is expressed as (Freeze and Cherry, 1979):
K = A × d10
2
Where,
K = hydraulic conductivity, (cm/s);
d10 = effective grain diameter, (mm) which is determined from the grainsize distribution curve;
A = constant, which is usually taken as 1.0 (Freeze and Cherry, 1979).
 The advantage of the correlation methods is that an estimate of the K value is often simpler and faster than its direct
determination.
 However, the major drawback of these methods is that the empirical relationship may not be accurate in all cases,
and hence may be subject to random errors.

27. Determination of drainable
porosity
27
4/16/2018

28. 4/16/2018
28
Determination of Drainable Porosity
 Drainable porosity can be measured in the laboratory or in the field. In the laboratory, drainable porosity can be
measured using Hanging WaterColumn apparatus, which is suitable for a tension range of 0150 cm.
 Hanging WaterColumn apparatus consists of a glass funnel with a porous plate, a burette, and a flexible transparent tube
connecting the glass funnel and the burette.
HangingWater Column apparatus: (a) Initial saturated
sand column; (b) Lowered burette.

29. 4/16/2018
29
 Undisturbed soil sample is taken from the field and it is saturated in the laboratory with the help of Hanging Water-
Column apparatus .
 The saturation may take 24 hours or more depending on the soil type. The water level in the burette is maintained at the
same level as the top of the porous plate.
 Thereafter, the burette is lowered by a certain distance (usually in steps of 10 cm), which imparts a suction to the
saturated soil sample, and hence water starts draining slowly. The drained water raises the water level in the burette.
 At a given suction, this rise in water level is adjusted by readjusting the burette height such that the originally applied
suction is closely maintained.
 When there is no further rise in water level in the burette, the elevation difference between the top of the porous plate
and the water level in the burette are noted down, which gives the value of average suction applied to the soil sample.
 The difference between the initial and the final burette readings gives the volume of water drained from the soil sample
due to the applied suction.
 This process is repeated by lowering the burette in steps of 10 cm initially and more lately until the desired suction
(corresponding to the maximum possible depth of the subsurface drain or any other criteria) is obtained.

30. 4/16/2018
30
 If the water retention characteristic of the soil is known and if the pressurehead profile is known for two different
levels of water table, the drainable porosity (m) can be calculated from the following equation:
Where,
z1 = water table depth (m) for Stage 1 (say at t = t1),
z2 = water table depth (m) for Stage 2 (say at t = t2),
q1 (z) = soilwater content as a function of soil depth for the watertable position at t1
q2 (z) = soilwater content as a function of soil depth for the watertable position at t2.
 Thus, ‘drainable porosity’ can also be defined as “the ratio of the change in soilwater content in the soil profile above
the water table to the corresponding rise/fall of the water table in the absence of evaporation”.

31. THANK YOU
Presented By
Akhila Shiney (2017-18-015)
31
4/16/2018

32. 32
4/16/2018