EXPERIMENT 9
MEASUREMENT OF HYDRAULIC CONDUCTIVITY OF GRANULAR SOILS
I. INTRODUCTION:
Applicable ASTM Standards
ASTM D2434: Standard Test Method for Permeability of Granular Soils (Constant
Head)
Purpose of Measurement
It is important to quantify the volume of groundwater flow from areas of high potential
to low potential. This information is useful in estimating the performance of landfill
liners, the migration of contaminated groundwater, and other applications. To quantify
flow through soil, the hydraulic conductivity (a.k.a. permeability) of the soil must be
known. Hydraulic conductivity of granular soil, including sands and gravels, is
measured in the laboratory using a fixed-wall permeameter. In this exercise, hydraulic
conductivity will be used using the constant head and falling head test methods.
Definitions and Theory
Darcy’s Law and the Constant Head Test
Water moves through soil in accordance with Darcy’s Law. Given a cylinder of soil with
length L and cross-sectional area A subjected to a constant head difference of Δh
(Fig.10.1), the rate of flow through the soil, q, can be expressed as:
In this expression, k is the hydraulic conductivity of the soil. The flow rate q can be
expressed as flow volume Q per unit time t,
The ratio of Δh to L is defined as the hydraulic gradient i:
such that Darcy’s Law can be rewritten as:
q = kiA
Darcian velocity, vD, can be expressed as:
vD = ki
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and Darcy’s Law can also be expressed as:
q = vDA
Darcian velocity is also referred to as discharge velocity. Darcian velocity is not equal to
seepage velocity, vs. Darcian velocity is always less than vs, and the two terms are
related by porosity, n:
Flow of water through soil under constant head conditions
Flow of water through soil under constant head conditions
Darcy’s Law is based on the assumption of laminar flow. Under conditions of laminar
flow, k is independent of i. To ensure laminar flow, ASTM D2434 states that i should be
in the range of 0.2-0.3 and 0.3-0.5 for loose soils and dense soils, respectively. The low
end of these ranges corresponds to coarser soils, while the high end of these ranges
corresponds to finer soils. This assumption can be validated by performing the test over
a range of i, and creating a plot of q versus iA. The slope of this curve is k. For lower
values of i, flow is laminar, the relationship between q and iA is linear, and k is
independent of i. For higher values of i, flow becomes turbulent and the relationship
between q and iA becomes nonlinear. When applying laboratory test results, k should
be measured under a hydraulic gradient representative of anticipated field conditions
regardless of flow regime to obtain appropriate results.
Falling Head Test
The constant head test is described in ASTM D2434. The falling head test is not included
as part of the ASTM D2434 standard, but is a simpler test because 1) it does not require
a water source to keep the influent reservoir at a constant level and 2) measurement of
flow volume is not necessary. The test configuration includes a fixed-wall permeameter
and a supply reservoir with a cross-sectional area a. By measuring the head at the
beginning of the test, H1, and at the end of the test, H2, after a permeation period of t, k
can be calculated. 2
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Flow of water through soil under falling head conditions.
Darcy’s Law is used to derive the expression for k using the falling head test method.
For the falling head test configuration, Darcy’s Law can be expressed as:
A
where H is the instantaneous head across the specimen. Instantaneous flow rate, q, can
be expressed as a function of the incremental change in head Δh during an increment in
time Δt:
Combining equations:
= A
The terms in Eqn. 10.10 can be rearranged, and each side of the expression can be
integrated:
where H1 is the head at time = 0, and H 2 is the head at time = t. Integrating both sides
and solving for k,
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II. EQUIPMENT AND MATERIALS
Constant Head Test
ASTM D2434 describes the procedure for performing a hydraulic conductivity test of
granular soils using a fixed-wall permeameter while maintaining a constant head across
the specimen. To perform the test, the following equipment and materials are required:
Coarse-grained soil;
permeameter or permeability apparatus;
constant-elevation water reservoir;
tap water source;
measuring tape or yardstick;
large vessel for collecting effluent;
scale capable of measuring to the nearest 1.0 g; and
timing device capable of measuring to the nearest second;
The permeameter is illustrated in the figure. All four ports on the permeameter should
have valves that can be closed. To prevent dislodging of soil particles at the top of the
specimen, a spring is placed between the top cap and the top porous stone or wire
screen. The spring should apply 5-10 pounds of force to the specimen. The spacing
between manometer ports, Lc, should be greater than the specimen diameter D. The
purpose of the porous stones or wire screens is to prevent particle migration during
permeation, but it is also helpful to place filter paper between the soil and the porous
stones or wire screens. If porous stones are used, the hydraulic conductivity of the
porous stones should be greater than the hydraulic conductivity of the soil.
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Illustration of the fixed-wall permeameter:
a. cylindrical soil specimen;
b. permeameter side wall;
c. permeameter top cap;
d. permeameter bottom cap; e. influent port;
f. effluent port; g. porous stone or wire screen;
h. manometer ports;
i. spring w/ 5 to 10 lb force
Constant-head hydraulic conductivity test configuration.
For all soils, the fraction retained by the ¾ in. sieve should be removed prior to testing.
The minimum required diameter of the specimen, D, is dependent on the maximum
particle size of the fraction passing the ¾ in. sieve, and the percent retained by the #10
sieve (2.00 mm) or the 3/8 in. sieve, as detailed below:
If max. particle size is bet. 2.00 mm and 3/8 in. and P+#10 < 35% → D > 3.0 in.
If max. particle size is bet. 2.00 mm and 3/8 in. and P+#10 > 35% → D > 4.5 in.
If max. particle size is bet. 3/8 in. and ¾ in. and P+3/8 in. < 35% → D > 6.0 in.
If max. particle size is bet. 3/8 in. and ¾ in. and P+3/8 in. > 35% → D > 9.0 in.
Falling Head Test
The falling head test is a simpler alternative to the constant head. To perform a falling
head test, the following equipment and materials are required:
Coarse-grained soil;
fixed-wall permeameter;
influent water vessel;
measuring tape or yardstick; 5
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timing device capable of measuring to the nearest second; and
vacuum source capable of achieving a vacuum of 500 mm Hg (-9.67 psi).
Falling-head hydraulic conductivity test configuration.
The same permeameter can be used for both the constant head and falling head tests,
but the manometers are not used for the falling head test and the manometer valves
should remain closed. It is also important to note that the length term is different for the
constant and falling head tests. For the constant head test, the length Lc is the distance
between the manometer ports. For the falling head test, the length Lf is the total length
of the soil specimen.
II. PROCEDURE:
Constant Head Test
1) Obtain a soil-filled permeameter from your instructor and assemble the constant
head test configuration as shown in Fig. 10.4. Measure the distance between the
manometer ports (Lc) and the diameter of the soil specimen in the permeameter
(D). Calculate the specimen cross-sectional area A:
2) Soil must be saturated for Darcy’s Law to be valid. Saturate the specimen.
3) Open the influent valve, effluent valve, and manometer valves, and begin
permeating tap water through the specimen while maintaining a constant head.
Once the water level in the manometers has stabilized, record effluent flow
volume Q during time t. If your vessel is not graduated, you can calculate Q
using the conversion factor 1.00 cm3 = 1.00 g. For coarse-grained soil, you should
be able to permeate a sufficient amount of water (a few liters) in about 10
minutes or so. Also measure the corresponding head loss Δh between the two
manometers. 6
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4) Repeat Step 3 a total of 4 times. For each trial, vary i so that the tests span a range
in i from 0.2 to 0.5.
5) Calculate k for each trial using the following relationship:
6) Create a plot q versus iA using the four test points to identify the laminar and
turbulent flow regimes.
Falling Head Test
1) Assemble the falling head test configuration as shown using the permeameter
from the constant head test. Measure the length of the specimen (Lf) and the
diameter of the specimen in the permeameter (D). Calculate the specimen cross-
sectional area A. Close the two manometer valves and leave them closed for the
experiment.
2) Soil must be saturated for Darcy’s Law to be valid. Saturate the specimen.
3) Calculate the cross-sectional area of the falling head water reservoir, a.
4) Measure the initial head, H1.
5) Open the valves and permeate water through the specimen. Record the time, t,
required for the head to drop to H2.
6) Repeat Steps 4 and 5 a total of 4 times. For each trial, vary the initial hydraulic
gradient ii = H1/Lf so that the tests span a range in ii from 0.2 to 0.5.
7) Calculate the hydraulic conductivity of the specimen, k, in cm/s for each trial
using the following relationship:
Expected Results
The permeameter tests described in this exercise are intended for coarse grained
granular soils with less than 10% fines, which include the USCS group symbols SP, SW,
GP, GW, SP-SM, SP-SC, GP-GM, and GP-GC. For these soils, k is typically on the order
of 10-2 to 10-3 cm/s. Coarse-grained soils with greater than 10% fines, including SM, SC,
GM, and GC, typically have k on the order of 10 -5 to 10-6 cm/s. Fine-grained soils,
including ML, CL, and CH, typically have k on the order of 10-6 to 10-8 cm/s.
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IV. DATA AND RESULTS
Hydraulic Conductivity of Granular Soils for Constant Head
(ASTM D2434) Laboratory Data Sheet
I. TEST DETAILS
Soil description: Coarse Grained, varying in shape
Maximum Particle Size: Water Head “h” (cm):
1.26 137.7
Specimen diameter (cm): Specimen height (cm):
6.32 15.8
Specimen Area (cm2):
31.37
II. MEASUREMENT AND CALCULATIONS
Test Volume Time, t Hydraulic Conductivity, k
Number Discharged (sec) (cm/sec)
(Q)
1 180 15 0.04389
2 230 20 0.04206
3 300 25 0.04389
Average: 0.04328 cm/sec
III. EQUATIONS AND CALCULATION SPACE
Specimen Area = = 31.37 cm2
k1 = = 0.04389 cm/sec
k2 = = 0.04206 cm/sec
k3 = = 0.04389 cm/sec
kaverage = = 0.04328 cm/sec
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Hydraulic Conductivity of Granular Soils for Falling Head
(ASTM D2434) Laboratory Data Sheet
I. TEST DETAILS
Soil description: Coarse Grained, varying in shape
Maximum Particle Size: Area of the pipe (cm2):
1.26 0.372
Specimen diameter (cm): Specimen height (cm):
6.32 15.8
Specimen Area (cm2): Influent Reservoir Area (cm2):
31.37
II. MEASUREMENT AND CALCULATIONS
Test Initial Initial Final Time, t Hydraulic
Number Head Hydraulic Head (sec) Conductivity, k
(cm) Gradient (cm) (cm/sec)
1 99.5 5.759 8.5 16 0.12685
2 90.7 5.266 7.5 16.34 0.12853
3 97.5 4.937 19.5 5.9 0.08299
4 96.3 5.089 15.9 5.31 0.09287
Specimen Area = = 31.37 cm2
Pipe Area = = 0.372 cm2
i= = 5.759
k= 2.303 ( ) = 0.12685 cm/sec
i= = 5.266
k= 2.303 ( = 0.12853 cm/sec
i= = 4.937
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k= 2.303 ( = 0.08299 cm/sec
i= = 5.089
k= 2.303 ( = 0.09287 cm/sec
IV. ILLUSTRATIONS
Fig 9.1 Getting the size of the Fig 9.2 Filling on the Fig 9.3 Compacting the sand
largest particle permeameter with using a hammer
ocean sand
Fig 9.4 Placing a cylindrical Fig 9.5 Getting the elevation Fig 9.6 Filling in the funnel
plate on top of the sand of the funnel to the with water to saturate
permeameter the sand
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Fig 9.6 Extracting excess Fig 9.7 Filling the standpipe
water in the permeameter with water
Fig 9.8 Measuring the initial Fig 9.9 Recording the time
head, repeat 4 times required, repeat 4 times
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V. OBSERVATION
For this experiment, two tests were conducted to determine the hydraulic
conductivity of granular soils with the use of permeability apparatus. The
coarse-grained soil has maximum particle size of 1.26. The distance between the
manometer ports and diameter of the soil specimen in the permeameter was
measured as 6.32 cm while the specimen height is 15.8 cm. The water head is
137.7cm and the calculated specimen cross-sectional area is 31.37cm2. In the
constant head test, the flow of the water in the hose is continuous and the
bubbles were minimal. The volume discharge and time varies per trial from
which the hydraulic conductivity will be acquired. The volume discharged
were 180, 230 and 300 with their corresponding time 15, 20 and 25 seconds
respectively. The hydraulic conductivity of three trials were computed to be
0.04389, 0.04206 and 0.04389 cm/sec. The average of hydraulic conductivity is
0.04328 cm/sec. While in the falling head test, the flow of water inside the
standpipe is not continuous that is why the bubbles occurred. The calculated
area of the pipe is 0.372 cm2. The four hydraulic conductivity tests were also
computed to be 0.12685, 0.12853, 0.08299 and 0.09287 cm/sec and with their
corresponding time 16, 16.34, 5.9, 5.31 seconds respectively.
VI. CONCLUSION
The constant head test was used to determine the hydraulic conductivity of
the soil sample in this experiment. Based on the gathered data, the value of the
hydraulic conductivity was 0.04328 cm/sec. Thus, the group concluded that the
hydraulic conductivity is constant even if the time for water discharge changes.
Meanwhile, for the falling head test, only a short amount of time was
considered to determine the water discharge thus the hydraulic conductivity
obtained was 0.43124. Therefore, it was concluded that the sample used is a
coarse grained granular soil with less than 10% fines. It is also classified as SP.
VII. RECOMMENDATION
In this experiment, the researchers recommend to handle the porous stone
carefully for this is very fragile. Also, weigh the specimen in the same weighing
scale for an accurate results and get the dimensions using the caliper instead of
ruler. Additionally, do not put too much sand in the vessel for the stone and the
container might break due to heavy pressure, remove the air of the hose before
pouring the water because it affects the behavior of the water, and lastly
thoroughly compute the acquired date to avoid errors.
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