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.).

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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.

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