PROJECT COMPLETION REPORT DEVELOPMENT OF A MATHEMATICAL MODEL OF INFILTRATION

PROJECT COMPLETION REPORT DEVELOPMENT OF A MATHEMATICAL MODEL OF INFILTRATION

PROJECT COMPLETION REPORT

OWRT PROJECT NO. A- 027 -ARIZ

DEVELOPMENT OF A MATHEMATICAL MODEL OF INFILTRATION

WHICH INCLUDES THE EFFECTS OF RAINDROP IMPACT

Agreement No. 14 -31- 0001 -3503

Project Dates:

July 1971- December 72

Principal Investigators:

C. B. Cluff

D. D. Evans

Student Graduate Assistant:

J. G. Morse

The University of Arizona

Tucson, Arizona

Acknowledgment - The work upon which this report is based was supported by funds provided by the United

States Department of the Interior, Office of Water

Research and Technology, as authorized under the Water

Resources Research Act of 1964.

Acknowledgements

The authors thank Dr. G. R. Dutt and A. W. Warrick of the Department of Soils, Water and Engineering for their help and for the use of the Gamma

Ray Attenuation Equipment.

The authors also express thanks to Dr. Roger Smith who not only willingly provided the infiltration model but also spent considerable time in help with its operation.

Finally the authors appreciate the incentive provided by funds provided by the United States Department of the Interior, Office of Water Research and

Technology, as authorized under the Water Resources Research Act of 1964.

i

ABSTRACT

The purpose of this investigation was to use an existing mathematical model of infiltration to assist in determining which factors, including raindrop impaction, were responsible for infiltration characteristics of a bare semiarid watershed.

The infiltration model developed by Roger Smith was selected as best suited for this investigation.

Several laboratory and field rainfall simulator runs were modeled.

Good correlation was found between the modeled and experimental results for both the infiltration data and the saturation profiles, for both bare and grass covered plots.

For the lab and field experiments a realistic rotating disk rainfall simulator was used.

In the field tests bare and grass covered plots were tested.

In the lab specially constructed soil boxes were used that permitted measurement of infiltration and saturation profiles with time.

Gross changes in saturated hydraulic conductivities due to crusting effects were also measured.

Gamma ray attenuation techniques were used to obtain density and soil moisture profiles for the laboratory experiments.

It was found that the Smith model can be used to simulate infiltration from different surface conditions as long as there is some method to calibrate the model.

Carefully obtained saturated and unsaturated hydraulic properties for the soil types present in the watershed are needed in addition to infiltration data from a realistic rainfall simulator or through hydrograph analysis from unit subwatersheds.

ii

TABLE OF CONTENTS

ACKNOWLEDGEMENT

ABSTRACT

LIST OF FIGURES

LIST OF TABLES

INTRODUCTION

OBJECTIVES

DESCRIPTIVE REPORT

Mathematical Model of Infiltration

Model Description

Model Simulations

Field and Laboratory Experiments

Field Studies

Laboratory Studies

CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE STUDY

REFERENCES

Page i

1

1

23

25

3

3

3

6

2

2 iv v

1 iii

LIST OF FIGURES

Figure

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

Cross Section of Soil Profile

Diagram of Soil Box

Rainfall Distribution Under Rainfall Simulator

Arrangement of Soil Boxes

Schematic of Dual Source System

Typical Packing Density Distribution for Oven Dried Soil

.

Typical Saturation Profiles Before and After Two

Week Drying Out Cycle

Infiltration Capacity Curve for First Laboratory

Infiltration Test with Oven Dry Soil

Infiltration Capacity Curve for Sixth Laboratory

Infiltration Test with Initial Water Content of Thirty Percent Saturation

Infiltration Capacity Curve for Third Laboratory

Infiltration Test with Initial Water Content of Fifty Percent Saturation

Infiltration Capacity Curve for Field Infiltration

Tests with Initial Water Content Between Forty and Sixty Percent Saturation

Saturation Profiles for Laboratory Soil with

Initial Water Content of Thirty Percent Saturation

Page

4

8

9

10

14

15

17

19

20

21

22

24 iv

LIST OF TABLES

Table

1.

2.

3.

Soil Tension, Saturation and Relative Conductivity.

.

Single Source Gamma Equations

Dual Source Gamma Equations

.

Page

5

11

13 v

INTRODUCTION

Hydrologists are continually required to estimate runoff from ungauged watersheds.

Even when the watershed is gauged, estimates of runoff are needed for extreme events such as floods.

An important factor in runoff estimation is the infiltration rate.

The infiltration rate determines what portion of the rainfall appears as runoff or what is often referred to as rainfall excess.

Runoff usually occurs first as overland flow which then feeds the stream channel network and ultimately appears as the total runoff at the lower end of the watershed.

For this study, only the infiltration characteristics of overland flow areas were examined. Overland flow areas are defined for this study as those portions of a watershed where interception, evapotranspiration, saturated hydraulic conductivity, as well as rainfall impaction and inwash are the controlling factors of infiltration.

Many studies have shown that when the soil surface is exposed, as is the case of cleared land or on semi -arid watersheds where vegetative cover is lacking, that surface crusting caused by the momentum and impact energy of rainfall can sometimes be the controlling factor in infiltration (1)

(2) (3).

Infiltration has been shown to be over -estimated by as much as a factor of ten if the differences in infiltration characteristics between bare and covered soil are not taken into account. This is one important reason that semi -arid watersheds devoid of vegetation produce excessive flood peaks.

OBJECTIVES

1.

To use an existing mathematical model of infiltration for stuying bare semi -arid watersheds.

To evaluate this model for use in simulating a watershed response, which includes the effects of raindrop impaction, for a given rainfall input.

To use the model to assist in determining which factors are controlling infiltration.

2.

To use laboratory and field rainfall simulator runs to obtain infiltration and runoff data for differing soil moisture and rainfall conditions.

To use various analytical techniques in the laboratory to assist in describing infiltration dynamics of the soil being studied, specifically the contribution of rainfall impaction on infiltration.

3.

To use the laboratory data to evaluate the mathematical model for use in describing soil moisture movement in the field soil profile, and to then use the results of the laboratory studies in conjunction with model simulations to describe factors controlling infiltration in the field.

DESCRIPTIVE REPORT

The procedures used, principal findings and general discussion of results are presented in this section.

A more detailed account of most of this work can be found in the Master's Thesis prepared by J. G. Morse (9).

Mathematical Model of Infiltration

The use of a mathematical model of infiltration for bare semi -arid watersheds was studied.

Several existing mathematical models were evaluated, and a hydraulic model of infiltration developed by Smith (4) was selected as best describing the movement of water into soils.

The model provided an output of infiltration and runoff values as a function of time.

The model also can be applied to layered soils, a feature which could be used to model soil crust effects.

Model Description

The model as developed by Smith is a one -dimensional, finite difference solution to the "Richard's Equation" (4): a(cPSw) at

= K

2.¡Kr3Z) aZ

K = Hydraulic Conductivity

= Capillary Potential

Sw= Percent Saturation aZ e

Kr = Relative Hydraulic Conductivity q

= Porosity

= w

Solution of the equation depends on knowing the functional relationships among p, Kr, and Sw for the particular soil being examined.

This equation is solved for the rainfall -to- ponding upper boundary condition, which provides a sensitive means to describe the infiltration rate as a dependent function of the upper boundary condition.

A nonlinear Crank -Nicolson implicit finite difference scheme is used to develop a solution.

The solution matrix is solved iteratively for each time step, choosing At by considering current soil conditions.

The solution allows for swelling soils, layered soils and nonuniform depth increments, AZ.

Basic assumptions behind this model are that the flow system is one dimensional, which assumes the soil surface to be a plane; capillary suction

I and unsaturated Kr are unique time invariant functions of water content e; Darcy's law is valid for unsaturated flow provided the previous assumption holds; the relations between

Kr and a which can be evaluated in steady state soil tests, are true as well for a dynamic or unsteady flow situation

(4); and air entrapment in the soil column is negligible.

Two forms of the Smith model were examined, the INFLO 3 and INFIL 5 programs.

The INFLO 3 model combines the infiltration solution with a kinematic wave approximation to equations of unsteady overland flow on cascaded planes.

The INFIL 5 model contains just the infiltration solution, with no provision for routing the surface flow.

Due to the small size of the laboratory and field plots used, the INFIL 5 model was found to be more convenient for use in this study.

2.

Model Simulations

Applying this model to the soil profiles investigated proved to be a relatively straight forward procedure.

Basic hydraulic properties of the soil to be investigated, rainfall characteristics, and soil depth increments to be used made up the input data for the program.

Unsaturated characteristics for i,, Kr and Sw for the Page Ranch, Whitehouse soil investigated were obtained from work done by Dutt and McCreary of the Deaprtment of Soils, Water, and

Engineering of the University of Arizona (5).

In modeling the laboratory experimental arrangement, a uniform soil profile was assumed.

The saturated hydraulic conductivity as measured for the reconstructed laboratory soil profiles was used.

Starting from the soil surface and going down, the profile was divided into AZ increments as follows: ten .25 cm, ten .5cm, ten 1.0cm, and nine 2.0cm.

The smaller steps near the soil surface provided a smoother solution at the boundary, while increasing the step size going down the profile improved the efficiency of the prgram.

In simulating the laboratory arrangement it was unnecessary to model a special surface layer with a lower hydraulic conductivity in order to account for possible soil crust formation.

Using the basic soil properties described above, the computer simulation yielded results very close to the experimental data for both the infiltration values and the saturation profiles on the bare soils in the laboratory.

In modeling the field soil profile the upper two layers shown in Figure

(1) were used.

The soil tension and corresponding relative saturations used are listed in Table (1).

Saturated hydraulic conductivities used are shown in

Figure (1).

lation.

The AZ increments were the same pattern as used in the lab simu-

As in the laboratory simulations it was unnecessary to model a special surface layer with a lower hydraulic conductivity in order to account for possible soil crust effects due to rainfall impaction.

Using the basic hydraulic properties for the field profile the computer simulation produced an infiltration curve which closely approximated the curve obtained in the field for the bare test plot.

However it was necessary to increase the saturated conductivity from 0.009 cm /hr to 0.36 cm /hr to simulate a grass covered plot.

This is an increase of 40 times.

Field and Laboratory Experiments

In both field and laboratory studies the rota -disk rainfall simulator was utilized (6).

This type of simulator was developed at the WRRC after earlier work studying crusting with a Purdue simulator (

10 ) indicated the importance of impact velocities and drop size.

This device provides impact velocities and drop size distributions closely approximating natural rainfall.

Momentum and kinetic energy of drops are also similar to natural rainfall, and the intensity can be varied over a wide range.

In both studies the infiltration rate was obtained indirectly by measuring runoff and subtracting it from the rainfall.

Erroneous runoff data or rainfall simulator calibration can be a source of significant error in infiltration data.

Field Studies

Over a period of several years, rainfall simulator runs were made on experimental plots at Page Ranch, northeast of Tucson, Arizona.

There were ten plots, each was 1.50 x 1.50 meters on about a one percent slope.

Eight runs were made on each plot.

The amount of grass cover on the plots varied

3.

/ /

TABLE 1

Soil Tension, Saturation and

Relative Conductivity

+.000313

0.0

-3.400

-4.000

-5.000

-7.100

-10.00

-15.80

-19.90

-25.10

-31.60

-56.2

-100.0

-177.8

-.000313

-.04652

-.12647

-.2085

-.3438

-1.0008

-1.3995

-1.699

-1.999

-2.200

-2.400

-2.540

-2.600

-2.800

-3.000

-316.2

-562.3

-1000.0

-1778.3

-3162.3

-5623.3

-10000.0

Soil Tension: 1P

(cm)

Saturation: Sw (fraction)

Soil Profile

(0 -8.5 cm)

Kr

Sw

1.0001

1.0

.9999

.9980

.9924

.990

.985

.969

.963

.957

.951

.947

.944

.942

.938

.929

.920

.904

.883

.856

.814

.776

.727

.704

.681

.660

.608

.560

.517

.476

.439

.405

.373

.344

.317

.292

1.0

1.0

.999

.997

.995

.994

.992

.900

.780

.650

.581

.551

.521

.491

.470

.300

.250

.200

.120

.055

.021

.015

.0053

.0031

.0018

.0011

.0003

.00008

.00002

.000006

.0000016

.0000004

.0000001

.00000003

.000000003

.0000000002

-2.60

-2.80

-3.00

-3.40

-3.80

-4.00

-5.00

-10.0

-17.8

-31.6

-56.2

-100.0

-177.8

+.004

0.0

-.004

-.253

-1.00

-1.50

-1.60

-1.70

-1.80

-1.90

-2.00

-2.20

-2.40

-316.2

-562.3

-1000.0

-1778.3

-3162.3

-5623.4

-10000.0

-17782.0

Relative Conductivity: Kr (dimensionless)

Saturated Conductivity: Ks (cm /hr)

Soil Profile

(8.5 -15 cm)

Sw

1.0001

1.000

.9999

.999

.997

.993

.992

.989

.988

.983

.980

.975

.970

.966

.963

.958

.951

.710

.681

.653

.626

.600

.576

.552

.529

.508

.943

.938

.920

.876

.834

.805

.772

.740

Kr

1.0

1.0

.999

.995

.980

.970

.940

.900

.820

.720

.640

.530

.430

.360

.305

.260

.200

.155

.140

.084

.018

.005

.0014

.0004

.00011

.00003

.000008

.0000025

.00000066

.00000013

.000000051

.000000014

.000000004

.000000001

Ks = .009 CM/HR Ks = .00014 CM/HR

5.

from zero to almost fully covered.

For a given plot the amount of grass cover and debris present varied significantly over the period of time the runs were made.

As part of a concurrent experiment some of the plots were treated with salt to test its effect on infiltration.

One of the plots was carefully cleared between simulator runs to test differences in infiltration rates due to clearing.

These tests showed a 10 -fold decrease in infiltration when the protective vegetation was removed.

To conduct these rainfall simulation runs, a metal frame 1.50 x 1.50 meters was used to form the boundary for the plots and to provide a runoff collecting trough.

A narrow ditch was dug around the plot and the bottom half of the frame fitted into it.

Care had to be taken to assure that no water leaked out the sides or under the collecting trough of the frame.

Despite careful procedures some error in the runoff data was experienced due to improper sealing of the frame.

Water for the rainfall simulator contained approximately 100 to 200 ppm of dissolved solids which may have been a source of error.

To calibrate the rainfall simulator, plastic was placed over a plot and

100% of the input rainfall collected as runoff.

For both the calibration and infiltration runs, the simulator was leveled and operated at the same pressure and height above the plot.

On a few of the runs errors in estimating the input rainfall may have been as much as 5 to 10 percent.

Fluctuations in the portable power source, variation in the pressure, and difficulties with the nozzle accounted for most of these problems.

The average value for the input rainfall for the field infiltrometer runs was 4.27 cm /hr.

During the field tests, excessive ponding of water on some of the plots occurred due to small depressions in the test plot or entrapment by grass clumps.

Because the infiltration rate was calculated from the runoff rate, the ponded water was in effect included as part of the infiltration rate.

Although the water would eventually either infiltrate or evaporate, inclusion of this water as part of the infiltration rate for the sixty minute run was a significant source of error.

Laboratory Studies

The overall objective of the laboratory studies was to quantify Page Ranch,

Whitehouse soil infiltration characteristics under controlled conditions.

To accomplish this, experiments designed to measure various soil parameters were conducted.

As mentioned in the objectives an attempt to measure soil crust formation was made.

The procedure used involved a gamma ray attenuation device.

Besides measuring possible bulk density changes due to rainfall impaction, the gamma ray attenuation method was used to measure water content changes in the soil.

Measurements of changes in saturated hydraulic conductivities due to surface compaction were made using the soil boxes as permeameters.

Infiltration rates for different initial moisture conditions and rainfall input were also measured.

To conduct the experiments, soil samples were obtained from the upper portion of the profile at Page Ranch.

The soil was then oven dried and packed into specially constructed steel boxes.

The boxes were 9 cm wide, 25 cm long, and 17 cm high.

A slot for collecting the runoff was placed at one end of each box.

A coarse sand filter was placed in the bottom of the boxes to prevent air entrapment and permit a direct measurement of the saturated hydraulic conductivity in each box.

The steel boxes were sufficiently rigid to have a minimum of bulging when packed with soil, yet the sides were thin enough to permit splash between adjacent boxes.

6.

In use six boxes were placed side by side with an additional border of boxes around them.

These boxes provided additional splash interaction to more closely approximate field conditions.

A diagram of the boxes, their location within the rainfall simulator test area and their arrangement are shown in

Figures (2), (3), and (4),respectively.

The soil boxes were placed under the rainfall simulator in the area of most uniform rainfall distribution.

Although the average intensity of rainfall over the simulator test area was 4.27 cm /hr, there was considerable variation in the intensity from one location to another.

Figure (3) illustrates the rainfall intensities obtained in the laboratory distribution test.

This type of test was conducted by placing containers at selected grid points under the simulator and then measuring the amount of precipitation collected at each point.

As measured in empty soil boxes the average rainfall intensity for the area selected was 3.68 cm /hr ±.04

cm /hr.

Between each infiltrometer run this input rainfall value was checked by placing empty soil boxes in place of the six experimental soil filled boxes, and then measuring the amount of water collected in each box after a sixty minute run.

Two infiltrometer runs were conducted using rainfall intensities of both

3.68 cm /hr and 1.47 cm /hr.

Calibration procedures for the 1.47 cm /hr were the same as for the 3.68 cm /hr.

The runs were made using each intensity for thirty minutes, with five minutes in between for changing the disk, for a total of 65 minutes per run.

Rainfall intensity produced by the rota -disk rainfall simulator is controlled by the size of opening in the disk which rotates under the nozzle.

The order of application of the intensities was reversed from one run to the next.

The purpose of these two runs was to observe the interaction of varied intensities on infiltration rates.

The rest of the infiltrometer runs were conducted using the 3.68 cm /hr intensity for 60 minutes.

In order to make the density and moisture measurements of the soil, a matching set of holes were drilled on each side of the boxes.

The holes helped to minimize attenuation losses and variations due to the steel sides.

The holes were 1.1 cm in diameter, and the box was fiberglassed on the inside to cover the holes.

Losses through fiberglassing were negligible compared to the steel.

In addition to minimizing gamma ray attenuation losses the portholes enabled one to observe the movement of the wetting front.

This feature provided a check on measurements made with the gamma attenuation device.

The 1.1 cm diameter porthole was selected to enable both the Cesium and Americium rays to pass unobstructed through the steel sides.

Americium is collimated in a 1.0 cm diameter beam and Cesium is collimated in a0.33 cm diameter beam.

As can be seen in Figure (2), the holes were spaced .8, 2.2, 3.6, 5.0, 8.0, 11.5, and 15.0 cm from the top of the box.

This feature enabled packing density and moisture profiles of the boxes to be made prior to, during and after the infiltrometer runs.

Attenuation of a beam of gamma rays, as used in this study, provides a non -destructive method for making rapid and frequent measurement of water content as a function of time.

If a collimated beam is allowed to penetrate a material, the number of rays passing through a given thickness depends on the density of the material.

Beer's Law is the basic relationship for measurement of gamma ray attenuation.

The incident radiation decreases as it passes through material in such a way that, for small thicknesses, the change in intensity is proportional to the thickness and to the initial intensity.

Table (2) lists the relevant equations when using a monoenergetic source gamma attenuation technique.

7.

FIGURE 3

4.56

Rainfall Distribution Under

Rainfall Simulator

(cm)

I BaCK 1

Area of Field Test

Plot Frame

195.0cm

3.07

2.91

3.32

3.40

3.40

3.18

2.97

4:60

1

2978 3:11 3,78 4.42

3.96

3.69

3.30

3.12

1

2.91

3.60

3.78

4.42

4.99

4.29

3.69

3.11

J 3.18

4:02 4.37

1

3.05

.11

3.9 8

5.05

5.14

5.24

5.14

4.85

4.75

4.65

3.88

4.02

199.0cm

3.11

I

291 311

4.3 7

.11111M

456

4.56

4.17 I 3.69

3.01

.

3.07

3.88

12 81

3 11 3.59

3.88

3.88

3.591

3.20

I

-2 .8-3. --

2791-1-3:11

.

.

- 3e.11- .11--

-3;112.52

.

4.40

3.88

4.21

3.69

.

3.69

.

3.01

.

2.43

Location of

Laboratory

Soil Boxes

I FRONT I

SIMULATOR

PERIMETER

9.

TABLE 2

SINGLE SOURCE GAMMA EQUATIONS

Beer's Law:

-oI = p *u *Io *oX p = The Mass Absorption Coefficient

(cm2 /gm) p = Density (gm /cm3)

X = Thickness (cm) oI = Change in Intensity of Incident Beam Io after penetrating material of thickness AX

Integration yields:

I

= Io *e

-1PX

For Use in Determining Soil Water Content:

I

= Io *(exp(- (psp +pwe) *X -pcXc)

X = Thickness of Soil Sample ps = Mass absorption coefficient of soil u

Mass absorption coefficient of water in soil p = Density of soil e = Soil moisture content pc = Coefficient of absorption for soil container

Xc = Thickness of container walls

To correct observed count rate for resolving time error:

I

= R /(I -TR)

I

= True count rate (cpm)

R = Observed count rate (cpm)

T = Resolving time

Resolving time T for the gamma unit used in this experiment was determined to be 2micro seconds

In addition to the monoenergetic or single source system a dual source technique was attempted for this study.

In theory the advantage of the dual source technique is the ability to make a simultaneous measurement of both density and water content.

In the single source system density must be assumed to remain constant in order to solve for the moisture content.

For this study

Cesium 137 was used in the monoenergetic system and Cesium 137 and Americium

214 were used in the dual- energetic system.

Any two gamma ray sources with different energies such that their mass absorption coefficient are sufficiently different could be used; however, when factors such as half -life, cost, self absorption of low energy rays, shielding of high energy rays, and compatibility with available electronic equipment are considered Am 214, and Cs 137 are logical sources (7).

The equations for obtaining the simultaneous solution of density and water content are listed in Table (3).

In both methods corrections to the measured count rates must be made before a solution of the density or moisture content can be made.

Both methods require a correction for resolving time error.

The dual source method requires additional corrections for Compton scattering and coincidence and interference losses.

For the dual source technique the correction equations described by

R.

S. Mansell et al.(8) were used.

Tables (2) and (3) list the correction equations usedin each method and the value of the coefficients used.

The source holder for gamma ray equipment was designed to minimize

Compton's scattering and self absorption difficulties.

The Cesium and Americium sources were mounted coaxially but were independantly removable for single source operation.

Figure (5) is a schematic diagram of the gamma unit and it's associated electronic equipment.

Calibration of the gamma unit was required prior to using it in the infiltrometer experiments.

In addition to determing the various count correction parameters, mass absorption coefficients for soil and water for both the Cs 137 and Am 214 sources had to be measured.

The use of these attenuation coefficients in finding the values of density and moisture content is shown in Tables (2) and (3).

To make measurements of these coefficients, aluminum cylinders of different axial length were filled with either water or dry soil and the attenuation as a function of thickness obtained.

Mass absorption coefficients determined by this method are as follows: water = .19849

Am uwater

Cs

= .08654

soil

Am

=

.2930

soil

Cs

= .0775

As mentioned earlier soil was packed into the experimental soil boxes.

A packing density close to 1.81 gms /cm3 was aimed for.

This is the bulk density of the upper portion of the Page Ranch soil profile.

After packing, the boxes were checked using the gamma unit.

Figure (6) illustrates a typical bulk density profile of one of the boxes.

At this stage in the research project a serious limitation to the dual source technique was discovered.

When checking the bulk density profiles of the soil boxes the density values obtained from the Cesium attenuation were not always identical to the values obtained

12.

TABLE 3

DUAL SOURCE GAMMA EQUATIONS

Dual Source Equations:

I'/Io' = expí(

-uSAmp

S

+u4JAme

) X )

I " /Iö

= exp((-ìSCspS +iWCse).X)

X = Thickness of sample (cm)

PS = Density of Soil

(gm /cm3)

I'

= Attenuated Am gamma ray intensity (counts /min.)

I'

= Incident Am gamma ray intensity

"

I" = Attenuated Cs gamma ray intensity

I" = Incident Cs gamma ray intensity e = Water content (gm /cm3) uWCs =

Cesium mass absorption coefficient for water uSCs =

Cesium mass absorption coefficient for soil uWAm =

Americium mass absorption coefficient for water uSAm =

Americium mass absorption coefficient for soil

When above equations are solved simultaneously:

PS

uWAm ln (I/Io)-uWCs ln

(I'/In)

WCs uSAm X - uSCs uWAm X e = uSAm in

(I/Io)-uSCs ln uWAm uSCs X- uSAm

WCs

X

(

/I o)

To correct for coincidence and interference losses, and Compton's scattering the following equations are used:

I' =

((1-gTI")/2T){1-COS(sin-1(2(TR'-fTR")1/2))}

1-gTI"

I" =

2T fl- COS(sin- 1(4TR ")2)} g = coincidence correction parameter = 3.3

f = Compton scattering correction parameter = .085

13.

NaI (TI)

D6TCTOR

LSAO

ThCTOR ii.014)ER

.661u.) SOURCt riauJER

I "

Collimator

II- 4-

4c-

4-

4- 4-1A

0E.7.47.:1-4t-g7

SOIL

BOX

Collimators

Gamma Rays

(30-800 kV)

.

NA-10 AC-22

a

NA-22 ariable haping

mear

Amp

Pulse deignt

Analyser

AGC

Amp

AS-3U

Scaler

L r"

Am

Counts

AS-30

Scaler

I ca

Cs

Counts

T i

m

N

T

-

2

7

AV425 kiin

Volt.

Supp.

8

5

N

A

_ r

BI

&

Po

Su,

FIGURE 5

SCHEMATIC OF DUAL SOURCE SYSTEM

14.

1.c80

.

1.80

.

1.77

'

1.81

1.64

1.82

1.81

.

1.83

,

1.78

.

1.60

1.82

1

80

1.81

-

SI1).6 Virw

179

,

_

1.80

1.75

1.79

,

1.78

.

1.78

1.61

FIGURE 6

TYPICAL PACKING DENSITY DISTRIBUTION

FOR OVEN DRIED SOIL

(gm /cni3)

15.

from Americium attenuation.

Since Am 214 is collimated into a beam 1.0 cm in diameter and Cs 137 is collimated into a beam .33 cm in diameter, this discrepancy may have in part been due to the Americium beam sampling a much larger slice of the soil profile.

Another cause of this discrepancy may have been the count rate error which for Am 214 was ( +1.8 %) and for Cs 137 was (+ .4 %).

As a result of these differences between the Cesium and Americium density profiles the simultaneous solution described in Table (3) tended to produce unrealistic values.

This had the effect of making the dual source technique unreliable for use in this study.

In addition, a boundary effect problem was detected near the surface of the soil profile which tended to make the Cesium and Americium measurements diverge even more.

Due to these difficulties the use of the dual source technique to directly measure near surface compaction due to rainfall was determined not to be feasible.

Despite this difficulty the remainder of the experiment was conducted successfully making use of the single source technique.

Bulk density values of the dry packed soil were assumed to remain constant and the moisture profiles for the infiltrometer runs calculated using the equations listed in Table (2).

A total of six infiltrometer runs were made in the laboratory.

The first and last run were conducted by removing each of the six experimental soil boxes from under the rainfall simulator at different times and measuring the soil moisture profile.

This procedure permitted the measurement of soil moisture movement as a function of time.

In addition at the completion of the first run the saturated hydraulic conductivities of the soil profile in each box was measured.

To do this a lid with a water column attached was placed over each box.

Constant head permeameter techniques were then used to obtain the hydraulic conductivity measured directly in the soil boxes.

This procedure was done to measure changes in the saturated hydraulic conductivities of the freshly packed soil as a function of time spent under the rainfall simulator.

No noticeable change in saturated conductivities as a result of rainfall impaction could be detected between the boxes.

Although this procedure could not determine if the uppermost portion of the profile was affected by rainfall impaction, it did indicate that the overall profile of Page Ranch soil as reconstructed in the lab showed no significant change in saturated hydraulic properties due to rainfall impaction.

There was considerable variation in saturated hydraulic conductivity between boxes making interpretation of these results difficult.

An average value of

0.36 cm /hr was measured for the laboratory soil.

The four other infiltrometer runs were conducted by leaving all six boxes under the simulator for the full sixty minutes.

Wetting profiles were obtained before and after each run.

In all six infiltrometer runs the unsaturated wetting front moved down the soil profile about eight centimeters.

As could be expected, initial moisture conditions controlled to some extent the movement of the unsaturated front into soil profile.

To "dry out" the soil boxes between runs they were placed outside the lab exposed to the summer sun for a period of about two weeks.

The moisture profile in the boxes was periodically checked and the boxes broughtin for another run when the desired moisture conditions were attained.

Figure (7) shows the typical wet and dry profiles observed during the laboratory experiments.

Even though the boxes were exposed to and heated by the sun on all sides and air was permitted to enter through the bottom of the profile, moisture movement out of the profile through the bare exposed surface was very slow.

As can be seen in Figure (7) a significant reduction in moisture content occurred only in the upper portion of the profile, and even this reduction after two weeks of exposure to the desert sun didn't produce a "dry" upper profile.

To obtain the 30% relative saturation desired

16.

for the last infiltrometer run it was necessary to place the boxes in a drying oven for three days in addition to the two weeks exposure to the sun.

To measure infiltration in the laboratory the basic procedure was similar to that used in the field.

For the lab the runoff from each box was measured separately in graduated cylinders and the amount collected checked at five minute intervals to obtain the increase in runoff as a function of time.

By collecting the runoff separately from each box, difficulties such as clogging of the runoff slot could be detected and possible errors in the runoff /infiltration calculations minimized.

To further improve the reliability of the results care was taken to prevent splash and rainfall from getting directly into either the runoff slot or the graduated cylinders.

As mentioned earlier, the boxes were located under the simulator in an area with the most uniform rainfall distribution.

Infiltration rates calculated from the runoff data varied somewhat between boxes.

This result was not too surprising considering the variation in hydraulic properties from one box to the next due to packing differences and tha variation in rainfall distribution.

In spite of these small variations the overall results of the laboratory tests yielded results which were consistent.

All except the first run produced terminal infiltration rates of about 1.0 cm /hr for a rainfall input of 3.68 cm /hr.

was higher than the average rate obtained in the field.

This infiltration rate

In the first run oven dried soil with basically a zero initial saturation was used.

A terminal infiltration rate was not reached at the end of the sixty minute run.

Considering the very steep suction gradient that would develop under these conditions, the much slower decrease in the infiltration rate observed on the first run was not unusual.

Figure (8) shows the infiltration curve obtained from the first laboratory rainfall simulator run.

Figures (9) and (10) show the experimental and simulated results for some of the other runs made in the lab.

As in the field situation the time required for the terminal infiltration to be reached could be seen to be a function of initial moisture conditions and grass cover.

The field infiltration tests were also simulated.

In Figure 11 the simulated and measured results from the field infiltration tests are shown.

When using the low hydraulic conductivity value of 0.009 cm /hr for the upper horizon, results of the model simulation very closely approximated the measured infiltration capacity curve obtained for the bare test plots.

When using the high conductivity value of 0.36 cm /hr for the All horizon, the results of the model simulation approximate the infiltration rates observed on the grass plots.

Both the laboratory soil and the All horizon of the grass plot were by coincidence modeled using a saturated conductivity of 0.36 cm /hr.

It is possible to adjust the output of the Smith model by introducing a surface layer (in this case 3 cm) with an appropriate value of saturated conductivity (0.36) to simulate a grass covered surface.

In a similar manner, if needed, a surface layer with lower value of saturated conductivity could be inserted to simulate a bare surface.

This approach requires sufficient data for calibration.

This data could come from use of a realistic rainfall simulator as used in this study or hydrograph analysis from a unit subwatershed.

Once calibrated the model could be used with caution to extend the data base in any given watershed.

18.

4.5

4.0

3.5

Input Rainfall = 3.68 cm /hr s

1

\

\ 3.0

o

2.5

U

.

ó

H

4..)

í-+ ir-1

.H

H

2.0 _.

1.5

1.0

\

\

`

\

.,

',ft..

.

-

0.5 -

0.0

0 5

10 15 t

20 25

30

35

40 45 50 55

Time from Start of Rainfall Simulator (min)

60 65

Figure 8.

Infiltration Capacity Curve for First Laboratory Infiltration

Test with Oven Dry Soil. -- Five soil boxes used for first data point, boxes removed at different times during test.

Last data point based on one box.

19.

4.5

4.0

3.5

3.0

2.5

2.0x i

Input Rainfall = 3.68 cm /hr

1

1

1 x h

1\

1\I

\

1.5

X t

Experimentally Measured Data

\ k

1

`x u

Computer Simulation Data

0.5

0.0

10 15

20 25

30 35 40 45

1

1

50

Time from Start of Rainfall Simulator (min)

!

55

!

60 t

65

Figure

9.

Infiltration Capacity Curve for Sixth Laboratory Infiltration

Test with Initial Water Content of Thirty Percent Saturation.

-- Six soil boxes used for first data point.

Boxes removed at different times during test.

Last data point based on two boxes.

20.

4.5

4.0

Input Rainfall = 3.68 cm /hr

2.5

I,

1.0

*a% X +.3.

~X- x,

Experimentally Measured Data

-

-

_k

... ...

r

.

7C

Computer Simulation Data

0.5

0.0

0 5

10 15

20 25

30 35

40

45

I

50

I

55

Time from Start of Rainfall Simulator (min)

60 f

65

Figure 10.

Infiltration Capacity Curve for Third Laboratory Infiltration

Test with Initial Water Content of Fifty Percent Saturation.

-- Infiltration data averaged over six soil boxes.

21.

4.5

Input Rainfall = 4.27 cm /hr

.111, _ OIM1

MOO

4.0

3. 5 ...,

X

1

1

1

1

1

3.0 -

1

1

\

2.5-- X

1

1

1

2.0--

1

X

1

1

`

,

1. 5

1 l.0__.,

\

X

1 i t

`

\

,

0 . 5 ....

X

Measured values x Simulated values

Curve for Simulation using High

Conductivity Value

41.1.

_ -

Curve for Grass -Covered

Plots

.....

am.

s ...

... .

X- -X ---X

Curves for Bare Soil and Simulation Using

Low Conductivity Value

0.0 ---i

0 t

5

10 15

I

20 25

30

I

35

é

40 45 f I

50

Time from Start of Rainfall Simulator (min) t

55

í

60 65

Figure 11.

Infiltration Capacity Curve for Field Infiltration Tests with

Initial Water Content Between Forty and Sixty Percent

Saturation. -- Averaged over eight tests on ten plots.

22.

The model also simulated the position of the wetting front as indicated in Figure 12.

These soil moisture profiles were obtained using the gamma probe.

These findings helped to increase the confidence level in using the

Smith model.

CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE STUDY

A model was found that can be modified to account for different surface conditions.

It was possible to simulate both the laboratory results and a bare soil field plot using the hydraulic characteristics pressure, water content versus hydraulic conductivity as measured in the laboratory.

An additional soil layer with high saturated hydraulic conductivity was superimposed on the soil system in order to simulate the infiltration of grass covered plots.

In a similar manner it should be possible to insert a surface layer with a lower value of saturated conductivity to simulate an essentially bare surface with a surface crust.

Unfortunately the funding available for this research did not permit further application of this model to other soil types.

This application needs to be made.

In addition, a sensitivity analysis needs to be made particularly at low values of hydraulic conductivity.

A need for this is evidenced by the fact that the model required a change of 4000% in the saturated conductivity in order to effect a 1000% change in the terminal infiltration rate.

Perhaps a relatively wide range of saturated conductivities could have been used in the lower ranges and still successfully simulated the laboratory and bare field plots.

This aspects needs to be investigated in the future.

In conducting the laboratory studies both single and dual source gamma ray attenuation techniques for measuring bulk density and soil moisture were tried.

Serious difficulties developed in using the dual source technique.

As a result the single source technique was used to obtain the bulk densities and soil moisture profiles.

Without the dual source gamma technique it was not possible to measure compaction of the surface layer due to rainfall impact.

Improvements which could be made to improve the dual source capability of the equipment utilized in this study are discussed in more detail in the thesis written as a part of this project (9).

23.

Percent Saturation

0.00

0. 50

-,

1.00 -

1.50'

2.00"

2.50 ,

3.00 -

3.50 -

4.00 -

4.50 -

5.00 -

5.50-

6.00 -

0

40

1

50

1

60 t

70 f

80

1

90

1

10

1

20 f

30

1

(

(

Initial

Saturation ,¡ r et

I i

..-

..-

..-°-

.

i

5 min.

_

x--'

'

.r

1 i

.

i

. / I

//

Ii

/

/

Il

/

X X.

/

1 il

!/

1

1

If

!C

(<

4

I

'

/

/

1( x

--'

20 min.

..

4.

//

40 min.

I

60 min.,/

/

X

/

/

/ l/ i

I

100

!

/

6.50 t

7.00 -

7.50 -

Measured saturation values at the various times and depths

8.00 -

8.50 ~

X Simulated saturation values at various times and depths

9.00 -

9.50

-

Figure

12.

Saturation Profiles for Laboratory Soil with Initial Water

Content of Thirty Percent Saturation.

24.

REFERENCES

1.

McIntyre, D. S., "Permeability Measurements of Soil Crusts Formed by

Raindrop Impact," Soil Science 85, (1958), pp. 185 -189.

2.

Moldenhauer, W. C., and D. C. Long, "Influence of Rainfall Energy on Soil Loss and Infiltration Rates:

I.

Effect Over A Range of

Texture," Soil Science Soc. Amer. Proc., 28, (1964), pp. 813 -817.

3.

Seginer, Ido, and J. Morin, "The Effect of Drop Impact on the

Infiltration Capacity of Bare Soils," State of Israel, Ministry of

Agriculture, Soil Conservation and Drainage Division, Research

Report No. 26, 1969.

4.

Smith, R. E., "Mathematical Simulation of Infiltrating Watersheds,"

Ph.D. Dissertation, Colorado State University, Fort Collins, Colorado,

1970.

5.

Dutt, G. R., with Hanks, J., "Predicting Nitrogen Transformations and Osmotic Potentials in Warm Desert Soils."

Research Memorandum,

RM 72 -39, Desert Biome, U. S. International Biological Program,

March 1972.

6.

Morin, J., C. B. Cluff, with W. R. Powers, "Realistic Rainfall

Simulation for Field Investigation," WRRC, University of Arizona,

Paper Presented at the Fifty -first Annual Meeting of the AGU,

Washington, D. C., April 24, 1970.

7.

Corey, J. C., S.

F. Peterson, and M. A. Wakat, "Measurement of

Attenuation of Cs 137 and Am 241 Gamma Rays for Soil Density and

Water Concent Determinations," Soil Science Soc. Ame. Proc.,

Vol. 35, pp. 215 -218, 1971.

8.

Mansell, R. C., L. C. Hammond and R. M. McCurdy, "Coincidence and

Interference Corrections for Dual- Energy Gamma Ray Measurements of Soil and Water Content," Soil Science Soc. Amer. Proc.,

Vol. 37, pp. 500 -504, 1973.

9.

10.

Morse, J. G., "Rainfall Infiltration Characteristics for a Semi -Arid

Watershed Soil, "Master of Science Thesis, Department of Hydrology and

Water Resources, University of Arizona.

Bertrand, A. R., and J.

F. Parr, "Design and Operation of the Purdue

Sprinkling Infiltrometer," Purdue Univ. Agric. Expt. Sta. Res. Bull.

723, 15 p., 1961.

25.

Was this manual useful for you? yes no
Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Download PDF

advertisement