Development and testing of a portable airpermeater for measuring compacted surfaces

Item Type text; Thesis-Reproduction (electronic)

Authors Gale, Robert David, 1941-

Publisher The University of Arizona.

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DEVELOPMENT AND TESTING OF A PORTABLE AIR PERMEAMETER FOR MEASURING COMPACTED SURFACES

byRobert David Gale

A Thesis Subroitted to the Faculty of theDEPARTMENT OF WATERSHED MANAGEMENT

In Partial Fulfillment of the. Requirements For the Degree ofMASTER OF SCIENCE

In the Graduate CollegeTHE UNIVERSITY OF ARIZONA

1.9 6 9

STATEMENT BY AUTHOR

This thesis has been submitted•in partial fulfillment of re­quirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library. '

Brief quotations from this thesis are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his judg­ment the proposed use of the material is in the interests of scholar­ship. In all other- instances, however, permission must be obtained ■ from the author.

APPROVAL BY THESIS DIRECTOR This thesis has been approved on the date shown below;

/ / JOHN L. THAMES 'issoc. Professor, Watershed Mngt.

Date

ACKNOWLEDGMENTS

I would like to express my sincere appreciation to Dr. John L. Thames for his guidance and assistance throughout my thesis pro­gram. I wish also to thank Dr. Malcolm J. Zwolinski for his help in the organization and presentation of this thesis and for his guidance- during my graduate program. Dr. Alan B. Humphrey and Dr. Phil Ogden offered help in the statistical analysis portion of this thesis and Dr. Daniel D. Evans lent knowledge and assistance toward the devel­opment of the air permeameter. To these men also goes my thanks.

I would like to acknowledge the U. S. Forest Service's cooper­ation in extending the use of the Bozeman Creek Watershed and Mr. Leon Logan for his interest and encouragement,

My appreciation also goes to Dr. John H. Ehrenreich who made my graduate program and thesis possible. And finally special thanks to my wife, Nancy5 for her understanding and encouragement through my graduate years and for her typing and reading-this thesis.

TABLE OF CONTENTS

PageLIST OF TABLES © © © © © © © © © © © © © © © © © c o e o o o V3.LIST OF ILLUSTRATIONS . . , . © » © , © © . , © © © © © © © viiABSTRACT © © © © © © © © © © © © © © © © © © © © © © • © © © © ilx

INTRODUCTION © © © © © © © © © © © © « © © © © © © © © © © © 1LITERATURE REVIEW © © © © © © © . © © © © © © © © © © © © 3DEVELOPMENT OF THE AIR PERMEAMETER © © © © © © © © © © © © © 7

Ls»Lox*s, coxy S oxici’ © © © © © © © © « © © © ©.©•© © © © © 7Laboratory Study No© I © © © © © © © © © ! © © © © 9Laboratory Study No© 2 © ©. © © © © © .© © © © © © © 11-Discussion of Laboratory Studies © © * . © © © © © 111

Construction of the Permesmeter © © © © © © © © © © © © 15Air Permeability Equation © © © © . © © © © © © , * * . 20

DESCRIPTION 0F STUDY AREA , . . * ......... 22Location and History © © o © © © © © © © * © © © # . © 22Geology and Soils © © © © © © © © © © © © © © © © © o © 22Climate © © © « © © © © © © © © © © © © © © © © © o © © 2

METHODS .AND PROCEDURES OP THE FIELD STUDY © * * . © . . © © 2?Air Permeability © © © © © © * © © © © © © © © © © © © 27Bulk Density © * © © © © © © © © © © © - © © © © © © © © 2SSoil Mois cure © © © © © © © © © © © ■ © © © » © © © © © © 28Site Variables © © © © - © © © o © © © © © © © © © © © © 2 9Soil Cracks « © © ©-» © © © © © © © © © © © © © @ © 0 © 2 9Time Variable © s © © © © © © © © © © © © © © © © © © © 30

■ 1, '

V

TABLE OF CONTENTS— Continued' Page

ANALYSIS AND RESULTS OF FIELD STUDY ' 31Analysxs of Famance © © c . . . . © . © . . © . . . . ® 31Response Simface © © © « © © © © © © « © © © © « . © © © © 33Co-Variance Analysis © © © . © . . © « © © . © © © © © © 3hMultiple Regression Analysis « , . © . . © . « » © © © . 33

DISCUSSION Aim SUMMARY ©'© © © . , © . . © © . © » . © © . © • i}3CONCLUS IONS © © © © © © © © © © © * © © © © © © © © © © © © ©APPENDIX As RES.UI,TS OF PRELIMINARY FIELD TESTS . . . . . . . 18APPENDIX Bs CALIBRATION CURVE 30APPENDIX C; PRECIPITATION DATA © © © . . © © . © © . © . © . 32APPENDIX D: SAMPLE FIELD FORM . 3HAPPENDIX Es ANALYSES OF VARIANCE . . . . . . . . . . . . . . 36APPENDIX F: RESPONSE SURFACE MODELS . © © . . © © . © . . © © 60.APPENDIX Gs CO-VARIANCE ANALYSES . © . . . © © . © . © . © © . 62LITERATURE CITED © © . © © © © . © @ . © © © . * © © . © © ^ 63

LIST OF TABLES

Table1.

2.

>

L

607o8.

9.

3Results in cm /sec of air flow at various pressures on ■ eight laboratory soil testsAnalysis of variance for double split-plot design overtime. This is the basic analysis used in testing thevariables air permeability, bulk density, and soil mois­ture 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . 0 0 0 0 0 0 0 0 0

Order of the variables as they entered the step-wise multi-linear and multi-linear quadratic regressions 0 The first two regressions are for the variables over distance« The second two are for the' variables over time . 0 0 0 0 0Analysis of variance for air permeability . . . . . . . .Analysis of variance for bulk density . . . . . o o . . .Analysis of variance for percent moisture « . . . « . . .Response surface modelsCo-variance analysis with air permeability as Y variable and soil moisture•as X variable . . . . . . . . . . . . .Co-variance analysis with bulk density as Y variable and soil moisture as X variable . . . . . . . . . . . . . . .

0

vl

Page

12

32

39575859 6l

63

6ii

LIST OF ILLUSTRATIONS.

Figure1*

2c

3o

itc

6c7.8c9.

10.

11.12.

13.

• PageApparatus for measuring air permeability in thelaborauory . . . . . . . . . . . . . . . . . . . . . . 8Curves showing the occurrence of turbulent flow athigh pressures and flow rates . . . . . . . . . . . . 10Shows curves with straight line segments indicating non-turbulenu flow . . . . . . . . . . . . . . . . . . 13Soxl contact head @. . . . . . . . . . . . . . . . . 17Photograph showing soil contact head in depressedposition ready for air.permeability reading . . . . . . 18Photograph of portable air permeameter ready for use. . 19Orxentauxon map . . .. . © . . © . * . . . . © ® © © 23Geology of Bozeman Creek Watershed . . . . . . . . . . 2k

Graph of air permeability5 bulk density, soil moisture and soil cracks over time. All site variables have been averaged . . . . . . . . . . . . . . . . . . . . . . . 3 6Graph of air permeability, soil moisture, bulk density and soil cracks over distance. Shaded area represents the percentage of sand in the soil. One inch vertically equals 20 percent sand content. 37A cummnlative graph of use over time . . . . . . . . . 38Diagram of path coefficients showing relationship of dependent variable to independent variables and their interactions. Numbers given are standard partial re­gression coefficients. . . . . . . . . . . . . . . . . h2

Graphed results of preliminary field tests. . . . . . . U9vii

LIST OF ILLUSTRATIONS— Continued

Figure PagelUc Calibration curve for flowmeter. Curve was con­

structed for normal atmospheric pressure and temper­ature conditions at study area . . . . . . . . . . . . 5>1

15. Precipitation measurements for three stations. Mystic.Lake Station was installed July 71 Lower Bozeman Creek, August 5® Bozeman is a permanent station. . . . . . . 5>3

l6. Sample field form . . . . . . . . . . . . . . . . . .

ABSTRACT

. This study concerns the development and testing of an air' per- meameter for measuring the permeability of compacted soil surfaces« Laboratory studies were conducted to determine optimum air flow rates and pressure ranges«, A modification of Darcy’s flow equation for steady state saturated flow was derived for use with the equipment»

The air permeameter developed is a constant flow type appara­tus which uses a compressed air cylinder for its air supply« The instru­ment is designed so it can be carried easily on the operator’s back* A rapid method of sealing the soil surface was devised which allows re­peated measurements at the same point. Measurements with the device were made on a 10-mile stretch of logging road in south central Mon­tana* Several physical soil factors were also measured in an attempt to equate them to air permeability.

Analyses of variance, co-variance* and multiple regression failed to point out any strong correlations, This was apparently due to the great amount of variation in the data and the presence of com­plex interactions between variables.

The air permeameter proved to be very usable under field con- d itions and appears to be capable of measuring a number of physical changes which take place in soil. However* further testing under controlled conditions will be required before it is recommended for field use,

ix

INTRODUCTION

A constant development of new equipment, an improvement of the old, and a diligent analysis of collected data are needed if the pro­cesses and relationships of nature are to be better understood. This is especially true in the.relatively new field of watershed manage­ment. Many pieces of equipment, already developed for other fields and requiring little or no modification, may prove to be of great value to the watershed scientist. The air permeameter is such a tool. This instrument was originally developed by the oil and water wellindustry for the study of subsurface geology. More recently, it has

1been modified to measure the permeability of soils.The primary objectives of this study are; (1) to develop an

air permeameter specifically designed for measuring compacted soil surfacesj (2) to demonstrate the usability of such a permeameter under field conditions; and (3) to attempt to give more meaning to air per­meability measurements . .

In recent years, hundreds of miles of temporary forest roads have been built to aid in transporting logs. The resulting soil com­paction creates a problem of particular interest to the watershed

1. Permeability can be defined as the ability of a medium to'transmit a fluid. .In this study, air was the fluid used.

1

scientist.. The. air permeameter offers a means of describing and evaluating this compaction. What effects does compaction have on the hydrologic properties of a watershed? How and at what rate do changes5 if anytake place? Can they be minimized by a better understanding of the processes involved? Some recent studies by Bethlahmy (1967), Packer and Haupt (1965), Lull (1959), and Packer (196?) have at­tempted to answer these questions.■ However, much work remains to be done. This paper will attempt to further explore some of these areas while demonstrating the usability of the air pemeameter. developed.

LITERATURE REVIEW

The measurement of air permeability, particularly in unsatu­rated soils, is a relatively recent development« In 19U1, Klinken™ berg, in a paper to the American Petroleum Institute, pointed out the value of using permeability as a means of describing the flow charac­teristics of a medium. Up until that time, permeability had been used primarily as an expression of how much fluid could be passed through a medium. A general lack of knowledge existed, and continues to exist, concerning the actual significance of the measurement.

Brooks and Reeve (1959) expressed the need for a better under­standing of the factors affecting permeability and suggested a great­er attempt be made to apply permeability measurements to field pro­blems. They used a ratio of air to water permeability, developed in

X1953 by Reeve as a method of measuring soil, stability, and found soil stability to increase as the permeability ratio approaches, one. The same study suggested that? (l) air permeability varies linearly with increases in soil moisture; (2) an increase in soil moisture has a much greater effect on reducing the air permeability of clay

1. A difference between air and water permeability exists due to a phenomenon known as gas slippage which is greatest in fine tex-- tured soils (Corey, 1957). Gas slippage is thought to result from the inability of a gas to cohere, as liquids do, to pore walls (Collins, 1961).

3\

soils than of loam- soils| and (3) soil moisture lowers air permeabi­lity by blocking air passages, reducing pore size and in some cases changing pore arrangement= .

Aljibury and Evans (1963) advocated using air, rather than water, for determining the permeability of soils since air is less susceptible to entrapment than water. Plugging of pores, a problem created by the foreign matter often present in water, is eliminated| and. air does not disintegrate the structure being measured, parti­cularly at the surface, as water tends to do.

Kirkham (191*70 pointed out that the Darcy Equation

V - . k. (dp/dx) (l)

is applicable to gas. as well as water flow. In the equation, V represents the volume of fluid per unit of time passing through a unit cross-section and perpendicular to the x direction; k represents the permeability of the medium; and dp/dx, the space rate of change of pressure. The assumption must be made that gas compressibility is negligible, since this factor is not accounted for in the equa­tion. This assumption is justified if low pressures (i.e., close to atmospheric) are used.

Kirkham (191*7) was the first to propose a method for determin­ing the air permeability of unsaturated soils. A falling head system with a manometer and air flowmeter was employed. Contact with the soil was made by inserting a tube of known volume. This procedure has two undesirable effects. Insertion of the tube disturbs the soil

and the walls of the tube increase gas slippage» Scheidegger (i960) stated that gas slippage can be nullified if the free path length is zero,

Evans and Kirkham (195>0) conducted further studies using equipment similar to that used by Kirkham (I9lt7) except that a new means of making contact with the soil was adopted, A small glass tube was placed in contact with, and perpendicular to, the soil surface.A layer of wax was then poured around the tube and over the surface to form a 6-inch diameter surface seal. Approximately one-half hour was required to set up and obtain a measurement with this device. In order to compute air permeability using Evans and Kirkham's wax sur­face seal method, the volume of soil through which air is flowing must be known. Air movement in soil follows stream lines and can be des-- cribed for 3-dimensional space with La Place's Equation, Kirkham (19U7) pointed out that this movement of air under low pressure gradi­ents is analogous to the flow of electricity in a conducting medium. With these assumptions and the use of an electrolytic tank, Evans and Kirkham (I9S0) constructed electrical analogue models for revealing theoretical boundary conditions of depth and width for various inlet and surface seal diameters... : A graph was constructed from which an , area factor (A) could be obtained for a given inlet and surface seal diameter. •

The electrolytic tank was also used by Evans and Kirkham (1950) to determine the effects on air permeability of stones, cracks, and worm holes of various sizes and distances from the air inlet.

6Wilde and Steinbrenner (1950) developed a. constant flow type

apparatus« A soil tube was inserted into the soil and manometer readings were obtained in inches of mercury. No flowmeter readings were taken and therefore an actual permeability figure could not be obtained. In 1959, Steinbrenner developed another permeameter.This instrument, like its predecessor, gave, only pressure readings and a similar method of inserting a tube into the soil was used. However, the new permeameter had many design advantages. Measurements could be obtained rapidly, and the instrument was light and portable (weigh­ing only 32 pounds). A harness arrangement was attached allowing it to be carried and used while on the operator’s back. The bulky air pump and constant volume tank used with the falling head system were eliminated. Instead, the new instrument employed a constant flow system using an air cylinder and pressure regulator for the air supply.

DEVELOPMENT OF THE AIR PERMEAMETER

A review of the literature indicated that none of the instru­ments already developed for measuring air permeability of soils would

%be suitable for a study on logging roads« An instrument was needed which would be light and portable, capable of making rapid repeated measurements at the same location, and usable on compacted soils.

A series of laboratory studies was undertaken to develop a suitable permeameter. One of the first considerations was to determine an adequate range of air pressure and flow rate, To accom-? ' plish this, a flowmeter and manometer system was set up (Figure l).One end of this pressure system was attached to an air supply while the other was connected to the top of a core sampler. As a result, all air entering the system could escape only after passing through the soil sample.

Air was applied to the system. Manometer pressure and rate of air flow were recorded. This procedure was repeated at various.

• 1. A logging road as used in this'text is defined as a bull­dozed road consisting of in-place soil without organic matter or natural structure.

7

flow m eter a m anom eter

air supply —>

s o ilsam ple

Figure 1. Apparatus for measuring air permeability in the laboratory.

CO

9flow rates and manometer pressures with several soil'samples, and the results were graphed. After reviewing the results of each test, the density of the liquid in the manometer and the air flowmeter range were changed. Adjustment was continued until the desired flow and pressure conditions were obtained with the equipment remaining sen­sitive enough for suitable readings.

Laboratory Study No. 1 .Three soil samples were tested using a mercury manometer

3(density 13.6 g/cm ) and a flowmeter with a range of 0.01 to 2.00 cmVmin. The results are shown in Figure 2,.

Sample 2 was run three times in succession to observe the effects of air passage on drying of the soil. Although a difference between readings for Sample 2 did occur, the curves remained roughly parallel. This indicates that some changes in permeability are due to soil moisture. In actual field use, this drying effect should be negligible because less air will be used and for a much shorter time duration.

Flow must be laminar or non-turbulent for Darcy’s Equationto apply. If pressure plotted against flow is linear, laminar flow .is assumed to be occurring. Since the curves in Figure 2 are notlinear, the flow can be considered to be turbulent and above the range

2desired.

2. See page lii for a discussion of laminar flow.

2C :2B '2 A

(.804

1 .4 0-

§

g 1.00-

.20-

22PRESSURE IN CM OF MERCURY

Figure 2. Curves showing the occurrence of turbulent flow at high pressures and flow o

11Laboratory Study No. 2 • -

The previous studies were repeated on additional soil samples using lower air pressures and more sensitive flow-measuring equipment.A manometer with Brodies solution (density determined to be 0.8825

3 ■ 3 ■g/cm ) and a flowmeter ranging from. 1 to 35 cm /sec were tested. Dueto the increased sensitivity, of the flowmeter, all flowmeter readingsnow had to be converted to cubic centimeters by using a calibrationcurve.

Samples 6, 3A and 2 were discarded (Table l). Soil Sample 6 was taken in grass rather than on bare soil. Analysis of the curve, suggests that measurements can be obtained, should they be desired, under this condition. Curve 3A was derived from Sample 3 after that sample had dried in the laboratory for 2ii hours. The difference between the data from 3A and 3 again demonstrates the apparent effect of drying. Both Samples 3A and 6 were made for comparison only and therefore will not be considered further. Soil Sample 2 was badly disturbed during collection and the results were not considered representative.

The curves of Samples 1, 3, It, 5, and 7 appear in Figure 3.All these curves have a straight line segment, breaking only in their upper portions or at the point where turbulent flow begins« Curves1, 3 and 7 become non-linear above 25 cm^/sec. Curve it becomes non-

3 3linear above 30 cm /sec and Curve 5, above 20 cm /sec.

12

Table, lo Results in c rrrV se c of air flow at various pressures on eight laboratory soil tests.'

SampleCm Pressure Brodies 1 2 . 3

<3ry 3 A h 5

grass6 7

7.3 1.6 3.0 1.8 2.1 2.7 1.01 2.0 ih.k 3.0 6.6 3.It it.7 6.1 1.81% 25.3 11.0 5.2 6.6 9.U2 lt.8 6.1 1)4.6 6.6 13.it 13.0 3.33 21.8 11.0 18.3 it.9h 10.0 13.2 33.9 17.6 2)4.55 17.6 21.8 29.0 7.76 15.2 19.2 25.3 32.97 23.6 28.8 11. it8 19.6 25.8 27.89 31.3 35.6 lit. 6

10 2)4.2 26.1 33.111 . 17.712 28.3 33.913 21.0Ih 32.015 2lu517 27.019 30.221 33.1

FLOW IN

CM'VSEC

40i

32-1

24-

164

PRESSURE IN CM OF BRODIES SOLUTIONFigure 3. Shows curves with straight line segments indicating non-turbulent flow. v>

litDiscussion of Laboratory Studies

The air permeability of a soil is a.numerical description of a porous medium and is usually referred to as "k". This value can be obtained by a form of Darcy's Equations

k = Q N » (2) •A P A pgf

This equation was developed to fit the air permeameter used in this study« Its derivation is given at the end of this chapter.

'

One of the basic assumptions of Darcy's'Equation is that flow be laminar or non-turbulent. It was, therefore, necessary to deter­mine when turbulent flow begins in a soil sample. Evans and Kirkham (19J?0) stated that turbulent flow occurs when a plot of flow rate over pressure becomes non-linear. Turbulent flow, as seen in Figure 3, does not occur at the same pressure or flow for each sample but varies with the slope of the curve for the particular soil. The slope is primarily a function of the permeability, being steeper for less permeable soils.. Based on these results, it was assumed that flow rates up to 20 cn rV se c could be considered laminar.

The soils used in the. laboratory studies varied in texture and were selected from foot paths and parking lots. It was.antici­pated that more compact soil, requiring higher pressures, might be encountered on the logging roads. This was later confirmed when the field permeameter was constructed and preliminary field tests were made on a compacted road surface. These results appear in Appendix

15Aj Figure 13 • No sign of turbulence was noted for pressures up to 55 centimeters with flows less than 16 cm?/sec.

The laboratory studies also confirmed that it was time- consuming and difficult to insert a core sampler or soil tube into a compacted surface,. The chances of disturbing the soil and thus changing its air permeability were quite high. Evans and Kirkham's method of sealing the surface with wax.seemed more practical although it, also, was time-consuming„ This method, in addition, created the possibility of the wax affecting the permeability when repeated readings were made at a given location.

Construction of the Permeameter In order to make the equipment as portable as possible, a

compressed air cylinder with an air flow regulator, was used for the air supply. A regulator with a built-in bleeder valve was found to •' work best under field conditions. It allowed adjustment of a few centimeters of pressure at a time while holding a very constant air flow.

A Fisher predictability flowmeter was used to measure the rate of air flow through the system. The meter was calibrated for local temperature and pressure conditions using the standard bubble flow method. The calibration curve (Figure111) obtained appears in Appen­dix B. Although temperature and humidity influence' the viscosity of air, as shown by Buehrer (1932), this influence has little effect on the final air permeability. Therefore temperature and humidity of the air supply were not measured. .

16A 50-cm manometer with unbreakable plastic tubing was used to

obtain pressure readings, Distilled water (density 1.0 g/cm )f with a few drops of bromcresol green indicator added to make it easier to read) was chosen for the manometer fluid. The Brodies solution used in the laboratory) although more desirable) was not readily available for field use.

Since a seal of the soil surface had to be obtained in order to take in-place soil permeameter readings5 a special "soil contact head" was designed (Figures It and 5)= This head consisted of a 2-inch thick) 6-inch diameter circular foam rubber pad coated on its lower side with cement. A %-inoh thick steel plate) slightly larger than the rubber pad, was placed above the pad. A housing, bolted to the top and center of the plate, acted as a guide for the plate and pad.An air inlet tube extended through the center of the head and allowed a constant ( g-inch I.D.) diameter to be maintained, • The surface was sealed when the. operator, stood on the steel plate, causing it to slide downward along the inlet tube. The plate depressed the rubber pad which molded itself to surface irregularities while at the same time making a tight seal around the inlet tube.

The soil contact head was joined to the permeameter by a . ii-foot piece of %-inch pipe (which helped the operator to keep the in­let tube at right angles to the surface) and a 6-foot length of rub­ber hose. The permeameter was mounted on a pack frame which made it made it very portable. Its total weight was approximately 2?.pounds (Figure 6).

I<------ 2 >11/2 pipe thread

SOIL CONTACT HEAD

- measurements in inches -pieces are all circular

1/4

<■ 1/2 > ID

1/2

3 / 4

1/8

foamrubber

Figure k.

18

Figure 5>. Photograph showing soil contact head in depressed position ready for air permeability reading.

19

Figure 6. Photograph of portable air permeameter ready for use.

Air Permeability EquationAn air permeability equation had to be specifically designed

for use with the permeameter developed in the study. This equation had to be applicable to a constant flow system and had to take into consideration the density of the fluid in the manometer, air visco­sity, and the effect of acceleration of gravity on air. It had, also, to incorporate an area factor. The needed equation was derived from an expression of the Darcy Equation, the basic equation for flow in a saturated medium.

The Darcy Equation, expressed in terms of quantity' (Kirkham, 19U7)5 can be written;

Q = KAP A1L (3)In this equation, Q is the quantity of flow per unit of time, K is the hydraulic conductivity,^? is the change in pressure gradient,A"*" is the cross-sectional area of a sample, and L is the length of the sample.

The permeability "k" is contained in the function K which describes both the porous medium and the. fluid passing through it.The acceleration of gravity is indicated by g, the viscosity of the fluid air by N.

21The symbol Vs should be added to the equation to allow for the density of the fluid being used to measure pressure« Darcy’s Equation may then be written:

Ti L (5)orQ N L

g-fA? A (6)

In the method used in this study to test the air permeability of soil; no definite boundaries exist because no device was inserted into the soil* It therefore was. necessary to estimate the dimensions of the area sampled.

In a study by Evans and Kirkham (195>0), it was found that for a g-inch (1.27 cm) diameter air inlet tube with a 6-inch soil sur­face seal$ an area factor (A) could be obtained by multiplying the radius of the inlet tube by four. This area factor represents the dimensions of length (bj and cross-sectional area (A’*') , of the sample; and is 5-OS for the permeameter used in this study.

Substituting A into Darcy’s Equation; the equation for a continuous flow-type air permeameter is:

k = Q NA P Ay*g (7)or

k (cm) = Q x .000,182;7^ T 3 T ^ 6 F i n ^ o l E o 3 r (8)

DESCRIPTION OF STUDY AREA

Location and History Field studies were conducted within the £3 <,000-acre Bozeman

Creek watershed on the Gallatin National Forest five miles southeast of Bozeman5 Montana (Figure 7)« Since it is a primary supply of water for the City of Bozeman5 the watershed has a high resource value and is closed to the public«,

In 1958 a road was constructed into the watershed to provide general access and to allow logging operations» As the logging pro­gressed, the road was extended up the drainage to its present termin­ation point approximately one mile below the upper divide. The lower end of the road, consequently, is the oldest and has received the most use. During this study, however, all major traffic traveled the road’s entire length.

Geology and Soils The geology of the upper three-quarters of the watershed was

extensively mapped by Roberts in 196!t« The area has undergone exten­sive folding and faulting resulting in complex formations. A traverse of the road revealed the following general categories of geology (Figure 8) and soils. The lower end consists of Precambrian gneiss,

22

23

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/\ P/\ zxiZ \ Z \A

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20 30 4 0ov>v>

Ml LES

BozemanBOZEMAN t

WATERSHED 4

WYOMING

Yellowstone ' National Park

MONTANA/7n x— — z;IDAHO z

, „ A

F igu re 7 .

2b

GEOLOGYof

BOZEMAN CREEK WATERSHED

Pvvvl Granitic

1 X 1 Limestone

[vivlvl Volcanic

Lava f low

| ) Und i f fe ren t ia te d

= Road

Creek

tr0 1 2 Mi le shH3Z=zi^^^

F igu re 8 .

. 25schist and granite which have yielded coarse-textured soils. Approxi­mately five miles from the lower end of the road, a series of greatly distorted Cambrian formations is encountered for the next two and one- half miles. Soil textures vary greatly in this area (clay to sand). Progressing up the road, the next one and one-half miles are heavy clays derived primarily from Hississippian limestone. Above this, the road crosses one and one-half miles of a large landflow deposit which consists of volcanics intermixed with sandstone and limestone. The soils here are mostly clay with some coarse sands. The upper one-half mile of the road is mainly sandy , soils originating from Cretaceous sandstone.

ClimateThe climate of Bozeman Creek varies greatly due to the large

range of elevation (5300 to 9b22 feet above mean sea level) and local topography within the watershed. The nearest weather station to Bozeman Creek is located on the campus of Montana State University in the Bozeman Valley. The.long-term average annual precipitation, as recorded at that station, is 16 to 18 inches with May being the wettest month and February the driest.. The long-term mean annual temperature is lil«9 degrees Fahrenheit. Long cold winters and short cool summers are characteristic.

During the summer in which the study was conducted, two precipitation storage gauges were maintained.on the watershed. One gauge was located approximately two miles from the lower end of the

26road (5>5>00 feet elevation) j the other was approximately two miles be­low the upper end at Mystic Lake (elevation 61)00 feet) e Although these records are for a very short time duration, they suggest that precipitation on the watershed is at least $0 percent greater than at the Bozeman Station. Within the watershed, greater precipitation was measured on the lower area. This internal variation is most likely due to topographic barriers and prevailing southwesterly winds„ The precipitation records have been graphed (Figure 13>) and appear in Appendix C.

METHODS AND PROCEDURES OF THE FIELD STUDY

To better define air permeability and the factors which affect it; several physical measurements were taken with each air per meability reading. Although these variables are not the only factors affecting permeability; they are thought to be some of the more im­portant ones. An example of the field data sheet appears in Appen­dix D; Figure 16.

Air Permeability. The prime variable; permeability; was determined with the

previously described air permeameter. Measurements were taken aboutevery one-half mile at 25> different stations along 1C% miles oflogging road. At each station four points, approximately six feetapart; were sampled. Two of these points lay on the cut, or uphill,

• 1side of the road and two on the downhill, or fill side. The measure ments were all taken in the road tread, or that portion of a single lane road over which tires normally pass. Sample points were sur­veyed to four stakes at the side of the road so that they could be relocated each week. Since it was not practical to relocate each point exactly, successive measurements were made within two inches

1. The cut side is the side which has been notched out of the slope. The fill side is the side on which the fill material has been deposited.

28

of the original point. Measurements were taken at each station approximately one week apart for six weeks, A total of 600 air per­meability readings were obtained. .

Bulk DensityA soil sample for bulk density was taken with every permea­

bility reading. The clod method, as described by Reeve (1965), was employed. , Lumps of soil were randomly extracted each week from an 8-inch radius around the permeability measurement point. Each clod was 1 to inches in diameter and was taken from the tread surface. For each permeability measurement point, the bulk density of three clods was determined in the laboratory. The mean of these readings was taken as the bulk density value for the point.

Soil MoistureSince moisture occupies pore spaces within the soil, it was

concluded that the degree of soil saturation must be considered in a comparison of air permeability readings. The gravimetric method with oven drying was used to determine soil moisture. Two samples, weighing approximately liO grams apiece, were taken at each road station: one from the cut side and one from the fill. Only one sample from each side of the road was needed because moisture varia­tion between samples taken on the same side was found to be non­significant.

Site VariablesSeveral non-dynamic variables were measured for each station

to describe the site and to estimate the' effect of location on air permeabilityo The elevation of each station was obtained using a standard pocket altimeter. Aspect was measured with a box compass and the readings were grouped.into 30-degree quadrants. Two slope measurements (regional slope, or the slope of the adjacent mountain­side, and the slope of the road surface) were taken at each station using an abney hand level with a percentage scale.

A soil sample to determine texture was collected at each station. Each sample was run through a 2-mm sieve in the laboratory. The resulting coarse fragments were expressed as a percent of the total sample. The remaining material — that.less than two milli­meters -- was analyzed for sand, silt and clay content using Day's (1956) modification of the Bouyoucos hydrometer method.

Soil GracksJust prior to taking the first field measurements, it was

noted that cracks were appearing in the road surface. In order to estimate their number and to keep track of their occurrence from week to week, a grid system was devised to count the cracks. A . 1-foot square wooden frame was constructed and divided, using string, into 1-inch square segments. As each permeability measurement was made, the grid was randomly placed over the measuring point, A crack was recorded if it crossed one of the II4I4 grid intersections. Size was indicated as small (hairline), medium (up to l/l6-inch)

30and large (greater than l/16-inch). In this manner5 the size and number of cracks could be quickly estimated.

In analysis5 the number of small cracks was multiplied by one, the medium by two, and the large by three. The sum attained by combining the values thus obtained was used as an expression of the cracks at a given measuring point.

Time Variable 'The use. or time variable was considered as a treatment

effect to determine if changes in air permeability due to use could be measured. To test this, measurements of permeability, bulk den­sity, and soil moisture were taken on a weekly basis as mentioned previously. In addition, an exact record was kept of all vehicles using the road during the time of the study.

The number of vehicles was recorded by placing a traffic counter across the lower end of the road. The specific weight of each truck and its load was made available by the Idaho Pole Company, the logging company operating in Bozeman Creek. Traffic other than logging trucks (only 12 percent) consisted, almost entirely, of Forest Service and Idaho Pole Company pickup trucks, An average weight for a partially loaded pickup (U500 pounds) was used to estimate this remaining traffic.

ANALYSIS. AND RESULTS OF FIELD STUDY

Several statistical methods were used in an attempt to ex­plain the results. These methods were: (l) split plot analysis of variancej (2) response surface5 (3) co-variance analysis | and (i;) multiple regression with path coefficient.

Analysis of Variance Analyses of variance were ‘used to determine if there were sig­

nificant differences with time and distance in the quantities air per­meability, bulk density, and soil moisture (Appendix E, Tables It, £ and 6), For each of these variables, an analysis was run using the main effects of side, time, and distance. Interactions were also tested. The analysis used for permeability and bulk density was a double split plot over time. A split plot over time was used for soil moisture for which only one sample per side was taken. In the analy­ses for bulk density and permeability,. the.word sample is used to de­note replication. In the analysis for soil moisture, the word side, is used.

Table 2 summarizes the analyses.of variance and gives the error components. The side-time-distance (STD) interaction was the error term for testing all the effects in the soil moisture variable. Air permeability and bulk density were, tested using error terms A,B, and C.

31

Table 2 . Analysis of variance for double split-plot design over time. This is the basic analysis used in testing the variables air permeability, bulk density, and soil moisturee

Source Degrees of Freedom

Side 1Sample 1Side Sample 1

Error A 2Distance 2k

Distance Side 2kDistance Sample , 2kDistance Side Sample . 2k

Error B lt8Time 5>Time SideTime Distance 120Time Distance Side * 120

Time Sample . 5Time Sample Side .5 . ..Time. Distance Sample 120Time Distance Side Sample 120

Error 0 2$0

Total 5>99

# Error term for testing all effects in soil moisture variable»

33All 'variables5 excepting side, had significant main effects.

Most interactions were also significant with the exception of the side­time interaction for permeability and soil moisture, and the time- distance interaction for soil moisture. The analyses strongly indica­ted that significant changes with time and distance were measured for the variables air permeability, bulk density, and soil moisture. How­ever, because of the significance of several interactions, definite statements could not be made about the causal relationships of the main effects unless it was known how they reacted at various levels.

Response SurfaceA response surface analysis was attempted to provide a method

for expressing the main effects and interactions noted in the analysis of variance. A response surface presents the results as a surface and shows what happens to a dependent variable (Y) when it is influenced by a number of quantitative factors. The response surface method can also be used to show how Y is affected when the level of a factor is changed (Cochran and Cox, 1966).

A quadratic equation was obtained for each, of the three varia­bles (permeability, bulk density, and soil moisture) used in the analy­sis of variance. These equations were determined using the regression .coefficients from a forced multiple regression analysis as explained by Cochran and Cox (1966). The fitted equations for each variable are. given in Appendix F, Table 7« They can be used either as prediction

3Uequations or to construct response surface diagrams». The following basic equation was used;

Y = b0 -}- b^t * b^t^ ^ bgd + b22d2 + b:L2tld2

where Y is the dependent variable, bQ is the beta constant for the2regression, b t is the linear time component, b t is the quadratic 1 11 2time component, bgd is the distance linear component, b^d represents

the quadratic distance factor, and b^2t^d^ is the residual time- distance factor.

The F tests indicated that the response model did not fit the data for any of the dependent variables. For this reason, the actual response surfaces were not constructed. Evidently the data had either too much variation or variables, not accounted for by the model, were exercising too strong an influence on the response surface.

Co-Variance AnalysisIt was believed that the effect of soil moisture could have

been masking the effects of permeability and bulk density. Thus, co-variance tests'adjusting .for soil moisture were made. Tables 8 and9 in Appendix G summarize the results of the co-variance analyses.

The F test for slope of the regression (b ) was non-significanto •

for both permeability versus moisture and bulk density versus moisture. An F test of the adjusted main and secondary effects was also non­significant, except for the main effect of distance. The co-variance analyses supported the belief that the variables thus far tested and

included in the response surface model.were being overshadowed by other non™tested variables»

Multiple Regression Analysis The significance of the main effect, distance, in the co-

variance analyses suggested that the effects of the site variables texture, elevation, slope and aspect might be brought out by an ex­panded regression analysis„ Two additional variables, use and number of cracks, were also included in this analysis» Bulk density and soil moisture were also retained. Texture was broken down into four separate variables? clay, silt, sand and coarse fragments (greater than 2 millimeters). ■

Four multiple step-wise regression analyses for air permeability were run. The regression was first run.with the time intervals averaged for each distance and then with all distances averaged for each time. Averaging the time and then the distance variables was necessary in order to enter the variables into the regression. The means of select­ed variables with time and distance averaged respectively are represent­ed graphically in Figures 9 and 10. A-graph.'representing; use oyer time is given in Figure 11. .

The step-wise linear regression, with time, averaged, entered' the variables into the regression in the order shown in Table 3 with

' ' ' ' osoil moisture accounting for the most, variation. Unfortunately, the R'value for the final step of the regression was only 0.28, indicating

CRACKS BULK

DENSITY

36

3525

9.3g 8.3H5 7.3

6.3

2.20

2.00

20

H

VO J

TIMEFigure 9. Graph of air permeability, bulk density, soil moisture

and soil cracks over time. All site variables have been averaged.

756045 0 30 8

2.5; 2.2

W 2.i85 2.0

3 20 -

I Ig 15-G3X 10-o!

H

24DISTANCEFigure 10. Graph of air permeability, soil moisture, bulk density and soil cracks over

distance. Shaded area represents the percentage of sand in the soil. One inch vertically equals 20 percent sand content.

Figure 11. A cumulative graph of use over time.

39Table 3, Order of the variables as they entered the step-wise

multi-linear and multi-linear quadratic, regressions.- The first two regressions are for the variables over distance. The second two are for the variables over time.

Regressions with time variables averaged

clayaspectsoil moisture bulk density silt sandelevation road slope coarse fragments regional slope

Linear and Quadratic .1*0clay2 aspect^ road slope soil moisture soil moisture silt2 sand sand2 elevation

-x-elevation

Variables R2 ValuesLinear 28

Regressions, with distance variables averagedLinearsoil moisture usenumber of cracks bulk density

.72

Linear and Quadratic 89us esoil moisture

-x-use

soil moisture^

Variables after this step were not listed.

1*0

that the variables tested accounted for only 28 percent of the varia­tion in the dependent variable,

A quadratic regression was then run on the same data to see if some of the variation was due simply to non-linear relationships among the variables, The quadratic equation accounted for hO percent of the variation,, The variable responsible for most of this variation was (soil moisture) ,

All variables which changed with distance were averaged in order to analyse the change in air permeability over time. The varia­bles used in the regression analysis, were soil moisture, bulk density,

2use and cracks, An R ' value of 72 percent was obtained (Table 3)°Clay accounted for more of the. variation than any other variable,

A quadratic regression was run on the same data which in-pcreased the R value to 0,89, thus accounting for most of the varia­

tion in regression. The order that the variables entered the regressionis shown in Table 3, Of the eight variables in this regression,

2(clay) accounted for, the largest amount of the variation.An F test run on the regression,revealed that the slope of the

regression was non-significant. According to Snedecor (1961), if the F test is non-significant, a predictability equation constructed from the regression should not be relied upon for predicting Y, However, the relative importance of the variables as they effect air permeability was indicated. Whether the variables were linear or quadratic was also shown.

h i

Path coefficients 5 as described by Li (195>6) for multi-linear regression models 5 were developed to express t (l) the portion of the regression due to each variable: and (2) the portion of each inter­action acting on a variable„ The path coefficients were constructed

2only for regression over time, which had a relatively high R value (O.71)» A diagram of the variables and their interactions appears in Figure 12. The standard partial regression coefficients are used to show the relative importance of each, variable interaction. Due to the non-significant F values for these regressions, the actual portion that each value represents cannot be given too much consideration.

ALL POSSIBLE RELATIONSHIPS

a i rpermeabi l i ty

F ig u re 12.

.4 5

bulk d e n s i t yt

- . 9 8

- . 5 8

-.12

- . 0 6

- . 0 9

soi I moi sture

.00

use

- . 6 9

Ic rocks

t- . 0 3

- . 9 8

.55

.08

. 4 9

.04

. 0 4

MOST IMPORTANT RELATIONSHIPS

bulk density

airpermeability

- .09 - .98- . 9 8

.45 soi l m o is tu re .55

.08use

- .06

- . 69c r a c k s

Diagram of path coefficients showing relationship of dependent variable to independent variables and their interactions. Numbers given are standard partial regression coefficients.

DISCUSSION AND SUMMARY

Because of the largely non-significant results and the great amount of variation in the data, no strong conclusive statements could be made about the variables and their relationships to air permeability« The failure to show significant trends with the analyses used in the study might be due to the complex inter-relationships between the variables used* The most confounding relationships were found to be associated with soil texture«

Variation in permeability measurements was greatest on soils from the upper part of the watershed. This is shown in Figure 10 by comparing the measurements made at sites 1 through 1$ on the upper watershed with those of the group 15 through 2$ on the lower watershed. Clay content of the soils in the former group was usually higher.

In the regression analysis, with all variables except time entered, clay accounted for more of the variation than did any other variable. However, the relationship between soil texture and the variation in the measurements could not be explained simply by the amount of clay in the soil since, contrary to what would be expected, clay was positively correlated with permeability and sand was nega­tively correlated.

It appears that, if the data had been analysed separately for the upper and lower site groups, more distinct relationships might

ii3

ItUhave emerged which were otherwise masked by the complex inter­relationships of soil particle sizes. For.example, on the lower sites a strong positive relationship was found between the sand content and permeability whereas essentially no relationship was found between the clay content and permeability.

The interaction effect of variables other than those of soil texture was also more clearly brought out when upper and lower sites were considered separately. Bulk density was very poorly correlated in both regression analyses. In the regression analyses with all .variables except time entered, the correlation was positive, but in the analysis with site variables averaged over time the correlation was negative. It seemed likely that soil texture, which was entered only in the latter analysis, masked the effect of bulk density,

A fair positive relationship was found between bulk density and permeability for the upper sites, but essentially no relationship existed on the lower sites. The masking effect of soil texture may be due to the fact that higher bulk densities are usually associated with coarser soils. Coarse textured soils are normally the most per­meable.

Results of the study may be summarized as follows:1. The analyses of variance strongly indicated that signi­

ficant changes with time and distance were measured with the equipment used for the variables air permeability, bulk density, and soil mois­ture. However, this does not mean that there is a relationship be­tween the three variables.

2, The response surface model., which was constructed to study the interactions within the three variables, did not fit the data. This indicated that the data had: (a) too much variation; or (b) the varia­bles not accounted for in the model were exercising too strong an in­fluence,

3« The co-variance analyses did not reveal any relationship between air permeability and soil moisture, or bulk density and soil moisture. Therefore, the relationships either did not exist; could not be detected; were due to large amounts of variation in.the data; or were being masked by other variables which were exercising a strong influence on the data,

it. The multiple step-wise regressions indicated that the site variable of clay content accounted for the most variation where mois­ture and clay were both in the same regression. In the regressions which did not contain site variables, moisture was the most influen- cial effect. The quadratic regressions suggested that many of the relationships of variables were quadratic and not linear, as they were applied in the other analyses.

CONCLUSIONS

The most important result of this study has been the develop­ment of a portable air permeameter which can be used on a compacted surface. This permeameter would probably be suitable for most surfaces where it is desirable to avoid disturbing the medium being measured.The air permeameter proved to be very convenient and usable under field conditions and it appeared to have measured significant changes with time and location.

Additional laboratory studies should be conducted with the instrument to attempt to reduce the variability of the measurements. Temperaturemoisture content of the gas, gas slippage and the effect of continuous air flow into a medium should be studied in detail.

The problem of better defining the measurement of air permea­bility would have been better served with a laboratory type experi­ment where.as many variables as possible would have been known and could have been controlled, . This might be accomplished with large boxes filled with a uniform-textured soil. Compaction could be accomplished by artificial controlled packing. Moisture could be monitored with a neutron probe and all site variables could be held con­stant or controlled. Care should be taken to assure sufficient repli­cation for good and convenient statistical analysis.

It was evident from the statistical analysis that the relation­ship of air permeability to any specific variable was not a simple

1|6

U7one. Several of the relationships were non-linear and a number of interactions existed between the variables0 The results suggested that if measurements are confined to a given sites or to similar sites, then air permeability measurements can be made quite useful in detecting phy­sical changes that occur in soils. As a better understanding of the factors which affect air permeability is developed, use of the measure­ment will increase both in research and management situations.

APPENDIX A

RESULTS OF PRELIMINARY FIELD TESTS

FLOW IN

CM'VsEC

8-1

4030 5020100PRESSURE IN CM OF BRODIES SOLUTION

Figure 13. Graphed results of preliminary field tests.

APPENDIX B

CALIBRATION CURVE

FLOW METER

READINGS

I6r

14

12

10

8

:/

0 0.5 1.0 .5 2.0 2.5 3.0 3.5FLOW IN CM /SEC

Figure lb. Calibration curve for flowmeter. Curve was constructed for normal atmospheric pressure and temperature conditions at study area.

APPENDIX C

PRECIPITATION DATA

52

PRECIPITATION IN

INCHES

Mystic Lake StationLower Bozeman Creek Station

Bozeman Station.70JDate of Permeability Measurement

.50-

.30-

20 25 3020 25 30 AUGUST SEPTEMBERJULYFigure l£. Precipitation measurements for three stations. Cystic Lake Station was installed

July 7; Lower Bozeman Creek, August 5>. Bozeman is a permanent station.

APPENDIX D

SAMPLE FIELD FORM

AIR PERMEABILITY SURVEYSample No. ___________ Watershed Bozeman Creek______Date Location Gallatin National Forest

Elevation CracksSlope

PositionRoadRegional

Road Class Road StatusAspect ____ErosionRoad AgeAmount of Use Remarks:

Size No.Permeability Q P X

XCut y

XFill y

Wet Wt.Soil

Dry Wt.Moisture Wt. Loss % Moisture Can Wt.

CutFill

Soil TypeTexture Parent Material % Coarse

Bulk Density Cut Fill

Figure 16. Sample field form

APPENDIX E '

ANALYSES OF VARIANCE

56

57Table In , Analysis of variance for air -permeability,

Source

S = Side A = Sample . T = Time D = Distance

Degrees of Preedbm. .

MeanJiati&ES. M .Test.

» S 1 , 213.576a 1 272.660

T 5 732.1 57D " 2h 628.21:7

SA . 1 78.229ST 5 152.512AT 5 79.557SD 2U.. 378.286

AD, 2h 150.126

TD 120 267.550

SAT 5 120.1:92

SAD 2h 92.159STD 120 178. W 7ATD • 120 118.628

SATD 120 159.31:1Total 599

Error termsError A 2 • 160.902Error B lt8 121.11:3Error C 250 137.1:26

F = 1.388Error A

F f T = 5c330 *Error G

F - D = 5.186 -x-Error B

F = ST = 1.110 Error G

F = SD - = 3.123 *Error B

F = TD = 1.917 *Error C

F = STD = 1.299 Error C

* = Significant at 95 percent level

Table 5- Analysis of variance for bulk density*

Source

Degrees of Freedom

Mean■Square

s 1 .00056A 1 .00355T 5 .08501D 2h .21878SA 1 • .00763ST 5 .03651AT 5 .00265SD . 2h / .03815AD 2h .001*00TD 120 .05052SAT . . 5 .00251SAD . 2U .00201*STD 120 .0261*1*ATD. . 120 .00309SATD 120 .00352Total 599

Error termsError A ’ 2 . .00559Error B ^8 .00302Error C 250 .00328

S = Side A = Sample

D = Distance T = Time.

# =

F Test

F = = 0.010Error A

F = T = 25.933*Error C

F = D = 72.162*Error B

F = ST 11.138*Error C

F = SD = 12.635*Error B

F = TD = l5.iill*Error.0

F = STD = 8.O67* Error 0

level

59

Table 6« Analysis of variance, for percent moisture.

Source

Side

Time

Distance

Side-Time

Side-Distance

Time-Distance

STD = error

Total

Degrees of Freedom

5

2h

5

2k

120

120

299

■ Mean Square

17,832

29,363

72.157

1.515

16.770

it,9li5

5,213

F Test

F = S = 3.101error

F = T = 5.600*error

F = D = 13.762*error

F = ST = 0.289error

F = SD = 3.198*error

F = TD = 0.9lt3error

* Significant at 95 percent level.

APPENDIX F

RESPONSE SURFACE'MODELS

60

61

Table ?• Response Surface Models„

Dependent = b0 * bit + b ^ ■+ bod + bood^ +' b-,pt-,dVariable T 0 x 11, 2 22 12 J-

Air Permeability =:» llt„lj.89 - ,228 - «011i + - .676 - ,093

Bulk Density = 2,112 + ,009 - ,000 + ,010 - ,002 - ,001

Soil Moisture = 6,1|12 - ,205 + ,007 - ,373 ,102 + ,009

APPENDIX G

CO-VARIANCE ANALYSES

62

63Table 8. Go-variance analysis with air permeability as J. variable and

soil moisture as X variable =,

Source Degrees of Freedom

MeanSquare F Value

Time 4 52.071 O.bOSide 3 2ljli.Oli8 1.88Time-side 5 232.696 1.79Distance 2h 312.871 2.bOTime-distance 120 117.528 0.90Side-distance 2h 11b.632 0.88STD = error 119 130.Ib5

The following is a test for Beta significance from the co- variance analysis.

F = gCxy^/^xxresidual within MS

F = (-372.6l66)2/509»069h, --------D o z m ; —

F = 2.0956,F = non-significant

Table Co-variance analysis with bulk density as Y variableand soil moisture as X variable.

Time 5 .030 1.75Side 1 .0% 3.15Time-side 5 .022 1.27Distance 2lt .076 lt.li2Time-distance 120 .018 1.03Side-distance 21} .039 2.28STD = error 119 ■ - .017

The following is a test for Beta significance from the co- variance analysis.

F = jE" xy^/^x%' residual within MS

2F = (1.31U5) /5Q9.o69lt 6.0171F = 0.198F = non-significant •

LITERATURE;CITED

Aljibury, F« K, , and Evans«, D. D„ 1965® Water permeability of satu­rated soils as related to air permeability at different moisture tensions® Soil Sci® Soc. Am®, Proc® 29:366-368®

Bethlahmys Nedaria® 196?. Effects of exposure and logging on runoff ■ and erosion® U®S®D®A® Intermt® For® and Range Exp, Sta, Res.Note INT-61®

Brooksj> R® H® and Reeves R. C® 1959® Measurement of air and. water permeability of soils® Am® Soc® Agr® Eng® Trans® 2:125-126, 128®

Buehrer, T® F® .1932® The movement of gases through the soil as acriterion of soil structure® Aria® Agr® Exp® Sta, Tech® Bui® 39®

Cochran, William G®, and Cox, Gertrude M® 1966® Experimental Designs 2nd.ed® John Wiley and Sons, Inc®, New York.

Collins, Royal Eugene» 1961® Plow of Fluids through Porous Materials Reinhold Pub® Corp®, New York®

Corey, A® . T. 1957® Measurement of water and air permeability in unsaturated soil. Soil Sci® Soc, Am® Proc. 21:7-10.

Day, P® R. 1956. Report of the committee on physical analyses,195^-55/ Soil Science Society of America, Soil Sci. Soc. Am® Proc

. 20:167-169.Evans, D, D®, and Kirkham, Don®. 1950. Measurement, of the air permea­

bility of soil in situation. Soil Sci. Soc® Am® Proc® (19U9)1U:65-73.

Kirkham, Don® 19i7 ® Field method for determj.nation of air permeabil­ity of soil in its undisturbed state. Soil Sci® Soc, Am® Proc. (1916) 11:93-99®

Kl.inkehberg, L® J. 19^1® The permeability of porous media to liquids and gases® American Petroleum Institute, Drilling and Production Practices, 200-21^®

Li, C® C® 1956,, The. concept of path coefficient and its impact on population genetics. Biometrics 12(2): 190-2.09®

65

66

Lull, Howard W» 1959« Soil compaction on forest and range lands«,UoSo Forest Serv* Misc0 Puble. 7680

Packer, Paul E« 196?« Criteria for designing and locating logging roads to control sediment = For« Science 13 22-18 =,

Packer, Paul E0, and Haupt, Harold F„ 1965« The influence of roads oh water quality characteristics <, Proc0 Socc Am6 For,, 112-3.15<>

Reeve, R, C, 1953» A method of determining the stability of soil structure based upon air and water permeability measurements,Soil Scio Socp Am, Proc, 17s 32li-329«

Reeve, R, C, 1965, Air-to-water permeability ratio. In C, A, Black, ed. Methods of Soil Analysis Part I, Am, Soc, of Agronomy, Madison, W s cons in, lil;520-531»

Roberts, Albert E, 1965, Geologic I4ap of the %stic Lake Quadrangle, Montana, U,S,G,S, Mis, Geol, Investigations Map 1-398j scale112i(,000,

Scheidegger, Adrian E, i960. The. Physics of Flow through Porous Media, Macmillan Co,, New York.

Snedecor, George ¥. 1961, Statistical Methods. 5th ed. The IowaState Univ., Press, Ames, Iowa»

Steinbrenner, E. C, 1959• A portable air permeameter for forestsoils. Soil Sci. Soc. Am. Proc. 23 $578-581.

Milde, S. A., and Steinbrenner, E. C. 1950, Determination of airpermeability of soil by means of a sphygmomanometer. J. Forestry58; 850-851,