study guide for an exam (geotechnical)
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4WaterinSoil.pptGeotechnical Engineering A
4
Water in Soil
Contents
Groundwater
Permeability
Coefficient of permeability:
Coefficient of permeability published data
Coefficient of permeability laboratory tests
Coefficient of permeability in-situ tests
1. Groundwater
- Groundwater in soil may be one of two types, occurring in two distinct zones separated by the water table (or phreatic surface).
The zone below the water table is known as gravitational water (or phreatic), which:
- Is subject to gravitational forces.
- Saturates the pore spaces in the soil below the water table.
- Has an internal pore pressure greater than atmospheric pressure.
- Tends to flow laterally.
The zone above the water table is known as vadose water, which is the unsaturated zone and comprises:
- Slow moving water, percolating downwards to join the phreatic water below the water table.
- Capillary water held above the water table by surface tension forces (with internal pore pressure less than atmospheric).
Normal and Perched water table
- The water table is the level at which the pore water pressure is equal to the atmospheric pressure.
- In general, the water table corresponds to the free water surface; such as may be found at a river or lake or in an excavation,
- where groundwater lies above isolated bodies of soil, perched water tables may occur.
Confined groundwater
- Artesian conditions are said to exist where the water table ties above ground level.
- Sub-artesian conditions occur when the water table lies between the surface and the aquifer.
Artesian conditions
(water table above ground)
Sub-artesian conditions
(water table below ground)
Where a stratum of reasonably high permeability, is confined above and below strata of low permeability = an aquifer - there may be no obvious groundwater table. However, the water level in standpipes or wells would indicate the level of the water table. The porewater pressure in a confined aquifer depends on the condition at the place where the layer is unconfined. If a rise in the water table occurred in this area, it is likely that the artesian pore water pressure will also rise
Capillary water
- Capillary water is held above the water table by surface tension
hc can be established theoretically from an understanding of the vertical forces at the surface of the liquid
Capillary rise hc
For a soil an approximation, based on the voids ratio, e, and the effective size of the soil particles, D10, may be established from:
- While the value of hc represents the maximum capillary rise, the soil will only be saturated with capillary moisture up to the capillary saturation level hcs. The approximate relationship between capillary rise and capillary saturation level is given on the graph below.
Effective size, D10, (mm) (log scale)
Capillary Rise (mm) (log Scale)
Approximate relationship between capillary rise and soil type
Groundwater zones
Excavation
2. Permeability
- Permeability may be defined as the rate at which water under pressure can flow through the interconnected voids (or pore spaces) within a soil.
- The flow properties of water through soil was first investigated
by H. Darcy in 1856.
- He showed that under steady flow conditions through beds of sand of varying thickness and under various pressures, the rate of flow, q, was always proportional to the hydraulic gradient, i, (the fall in hydraulic head per unit thickness of sand).
- This principal is known as Darcy’s Law, which is given below. This equation has been found to be valid for most types of fluid flow through soils.
q=Aki
where: q = rate of flow (m3/sec)
A = area of flow (m2)
k = coefficient of permeability (m/sec)
i = hydraulic gradient
- The hydraulic gradient, i, is the ratio of the difference in total head on either side of a soil layer, to the thickness of the layer measured in the direction of the flow. This can be illustrated using the examples given below.
Hydraulic gradient
X
If a standpipe or piezometer tube is inserted in the soil at any point X, the water will rise in the tube up to a level (h) which indicates the static pressure of water at X.
The level of water in the pipe is called the piezometric level and the pressure of the water is the height of the column of water in the pipe above point x
The difference in piezometric level between P & Q is the hydraulic head between these two points, which may be denoted as h1-h2.
The hydraulic gradient, i, is the ratio of the difference in head to the distance, L, between P & Q
Pressure = rgh
Inclined flow under a hydraulic gradient
- If the flow of water is not horizontal, as illustrated below, the difference in level between points S and T must be taken into account. This is achieved by measuring the heights of the piezometric levels h3 and h4 above a common datum, which gives the total head at each point. The length, L, is the distance between points S and T measured along the direction of flow. The calculation of the hydraulic gradient is similar to that given above:
Coefficient of Permeability, k
- The coefficient of permeability, k, may be defined as the mean discharge velocity of water flow under the action of a unit hydraulic gradient and is usually expressed in m/s.
- The coefficient of permeability may be assessed from:
- Published data,
- Laboratory or in-situ permeability tests or Derived from other empirical (based on observation and experiment) relationships.
These methods of assessment are considered in more detail below.
3.1 Coefficient of permeability – published data
266.tiff
3.2 Coefficient of permeability – laboratory tests
- There are two basic methods of determining the coefficient of permeability of a soil in the laboratory:
The Constant Head (used for soils of high permeability e.g. gravels & sands k >10-4m/s)
The Falling Head (used for soils of low permeability e.g silts & clays)
- The rate of flow of water through the sample may be calculated by measuring the quantity of water, Q, collected in a measuring cylinder in a measured time period. The rate of flow, q, may then be calculated from the expression:
268.tiff
- Given that the cross sectional area of the sample is known, the coefficient of permeability may be calculated from Darcy’s equation rearranged as follows.
q = Aki (Darcy’s equation)
or
NB Care is required to ensure that the units used when calculating values of k are appropriate.
Example 1: during a constant head permeability test the following data was recorded for a sample having a diameter of 75mm. Determine the average value of the coefficient k.
Distance in manometer levels (mm) =120mm
Length of flow path =120mm
Cross-sectional area of sample =
Q = Q(ml) x103 mm3
t = 3 x 60secs = 180sec
Average k = (2.81+3.02+3.22+3.21+3.97)/ 5
= 3.25x10-3 m/s
= 3.25mm/s
Sheet1
| 1009 | 942 | 757 | 606 | 474 | ||||
| Flow quantity for 3 minutes (ml) | 1509 | 1442 | 1257 | 1106 | 974 | |||
| Difference in manometer levels (mm) | 81 | 72 | 59 | 52 | 37 |
Sheet2
Sheet3
- Steady flow conditions are impossible to attain through soils of low permeability and the rate of flow would be too low to record using the constant head method of test.
- Consequently, the falling head test was developed specifically for low permeability soils.
- The falling head permeability test utilises a similar sample to that described above, but in this case a vertical standpipe leads directly to the top of the sample.
- The bottom of the sample is immersed in a dish in which the water level is kept constant.
2. The Falling Head Permeability
- At any instant in time, the difference in height between the water level in the standpipe and that in the dish is effectively the head loss over the sample length L.
- The flow rate is related to the drop in height of the water in the standpipe and the cross sectional area of the standpipe.
- However, the solution is complicated by the fact that the head, hence the flow rate, are constantly changing with time.
- The formula for the calculation of the coefficient of permeability, k, is derived using integral calculus, and is:
286.tiff
where:
a = cross sectional area of standpipe
A = cross sectional area of sample
L = length of sample
h1,h2= heights of water in the standpipe measured from the water level in the dish, at times t1 and t2 respectively
ln = logarithm to base e
or
log
Example 2: during a falling head permeability test the following data was recorded for a sample having a diameter of 100 mm and a length of 150 mm. Determine the average value of the coefficient k (standpipe diameter 9.00 mm).
Cross-sectional area of sample =
Average k =5.32x10-3 mm/s = 5.32x10-6 m/s
Cross-sectional area of standpipe =
=5.38x10-3 mm/s
=5.40x10-3 mm/s
=5.19x10-3 mm/s
Sheet1
| 1009 | 942 | 757 | 606 | 474 | ||||||||||||||
| Flow quantity for 3 minutes (ml) | 1509 | 1442 | 1257 | 1106 | 974 | |||||||||||||
| Difference in manometer levels (mm) | 81 | 72 | 59 | 52 | 37 | |||||||||||||
| k (mm/sec) | 2.81 | 3.02 | 3.22 | 3.21 | 3.97 | 16.24 | Initial standpipe level (mm) | 1200 | 900 | 750 | ||||||||
| Final standpipe level (mm) | 900 | 750 | 500 | |||||||||||||||
| Time onterval (s) | 65 | 41 | 95 |
Sheet2
Sheet3
3.3 Coefficient of permeability
in-situ test
- Laboratory measurement of permeability may be unreliable because, among other reasons, it is difficult to obtain undisturbed samples of granular soils. In addition, the small sample used may not be representative of the soil mass (macrostructure).
- There are three basic types of in-situ test, which are:
Constant/Falling head tests,
Packer tests,
Pumping tests.
- These methods are briefly discussed below.
- These tests are undertaken within boreholes sunk using any of the various drilling techniques.
- It should be noted that these tests are only applicable to soil below the water table and are not normally undertaken in rock.
- During the site work it is necessary to take the following measurements:
i) Constant head and falling head permeability in-situ tests
f is a shape factor which is depends on the conditions at the bottom of the casing (cases A to F)
Flow Rate (q)
SAND
CLAY
Ref. Soil Mechanics Principles and Practice by GE Barnes
ii) Packer in-situ permeability tests
Flow Rate (q)
Double Packer
(used in completed borehole)
Applied head (Hp)
Total head (H) = Hp+Hg
Fully Penetrating well in an unconfined aquifer; overlying impervious layer, with observation wells
iii) Pumping in-situ permeability tests
Constant Head Pumping Test
An approximate value of k can be obtained from the above expression even if the well is not fully penetrating but the depth H must be known in order to calculate values of h from draw down z. h can be found approximately if there are 3 observation wells spaced such that r/r2 = r2/r1
CLAY
CLAY
SAND
h1
h2
h3
Fully Penetrating well in an confined aquifer; between impervious layers, with observation wells
Constant Head Pumping Test
Strictly, only two observation wells are needed but the third well acts as a check. The formula for k is true only for confined flow: the piezometric head in the main well must be above the top of the aquifer
Pumping water out at a rate q
CLAY
CLAY
SAND
h1
h1
h2
Fully Penetrating Trench; in an unconfined aquifer with a line source
Constant Head Pumping Test
These expressions assume flow into one side of the trench only
Example 3: A pumping test was carried out to determine the permeability of a sand layer in an unconfined aquifer with a well arrangement as shown below. At steady-state pumping rate of 58.7 m3/h, the draw downs in the observation wells were respectively 2.91 m and 0.88 m. Calculate the coefficient of permeability k.
SAND
CLAY
15 m
35 m
16.2 m
GW
2.91 m
58.7 m3/h
1.85 m
= 0.0163 m3/s
h1= 16.2 - 1.85 - 2.91 = 11.44 m
h2= 16.2 - 1.85 - 0.88 = 13.47 m
= 11.44 m
= 13.47 m
= 8.70x10-5 m/s
0.88m
1.85 m
CLAY
CLAY
SAND
D = 7.6 m
15 m
32 m
5.7 m
2.18 m
1.62 m
0.47 m
Example 4: A permeability pumping test was carried out in a confined aquifer.the arrangement of wells and relevant dimensions is shown below. The draw downs indicated were observed at a steady-state pumping rate of 15.6 m3/h. Calculate the coefficient of permeability k.
= 4.33x10-3 m3/s
h1= 5.7+7.6-2.18-1.62 = 9.50m
h2= 5.7+7.6-2.18-0.47 = 10.65m
= 6.0x10-5 m/s
h1
h2
15.6m3/h
10
30
.
hc
eD
=
12
hh
h
i
LL
-
D
\==
34
hh
h
i
LL
-
D
\==
12
hh
i
L
-
=
Q
q
t
=
q
k
Ai
=
(
)
Q
qrateofflowofwater
t
=
(
)
12
hh
h
ihydraulicgradient
LL
-
D
==
q
k
Ai
=
.
..
QL
k
tAh
=
D
Q
k
tAi
=
Flow quantity for 3 minutes (ml)1509144212571106974
Difference in manometer levels (mm)8172595237
2
2
75
4418
4
Amm
p
´
==
3
10120
4418..180
Q
k
h
´´
==
D´
1
1509
0.151
81
k
=
2
1442
0.1513.02/
72
kmms
==
345
3.22,3.21,3.97
kkk
===
2.81/
mms
=
0.151(/)
Q
mms
h
D
(
)
(
)
12
21
ln/
aLhh
k
Att
éù
ëû
=
-
(
)
(
)
1012
21
2.3log/
aLhh
k
Att
éù
ëû
=
-
...
kAhdt
L
=
22
11
ht
ht
dhkA
dt
haL
-=
òò
(
)
2
21
1
log
h
kA
tt
haL
-=-
Initial standpipe level (mm)h
1
1200900750
Final standpipe level (mm)h
2
900750500
Time onterval (s)t
2
- t
1
654195
A= π ×100 2
4 = 7854.0mm2
A=
p´100
2
4
=7854.0mm
2
A= π ×9 2
4 = 63.6mm2
A=
p´9
2
4
=63.6mm
2
(
)
(
)
12
21
63.6150ln/
7854
hh
k
tt
éù
´
ëû
\=
´-
(
)
(
)
12
21
1.215ln/
hh
k
tt
éù
ëû
\=
-
(
)
1
1.215ln1200/900
65
k
éù
ëû
\=
(
)
2
1.215ln900/750
41
k
éù
ëû
\=
(
)
1.215ln750/500
3
95
k
éù
ëû
\=
c
q
k
fdH
=
(
)
ln/
.
ot
HH
A
k
fdt
=
fdk
gradient
A
=
q
k
Hfd
=
(
)
(
)
3
2
2
1
2222
2132
log
log
e
e
r
r
q
q
r
r
k
hhhh
pp
æö
æö
ç÷ç÷
èøèø
==
--
(
)
222
123
123
2
zzz
h
zzz
++
=
++
(
)
(
)
3
2
2
1
2132
log
log
22
e
e
r
r
q
q
r
r
k
DhhDhh
pp
æö
æö
ç÷ç÷
èøèø
==
--
(
)
(
)
12
2222
12
22
oo
qLqL
k
hhhh
==
--
(
)
(
)
2222
12
12
22
oo
khhkhh
orq
LL
--
==
3
58.7
/
6060
Flowrateqms
=
´
(
)
2
1
22
21
log
e
r
q
r
k
hh
p
æö
ç÷
èø
=
-
(
)
(
)
22
35
0.0163log
15
13.4711.44
e
k
p
\=
-
(
)
2
1
21
log
2
e
r
q
r
k
Dhh
p
æö
ç÷
èø
=
-
3
15.6
/
6060
Flowrateqms
=
´
(
)
(
)
3
32
4.3310log
15
27.610.659.50
e
k
p
-
´
=
´´-
