-
LAB #7 Infiltration and Infiltrometers for Measurement of Soil
Intake Properties
(Environmental Measurements CE/ENVE 320-04) Objectives The
primary objective of this experimental module is to conduct a
series of infiltration experiments to quantify soil intake
properties using measurement devices known as infiltrometers or
permeameters. These devices are designed to facilitate such
experiments by confining the flow to certain geometry, or boundary
conditions, or provide other information on the various flow
attributes. The common Double-ring Infiltrometer and related
designs will be used for strictly one-dimensional infiltration
problems. Subsequently, we will test disc infiltrometers that
generate 3-D flow fields for ponded and tension surface boundary
conditions (a tension mode enables exclusion of target pore sizes
thereby providing information on soil unsaturated hydraulic
conductivity). The specific objectives are to:
1.) conduct a vertical infiltration experiment into a column of
dry soil (ponded surface). 2.) infer intake parameters for an
algebraic infiltration equation (Lewis-Kostiakov). 3.) analyze the
1-D infiltration measurements based on Philip's solution 4.)
predict wetting front propagation based on the Green-Ampt
approximation 5.) use a ponded disc-permeameter for measurement of
soil hydraulic conductivity. 6.) introduce and use tension
disc-infiltrometer unsaturated hydraulic conductivity 7.) analyze
and discuss advantages and limitations 1-D and 3-D infiltration
methods .
Theoretical Background Infiltration An important class of flow
events involves water entry through soil surface in a process known
as infiltration. The rate of this process relative to the rate of
water supply to the surface determines how much water will enter
the soil, and how much, if any, will pond and create overland flow
(runoff). The leading edge of the wetted soil volume, the wetting
front, advances into the drier soil region in response to matric
potential and gravitational gradients.
Based on field observations, the infiltration rate denoted as i
is found to be dependent upon the initial soil water content, the
hydraulic conductivity of the surface soil, the elapsed time since
the onset of water application, and the presence of impeding layers
and other heterogeneities within the soil profile. In most
situations the infiltration rate (i) is highest when water first
enters the soil, and gradually decreases with time until a constant
final rate (if) is attained (Fig.2-1). This behavior is also
reflected in the cumulative infiltration (I) showing a rapid
increase in the volume of infiltration at short times, which
decreases gradually to a nearly linear rate of cumulative
infiltration at large times.
In many natural situations the initial rate of water application
such as the rainfall rate or sprinkler irrigation rate is less than
the soil's initial infiltration capacity (i), but higher than
the
0
0.1
0.2
0.3
0.4
0.5
Infil
trat
ion
rate
(cm
/min
)
0 10 20 30 40 50 60 70 80 Elapsed time (min)
Exp. 1
Exp. 2
Exp. 3
Millville Silt Loam
if
0
1
2
3
4
5
6
7
Cum
ulat
ive
infil
trat
ion
(cm
)
0 10 20 30 40 50 60 70 80 Elapsed time (min)
if
Fig.2-1: Time dependent infiltration rate and cumulative
infiltratrion into Millville silt loam soil
-
potential final rate (if) for the soil under the given
conditions. This common situation means that a transition must
occur in which water application rate will eventually exceed the
soil's infiltration rate, and ponding possibly followed by runoff
is likely to occur. Given an application rate (P) we may use the
infiltration equation to predict the time to onset of ponding,
hence, runoff.
Empirical Infiltration Equations Based on a predictable and
well-behaved shape of the infiltration rate vs. time relationship,
several functions having shapes similar to the expected behavior
have been proposed as predictive equations. Attempts were sometimes
later made to attach physical significance to the various
parameters of these empirical equations.
The Lewis (Kostiakov) Equation: One of the most widely used
empirical expressions was originally proposed by Lewis (1937) but
was erroneously attributed to Kostiakov (1932; see discussion by
Swartzendruber, 1993):
1=== aa aktdtdIiratektIcumulative :: (1)
where I is the cumulative depth of infiltration or the volume of
water per unit soil surface area, t is the elapsed time, k and a
are empirical parameters, and i = dI/dt is the infiltration rate.
The main disadvantages of this equation are: (1) its disregard for
different initial water contents; and (2) for long times it
erroneously predicts a zero infiltration rate. The latter problem
can be fixed by adding a parameter, f0, to Eq.(1) representing a
final infiltration rate for long times resulting in the following
modified equations: I = kta + tf0, and i = akt(a-1) + f0.
The Horton Equation: Horton (1940) proposed another empirical
equation based on an exponential form:
[ ] tfftff eiiiirateeiitiIcumulative +=
+= )(:: 0
0 1 (2)
where i0 and if are the initial and final infiltration rates,
respectively, and is an empirical parameter.
Physically-Based Infiltration Equations The Green-Ampt
Approximation
In contrast to the empirical approach, Green and Ampt (1911)
adopted a simplified, yet physically-based, approach to describe
the infiltration process. Their approximate solution was found
particularly useful for cases of infiltration into initially dry
soils which exhibit a sharp wetting front. The basic assumptions of
Green and Ampt were: (1) a distinct wetting front exists such that
the water content behind it (0) remains constant, and abruptly
changes to initial water content (i) ahead of the wetting front;
(2) the soil in the wetted region has constant properties (0, K0,
and h0), and (3) the matric potential at the wetting front is
constant and equals hf (Fig.2-2).
We begin by applying a simplified form of Darcy's law for
horizontal flow, hence no gravitational component, over a wetted
region of thickness Lf (i.e., the depth of the wetting front)
as:
f
fw L
hhK
LhKiJ
=
== 000 (3)
where h0 is matric head at the soil surface (or within the
wetted soil volume), hf is the matric head at the wetting front,
and K0 is the hydraulic conductivity of the wetted soil
(transmission zone). Additionally, we use the equality between
cumulative infiltration and depth of wetting (Lf) times change in
soil water content ( = 0-i):
dtdL
dtdIiLI ff === (4)
-
Fig.2-2: Green and Ampt's approximation - definition of the flow
domain (top, Hillel, 1980), and propagation of the wetting front
and total head (bottom, Smith and Williams, 1980).
This means that the infiltration rate (i) is equal to the rate
of advance of the wetting front times the change in soil water
storage. Equating Eqs.(3) and (4) provides an integral equation in
the form:
=tL
dthKdLLf
00
0 (5)
and the result is:
thKLf
= 02
2 (6)
To simplify the notation we define the effective diffusivity of
the wetted soil as: D0 = K0 h/. We are now able to predict the
wetting front depth, cumulative and instantaneous rates of
horizontal infiltration as:
tDi
tDLI
tDthKL
f
f
2
2
22
0
0
00
=
==
=
=
(7)
For the case of vertical infiltration, we need to include the
effect of gravity. If we take the soil surface as z = 0, then Hz=0
= h0+0; and at z = -Lf we obtain Hz=Lf = hf - Lf. Introducing these
heads into Darcy's law for vertical infiltration yields:
-
f
fff
LLhh
Kdt
dL = 00 (8)
and the integral form:
=+tL
dtKLh
dLLf
0
0
0 (9)
The solution to this integral, found in standard tables of
integrals, is given by:
=
+tK
hL
hL ff 01ln (10)
We may convert Eq.(10) to include cumulative infiltration vs.
time using I =Lf:
tKhIhI 01 =
+
ln (11)
There is no simple form to express I or i vs. time. However, for
short times this solution converges to the solution for the
horizontal case, and for long infiltration periods it converges to
i = Ko. Note that from Eq.(8) i = -Ko h/Lf + Ko, so as Lf
approaches infinity, i approaches Ko.
Philip's Solution
Philip (1957, 1969) presented the first analytical solution to
the Richards equation for vertical and horizontal infiltration. For
horizontal infiltration Philip showed that the cumulative and
instantaneous infiltration rates are given by:
21
21
21
== tSiratetSIcumulative :: (12)
with S as the sorptivity which is a function of initial and
boundary water contents, S = S(0,i), and t is time since water
application. When a sharp wetting front exists, the sorptivity may
be approximated by:
210
0 tL
S fii)(
),(
= (13)
where Lf is the distance from the surface to the wetting
front.
For vertical infiltration, Philip's solution to Eq.Error!
Reference source not found. describes the time dependence of
cumulative infiltration as an infinite series in powers of
t1/2:
K+++= 23
222
121
tAtAtSI (14) where the parameters A1, A2,... are dependent upon
the soil properties and on initial and boundary water contents. In
practice, the series is truncated and only the first two terms are
retained, resulting in the following equations, which are valid for
short times:
121
121
21 AtSiratetAtSIcumulative +=+=
:: (15)
The first term in each describes the influence of
capillary/sorptive forces of (relatively) dry soil, and the second
term the contribution of gravity. The influence of the first term
diminishes with time and reflects the reduction in the hydraulic
gradient as the soil becomes more saturated. For long infiltration
times when water is ponded on
-
the soil surface (0 =s at the surface), the final infiltration
rate approaches K(s), and thus the ratio A1/Ks is bounded by 1/3
A1/Ks 2/3.
For flux-limited infiltration rate such as low intensity
rainfall, P, we may approximate the time to ponding tp from the
time at which i = P (note that P is a flux), which is given by:
21
2
4 )( APSt p
= (16)
This is particularly useful for predicting whether and when
surface runoff will occur. This matching method however, ignores
the modification of the original infiltration curve (established
under complete surface ponding) due to the limited rainfall flux
and potential dependency based on rainfall rate. This situation
requires and a correction known as "time compression approximation
- TCA" (Kim et al., 1996) which for Philip expression takes on the
form:
21
12
42
)()(
APPAPStc
= (17)
and the actual infiltration curve is now shifted by the amount:
tshift = tc - tp. Hence calculations of infiltration rates for
times t>tc should consider the "tshift" correction. In essence
the TCA considers the time for equal cumulative infiltration as the
matching criterion, the amount of time-shift is set such that the
areas are equal (see figure).
Infiltration From a Surface Disk Source (3-D Flow) All flow
examples discussed thus far have been one-dimensional. In many
cases we are interested in solving flow problems in two or three
dimensions. For example, predicting water distribution from drip
irrigation systems, flow and wetting patterns from an irrigated
furrow, or flow rates and patterns from leaking underground tanks.
Detailed solutions of two or three-dimensional flow using the
Richards equation are feasible only by means of numerical methods.
However, under steady state flow conditions (i.e., no changes in
flux and soil attributes with time), and assuming that the soil
unsaturated hydraulic conductivity function K(h) can be expressed
in an exponential form proposed by Gardner (1958Error! Reference
source not found.):
hsKhKexp)( = (18)
where h is the matric head (note it is a negative value), Ks is
the saturated hydraulic conductivity, and is a parameter related to
typical pore size of the media. This exponential form of K(h)
allows for a variety of analytical solutions to multidimensional
flow from various source geometries to be developed. Philip (1969)
discussed a variety of multidimensional solutions from surface and
subsurface point, and line sources. A unique feature of these
multidimensional flow regimes as compared with 1-D flow is the
attainment of a finite and constant distribution of matric head and
water content about the source of water. Unlike 1-D vertical flow,
where the wetting front advances indefinitely, these 2- or 3-D
steady distribution of h is the result of a force balance between
sorptive (capillary) and gravitational forces. An approximate
solution to steady state infiltration rate from a shallow and
circular pond of water on the soil surface was derived by Wooding
(1968):
ss
sf rKKi 4+= (19)
where rs is the radius of the circular pond, and K(h) is given
by: K(h)=Ks eh . There are two terms in Eq.(19); one is the
contribution of gravity to the flow (Ks), and the second term
contains contributions due to sorptive forces or capillarity. Note
that unlike one-dimensional flow (Eq.(15)), the steady state or
final infiltration rate exceeds Ks, which has one-dimensional units
of length per time. This approximate solution provides a simple
-
means by which Ks and may be measured in situ, which is very
important due to the likely non-representative nature of collected
samples.
Other Field Methods for Estimating Soil Hydraulic Functions It
is imperative to measure soil hydraulic properties in the field.
The main reason is that small samples used in the lab may not
represent the conditions in the field accurately, particularly for
hydraulic conductivity determination. Soil cores may not adequately
represent the true macroporosity of the bulk soil, for example
because of dead-end pores resulting from the finite sample volume,
and the sampling may alter the structure of the soil matrix,
resulting in biased estimates of conductivity. Realistic modeling
and prediction of water flow and solute transport is therefore
dependent upon reliable and representative estimates of soil
hydraulic properties inferred from field experiments and
measurements made at scales larger than that of small lab cores. In
the following section we discuss several methods for inferring soil
hydraulic properties, with emphasis on saturated and unsaturated
soil hydraulic conductivity.
The Instantaneous Profile Method
The instantaneous profile method (Watson, 1966) is based on
simultaneous monitoring of changes in soil water content and matric
potential within a soil profile that was initially saturated and is
undergoing internal drainage. The soil surface which represents the
top boundary of the soil profile is covered and insulated to
prevent evaporation and thermal gradients. The measurements and the
controlled boundary conditions allow the application of the mixed
form of the Richards equation in a discrete form. The equation is
rearranged to provide direct estimates of the unsaturated hydraulic
conductivity using measurements of other attributes:
00
=
=
=
zL
Lz zHK
zHKdz
t
(20)
Since there is no flow across the plastic cover, the second term
on the right hand side (RHS) is zero. The changes in water content
between two consecutive measurements taken at two times, t1 and t2,
are integrated or algebraically summed from the soil surface z = 0
to a desired depth, z = -L, and the corresponding changes in the
matric potential are measured (see Fig.2-3 for the measurement
scheme). The working equation is:
Lz
L L
zHK
tt
dztzdztz
=
=
)(
),(),(
12
0 012
(21)
where the hydraulic gradient zH is an average gradient
calculated at two different times across the control plane z = -L,
and K() is related to the average water content between t1 and t2
at the profile between 0 and -L, or between two control planes in
the profile with known boundary conditions. Hence a tensiometer
should be installed at known depths above and below the plane z =
-L to obtain the mean hydraulic potential gradient. The term on the
RHS of Eq.(21) is an approximation of the flux that flows through
z=-L. The flux is divided by the hydraulic gradient on the LHS to
obtain the unsaturated hydraulic conductivity K():
[ ]
+
=
+
+
11
01
zhtt
dzzzK
ii
L
ii
)(
)()()(
(22)
where =[i+1(-L)+i(-L)]/2, and the hydraulic gradient is averaged
similarly.
-
Fig.2-3: A scheme of the Instantaneous Profile method
calculations
(Source: Flhler et al., 1976, SSSAJ 40:830-836).
An experimental plot for application of the instantaneous
profile method should be large enough to ensure that measurements
made at its center are unaffected by the conditions at the lateral
boundaries; a plot of a few m on each side should suffice. There
are several limitations to this method: (i) the soil should be
quite homogeneous; otherwise the use of "noisy" data with the
Richards equation for an assumed uniform soil may result in
unreasonable estimates of K(), (ii) the burden of measurements is
heavy, especially at the initial stages where measurements should
be taken frequently enough to capture the rapid changes in water
status. A study to analyze and quantify the errors associated with
the method was presented by Flhler et al. (1976).
Infiltrometers and Permeameters
Many field methods for measurement of Ks and K() or K(h) are
based on conducting controlled infiltration experiments with known
flow geometry, intake area, flow rate, and boundary conditions.
Knowledge of these flow variables enables the application of
various solution techniques to infer the unknown hydraulic
properties Ks and K(,h) from the results of the experiment, e.g.
from the changes in flux with time, or from final flux rate.
Devices that are designed to facilitate such experiments by
confining the flow to a certain geometry, or boundary conditions,
or provide other information on the various flow attributes are
called infiltrometers, or permeameters if designed specifically for
measuring hydraulic conductivity. One of the most common
infiltrometer designs for one-dimensional flow is the Double-ring
Infiltrometer.
The double-ring infiltrometer (Swartzendruber and Designs, 1961)
consists of two thin-walled metal cylinders. The two cylinders are
concentrically placed and driven into the soil to a depth of 5 to
10 cm (Fig.2-4). Water is ponded to the same shallow depth in both
the inner and outer rings. The flow in the inner ring is presumed
to be one dimensional with vertical streamlines. Flow from the
outer ring may diverge laterally due to "edge effects" (Bouwer,
1986). The idea behind such a design is to establish 1-D flow
conditions for the inner ring, while satisfying edge effects and
lateral flow by the presence of the outer ring.
-
OuterRing
InnerRing
1-DFlow
Fig.2-4: Sketch of a double-ring infiltrometer and flow field
(top), and commercially
available double-ring infiltrometer with installation tools
(bottom)
Water flow rate vs. time from the inner ring is monitored by
means of a Mariotte flask or other constant head water supply until
it reaches a constant value. The assumption is that the soil layer
immediately below the ponded area is fully saturated and thus the
matric potential is essentially zero. Under these conditions the
hydraulic gradient is unity which presumably renders the final
infiltration rate (final flux) equal to the soil's saturated
hydraulic conductivity, Ks:
-
sssf KzzK
zzhKi
+=
)( (23)
However, as we have seen from Philip's analyses (Eq.(15)) the
long-time flux if is actually a fraction of Ks, bounded by 1/3
if/Ks 2/3; a value of if/Ks = 0.5 is usually a good assumption for
practical application of this technique.
Ponded Disc Permeameter and the Dripper Method Wooding's (1968)
approximate solution for infiltration from a circular shallow pond
into the underlying soil facilitates a host of infiltration
experiments based on the use a single disk-shaped water source to
infer the soil's Ks and K(h). Disc-shaped permeameters (Perroux and
White, 1988) apply water under saturated and unsaturated (i.e.,
negative pressure at the supply inlet) conditions for field
application of Wooding's solution. In its simplest design
(Fig.2-5), the disk permeameter consists of a metal ring having a
radius of 10 to 15 cm, and about 3 to 5 cm in height. The ring is
pushed into the soil to a depth of slightly less than 1 cm. A
graduated Mariotte tower is placed over the metal ring to supply
water to the soil surface inside the ring at a constant head and at
measurable rates. The time-dependent infiltration rate i(t) is
determined from the time-dependent changes in the height (h) of
water in the graduated Mariotte tower, and the cross-sectional soil
area Asoil, as i(t) = Vwater/Asoil = (hAtower)/Asoil. In addition,
initial and final water contents (i, and f = s) at the soil surface
must be measured or estimated.
Analysis of the results involves a series of assumptions and
steps. A primary assumption is that the infiltration rate at very
short times may be approximated by Philip's solution for 1-D
infiltration at short times, i.e., I = St1/2. The main steps in the
analysis of i vs. t include: (1) approximating the sorptivity (S)
from the slope of I vs. t1/2 for the first several measurements
over a short time; then (2) approximating the ratio Ks/ using:
( )if
2s SbK
(24)
where b is a shape parameter bounded between 1/2 and /4. A value
of b=0.55 is suitable for many field soils; (3) Ks is estimated
using Eq.(19):
( )ifs
2
fs rSb4iK
= (25)
Finally, is estimated from Eq.(24) using the value of Ks
resulting from Eq.(25) as:
2sif
SbK)( = (26)
Fig.2-5: Sketch of a disc permeameter based on Woodings (1968)
solution.
-
One of the main limitations of the foregoing analysis is the
over-reliance on measurements at early infiltration times. These
measurements are difficult to reliably obtain due to the rapid and
unstable infiltration rates. In some cases, the "short time"
behavior (where the relationship I=St1/2 holds), is too short to be
measured accurately (e.g., less than a minute), rendering estimates
of S unreliable. Philip (1969) provided an estimate for the time
after which the 3-D geometry swaps the initially 1-D character of
the flow:
2
=
Srt sgeom
(27)
Warrick (1992) developed an expression for "short time" behavior
that holds for extended periods (> 3 hrs)):
222
1
21 880
)(.
+=
srtSbStI (28)
Equation (132) is quadratic in S; the positive solution (root)
for S is:
+
= 16321311
21
21
2
)(.
.
)(
s
s
rI
t
rS (29)
Sorptivity should be approximately constant for times smaller
than: t < 3(r /S)2.
The Dripper Method developed by Shani et al. (1987) is another
technique for estimating soil hydraulic properties based on
Wooding's approximation. In this method a steady flux (if) rather
than the saturated radius (rs) is maintained constant using a
dripper having a fixed discharge rate (Q). The establishment of a
steady radius of ponding on the soil surface is monitored. After a
period of time, which is dependent upon the soil type, initial
conditions, and dripper discharge, rs reaches a final size
corresponding to its steady state value. The measurement is then
repeated with a different discharge rate (Q). Knowledge of several
values of rs vs. if (=Q/rs2) enables solution of Eq.(19) by linear
regression of if vs. 1/rs. The intercept of the regression line is
Ks, and is computed from the slope of the line (s) as: = 4Ks/s.
Example - Disc Permeameter (Measurement and Analysis)
Problem Statement: A disc permeameter was used to measure intake
properties of a sandy soil in Goshute Valley in eastern
Nevada. The diameter pond at the soil surface (defined by a
metal ring) was 210 mm, and the cylindrical water supply tower was
57 mm. Initial and saturated water contents were i = 0.07 m3/m3,
and s = 0.38 m3/m3. The following measurements of water height in
supply tower vs. elapsed time where acquired:
Time [sec]
Height [cm]
Time [sec]
Height [cm]
Time [sec]
Height [cm]
0 0.0 1846 5.0 3952 9.0 22 1.0 2040 5.5 4480 10.0
140 2.0 2362 6.0 5044 11.0 810 3.0 2609 6.5 5623 12.0 1068 3.5
2877 7.0 6210 13.0 1326 4.0 3126 7.5 6813 14.0 1588 4.5 3407 8.0
7404 15.0
(1) Find the sorptivity assuming I = St1/2 for short times (use
the first few measurements)
-
(2) Determine the steady state infiltration rate (use the last
5-8 measurements) (3) Determine Ks and for this soil.
Solution: (1) First we calculate cumulative infiltration volume
I for each time step according to:
where ds is the diameter of the supply tower, dr is the diameter
of the metal ring, and h is the water height in the supply
tower.
(2) For each time step we take the square root of the elapsed
time (t1/2) and plot the values against the cumulative
infiltration. This data set is the basic input for the
determination of sorptivity.
(3) To find the sorptivity we take the first three data pairs
(22, 140, and 810 sec) and perform a linear regression analysis
using the statistical tools provided in most computer spreadsheets
(e.g. Excel). For linear relationship between I and t1/2 the
sorptivity is simply the slope of the regression line (we set the
intercept to zero).
(4) To determine the steady state infiltration rate we perform a
regression analysis with the last 8 data pairs of I versus time
(t). The slope is the steady state infiltration rate.
(5) With known steady state infiltration rate if and sorptivity
S we now can calculate Ks and using the following
relationships:
)( ifsfs r
SbiK
=24
2SbKsif )(
=
where b is a shape parameter (b=0.55 is suitable for most field
soils), rs is the saturated radius (radius of the metal ring), and
i and f are the initial and saturated water contents
Tabulated Calculation:
Measurements Calculation
Time [sec]
Height h [cm]
Time [min]
Time1/2 [min1/2]
Height h[mm]
Cumulative infiltration [mm]
Regression line for sorptivity
Regression line for infiltration
rate 0 0.0 0.00 0.00 0 0.000 0.000
22 1.0 0.37 0.61 10 0.737 0.404 140 2.0 2.33 1.53 20 1.473 1.020
810 3.0 13.50 3.67 30 2.210 2.454
1068 3.5 17.80 4.22 35 2.579 2.817 1326 4.0 22.10 4.70 40 2.947
3.139 3.271 1588 4.5 26.47 5.14 45 3.315 3.435 3.609 1846 5.0 30.77
5.55 50 3.684 3.704 3.941 2040 5.5 34.00 5.83 55 4.052 3.894 4.190
2362 6.0 39.37 6.27 60 4.420 4.190 4.605 2609 6.5 43.48 6.59 65
4.789 4.403 4.923 2877 7.0 47.95 6.92 70 5.157 4.624 5.268 3126 7.5
52.10 7.22 75 5.526 4.820 5.588 3407 8.0 56.78 7.54 80 5.894 5.032
5.950 3952 9.0 65.87 8.12 90 6.631 5.419 6.652 4480 10.0 74.67 8.64
100 7.367 5.770 7.331 5044 11.0 84.07 9.17 110 8.104 6.123 8.057
5623 12.0 93.72 9.68 120 8.841 6.464 8.802 6210 13.0 103.50 10.17
130 9.578 6.793 9.558 6813 14.0 113.55 10.66 140 10.314 7.116
10.334 7404 15.0 123.40 11.11 150 11.051 7.418 11.095
122
22
= rs dhdI
-
Regression - Sorptivity S = 0.6678 mm/min1/2 r2 = 0.6543
Steady State Rate Constant: 1.5644 Coefficient(Infiltration
rate) if = 0.0772 mm/min r2 = 0.9995
(3) Saturated Conductivity and
[ ]min.)..(
... mmKs 067600703801056680550407720
2
=
=
( ) [ ] =
= 0 38 0 07 0 0676
055 0 6680 08542
1. . .. .
. mm
0 2 4 6 8 10 120
2
4
6
8
10
12C
umul
ativ
e In
filtr
atio
n I [
mm
]
t1/2
0 20 40 60 80 100 120 1400
2
4
6
8
10
12
Cum
ulat
ive
Infil
trat
ion
I [m
m]
t
-
Tension Disc Permeameter
A modification of the pond-type disc
permeameter is depicted in Fig.2-6, in
which water is supplied trough the
base-plate under negative pressure
using a bubbling tower to control the
pressure, and a fine-mesh nylon
membrane for the base. The
modifications allow for controlled
negative pressures at the supply
surface (membrane) up to the air
entry value of the saturated
membrane. The main advantages of
such a design are: (i) the ability to
exclude macropores from the
measurements (by controlling the
negative pressure); and (ii) the ability to
measure "directly" and in-situ the unsaturated hydraulic
conductivity.
Complete contact between the supply membrane and the soil
surface is absolutely essential, and is
often achieved by capping the uneven soil surface by a thin
layer of coarse sand (or other highly permeable
contact material). The analysis of the results follow a similar
path as that of the saturated (pond) case, except
that K(hs) is used instead of KS in Eq.(25) :
( )ifsfi
fs rSb
ihK
=24 ),(
)( (30)
where hs is the negative head at the supply surface. Note that
S(2i,2f) is expected to be smaller than for the
saturated case (2f
-
The unsaturated conductivity values and $ may be estimated
without requiring sorptivity or water content
measurements, using the following equations:
1
2
1
221
2
11
1
12
QQ
QQhhr
r
QhK
+
+
=)(
)(
(33)
1
122 Q
hKQhK )()( = (34)
)]()()[(
)]()([
2121
212hKhKhh
hKhK
= (35)
where Q are the steady-state volumetric flow rates (m3 s-1), or
Q/Br2=q. These equations were developed based
on the following assumptions: (i) the ratio K(hi)/N(hi) is
constant; and (ii) N(h1)-N(h2) = (h1-h2){K(h1)+K(h2)}/2,
which along with eq. (30) provides a system of four equations
for the four unknowns (Ankeny et al., 1991).
Hussein and Warrick (1993) have used the exponential hydraulic
conductivity function (Eq. 18) to write Eq. 31
for two different steady state flow rates and obtain a simpler
expression for $ as:
12
12
hhQQ
=
]ln[ (36)
Similarly, Eq. 31 can be expressed directly as:
+=
rK
rQ
ihs
i
412 exp (37)
and rearranged to solve for the saturated hydraulic conductivity
(Ks). These two analyses are equivalent;
however, the analyses of Ankeny can be generalized to admit
different models for the unsaturated hydraulic
conductivity function.
Procedures 1-D Infiltration into a Soil Column
1.) An infiltration column will be assigned to each group.
Groups performing the experiments with Sand will use long
infiltration columns; groups with Silt Loam will use shorter
columns.
2.) Weigh the column and fill it with a known amount of
air-dried and sieved soil to about 3 cm below the columns top.
Calculate the soils bulk density and porosity (measure the columns
inner diameter and length).
3.) Place the empty infiltrometer on top of the prepared column,
und use the adjustment screws to level the infiltrometer and to
adjust the gap between soil surface and infiltrometer to about 1
cm. Calculate the volume of water required to fill the 1 cm
gap.
4.) Fill the supply and prime towers of the infiltrometer
(Fig.2-7) by submerging the infiltrometer base into water-filled
bucket and using a hand-held vacuum pump to fill the towers.
When
-
you disconnect the vacuum pump the connectors automatically
close; the water is under subatmospheric pressure (negative
pressure), therefore should stay in the towers. The volume
contained in the prime tower should be approximately equal to the
volume that is required to fill the 1 cm gap between soil surface
and infiltrometer base.
5.) Carefully place the water-filled infiltrometer on top of the
column, and prepare a ruler and a timer to measure the elapsed
time, the wetting front position from the surface, and the
infiltration rate from the change in the height of water in the
infiltrometer supply tower.
6.) Before you start the infiltration experiment ensure that the
drainage port line at the bottom of the soil column is open, and
then remove the rubber stopper from the priming (small) tower to
fill the gap between the soil and the infiltrometer base. Be
prepared to quickly add known amounts of water as needed to create
hydraulic continuity between the pond and supply tower! A small
hole connects the towers at the base, when the water level falls
below the connecting hole, air bubbls and the supply tower acts
like a Mariotte device.
7.) Start recording the time and discharge from the supply tower
(change in height) as soon as the first air bubble enters the
tower.
8.) Measure the time at fixed intervals of water height
(vertical distance on the tower). Assign one person to observe
changes in water height in the Mariotte tower.
9.) Measure the wetting front position with time (make remarks
regarding its uniformity around the column).
10.) We may install two TDR probes to provide additional
information on soil water content close to the surface and within
the wetted volume.
11.) Collect data until the initiation of drainage from the
bottom of the column. 12.) Obtain soil samples from two depths in -
near soil surface and 5 cm below surface.
1-D infiltration Data Analyses:
1.) Compute (a) cumulative infiltration vs. time (I vs. t); (b)
infiltration rate vs. time (i vs. time); and (c) wetting front
depth vs. time (Lf vs. time).
2.) Estimate the parameters of the "modified" Lewis-Kostiakov
equation for i vs. t, and plot the prediction vs. observations of
i-t pairs (Use the solver tool of your spreadsheet software for the
least square fit procedure)
3.) Estimate the parameters for Philip's solution for vertical
infiltration (S and A1) by fitting i vs. t data.
4.) Estimate S from the short time behavior (for t less than the
first 2-3 minutes) assuming 1-D horizontal flow; and soil water
content information.
5.) Use your estimates of S for short times to obtain an
estimate for Green and Ampt's wetting front matric potential hf
assuming horizontal flow
Fig.2-7: Experimental setup for 1-D infiltration into a soil
column the infiltrometer is used here as constant head water supply
(note - this is not 3-D disc infiltrometer test!)
-
6.) Use nonlinear curve fitting to estimate the soils K0 and hf
using and your Lf vs. t data. Plot observed and predicted Lf vs.
t.
Ponded Disc Permeameter
1) Your group will be assigned a large pan with one of two soil
types (sand or silt loam); take a small sample prior to wetting to
determine the soil's initial water content, i.
2) Smooth the soil surface and insert the metal ring to a depth
of less than 1 cm (use a level). 3) Prepare your disc permeameter;
measure or obtain from instructor all relevant dimensions
(tower cross-sectional area, metal ring area, etc); set the
permeameter on the ring, maintain a 1 cm clearance above the soil
surface and level the base of the permeameter (remember the exact
orientation of the permeameter for later use)
4) Dip the permeameter into a water-filled bucket and use a
hand-held vacuum pump to fill the main and primer towers.
5) Prepare a table to record the water level in the main tower
vs. elapsed time, you will need a stopwatch.
6) Position (carefully !) the water-filled disc permeameter on
top of the ring (use the same orientation as in preparation step);
when ready, release slowly the stopcock on the primer tower (add
water through the primer tower if necessary to create continuity
with the water in the main tower).
7) Record the height of water in the main tower vs. time
(initially, it will move fast). 8) Continue until the infiltration
rate is constant for 5-8 consecutive readings. 9) Close the
stopcock in the primer tower and remove the permeameter. 10) As
soon as the free water recedes, take a soil sample from the surface
to determine soil's s.
Tension Disc Permeameter for Unsaturated Flow Measurements
1) The key difference between from ponded permeameters, is that
water is supplied under negative pressure (tension) to the soil
surface. This is achieved by using a fine-mesh nylon screen
attached to the lower part of the base, which can remain saturated
even under negative pressures up to about -250 mm (Fig. 2-6).
2) The dimensions of the "pond" are determined by the area of
the screen-covered base. 3) To ensure good contact between the base
of the permeameter and the soil, a thin layer of fine
sand with high hydraulic conductivity is placed on the soil
surface, and the permeameter is placed on top of the sand layer. In
some cases when the soil is flat and smooth, it is possible to
place the tension permeameter directly on the soil surface.
4) The priming tower is now used to maintain a negative bubbling
pressure ,i.e., air enters into the permeameter to replace
infiltrating water, only when a prescribed negative pressure
(equals to the height below the free surface of water in the tower)
develops.
5) One group will start measurements sequence from wet (zero
tension) to dry (-80 mm tension) at -20 mm increments, the other
group that was assign the same soil type will start their
measurements from dry -80 mm tension to wet (please share results
for the report)
6) Apply the target suction in the priming tower (0,-20,-40,-60,
or -80 mm) and measure infiltration until the system reaches steady
state (no need to collect transient information for short
times).
7) For the dry end you may need to wait > 5 min between
readings; steady state is considered after 3 consecutive (nearly)
identical readings.
-
8) Data analyses follow a similar path as the ponded analysis,
except that the hydraulic conductivity is not the saturated (Ks)
but the unsaturated conductivity (K[h]) corresponding to the
negative pressure (h) of the supply.
Report Disc Permeameter Experiments: 1) Present samples of all
your calculations and the data you used. 2) For the ponded
experiment - plot the cumulative infiltration vs. t1/2 to estimate
the sorptivity from short
time behavior; and plot the cumulative infiltration vs. time to
estimate the steady state infiltration rate (if) from the slope of
I vs. t (recall that i=dI/dt).
3) Calculate the soil's Ks and . 4) Present the data and the
calculated unsaturated conductivity K(h) measured by the tension
disc
permeameter. 5) Synthesize the results from all experiments, and
discuss advantages and limitations of each of the
methods presented in this lab (consider assumptions, ease of
use, etc.).
References Ankeny, M.D., T.C. Kaspar, and R. Horton. 1988.
Design for an automated tension infiltrometer. Soil Sci. Soc. Am.J.
52:893-896. Ankeny, M.D., M. Ahmed, T.C. Kaspar, and R. Horton.
1991. Simple field method for determining unsaturated hydraulic
conductivity. Soil Sci. Soc. Am. J. 55:467-470. Fluhler, H, M.S.
Ardakani, and L.H. Stolzy, 1976. Error propagation in determining
hydraulic conductivities from successive water content and pressure
head profiles. Soil Sci. Soc. Am. J. 40:830-836. Gardner, W.R.
1958. Some steady-state solutions of the unsaturated moisture flow
with applications to evaporation from a water table. Soil Sci.,
85(4):228-232.
Green, W.H. and G.A. Ampt. 1911. Studies in soil physics. I.
Flow of air and water through soils. J. Agr. Sci. 4:1-24.
Hanks, R.J. 1992. Applied Soil Physics. 2nd Ed., Springer
Verlag, New York, NY.
Hillel, D. 1980. Fundamentals of Soil Physics. Academic Press,
San Diego, CA.
Horton, R.E., 1940. An approach towards a physical meaning of
infiltration capacity. Soil Sci. Soc. Am. Proc. 5:399-417.
Hussen, A.A., and A.W. Warrick. 1993. Alternative analyses of
hydraulic data from disc tension infiltrometers. Water Resour. Res.
29(12):4103-4108.
Kostiakov, A.N., 1932. On the dynamics of the coefficient of
water percolation in soils and on the necessity of studying it from
a dynamic point of view for purposes of amelioration. Trans. Sixth
Comm. Int. Soc. Soil Sci., Part A 17-21.
Lewis, M.R. 1937. The rate of infiltration of water in
irrigation practice. Eos, Trans. AGU, 18:361-368.
Logsdon,S.D. and D.B. Jaynes. 1993. Methodology for determining
hydraulic conductivity with tension infiltrometers. Soil Sci. Soc.
Am. J. 57:1426-1431 Perroux, K.M., and I. White. 1988. Designs for
disc permeameters. Soil Sci. Soc. Am. J. 52:1205-1215.
-
Reynolds, W.D. and D.E. Elrick. 1991. Determination of hydraulic
conductivity using a tension infiltrometer. Soil Sci. Soc. Am. J.
55:633-639. Shani, U., R.J. Hanks, E. Bresler, and C.A.S. Oliviera.
1987. Field method for estimating hydraulic conductivity and matric
potential-water content relations. Soil Sci. Soc. Am. J.
51:298-302.
Smith, R.E., and J.R. Williams. 1980. Simulation of the surface
water hydrology. In: A field scale model for Chemicals, Runoff, and
Erosion from Agricultural Management Systems. Ed: Knisel W.G.
U.S.D.A. Consev. Res. Report 26.
Swartzendruber, D., 1993. Revised attribute of the power form
infiltration equation. Water Resour. Res. 29(7):2455-2456.
Swartzendruber, D., and T.C. Designs. 1961. Sand-model study of
buffer effects in the double-ring infiltrometer. Soil Sci. Soc. Am.
Proc. 25:5-8.
Watson, K.K., 1966. An instantaneous profile method for
determining the hydraulic conductivity of unsaturated porous
materials. Water Resour. Res. 2:709-715.
Wooding, R.A., 1968. Steady infiltration from a shallow circular
pond. Water Resour. Res. 4:1259-1273