•STUDIES ON SOIL PERMEABILITY

by

EUGENE FREDERICK GYAMPO MANTE

B. Sc. U n i v e r s i t y o f C a l i f o r n i a , I960

A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF SCIENCE IN AGRICULTURE

i n the Department of

S o i l Science

We accept t h i s t h e s i s as confirming t o t h e

r e q u i r e d standard.

THE UNIVERSITY OF BRITISH COLUMBIA

October, 1 9 6 3

i i i

In presenting this thesis in partial fulfilment of

the requirements for an advanced degree at the University of

British Columbia, I agree that the Library shall make i t freely

available for reference and study. I further agree that permission

for extensive copying of this thesis for scholarly purposes may be

grant ed by the Head of my Department or by his representatives.

It is understood that copying or publication of this thesis for

financial gain shall not be allowed without my written permission.

Department of < J t n JL

The University of British Columbia, Vancouver 8 , Canada.

Date

i i i

ABSTRACT

\

Laboratory t e s t s were performed t o i n v e s t i g a t e the

p o s s i b i l i t i e s of u s i n g a modified form of Stein b r e n n e r 1 s apparatus

to estimate the i n t r i n s i c p e r m e a b i l i t i e s of f o u r d i f f e r e n t s o i l s .

Readings were taken on s o i l s a t the same moisture content but d i f f e r ­

ent v o i d r a t i o s ; and on s o i l s a t the same v o i d r a t i o but d i f f e r e n t

moisture contents. S t r a i g h t l i n e graphs of p o s i t i v e slopes were

obtained when the l o g a r i t h m of i n t r i n s i c p e r m e a b i l i t y was p l o t t e d

a gainst v o i d r a t i o f o r peat, a sandy loam and s y n t h e t i c s o i l s .

R e s u lts were extremely v a r i a b l e i n the case of a c l a y s o i l .

An attempt was made t o r e l a t e the p e r m e a b i l i t y estimated

wit h the apparatus and u s i n g a i r as the permeant t o the p e r m e a b i l i t y

estimated w i t h water on core samples. Some c o r r e l a t i o n was observed

between the two types of t e s t s on the sandy loam and s y n t h e t i c s o i l s ;

but there was no c o r r e l a t i o n i n the case of the peat and c l a y s o i l s .

R e s u l t s , i n gene r a l , were v a r i a b l e .

ACKNOWLEDGEMENTS

The author wishe s to express his appreciation to

Dr. H. E. Gardner and Professor N, D. Nathan for their

criticisms and helpful suggestions; to Mr. G. Dargie and

Dr. J . Basaraba for their help and words of encouragement; to

Dr. C. Rowles who was the graduate committee chairman until

his departure to Venezuela on a United Nations assignment,

and to Professor L. Staley and Dean B. Eagles who were

invaluable members of his graduate committee.

/

TABLE OF CONTENTS

Item Page

T i t l e Page i Abstract i i i Table of Contents i v - v l Acknowledgement v i i I n t r o d u c t i o n 1 - 2

A. L i t e r a t u r e Review 3 - 1 4

Types of P e r m e a b i l i t y Flow 3

Laminar Flow i n S o i l s 4

The Darcy Equation 5

Laws of S o i l Moisture 6

Factors That Influence S o i l P e r m e a b i l i t y 6 - 1 2

Methods of S o i l P e r m e a b i l i t y Measurement 12 - 13

B„ Experimental 15

Introduc t i o n 15

Steinbrenner's Apparatus 15 - 17

Steinbrenner's M o d i f i e d Apparatus 17

Theory 17 - 20

M a t e r i a l s and Methods 21 - 25

1. Preparation and S a t u r a t i o n of S o i l Samples 22

2. Treatment t o Show the E f f e c t of S o i l Moisture content on K' and K, " 22

3 . Treatment t o Show E f f e c t of Compaction 24 4. Measurement of K w Using Water 24

5. Measurement of Void R a t i o 25

6. Measurement of K 1 With the Mo d i f i e d S t e i n b r e n ­ner' s Apparatus Using A i r as Permeant 25

C. Results & D i s c u s s i o n 27 - 40

Designations 27

Logarithm of I n t r i n s i c P e r m e a b i l i t y ( l o g K*a) versus Void R a t i o (e) 27

I n t r i n s i c P e r m e a b i l i t y (K'a) versus S a t u r a t i o n (S) 28 I n t r i n s i c P e r m e a b i l i t y a t Zero S a t u r a t i o n 32

Comparison of (Ka) and(Kw) 38

Table of Contents Continued Item Page

Conclusions Appendix Bibliography-

Table 2 Table 2 Tables 3

Tables 6

Table 1 9

F i g . 3

F i g . 6

F i g . 8

F i g . 9

F i g . 1 0

F i g . 1 1

F i g . 1 2

F i g . 1 3

F i g . 1 4

F i g . 15

F i g . 1 6

5

18

L i s t of Tables

Values f o r C a l i b r a t i o n Curve T y p i c a l A i r P e r m e a b i l i t y Readings E f f e c t of Void R a t i o on I n t r i n s i c P e r m e a b i l i t y E f f e c t of S a t u r a t i o n on I n t r i n s i c P e r m e a b i l i t y R e l a t i o n s h i p Between Ka, and K w

L i s t of Figures

Diagram of Steinbrenner's Apparatus Diagram Showing Method of Sub-sampling Diagram of Apparatus i n Operation Alderwood Sandy Loam; E f f e c t of Void R a t i o on I n t r i n s i c P e r m e a b i l i t y Synthetic S o i l ; E f f e c t of Void Ratio on I n t r i n s i c P e r m e a b i l i t y Peat S o i l ; E f f e c t of Void R a t i o on I n t r i n s i c P e r m e a b i l i t y Peat Soil; E f f e c t of S a t u r a t i o n on I n t r i n s i c P e r m e a b i l i t y Measured w i t h M o d i f i e d Steinbren­ner's Apparatus Alderwood Sandy Loam; E f f e c t of Sa t u r a t i o n On I n t r i n s i c P e r m e a b i l i t y Measured With M o d i f i e d Steinbrenner's Apparatus Alderwood Sandy Loam; E f f e c t of S a t u r a t i o n On I n t r i n s i c P e r m e a b i l i t y Measured With M o d i f i e d Steinbrenner's Apparatus Synthetic S o i l ; E f f e c t of S a t u r a t i o n on I n t r i n ­s i c P e r m e a b i l i t y Measured With M o d i f i e d S t e i n ­brenner's Apparatus Synthetic S o i l ; E f f e c t of S a t u r a t i o n on I n t r i n ­s i c P e r m e a b i l i t y Measured w i t h M o d i f i e d S t e i n ­brenner's Apparatus

4 0

4 1

7 0

45

4 6

5 2 -

55 -

6 8

1 6

21

2 3

2 9

3 0

3 1

3 3

3 4

3 5

3 6

3 7

6 9

75

54

6 7

VI Table of Contents Continued

Item Page

F i g . 17 R e l a t i o n s h i p Between C o e f f i c i e n t of Perm­e a b i l i t y ( K a ) Obtained w i t h Modified S t e i n ­brenner' s Apparatus•& C o e f f i c i e n t of Perm­e a b i l i t y (K ) Obtained w i t h Water on Core Samples, and Void R a t i o (e) 40 (a)

F i g . 18 D e t a i l e d Drawing of M o d i f i e d Steinbrenner's Apparatus. 69

P l a t e s

F i g . 1 Steinbrenner's O r i g i n a l Apparatus 14

F i g . 2 Steinbrenner's O r i g i n a l Apparatus i n

Operation 14

F i g . 4 Apparatus Empty 18

F i g . 5 Apparatus Showing S o i l i n Tube T. 18

F i g . 7 Apparatus i n Operation 23

1. INTRODUCTION

The f a c i l i t y with which a f l u i d i s able to travel through s o i l

pores i s referred to as permeability. The permeability of a s o i l has

a great influence on plant growth since plants obtain t h e i r water and

nutrient s from the s o i l . Plants growing on highly permeable s o i l may

wilt i f they are not watered regularly becaus e water passes so rapidly

through the s o i l that there is not enough stored i n the s o i l pores for

plant use. On the other hand a highly permeable s o i l i s well aerated.

Soils of low permeability generally tend to be water-logged;

and are consequently poorly aerated. Plants growing on such soils

have enough water but not enough a i r ; therefore they suffocate and die.

Water, moving through the soil, has, dissolved i n i t , important

salt nutrients for the plant. The rate at which this water moves through

the s o i l determines the rate at which the dissolved nutrients can reach

the roots of the plant, from where they are absorbed into the plant.'

Apart from agriculture, knowledge of permeability i s useful i n

the solution of problems involving drainage of airports, highways and

playing fields etc., u p l i f t pressures beneath dams and buildings, land­

slides, seepage through earth dams, dewatering of excavated sites, and

many other problems.

The importance of permeability i n many s o i l problems makes i t

desirable that i t be measured as accurately and as rapidly as possible.

Unfortunately, most of the present-day methods available for the measure­

ment of permeability take a considerable amount of time, and succeed i n

giving only an estimate of i t .

This work was directed at exploring the possibility of using a

2 .

modified Steinbrenner's apparatus as an instrument for the rapid esti­

mation of soil permeability. If the relationship between void ratio

and permeability measured with the apparatus was found to correspond

to the empirical relationships proposed by other investigators, this

fact was taken as evidence that the apparatus could be used to estimate

soil permeability.

LITERATURE REVIEW.

Types of Permeability flow of water in s o i l s .

There are two types of flow: (6)

(1) Saturated flow e.g. the flow of water below the per­

manent ground-water level, with voids f u l l of water (100$ saturated)

(2) Unsaturated flow or flow of water below a temporary

elevated ground water level - i.e. a free water surface with different

degrees of saturation and a i r clogging of s o i l voids. Important

examples of this are: (a) flow of water through river banks or levees

caused by r i s i n g flood stages of a river; (b) flow of water through

earth dams caused by rising water level i n a reservoir; (c) the i n f i l ­

tration of rain water downward into the s o i l . In these cases permea­

b i l i t y flow applies some distance back from the advancing front of

capillary flow, where the s o i l is completely saturated with water.

Another method of classifying flow is to differentiate i t into

(1) laminar flow (also called streamline or viscous)

(2) turbulent flow (non-viscous)

In laminar or streamline flow, the velocity of flow i s dependent on the

hydraulic gradient. Viscous forces shape the character of flow. This

type of flow i s regarded as being stable i n character; and i s sometimes

called "Darcy flow". The diameters of s o i l pores are generally of such

small sizes, and the velocity of water flowing through the s o i l i s so

small, that laminar flow conditions are assumed to exist during permea­

b i l i t y flow of water through s o i l s .

Turbulent flow conditions exist at high flow velocities. Flow

occurs i n the form of eddies and vortices (especially i n the larger

void spaces), due to expansion and contraction of air in the soil pores,

and change of direction effects. In soils this may occur at relatively

small velocities. However, as explained above, the flow velocity in

soils is generally small enough to ensure the existence of laminar flow

conditions.

Laminar (Viscous) Flow In Soils.

The basic ideas involved in understanding soi l permeability

phenomena have been given by Darcy and others ( 1 5 , 3 6 , 6 7 ) . According to

Darcy's Law, the velocity for purely viscous flow (Vx) through an element,

for a pressure differential (dp) between faces of unit area and a dis­

tance (dx) apart is given by

The quantity (Kj) is called the coefficient of permeability and is deter­

mined by the geometry of the pore system and the nature of the f luid.

If uniform, the flow (Q) through a section of area, (A), is equal to

AVx (Q = AVx) and thus:

Q = -KA ^ or K = Qd_ (2 ) A dx

so that the coefficient of permeability K is seen to be simply the quan­

tity of fluid driven through unit area by a pressure gradient of unity.

Richards (55) pointed out that the discharge velocity in the

Darcy equation was related to the hydraulic gradient. In other words

the quantity (dp) in equation (2 ) must be looked upon as a small differ­

ence in total head (hydraulic head plus pressure head). For vertical

flow, he suggested the more appropriate form:

Q = KS (H + e) (3) e

where:

5.

K = coefficient of permeability H = head of water above soil column e = the length of the soil column S = surface area

The Darcy Equation.

The constant K in the Darcy equation is commonly expressed in

units of cm/sec or in/hr. For use with the one fluid (water), within

the usual range of temperature found in soils, the Darcy equation is

satisfactory. However, the value (K) wil l vary not only with the prop­

erties of the soil but also with those of the liquid. It is desirable,

therefore, to have also a permeability constant which wil l reflect only

the properties of the soil (47)» Thus the sub-committee of the Soil

Science Society of America on Permeability and Infiltration (Richards,

Chairman, 1952) (58) recommended the use of the term "intrinsic permea­

bil ity" (K l) which is given by the equation:

Q = -K! df (5) . }x dL

where:

}i = viscosity of the fluid & = the potential per unit volume of fluid in ergs/cm^

2

K* = intrinsic permeability of the so i l in cm

For coarse textured soils (e.g. sand), K* reflects only the properties

of the soi l . K, the coefficient of permeability in the Darcy equation

is related to K' the physical permeability in the general equation of

flow by the relationship (68):

K = K«tf = K £ £ (6)

where: X — unit weight of permeant used p = density of permeant us ed

v g = acceleration due to gravity

= viscosity of permeant

It should be noted that the Darcy's equation applies only to

saturated flow which must also be laminar.

The Two Laws of Soil Moisture

L. A. Richards (55) in his paper "Laws of Soil Moisture" recog­

nized two main laws that govern the flow of water through soils. The

first is the Darcy Flow Law which has already been discussed. The

second law of soil moisture is the Outflow Law. It may be stated thus:

"Outflow of free water from soil occurs only i f the pressure in the

soil water exceeds atmospheric pressure.,l:w.'.Richards, Neil and Russel (60,

Kohke, Dreibelbis and Davidson (41) and many other experimenters work­

ing with either lysimeters or centrifuges have confirmed this law.

The law applies to the entry of water into underground t i le drains and

drainage of water from lysimeters and soi l pots used for growing plants.

It is best explained and illustrated by the anomalous field drainage

case where a shallow soil layer of fine texture is underlain with coarse

material. Instead of providing improved drainage, the abrupt transi­

tion zone from fine to coarse texture acts like a perched water table

because the soil moisture at the lower boundary of the fine-textured

layer must come practically to atmospheric pressure before i t wi l l move

into the coarse material (55) .

Factors That Influence Soil Permeability.

According to Winterkorn (77) the movement of liquids through

porous solid systems depends on the proportion and geometrical charac­

teristics of the pore space, the physical properties of the l iquid,

7.

the interaction between liquid and solid internal surface, the energy-

potential in the direction of flow, the cross section considered, and

the time allowed. Soils are porous solid systems, but they do not

follow simple concepts and patterns of behavior as many of the common

structural materials do. The character and responses of soil are pre­

determined and controlled by its enviroment and are always conditioned

and modified by changes in the enviroment ( 6 ) . Therefore the character

and specific behavior of a soil must always be considered in relation

to existing enviromental conditions. These include, among other things:

(1) presence of subsoil layers in the field (or horizon differences.

(2) presence of structures e.g. fences, pipes etc. in the field.

In addition to enviromental conditions some inherent characteristics of

the soil influence its permeability.

Influence Of Soil Material and Soil Texture:

The texture of a soi l (i.e. % gravel, sand, s i l t , clay) affects

its permeability. During the movement of liquid through the soil the

finer textural fractions move with the liquid and clog the soil voids.

The volume of soi l voids, therefore, changes continuously with time until

movement of these fine fractions cease. It may also be that the shape

and arrangement of the voids may change without any change in their aver­

age volume, i .e . local changes in volume without any charge in total vol­

ume. This explains why flow through the finer textural fractions of

soil takes some time before reaching the steady state. For the coarse

textured consolidated fraction, however, no changes in void volume

occurs during or as a result of flow, and the basic equations of flow

apply in the soil mass.

8 .

Effect of Structure:

There are two types of structure in the soil - primary and

secondary - each of equal importance (51). The arrangement of the

single soi l particles is called primary structurej in turn the single

particles are generally combined into aggregates which are the units of

secondary structure. The aggregates fa l l naturally into four simple

patterns: granular, platy, prismatic, and blocky. There are character­

istic pore spaces between the secondary units. In addition, each single

aggregate, such as a prism, has a characteristic porosity formed by the

spaces included between the primary particles. The movement of liquid

through the soil depends upon the type of secondary porosity (non-capil-

ary) as well as the primary porosity (capillary). The stability of the

aggregates is also important. Some aggregates easily disintegrate in

water, thus clogging most of the secondary pore space. It has been

observed that the greater part of infiltration, especially in the in i t ia l

stages, occurs in the secondary pore space (66).

Porosity, Void Ratio, Relative Density arri Bulk Density.

These four.- terms are used to characterize the denseness of a

soi l . Porosity is defined as the ratio of the total volume of soil

pores to the total volume of so i l . Void Ratio is the ratio of total

volume of soi l pores to the volume of soi l solids; and Relative density

is defined as:

Q m a x ~ e

emax - emin

where: ^ax = maximum void ratio of the soi l

where: emin = minimum " " " " " e = measured " " 11 " "

;Bulk density is the ratio of the weight of the bulk so i l to i ts total

volume. Even though a l l four properties are known to affect the permea­

b i l i ty of a soi l , the exact nature of the'relationship is difficult to

establish ( 5 , 3 1 , 3 3 , 4 4 , 7 7 ) . Lambe (44) states that: "permeability

depends not only on the void ratio but on the method by which the void

ratio is obtained. The normal soil testing procedures consider absorbed

fluid as normal pore fluid rather than part of the soil particle. Since

the absolute amount of immobile fluid probably depends on pore size and

water content (among other things), the commonly measured void ratio is

not equal to the effective one nor is i t a constant percentage of it:! 1

However differences in permeability of sands have been related to their

void characteristics ( 6 , 3 3 ) . The term "void characteristics" was used

to refer not only to the amount of voids (soil pores) in a sample but also

to other related variables such as the size distribution and continuity

of the voids.

Considerable data (69'):-,fiavs shown that generally the plot of

void ratio versus the logarithm of permeability approximates a straight

line. This relationship holds, of course, only when a l l other soil

characteristics are kept constant, since void ratio is a dependent vari­

able.

Effect of the Degree of Saturation.

Soil pores f i l led with entrapped air do not serve as channels

for flowing water. A partially saturated soil does hot, therefore

transmit its maximum amount of liquid during permeation (44) . The influ­

ence of the degree of saturation on permeability is relatively minor

in comparison with texture, structure and void ratio. The effects of

10.

the degree of saturation are usually masted. For example Lambe (44)

found from an experiment on a sample of Maine s i l t compacted at 20.4$

moisture that there was a decrease in permeability during permeation

whilst a decrease in density and an increase in the degree of satura­

tion occurred. This means that the permeability decreases caused by

the alteration of structure more than outweighed the combined effects

of the degree of saturation and density alteration.

Effects of Electrical Properties of Soil .

Moist soils possess thermal and electrical properties. When

clay is in contact with water i t affects the properties of the water in

its immediate vicinity, partly through the exchangeable ions at or near

its surface. If the water with which soil is in contact is free of,

or very low in electrolytes, some of the ions from the surface of the

soil particles dissociate from the soi l surface and move into the water.

But some do not move very far and what is known as a diffuse double

layer is formed. It is called a double layer, because the soil surface

carries a net negative charge whilst the rest of the system carries a

net positive charge; and i t is diffuse because the net positive charge

is distributed throughout a volume instead of over a surface. This

double layer has many properties, including the ability to influence the

movement of water (63).

Effect of Organic Matter.

Organic matter of the soil contains waxes and other similar

materials which bind the soil particles together into larger aggregates,

thus improving the structure of the soil and allowing for rapid trans­

mission of water (63).

11.

Effect of Permeant.

Michaels and Lin (48) showed that the intrinsic permeability

of kaolinite at a given void ratio varied for different fluids. They

also noticed that viscosity and density are not the only permeant

characteristics, as indicated by the theoretical equations that influence

the permeability of fine-grained soils. Some of the permeant, they

observed, is immobilized during the permeability process. The thick­

ness of the immobilized fluid increases with the polarity of the fluid;

and, therefore, they suggested that some measure of polarity might

well be included in the equations.

Effect of Time.

In the in i t ia l stages of flow of fluid through soi l , fine par­

ticles move to clog some of the non-capillary pores, resulting in a

decrease in permeability. Local changes in the volume of soil pores

occur continuously with time until movement of the fine particles cease

and a steady state is readied. During the movement of fine particles,

air in the soi l pores may contract, or,expand, causing the fluid flow to

be turbulent in nature. When a l l the air in the soi l pores has dis­

solved in the fluid or otherwise been expelled from the soil; and when

movement of fine particles have ceased, the flow becomes laminar. It

is only at this stage that the Darcy flow equation can be used to des­

cribe the flow. The length of time one has to wait before flow becomes

laminar depends on the type of soi l . If the velocity of flow is very

small, laminar flow conditions may be established in a clay or s i l t

soil within a few minutes, since movement of fine particles is consider­

ably reduced by small velocities. In gravelly soils flow is always

12.

t u r b u l e n t , w h i l s t i n sands, a gradient g r e a t e r than 0.5 w i l l cause

t u r b u l e n t f l o w (69).

Some Laboratory Methods of S o i l P e r m e a b i l i t y Measurement.

The most common method i s the use of core samples. S p e c i a l l y

made brass cores are used t o ob t a i n s o i l samples. The s o i l i n a core

i s s a t u r a t e d s l o w l y by standing the core i n a t r a y of water. The water

moving up s l o w l y through the s o i l d r i v e s out the a i r from the s o i l ,

thus ensuring completely uniform we t t i n g .

P e r m e a b i l i t y t e s t on such a saturated core sample c o n s i s t s

e s s e n t i a l l y of adding and ma i n t a i n i n g a constant head (g") of water

to the top of the s o i l and p e r i o d i c a l l y c o l l e c t i n g the water p e r c o l a t ­

i n g through the s o i l . U s u a l l y one does not c o l l e c t the p e r c o l a t i n g

water u n t i l a f t e r about 15 - 30 minutes, d u r i n g which period the move­

ment of p a r t i c l e s r e s u l t i n g i n minor s t r u c t u r a l changes i s supposed t o

be completed and a steady laminar f l o w stage i s e s t a b l i s h e d . With the

Darcy equation, the c o e f f i c i e n t of p e r m e a b i l i t y i s c a l c u l a t e d . Suppose

t h a t on the average V mis. of l i q u i d are c o l l e c t e d i n t seconds. Then

the volume of l i q u i d Q f l o w i n g per u n i t time i s given by:

t

Thus from Darcy's law (the form suggested by Richards (55) K, the c o e f f i ­

c i e n t of p e r m e a b i l i t y i s given by:

S(H+e) where:

e = l e n g t h of s o i l core S = c r o s s - s e c t i o n a l area of core H = head of water above the s o i l column Q = volume of water c o l l e c t e d i n u n i t time

13.

Some workers (24,36,50,70) have used air instead of water as

the permeant in permeability measurements. In general air is supplied

by a compressor storage tank to the top of a soil core and allowed to

flow through the soi l and out to the atmosphere at the other end of

the core. The pressure at the top of the core is measured with either

a Bourdon gauge or a mercury manometer at intervals of time. The mass

flow of air per unit time (from which the volume flow is obtained) is

calculated from the universal gas equation: PV = nRT

where: V = volume of air flowing at any instant P = pressure on top of the soil core at any instant T = temperature in degrees Kelvin R = universal gas constant n = number of moles of gas flowing

The intrinsic permeability of the soil is then obtained from the modified

general equation of flow: K« = QfxL

Ag(P-Pa) where:

Q = volume of air flowing per unit time

/A — viscosity of air L = length of soil core A = cross-sectional area of the soil core P = pressure on top of the soi l core

Pa = atmospheric pressure g = acceleration due to gravity

K' = intrinsic permeability

There are of course many modifications to the method of calcu­

lation of K l which will not be discussed here. It should be pointed

out, however, that the intrinsic permeability K1 may be converted to the

coefficient of permeability K by multiplying K1 by Jjf as already explained.

14

F i g . 1 Steinbrenner 1s O r i g i n a l Apparatus

F i g . 2 Steinbrenner's O r i g i n a l Apparatus i n Operation.

15.

EXPERIMENTAL

A. I n t r o d u c t i o n

The ideas used i n t h i s research were based on those of Grover

(24), Kirkham (36), Muskat (50^ and Weaver (70). An apparatus s i m i l a r

t o Steinbrenner's (68) was used. Steinbrenner's apparatus was designed

to measure macroscopic pore space of s o i l . A i r was introduced i n t o

the s o i l at a constant pressure of 15 p s i . The r e s i s t a n c e of the s o i l

t o the movement of a i r r e s u l t e d i n what Steinbrenner c a l l e d a "back

pressure" which was measured by a pressure gauge attached to the i n s t r u ­

ment. The back pressure was then r e l a t e d t o p o r o s i t y and root penetra­

t i o n .

I t was f e l t t h a t i f the "back pressure" reading was taken as a

^ p , then knowing the volume of a i r Q th a t passes through the s o i l i n

a given p e r i o d , and the average Ap f o r the p e r i o d , one could use.i the

equation:

Q = -K]_ d_ p dL

which has a l r e a d y been discussed on page 5 t o c a l c u l a t e K'. p i s sub-

s t i t u e d f o r d$; Q i s measured by means of a f l o w meter. dL i s the

le n g t h of the tube of the apparatus; _u i s the v i s c o s i t y of a i r . S u b s t i ­

t u t i n g these values i n t o the equation, one can c a l c u l a t e the average

K' f o r the short p e r i o d i n question.

B. Steinbrenner's Apparatus

Steinbrenner's apparatus i s i l l u s t r a t e d i n F i g . 1, page 14-

The compressed a i r c y l i n d e r ( l ) has a c a p a c i t y of 1980 p s i . A i r i s

d e l i v e r e d from the c y l i n d e r through a pressure r e g u l a t o r (2) which can

16

FM

46

T ;

1 I i P

F ig . 3 Diagram of the Modified Steinbrenner's Apparatus

17-.

be set to release any desired pressure. Air passes from the regula­

tor through a pressure hose to a toggle valve. ( 3 ) . From this valve

air passes through a pressure hose to a "back pressure" gauge ( 4 ) .

The gauge is connected to the stem by means of a standard \ inch

pipe T to which the soil tube ( 5 ) is attached to complete the system.

Fig. 2 shows the operation of the soi l permeameter for surface deter­

minations .

C. The Modified Steinbrenner's Apparatus

The apparatus is illustrated in fig. 3 page 1 6 . It is

simply an enlarged size of the original apparatus with a flow meter

and additional gauges. Pc is a pressure regulator (see f ig. 3 ) which

keeps the pressure of the air flowing into the apparatus constant.

Pg and Prp are gauges which measure the pressures at the bottom and top

of a flow meter FM. Pjy[ is another gauge between FM and Pp. For

details of the construction of the apparatus, see Appendix page .

D. Theory

Fig. 4 , page 1 0 shows the apparatus with the soil tube empty,

i t has been demonstrated in the laboratory that i f the pressure reg­

ulator Pc (see fig. 4 ) is set so that i t regulates the pressure of

the air flowing through i t at 5 ps i . , then with suitable adjustment

of the valve just below the gauge P^,

Pc = PB = PT = PM = 5 psi, whilst PD = y, where y is always

18.

F i g . 5 Apparatus Shewing S o i l i n Tube T.

19. '

less "than 5 psi. Steinbrenner has called y the "back pressure"

of the soil and stated that i t is related to the porosity of the

soi l . The volume of air passing through the flow meter, and being

measured by i t , depends on the volume of air that is able to pass

through the soi l in the tube, which in turn depends on the porosity

of the soi l in the tube T. The flow meter measures the volume of

air at pressure Pip = Pg = 5 psi. flowing per minute. The tempera-

ture of the laboratory during the test was 20°C. - 0.5°C. whxch was

regarded as constant. The volume measured by the flow meter can

be converted into volume per second which is then divided by the

cross-sectional area of the soil tube T to give Q in equation (5)

page 5. P Q indicates the pressure acting on top of the soi l . If

i t is assumed that the pressure of the air as it comes out of the

soil tube T is almost equal to atmospheric pressure, P ^ then

PD - PA = A P '

If atmospheric pressure is taken as zero, then

P d _ o = _P = P D

Thus the reading on the gauge P D gives the loss in pressure head

between the top and bottom of the soil tube T. A,p in energy units

can be substituted for d(j) in equation (5) page 5 . ytc for air at

the temperature of the experiment can be obtained from tables,

d L (length of tube T) is known.

20-

Thus K* can be evaluated from the equation:

K« = O^L (7)

By applying the relationship: K = Kljty to this K ! and substituting

into i t the values of j> and /t for water one can obtain an estimate

of the coefficient of permeability, commonly called the hydraulic

conductivity.

E. Materials and Methods

Soils used:

Ladner Clay

Alderwood Sandy Loam

Peat soi l

Synthetic soil (\ Alderwood sandy loam

+ ^ beach sand + \ Ladner Clay

+ z; peat soil)

Al l the above soils were obtained from the Lower Fraser Valley of

British Columbia. No mechanical analysis was done on the soils.

Samples were taken from a depth (0 - 1 f t . ) , since the textural

classification by which the above soils were classified applies to 1.

the surface texture .

1. ;- Soil Survey of the Lower Fraser Valley; Canada Department of Agricul­

ture, Technical Bulletin 20 .

21

F ig . 6 Diagram Showing Sub Sampling From large Sample Can

a — sample for v o i d rat io measurement

b =3 sample for s o i l tube ,

c = sample for permeability test with water

22.

The soils chosen are among the most important agricultural soils in the

Lower Fraser Valley.

1. Preparation ard Saturation of the Soil Samples.

The soil was air dried, ground and thoroughly mixed. It was then

passed through a 2 mm. sieve. Fruit salad cans (l5cms. diameter, 9cms.

height) with holes at the bottom, were used as containers. A cylindri­

cal 2500 gm. dropping weight was used to compact the so i l . The dropping

height was 30.5 cm. in each case. The soil in the can was then satura­

ted by placing the can in a tray of water, and the water level in the

tray was slowly raised. The water moved up into the soil driving the

air in the soil before i t , thus eliminating air pockets and ensuring uni­

form wetting.

2. Treatment to show the Effect of Soil Moisture content on K' and K.

The soils in this series were each compacted with five blows be­

fore being saturated. They were then equilibrated with different tensions

or pressures on either the tension table or in a pressure pot or a pres­

sure membrane apparatus (56,57) in the following way: The surface of the

soi l sample was carefully levelled by scraping off excess soil with a

spatula until the surface was flat and level" with the rim of the can.

A piece of cheese cloth was stretched across the surface of the soil and

held in place with the aid of a rubber band. The whole sample was then

quicklytransferred from the tray of water and placed on a tension or

pressure apparatus bottom-side up so that the surface of the soil was in

close contact with the membrane of the apparatus (blotting paper in case

of the tensiontable). The apparatus was properly closed and the required

tension or pressure was applied. The sample was removed from the appara­

tus and weighed every 24 hours until the weight was observed to be constant.

Fig. 7 Apparatus i n Operation

ii «

" 5 Soil TuViC

"1 IT joanaaq:

1 -wooden

Fig. 8 Apparatus in Operation Showing S o i l 'rube, Hollow Can, and Wooden Platform

2k:

- Air permeability tests were then performed on the sample. Tensions

or pressures applied ranged from 5cms. of water to 15 atmospheres.

3. Treatment to Show the Effect of Compaction (compaction was eval­

uated as changes.in Void Ratio)

Different samples of the same soil were compacted differently

by dropping the cylindrical weight a different number of times on the

samples. To obtain good differences in compaction levels, some of

the soils were wetted before being compacted. The number of drops

varied from 0 to 20. The sample s were then saturated as described in 1.

They were drained with a tension of 40 cms. as described in 2. above.

It has been observed (6l) that the non-capillary pares of most soils are

completely drained at 40 cms. of water tension. This is equivalent to

the condition of the soi l at its f ield capacity.

4. Measurement of IWusing water as permeant.

Samples were obtained as follows: A brass cylinder 5*6 cms. in

diameter and 4.8 cms. long was carefully driven into the bigger sample

from 2 or 3 (see f ig . 6 page 21). It was then very carefully removed

and the soi l inside i t was carefully trimmed so that the surfaces of the

soil at both ends of the core were level with the rim of the core. A

small cheese cloth was then stretched across one end of the core and held

in place by means of a rubber band. Another brass cylinder of the same

size was placed at the other end so that the rims of both cores were

flush with each other. The two cores were joined together with a thick

plastic tape, making sure that the ends and sides of the cores remained

flush with each other so that no water could escape from the joint. The

end of the core covered with the cheese cloth was then placed in a tray of

2$.

!)wat-er and the soi l inside the core was saturated by upward wetting as

described in 1. The saturated core was then used to estimate the Darcy

K as described in the Literature Review on page 11 under "Some Labora­

tory Methods of Soil Permeability Measurement".

5. Measurement of Void Ratio and Saturation.

Samples were obtained as follows: A brass cylinder 2.54 cms. in

diameter and 4.55 cms. in length was carefully forced into the big sample

from 2 or 3- It was then carefully removed and the soi l inside i t was

trimmed so that the surfaces of the soil at both ends of the core were

level with its rims. A small cheese cloth was then stretched across one

end of the core and held in place with a rubber band. The sample was

weighed accurately to two decimal places and was saturated with water as

described in 1. The saturated sample was then very quickly transferred

to a petri dish so that as l i t t l e water as possible was lost during the

operation and the weight of the saturated sample determined. The sample

was then oven-dried at a temperature of 105°C. and weighed every 24 hours

until the weight was observed to be constant. The soi l was then removed

from the core which was thoroughly cleaned and weighed. The petri dish

was also thoroughly cleaned and weighed. Results of the weighings were

used in computing the void ratio as described on page,42 under "Calcu­

lations and Tables.

6. Measurement of K' with the Modified Steinbrenner"s Apparatus Using

Air as Permeant.

The soil tube T of the modified Steinbrenner's apparatus was used

to obtain a sample from the large sample can (fig. 5 page 18 and f ig . 6

26.

page 21) to estimate K'.

The sample was placed over a hollow fruit salad can resting on

a wooden platform with holes drilled into it to allow for the escape of

air from the soi l tube directly to the atmosphere, (figs. 7 and 8 page

23). The air tubes were connected to the apparatus and air was intro­

duced at a constant pressure of 5 psi. Pressures recorded by the gauge

Pn and corresponding readings of the flow meter were recorded every

minute for 15 minutes. These were used to compute K' as explained on

page 15 under "Theory".

27-

RESULTS AND DISCUSSION 1. Designations

(a) I n t r i n s i c p e r m e a b i l i t y , estimated w i t h the modified Steinbren­

ner's apparatus using a i r as permeant was designated as ( K ' a ) .

(b) (K'<x) was evaluated u s i n g the most f r e q u e n t l y occuring value

of pressure (and i t s corresponding volume) w i t h i n a 15 minute p e r i o d .

For example f o r sample 1, Table 6 page 55 a pressure of 0.916 p s i . and

a volume of 14 l i t e r s were used t o c a l c u l a t e (fc'a,-) as explained i n the

Appendix, Section 3 pages 47 and 48.

^ (c) On the assumption that the i n t r i n s i c p e r m e a b i l i t y (K'a, ) e s t i ­

mated w i t h a i r r e f l e c t e d o n l y the p r o p e r t i e s of the s o i l (see page 5),

the Darcy c o e f f i c i e n t of p e r m e a b i l i t y (K) was obtained by m u l t i p l y i n g

K'a by the u n i t weight of water ( Yw) and d i v i d i n g by the v i s c o s i t y of

water (58), (see a l s o page 5). TKe:.value:.of the c o e f f i c i e n t of permea­

b i l i t y obtained by t h i s method was designated as Ka. One could estimate

the c o e f f i c i e n t o f p e r m e a b i l i t y d i r e c t l y w i t h o u t f i r s t having to estimate

the i n t r i n s i c p e r m e a b i l i t y , i f one used water i n s t e a d of a i r as the

permeant (page 5 ) . The c o e f f i c i e n t of p e r m e a b i l i t y estimated by t h i s

method was designated as K w.

2.

Logarithm of I n t r i n s i c P e r m e a b i l i t y ( l o g K'a) versus Void Ratio ( e ) .

As explained on page 9, many workers have shown t h a t t h e graph of

the l o g a r i t h m of i n t r i n s i c p e r m e a b i l i t y (K'a) versus v o i d r a t i o (e)

approximates a s t r a i g h t l i n e . This however i s not always the case, i t

has been found i n some instances (69,70) t h a t K'a versus e , K'a versus 2 e 3

e and K'a versus — - give s t r a i g h t l i n e graphs. The p l o t of l o g K'a versus e was found t o approximate a s t r a i g h t l i n e i n t h i s study. I t

28

was necessary t h a t t h e samples used i n t h i s case should a l l have the

same s a t u r a t i o n percentage. Since v o i d r a t i o was v a r y i n g , s a t u r a t i o n

(I) had t o vary w i t h i t even though the same s o i l was used, and a l l

samples were drained a t the same t e n s i o n (page 20 s e c t i o n 3 ) . The

r e s u l t s obtained showed t h a t s o i l s drained a t 40 cms of water t e n s i o n

d i d not a l l have approximately the same s a t u r a t i o n percentage. Thus

an attempt was made to s e l e c t at l e a s t s i x samples of each s o i l which

had almost the same s a t u r a t i o n percentages C*- 1%). 0n3y the values

obtained on such samples were used t o p l o t the graphs; the r e s t were

abandoned. In the case of the Ladner s o i l i t was not even p o s s i b l e t o

ob t a i n s i x samples w i t h more or l e s s the same s a t u r a t i o n percentages.

Consequently no graphs are presented f o r the Ladner c l a y s o i l . Fig.9-'

page 29, F i g . 10, page 3D and F i g . 11 page 3L are p l o t s of l o g K'a versus

e f o r Alderwood sandy loam, Synthetic s o i l , and peat s o i l r e s p e c t i v e l y .

These are a l l s t r a i g h t l i n e graphs, i n d i c a t i n g that t h e apparatus could

be used t o estimate i n t r i n s i c p e r m e a b i l i t y .

3-

. I n t r i n s i c P e r m e a b i l i t y (K'a) versus S a t u r a t i o n Percentage (S).

A l l samples were kept a t t h e same vo i d r a t i o (e) w h i l s t s a t u r a t i o n

percentage was v a r i e d by d r a i n i n g the sa t u r a t e d samples w i t h d i f f e r e n t

tensions (see page 22 s e c t i o n 2 ) .

Again, r e s u l t s f o r the Ladner c l a y samples were extremely v a r i a b l e .

Even though t h e r e was a general tendency f o r t h e I n t r i n s i c p e r m e a b i l i t y

t o decrease w i t h s a t u r a t i o n , there were not enough samples w i t h t h e same

vo i d r a t i o (e) but d i f f e r e n t s a t u r a t i o n percentages (&) w i t h which t o

p l o t a graph. F i g . 12 page 33 F i g s . 13 - 16 pages 3 ^ - 3 7 show a decrease

.540 .560 .5B0 ,600 ..620. Void Ratio (e) MO .660 .680 ,70(

Fig. 9 : .Alderwood Sandy Loam: Effect of Void Ratio on Intrinsic Permeability Saturation (S) -0.72%

32

_ i n I n t r i n s i c P e r m e a b i l i t y (Ka) w i t h s a t u r a t i o n (S) f o r Peat, Alderwood

Sandy Loam, and Peat S o i l s r e s p e c t i v e l y . In each case (except f o r Peat)

I n t r i n s i c P e r m e a b i l i t y was v i r t u a l l y zero above 90$ s a t u r a t i o n . This

i n d i c a t e s that the apparatus cannot be used at s a t u r a t i o n s higher than

90$. Peat can absorb a l a r g e amount of water without having t h e s o i l

pores completely blocked; i n other words a l a r g e amount of water may

be imbibed w h i l s t o n l y a small amount i s adsorbed on the c o l l o i d a l par­

t i c l e s of peat s o i l . Hence some s o i l pores remain open f o r the passage

of a i r , even at high s a t u r a t i o n s . Since s a t u r a t i o n i s d e f i n e d as volume

of water / volume of s o i l pores, i t i s p o s s i b l e t o o b t a i n s a t u r a t i o n

percentages of more than 100$ f o r peat, because i n a d d i t i o n to water

f i l l i n g the pore spaces the -organic matter i n peat s o i l can absorb and

hold l a r g e amounts of water.

In many in s t a n c e s t h e r a t e of movement of a i r through s o i l s at l e s s

than 20% s a t u r a t i o n was so great ( i . e . the r e s i s t a n c e t o a i r movement

was so small) that no pressure was recorded by the gauge P^ (see page 16

and consequently the i n t r i n s i c p e r m e a b i l i t i e s i n such cases could not be

obtained. The r a p i d l y moving a i r a l s o blew out some of the s o i l , or

otherwise caused a very appreciable disturbance of s o i l s t r u c t u r e .

Thus i t would seem that the apparatus could not be used s u c c e s s f u l l y on

samples a t l e s s than 20$ s a t u r a t i o n , f o r the Alderwood sandy loam,

the s y n t h e t i c and peat s o i l s .

4. I n t r i n s i c P e r m e a b i l i t y at Zero S a t u r a t i o n

Darcy's law f o r steady laminar f l o w c o n d i t i o n s , a p p l i e s o n l y when

the sample i s 100$ s a t u r a t e d w i t h water. Therefore, i f p e r m e a b i l i t y i s

33

20 40 60 80 100 Percen t S a t u r a t i o n (S)

F i g . 13 Alderwood Sandy Loan: E f f e c t o f S a t u r a t i o n on I n t r i n s i c ! " P e r m e a b i l i t y

Measured w i t h M o d i f i e d S t e i n b r e n n e r ' s Appara tus .

35

a o

to ' o r-i X

•P • H r-i • H &

e •

2Q

18

16

14

12

10

8 o •H 05 C

• H U 3. 6

0

.Ac* \* i \ o

\ \ 0 \ \ \-° \ Xvt \ V? \ \ -V \

V? \u\ \u\ \ \ V

V \o \ Y2 \ x >

\ \ \

L i j

-• '

V

> \ \*

1

i

\ "•

20 40 60 Percent Saturation (S)

80 100

F i g . 14 . Alderwood Sandy Loam: Jtffect of Saturation on Intr ins ic " V Permeability

. Measured withModified Steinbrenner's.Apparatus •

20 40 60 , 80 ' 100 Percent Saturation (S)

Fig. 15 Synthetic Soil: Effect of Saturation on Intrinsic ; Permeability

Measured with Modified Steinbrenner's"Apparatus

37

cv B o

>>

-p •H <H •H X)

cu a

•A. t>

•H W fl

•H

20

18

16

12

10

8

1

\&

\ ' j

V \ \

-\c>

\

• • V V

• -

20 40 60 80

Percent Saturation.(S)

100

Pig. 16 Synthetic Soil: Effect of Saturation on Intrinsic • j Permeability-

Measured with Modified Steinbrenner's Apparatus

38.

estimated using a f l u i d other than water, the sample must be 100$

s a t u r a t e d w i t h that f l u i d . In order t o convert the I n t r i n s i c permeabil­

i t y K'a estimated w i t h the apparatus, using a i r a s permeant to the co­

e f f i c i e n t o f p e r m e a b i l i t y Ka by the equation Ka = K'a^ a (70) (see a l s o /iw

page 5) i t i s necessary t h a t the samples used should be completely

d>r.,y 'i* i . e . completely s a t u r a t e d w i t h a i r . However, as pointed out

above, i n many cases the i n t r i n s i c p e r m e a b i l i t y could not be estimated

on samples at l e s s than 20$ s a t u r a t i o n . The i n t r i n s i c p e r m e a b i l i t i e s

were t h e r e f o r e estimated on samples at s a t u r a t i o n s between 30$ and 80$

and the graphs of i n t r i n s i c p e r m e a b i l i t y versus s a t u r a t i o n were then

extended to cut the i n t r i n s i c p e r m e a b i l i t y a x i s a t zero s a t u r a t i o n , t o

o b t a i n the value of i n t r i n s i c p e r m e a b i l i t y when the sample i s completely

saturated w i t h a i r . Again, i t was necessary t o choose samples w i t h

the same void r a t i o s . F i g s . 13 - 16, pages '2k - 37) show such graphs

f o r Alderwood sandy loam and s y n t h e t i c s o i l s . However, t h e r e was only

one set of s i x samples of peat s o i l f o r which a graph could be obtained.

(Fig. 12 page 33 ) In the other samples of peat s o i l , the v o i d r a t i o

measurements were as v a r i a b l e as was t h e case w i t h the Ladner c l a y s o i l .

No data was t h e r e f o r e presented f o r these. The method by which v o i d

r a t i o and s a t u r a t i o n were measured (see page 25 s e c t i o n 5) was not very

accurate because as f a r as i t can be i n f e r r e d from the r e s u l t s , most

of the v a r i a t i o n s were these of s a t u r a t i o n percentage or v o i d r a t i o .

5'.

,Comparison of C o e f f i c i e n t of P e r m e a b i l i t y (Ka) and the Darcy's C o e f f i c i e n t of P e r m e a b i l i t y (Kw)

The Darcy's c o e f f i c i e n t of p e r m e a b i l i t y Kw which i s a l s o c a l l e d

3 9 .

nbhe h y d r a u l i c c o n d u c t i v i t y or simply c o e f f i c i e n t of p e r m e a b i l i t y ,

was found e m p i r i c a l l y by Darcy to be given by equations 1 and 2 on

page 4. But t h i s equation i s c o r r e c t o n l y i f the permeant used i s water

(47). However, as explained on page 5 with equations (5) and (6) i t

i s p o s s i b l e , f i r s t to estimate the i n t r i n s i c p e r m e a b i l i t y (K') of a

s o i l , and then use the value obtained t o estimate v«hat the c o e f f i c i e n t

of p e r m e a b i l i t y would be f o r d i f f e r e n t f l u i d s by s u b s t i t u t i n g the

values of Ji a n d f o r the f l u i d s i n t o equation 6 page 5. This c o e f f i ­

c i e n t of p e r m e a b i l i t y was designated as Ka i n t h i s study, s i n c e i t was

not estimated d i r e c t l y w i t h water as the permeant, but i n s t e a d was com­

puted from a value of I n t r i n s i c p e r m e a b i l i t y K'a estimated with a i r as

permeant. I t was necessary t o f i n d out how accurate t h i s method was,

compared w i t h t h a t whereby the c o e f f i c i e n t of p e r m e a b i l i t y Kw was e s t i ­

mated d i r e c t l y w i t h water. Values of K'a a t S = 0 , obtained from f i g s .

13 - 16 pages 34 - 3 7 were, converted t o values of Ka by s u b s t i t u t i n g the

values ofy° and f o r water i n t o equation 6 page 5. Values of Kw

were obtained on samples s i m i l a r t o those on which Ka values were o b t a i n ­

ed (as explained i n s e c t i o n 4 page -24). The v a l u e s of t h e d i f f e r e n t

c o e f f i c i e n t s of p e r m e a b i l i t y (Ka and Kw) were p l o t t e d a gainst the v o i d

r a t i o of the samples on t h e same graph paper. F i g . 1'7 shows th a t Ka

and Kw values d i f f e r from each other but are f a i r l y c l o s e t o each other.

The values f o r the Alderwood sandy loam s o i l are c l o s e r to each other

than those of the s y n t h e t i c s o i l . As pointed out e a r l i e r i n the L i t e r ­

ature Review on pages 5 and 11 the equations used, apply w i t h l e s s

accuracy t o f i n e t e x t u r e d s o i l s than f o r coarse t e x t u r e d s o i l s . Since

Fig. 17 Relationship between Coefficient of Permeability (kaJ Obtained with Modified Steinbrenner's Apparatus and Coefficient of Permeability (l^J Obtained with Water on Core Samples, and Void Ratio (e)

40.

2 5 $ of the sy n t h e t i c s o i l was Langley c l a y one would expect t h e

equation to apply t o the s y n t h e t i c s o i l w i t h l e s s accuracy than t o

the Alderwood sandy loam.

CONCLUSIONS

There was too much v a r i a b i l i t y i n the readings obtained due mainly

to the d i f f i c u l t y i n o b t a i n i n g undisturbed sub-samples f o r the d e t e r ­

m i n a t i o n of v o i d r a t i o and percent s a t u r a t i o n .

The equations used i n the a n a l y s i s d i d not apply a c c u r a t e l y to

f i n e t e x t u r e d s o i l s .

A considerable amount of data had t o be discarded becaus e of

extreme v a r i a b i l i t y , before any reasonable a n a l y s i s could be c a r r i e d

out. Consequently i t i s f e l t t h a t a t the present stage t h e apparatus

i s not s u i t a b l e for the e s t i m a t i o n of s o i l p e r m e a b i l i t y . A much more

thorough e v a l u a t i o n of the apparatus, i n the l a b o r a t o r y , i s suggested.

The l a b o r a t o r y e v a l u a t i o n should be. f o l l o w e d by a very comprehensive

e v a l u a t i o n i n the f i e l d , before any d e f i n i t e conclusions can be a r r i v e d

a t , as t o the usefulness of the apparatus i n p e r m e a b i l i t y measurements

i n s i t u .

4 1 .

\

- APPENDIX -

42.

A. C a l c u l a t i o n s and Tables.

1. Flow Meter C a l i b r a t i o n Curve.

The use of t h e f l o w meter chart t o compute the q u a n t i t y of a i r

f l o w i n g through the f l o w meter i s e x p l a i n e d i n the accompanying c h a r t s . /

Values of v i s c o s i t y and d e n s i t y o f a i r (at the temperature and

pressure under which the experiment was performed) required f o r the use

of the c h a r t s were obtained from the "Handbook of Physics and Chemistry".

Now, with t h e I n d i v i d u a l C a l i b r a t i o n chart (page43) and the graph on

, page 44 the i n s t r u c t i o n s on page 44'were fo l l o w e d t o o b t a i n a c a l i b r a t i o n

curve f o r t h e co n d i t i o n s of fl o w a s f o l l o w s : (see step 3. page44) ^ = 1.042 Wf (jPf -f)p R3

U # From C a l i b r a t i o n c h a r t (page,43)

Wf = 2.715 gm ft = 2.53 _ and from the Handbook of mi

Physics and Chemistry,^= .0238199 and^»= .0015395 at 5 p s i . and 25°C.

Therefore St- = 1.042 x 2.715(2.53 - .00153959).00153959 R 3

(.0238199) (2.53)

= 7.6739 R 3

For R = 25 Scale Reading from C a l i b r a t i o n Chart (page 43) = 95

(see Step 1 page 44 )

Therefor e S t = 7.6739 R 3 = 7.6739 x 15,625 = 119,904.6

From C o r r e l a t i o n Chart (page 44) read o f f C R f o r St = 119,904.6 and R = 25 This gives = 0.97 (see step 4)

From C a l i b r a t i o n Chart (page 43) % = 0.500" (Step 5) Thus

£ = 59.8 x 0.500 x 0.97 12.715(2.53 - .00154) 25 + 2 (Step 5) J 2.53 x .00154 100

= 67091.0625 mt/min.

S/ZTE NO. 5

S T D .

A/R ML./

CAL/BRA T/OM CHART

*\J FLOH/METE R CATALOG A/O. F15oo

SER/AL NO. E /9Q Df = O. 500" = 2.7/5 GM. 2.53 GM / M L .

*STO. = /ATM. A A / D 7 0 ° F

•A3-

1 WATER

/MJAt. 25

eopoo--z

5,opo^A

/o 20 SO <40 SO 60 70 80 90 /OO S C A L E R E A P S MG A T CENTER OF BALL

-COPYRIGHT 1961 BY ROGER GILMONT INSTRUMENTS, INC.— MAY NOT BE REPRODUCED IN ANY FORM

D I R E C T I O N S F O R U S E

The individual calibration chart supplied with each meter is a plot of the percentage change in diameter ratio, fl, against the scale reading of the meter, which is a straight line. On the left side of the chart is a direct reading scale of the equivalent flow of air at standard conditions, and a similar scale for water is on the right side.

When cleaning the meter, great dare should be exer­cised not to lose the glass ball. It is possible to replace the glass ball; however, the calibration will not be as ac­curate, although deviations will only be minor.

The above dimensionless correlation chart of-flow coefficient, CR, against Stokes number, St, for different values of fl may be used to calculate the calibration curve for any fluid whose density and viscosity are known at conditions of flow:

1. Select a suitable value of R and read the corre­sponding scale reading from the individual calibration curve supplied.

2. Obtain the values of weight of float in .grams, Wf, and the density of float, pf, in grams/ml. from the cali­bration chart. Let P= density of fluid in grams/ml. and

viscosity of fluid in centipoises at conditions of flow. 3. Calculate the Stokes number from the following

equation: St= 1.042 W ' < * - * > *

umetric rate of flow in ml/min, q, from the following equation:

<7=59.8D/ CT

6. The volumetric rate of fluid flowing and measured at the conditions of flow may be converted into mass rate of flow by multiplying by the density.

7. To obtain a complete calibration curve several values of fl may be selected. Gases may be plotted against the standard air scale and liquids against the standard water scale on the calibration chart to give very nearly straight lines.

SAMPLE CALCULATION

Flowmeter Catalog No. F 1100, std. water at fl= 25 1. From individual calibration chart, scale reading is

100 at fl i= 25

Wf — .00530 grams, water: P— 1.0 grams/ml

4 2.53 grams/ml. For std.

3. St =

and /m 1.0 cp

1.042 x.00530 x 1.53 x 1.00

fl:

4. From the correlation chart read off the corre­sponding value of CR for the calculated value of St and the selected value of fl.

5. Obtain the value of diameter of float in inches, Df, from the calibration chart, and calculate the vol-

4.

5.

1.0x2.53

From correlation chart, CR

Df = .0625 inches and

x 15,625 = 53.2

.458

q = 59.8 x.0625 x.458 .00530 x 1.53 2.53x1.0 x 25(2.25) = 5.44ml/min

O G E R

I I L M O N T J _ N S T R U M E N T S , I N C .

Mass flow: 5.44 x 1.0 = 5.44 grams/min.

1 G R E A T N E C K R O A D • G R E A T N E C K . N E W Y O R K

COPYRIGHT 1961 BY ROGER GILMONT INSTRUMENTS, INC. — MAY NOT BE REPRODUCED IN ANY FORM

45.

Read 67,091.0625 mi/m±a. from left hand scale on Calibration

Chart (page 43). Move across to the corresponding scale reading of 95 for

R = 25 and plot the point as shown on the graph.

The whole process was repeated for R = 20, 10, 5, to obtain the

broken line calibration curve (page43).

Table 1. Values for Calibration Curve

R Scale Reading St C R .

25 95 119,904.6 0.97 67,091.06 20 75 61,391.2 0.97 53480.12

10 35 7,673.c9 0.9 23,728.95 5 15.25 959.2375 0.79 lCp.66.41

2. Volume of Air Flowing Through the Flow Meter.

A typical record of readings taken over a period of 15 minutes is

shown in Table 2 page 46.

With flow meter reading at center of flow meter ba l l , read volume

of gas flowing per minute from the corrected calibration curve (page 43)

These values are entered in the "volume" row of table 2, page 46.

TABLE 2

T y p i c a l Record of A i r P e r m e a b i l i t y Readings.

See Sample No. 1.-, Pg. 55

Compaction. = 1 blow; S a t u r a t i o n = 39.1$ Constant A i r Pressure used = 5 p s i . Temp. = 25°C

Time a f t e r l a s t Reading (mins. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Pressure P n ( o r p) 0.916 0.916 0.916 0.916 0.916 0.916 0.916 0.916 0.916 0.916 0.916 0.916 0.916 0.916 0.916 0.916

PB 5 5 5 5 5 5 5 5 5 5 5- 5 5 5 5 5 Pr 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

PM 5 4.8 5 5 4.8 4.8 4.8 4.8 4.8 4.8 4.8 4.8 4.8 4.8 4.8 4.8

Flow Meter Reading 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20

Volume ( l i t e r s ) 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14

3.. Value for the Intrinsic Permeability K' a and the Darcy Coefficient of Permeability K&

Let the average volume of a i r flowing per minute as determined

from the flow meter chart be V liters/minute. If ^ is defined as the

volume of a i r in m l l l i - l i t e r s flowing across a unit cross sectional

area of the so i l tube in one second then:

A = Vxl0 3/60 = 0.368 V mis/sec. + 3.14x(7.6)/4

where diameter of cross section of tube = 7.6 cms.

Length of so i l tube = 5 cms = dl~

Let the pressure measured by the gauge PJJ (see f i g . 7 page 2 3 ) ,

be equal to p ps i . (see "Theory" page 17)

Then the drop in head 4$ that occurs when a i r passes through the

so i l core 5 cms. long in the so i l tube T is given by

<(<_ = _ x (76x13.6x980) ergs (14.7 cms

= (7.9x10^) p. ergs cms

The int r ins ic permeability K' i s given by the equation

- K« a= 9.uc(L

= (l.83xl.3xl0~4) poises = (2.379xl0"^) poises s

Therefore by substituting the values above into this equation,

K'^can be evaluated.

P.S. pidL w i l l be constant ,', 2.379x5x10"^ = (11.895x10^)

Kq, = K<c&5 where = density of water •^t0 5 = acceleration due to gravity

p^j = v iscosity of water

48.

x P.S. £ , = 1. /Iv = 0.894 x 10 poises

Therefore Ko.= K'a __ = (109.61969 x 10) K!_

Example:

Consider Sample No. 1 (see Table 2 page 46)

Average of values of Ap = 0.916 psi.

" " corresponding values of V = 14.0 l iters

= 0.368 x 14 mis sec

and d$ = 7.9 x id* x 0.916 ergs cm

K _= 0.368 x 14 x 11.895 x 10~4 cm2

7.9 x 10 x 0.916 2

=8.5 cm i and KA = 8.5 x 1096.2 cms/sec

=9.3 cms/sec.

4. Darcy's Coefficient of Saturated Permeability K W estimated with water on Core Samples.

ml. of water collected per hour = Q.

ml. " » " " sec. = Q. 3600

2 Cross sectional area of core = 25.51 cm = S.

Diameter =5.6 cms.

* = Q ^ y , 3600x25.51 /cffl^ sec

49.

•Height of water above s o i l core, H = 1 inch = 2.54 cms

Length of s o i l core, e, = 4.8 cms.

Therefore total head H i e = (2.54 + 4.8) cms. = (7.34) cms.

From the Darcy equation:

^. = KwH+e , we have e

K = 3-e (H+e)

Therefore K w = (?$.31x10^) j . 8 ) 7.34

= Q x 4.8 x 1CT^ 9.31 x 7.34

= .0705 x 10 _ Z f Q

= 7.05 x 10*"6 Q

Again consider values for sample No. If Table 6, Page 55.

Table 4

Sample No. 1 Treatment mis. of water collected i n Average Percolation Average

1 hr 1 hr 1 hr 1 hr 1 hr Rate (Q) K^xlO5

Compacted with 2 blow 17 16 16 16 15 16 mls./hr. 11.252-

sec

Thus K w = 7.05 x 16 x 10~^cm = 11.2 x sec

10" 5 cm sec.

5. Void Ratio e.

In the f i e l d of s o i l science, void ratio i s defined as

e = Total Volume of voids Volume of Soil Solids

50.

e = (Saturated Weight) - (Oven dry weight) ( V o l . of sample core) - (Saturated weight - Oven dry

weight)

For sample l : ( s e e Table 6 page 55)

e = Column 4 = 6.84 = .421 Column 6 - Column 4 23.1-6.84

6. Percent S a t u r a t i o n S.

S = Volume of water (Assume u n i t weight of water = l ) Volume of v o i d s

Column 5 (see t a b l e 6 ) Column 4

For sample No. Iv Table 6, page 55.

S = 2.68 = .391 6.84

51.

B. Curve Fitting

The method of coefficients was used. This is an algebraic method. Observational equations were formed by substituting each pair of values in the equation y = mx+b, and then the most probable values of m and b were calculated.

Procedure: 1. Form the observational equations. 2. Add these to get the normal equation in b. 3. Multiply each equation through by its coeffi­

cient of m to get the normal equation in m.

4. Solve these two normal equations for m and b.

Example:

Steps 1 and 2

Step 3.

Table 10- K ' a vs S.

7.3 — .598m + b

6.5 .624m + b

6.3 = .649m + b

5.1 = .688m b 4.0 .727m + b

3.9 = • 740m + b

33.1 4.026m + 6b

4.4 .358m + .598b

4.1 = ,389m + .624b

4.1 = • 421m + .649b

3.6 = • 473m + .688b

2.9 .528m + • 727b

2.9 = • 547m + .740b

22.0 2.716 + 4.026b

Normal in b (l)

Normal in m (2)

From equations (l) and (2) m = -22 b = 20.

52. Table 3 Alderwood Sandy Loam. E f f e c t of Void Ratio (e) on I n t r i n s i c P e r m e a b i l i t y ' , • % Sa t u r a t i o n (5) = 12% - 1%

1 Saturated

Wt. •

2 Wt. after Drainage

on Tension Table

3 Oven-Dry Wt.

4 T o t a l Pore V o l .

1-3

5 V o l . of Water A f t e r Drainage

2-3

6 V o l . of Sample Core

7 Void R a t i o (c)

4 • 6-4

8 % Satura­t i o n (5)

5 4

9 A i r

Pressure

• P-p s i .

10 V o l . a i r Flow­i n g

V (L i t e r s )

11 I n t r i n ­s i c Permea­b i l i t y

K ' x l O 8 ^

12 . Coeff. . Of Perm.

K x l 0 5 c m •sec

13 Ave. P e r c o l a ­t i o n Rate

ml nr. .

14 Darcy 1s Goeff. Of Perm.

K w x l 0 5 c m . sec

15

1 98.87 96.43 90.20 8.67 6.25 23.1. .602 72.2 1.875 12.3 7.3 8.0 18.5 13.1

2 98.85 96.57 90.63 8.22 5.94 23.1 .607 72.4 1.663 10.72 7.1 7.8 23 16.2

3 99.95 97.36 90.71 9.24 6.65 23.1 .668 72.0 1.420 12.71 9.9 10.7 26 18.3

4 100.50 97.99 91.60 8.90 6.39 23.1 .627 71.8 1.500 11.00 8.1 8.9 21.8 15.3

.5 100.06 97.51 . 91.04 9.02 6.47 23.1 .641 71.7 1.433 11.20 8.7 9.5 24 16.9

6 99.66 97.35 91.43 8.23 5.92 23.1 .554 71.9 1.875 10.20 6.0 6.6 20 14.1

Table 4 Synthetic Soil: Effect of Void Ratio (e) on Intrinsic Permeability % Saturation (S) = 7 9 $ ± 1%

1 Satura­ted Wt.

2 Wt. After Drainage

On Tension

Table

3

Oven Dry Wt.

4

Total Pore Vol.

1-3

5

Vol. of Water After Drain­age

2-3

6

Vol. of Sample Core

7

Void Ratio (e)

4 6 - 4

8 % Satura­tion ( s )

5

4

9

Air Pres­sure

P-psi

10 Vol. air Flowing

V (Liters)

11 Intrin­sic Permea­bi l i ty

K'xlC&m2

12 Coeffi­cient of Perm

K xl05cm sec

13 Ave. Percola­tion Rate

ml hr.

14 Darcy1s Coeff. of

Perm.

KypclO cm sec

15

1 98.39 95.54 34.84 13.55 1 0 . 7 0 23.1 1.42 78.8 2.125 12.0 6 . 3 6.9 13.0 9.2

2 98.75 9 5 . 9 5 34.95 13.80 11.00 23.1 1.48 7 9 . 5 2.050 12.0 6.5 7 .1 10.3 7 . 3

3 9 9 . 6 0 96.80 35.40 14.20 11.40 23.1 1 . 5 9 80.1 1.710 12.45 8.1 8.8 11.8 8.4

4 98.11 9 5 . 5 0 35.12 12.99 10.38 23.1 1.28 79.7 2.435 11.214 5 .1 5 . 6 12.2 8.7

5 99.30 96.63 86.93 12.37 9.70 23.1 1.15 78.5 2.653 9.473 4.0 4.3 11.8 8.4

6 98.41 9 5 . 7 9 36.16 12.25 9 . 6 3 2 3 . 1 1.13 78.6 2.906 10.141 3 . 9 4 . 2 10.3 7 . 3

Table 5 Peat S o i l ; E f f e c t of Void Ratio (e) On I n t r i n s i c P e r m e a b i l i t y % S a t u r a t i o n (S) = 32% - 1%

1 Satur a ­ted Wt.

2 Wt. A f t e r Drainage On Ten­s i o n Table

3 Oven-Dry Wt.

4 T o t a l Pore Vol.

1-3

5 Vo l . of Water A f t e r D r a i n ­age 2-3

6 Vo l . of Sample Core

7 Void Ratio (e)

4 6-4

8 % Satur­a t i o n (s)

5 4

9 A i r Press­ure

P-p s i .

10 Vo l . A i r Flowing

V ( L i t e r s )

11 I n t r i n ­s i c Permea­b i l i t y K'xlO^cm2

12 Coeff. Of Perm.

K xD^cm sec

13 Ave. Perco­l a t i o n Rate

ml hr

14 Darcy's Coeff. Of Perm. K^xlO 5™

sec

15

1 89.60 79.55 74.80 14.80 4.75 23.1 1.78 32.1 2.0 9.99 5-5 6.1 125 88

2 89.93 79.36 74.61 15.32 4.75 23.1 1.97 31.0 1.75 11.6 7.3 8.1 194 138.1

3 88.93 78.39 73.46 15.47 4.93 23.1 2.02 31.9 1.625 11.0 7.5 8.2 186 108

4 89.58 79.06 73.98 15.60 5.08 23.1 2.07 32.6 1.71 12.45 8.1 8.8 200 142.4

5 89.70 78.82 73-70 16.00 5.12 23.1 2.25 32.0 1.279 11.51 10.0 10.9 185 106

6 89.83 78.97 73.93 15.90 5.04 23.1 2.20 31.7 1.420 12.71 9.9 2.4 190 134

Table 6 Alderwood,Sandy Loam; E f f e c t of S a t u r a t i o n (S) On I n t r i n s i c P e r m e a b i l i t y 55. Void R a t i o (e) = 0.42 - .01

1 ' ' \

1 Satura­t i o n Wt.

2 Wt.After Drainage On Tension Table

3 Oven-Dry Wt.

4 To t a l Pore V o l .

1-3

5 Vo l . of Water A f t e r Drainage

2-3

6 Vo l . o f Sample Core

7 Void R a t i o OO

4 6-4

8 % Satur­a t i o n (s)

5 4

9 A i r Press­ure

P. p s i .

10 V o l . A i r Flowing

V ( l i t e r s )

11 I n t r i n ­s i c Permea­b i l i t y

K'xlC&m 2

12 Coeff. of Perm

K xK)5cm sec

13 Ave. Perco­

l a t i o n Rate ' ml hr.

14 Darcy's Coeff. of Perm. KvxX)^cm

sec

15

1 128.7 124.54 121.86 6.84 2.68 23.1 .421 39.1 0.916 14.0- 8.5 9.3 16 11.2

2 130.8 126.68 123.90 6.90 2.78 23.1 .426 41.3 1.672 12.13 8.0 8.8 19 13.5

3 132.1 128.91 125.16 6.94 3.75 23.1 .430 54.0 1.913 10.20 5.9 6.5 21.8 15-3

4 131.93 129.20 125.11 6.82 4.09' 23.1 .419 60.0 2.146 9.598 5.0 5.4 19.8 14.0

5 130.90 128.49 124.02 6.88 4.47 23.1 .425 65.0 2.693 10.164 4.2 4.6 15.5 10.8

6 126.50 121.93 119.77 6.73 2.16 23.1 .411 32.0 1.167 10.098 9.6 10.5 18 12.6

Table 7 Synthetic S o i l ; E f f e c t of S a t u r a t i o n (S) On I n t r i n s i c P e r m e a b i l i t y Void Ratio (e) = 1.04 - .01

1 Satura­ted Wt.

2 Wt. A f t e r Drainage On Tension Table

3 Oven-Dry Wt.

4 T o t a l Pore Vo.

1-3

5 V o l . of Water A f t e r D r a i n ­age 2-3

6 Vol. of Sample Core

7 Void Ratio (e)

4 6-4

8 % Satur­a t i o n (s)

'5 4

9 S i r Press­ure

P-p s i .

10 Vol. A i r Flowing

V ( L i t e r s )

11 I n t r i n ­s i c Permea­b i l i t y

xl08cm2

12 Coeff. Of Perm.

K xlO^cm sec

. 13 Ave. Perco­l a t i o n Rate

ml hr.

14 Darcy*s . Coeff. Of Perm. KV(pd05cm

sec

15

1 104.16 97.57 92.80 11.85 4.77 23.1 1.050 .403 2.423 9.795 4.5 4.9 9.5 • 6.6

2 99.82 94.61 88.02 11.80 6.59 23.1 1.045 . 560 2.75 ' 8.05 3.2 3.6 6.0 4.3

3 100.50 95.47 88.53 11.77 6.94 23.1 1.035 .591 3.68 7.51 2.8 3.0 12.0 8.5

• 103.31 98.63 91.59 11.72 7.04 23.1 1.030 .610 3.617 9; 51 2.9 ' . 3.2 11 7.6

5 99.68 95.52 87.89 11.79 7.63 23.1 1.040 .649 3.225 7.36 2.5 2.8 . 12.0 8.5

6 101.78 97.98 90.11 11.67 7.87 23.1 1.039 .675 . 3.500 6.8 2.2 . 2.4

i —

• ' . 9.5 6.5

57. Table 8 Peat S o i l ; Effect of Saturation (S) On I n t r i n s i c Permeability-

Void Ratio = 2.51 - .01 1

Satur­ated Wt.

2 Wt.After Drainage On Tension Table

3 Oven-Dry Wt.

4 Total Pore Vol.

1-3

5 Vol. of Water After Drain­age 2-3

6 Vol. of Sample Core

7 Void Ratio (e)

4 6=4"

8 % Satur­ation (s)

5 4

9 A i r Pres­sure

P-p s i .

10 Vol.Air Flowing

V (Li t e r s )

11 I n t r i n ­s i c Permea­b i l i t y K' xloScm2

12 Coeff. Of Perm

KxIoScm sec

13 Ave. Perco­l a t i o n Rate ml hr.

14 Darcy's Coeff. Of Perm. K^xlO^cm

sec

15

1 . 90.41 77.11 73.90 16.51 3.21 23.1 2.51 19.4 1.625 11.00 7.5 8.2 200 142.4

2 90.23 78.03 73.73 16.50 4.30 23.1 2.50 26.0 1.599 12.269 8.5 9.3 205 146.3

3 92.11 81.91 75.66 16.45 6.25 23.1 2.52 38.0 1.903 12.00 7.0 7.7 182 130.7

4 90.34 81.26 73-85 16.49 7.41 23.1 2.50 45.0 1.875 12.30 7.3 8.0 194 138.1

5 94.20 90.21 77.68 16.52 12.53 23.1 2.51 76.0 2.504 11.055 4.9 5.4 184 131.3

6 94.31 91.30 77.79 16.52 13.51 23.1 2.51 82.0 2.710 10.67 4.4 4.8 184 131.3

1 58.

Table 9 Alderwood Sandy Loam; E f f e c t of Sat u r a t i o n (S) On I n t r i n s i c P e r m e a b i l i t y Void Ratio (e) = .62 - .01

1 Satura­ted Wt.

2 Wt.After Drainage On Tension Table

3 Oven-Dry Wt. .

4 T o t a l Pore V o l .

5 V o l . of Water A f t e r Drainage

2-3

6 Vol. of Sample Core

7 Void Ratio (e)

4 6-4

8 % Satur­a t i o n (s)

5 4

9 A i r Pres­sure

P-p a i .

10 Vol. A i r Flowing

V ( l i t e r s )

11 I n t r i n ­s i c Permea­b i l i t y K'xlO^m 2

12 Coeff. Of • Perm

K xlO^cm sec

13 Ave. Perco­l a t i o n Rate

ml hr.

14 Darcy's Coeff. Of Perm. K xQO cm

sec

15

1 99.52 96.10 90.72 8.80 5.28 23.1 .616 60.0 ,. 1.682 12.018 7.9 8.7 29 20.3

2 98.63 95.14 89.80 8.83 5-34 23.1 .621 60.5 1.708 . ' 11.880 77.7 8.5 28 19.5

3 100.06 97.01 91.19 ' 8.87. 5.82 23.1 ' .625 65.5 1.854 . 11.000 6.6 7.2 21 15.1

1

4 98.28 95.63 89.45 8.83 .6.18 23.1 • .619 70.0 2.000 9.990 5.5 6.1 23 16.0

5 99.42 97.58 90.64 8.78 6.94 23.1 .615 79.1 3.236 :10.504 .3.6 3.9 24 17.1

6 100.54 98.77 91.69 8.85 7.08 ;.. 23. i .623 80.0 2.938 .9.900 3.5 3.9 26 18.2

Table 10 Alderwood Sandy Loam; Ef f e c t of Saturation (S) on I n t r i n s i c Permeability 59. Void Ratio (e) = .58 - .01

1 Satura­ted Wt.

2 W t.After Drain­age On Tension Table

3 Oven-Dry Wt.

4 Total Pore Vol.

1-3

5 Vol. of Water A f t e r Drain­age 2-3

6 Vol. of Sample. Core

7 Void Ratio (e)

4 6-4

8 % Satur­ation (s) 5 4

A9 Air Pres­sure

P-p s i .

10 Vol.Air Flowing

V ( l i t e r s )

11 Int r i n -s i c Permea­b i l i t y

8 2 K'xlO cm

12 Coeff. Of Perm.

KxlD^cm sec

13 Ave. Perco­l a t i o n Rate ml hr.

14 Darcy *s Coeff. Of Perm. K^lD^cm

sec

15

1 98.40 94,95 89.80 8.60 5.15 23.1 .594 59.8 1.848 12.2 7.3 8.0 26 18.3

2 . 99.50 96.29 90.95 . 8.55 5,34 23.1 .589 62.4 1.750 10.2 6.5 7.1 24 17.5

3 100.50 .97.50 91.96 8.54 5.54 23.1 .587 64.9 . 2.125 12.0 6.3 \ 6.9 20 14.1 •

4 99.65 96.97 91.09 8.56 5.88 23.1 .590 68.8 2.435 11.214 5.1 5.6 27 19.0

5 100.25. 97.91 91.70 8.55 6.21 23.1 .588 72.7 2:653 9.473 4.0 4.3 23 16.3 '

6 . 99.66 97.43 91.09 8.57 6.34 23.1 • 591 74.0 2.810 9.96 3.9 4.3 24 17.1

60. Table 11 - Alderwood Sandy Loam; E f f e c t of S a t u r a t i o n (S) On I n t r i n s i c P e r m e a b i l i t y

Void Ratio (e) = .55 - .01

1 Satura­t e d Wt.

2 Wt.After Drainage On Tension Table

3 Oven-Dry Wt.

4 T o t a l Pore V o l .

1-3

5 V o l . of Water A f t e r D r a i n ­age 2-3

6 V o l . of Sample Core

7 Void R a t i o (e)

4 6-4

8 % Satur­a t i o n (s)

5 4

9 A i r Pres­sure P-

p s i .

10 V o l . A i r Flowing

V ( l i t e r s )

11 I n t r i n ­s i c Permea­b i l i t y K'xlC^cm2

12 Coeff. Of Perm.

K xlO^cm sec

13 Ave. Perco­l a t i o n

ml hr.

14 Darcy 1s Coeff. Of Perm. Kwxl0''cm

sec

15

1 98.00 94.71 89.78 8.22 4.93 23.1 .554 60.0 1.875 10.2 6.0 6.6 27 19 .1

2 99.40 96.26 91.14 8.26 5.12 23.1 .557 62 .0 2.000 9.99 5.5 6.1 25 17.6

3 100.45 97.66 92.18 8.27 5.48 23.1 .559 66.3 2.505 11.055 4.7 5.4 27 + 19.3

4 99.95 97.89 91.67 8.28 6.22 23.1 .560 75.1 2.913 7.838 3.0 3.3 27" 18 .9

5 100.03 98.23 91.85 8.18 6.38 23 .1 .549 78.0 3.413 7.280 2.4 2.6 23 16.4

6 98.15 96.49 89.97 8.18 6.52 23 .1 .550 79.7 3.633 6.475 2.0 2.2 25 17.3

Table 12 Alderwood Sandy Loam; E f f e c t of Sat u r a t i o n (S) On I n t r i n s i c P e r m e a b i l i t y Void R a t i o (e) = .67 - .01

1 Satura­ted Wt.

2 Wt.After Drainage On Tension Table

3 Oven-Dry Wt.

4 Tot a l . Pore V o l .

1-3

5 V o l . of Water A f t e r D r a i n ­age 2-3

6 Vol. of Sample Core

7 Void Ratio (e)

4 . 6-4

8 % Satur­a t i o n (s)

5

9 A i r Pres­sure

P-p s i .

10 V o l . A i r Flowing

V ( l i t e r s )

11 I n t r i n ­s i c Permea­b i l i t y K'xlC&m2

12 Coeff. Of Perm.

K xldW sec

13 Ave.

Perco­l a t i o n Rate

ml hr.

14 Darcy 1s Coeff. Of Perm. K^xlO^S

sec

15

1 100.95 96.88 91.69 9.26 5.19 23.1 .668 56.0 1.464 12.582 9.5 10.4 24 16.9

2 98.35 . 94.86 89.10 9.25 5.76 23.1 .669 62.2 1.583 12.140 8.5 9.3 31" 21.5

3 98.85 95.57 89.63 9.22 ' 5.94 23.1 .665 64.5 1.700 12.200 8.0 8.7 29" 20.2

4 - 98.48 96.02 89.21 9.27 6.81 23.1 .671 73.5 1.906 10.148 5.9 6.5 26 . 18.3

5 99.53 97.50 90.30. .9.23 7.20 23.1 .667 78.0 2.146 9.598 5.0 5.4 31 + 22.0

6 100.62 98.96 91.33 9.29 7.63 23.1 .675 82.1 2.846 10.200 4.0 4.4 22" 15.3

62. Table 13 Alderwood Sandy Loam; Effect of Saturation (S) On Intrinsic Permeability

Void Ratio (e) = .51 - .01

1 Satura­ted Wt.

2 Wt.After Drainage On Tension Table

3 Oven-Dry Wt.

4 Total Pore Vol.

1-3

5 Vol. Of Water After Drain­age

2-3

6 Vol.Of Sample Core

7 Void Ratio (e)

4 6-4

8 % Satur­ation (s)

5 4

9 Air Pres­sure P.

psi.

10 Vol.Air Flowing V

(l i t e r s )

11 Intrin­sic Permea­b i l i t y K'xI08cm2

12 Coeff. Of Perm.

K x!05cm Sec

13 Ave. Perco-l a t i on

ml hr.

14 Darcy's Coeff. Of Perm. K^xID^cm

15

1 9 9 . 7 9 96.67 92.09 7 . 7 0 4.58 23.1 . 5 0 2 59.5 1.750 11.600 7 . 3 8.1 24 17.1

2 101 .30 98.12 93.55 7 . 7 5 4 . 5 7 23.1 .505 59.0 1.942 11.838 6.6 7.4 22 15.8

3 98.87 96.08 91.09 7 . 7 8 4 . 9 9 23.1 .510 64.O 2.000 9.990 5.5 6.1 26 18.3

4 100.15 9 7 . 5 5 92 .37 7 . 7 8 5.18 23.1 .509 66.5 2.504 11 .055 4.9 5 . 4 27 18.7

5 100.65 98.15 92.85 7.80 5.27 23.1 .511 6 7 . 6 2.423 9 . 7 9 5 4 . 5 4 . 9 21 14.5

6 100.18 98.07 92 .37 7.81 5 . 7 0

1 23.1 .512 ' 73.0 3.360 8.360 2 .6 2 .9 21 + 14.6

63. Table 14 - Synthetic S o i l E f f e c t of S a t u r a t i o n (S) On I n t r i n s i c P e r m e a b i l i t y

Void Ratio = 1.12 - .01

1 Satura­t e d Wt.

2 Wt.After Drainage On Tension Table

3 Oven-D r y

Wt.

4 To t a l Pore V o l .

1-3

5 Vol . Of Water A f t e r D r a i n ­age 2-3

6 V o l . Of Sample Core

7 Void R a t i o (e)

4 6-4

8 % Satur­a t i o n (S)

5 4

9 A i r Pres­sure P-

p s i .

10 Vo l . A i r Flowing

V ( l i t e r s )

11 I n t r i n ­s i c Permea­b i l i t y K'xlO^m

12 Coeff. Of Perm.

Kx]0 5cm sec

13 Ave.

Perco­l a t i o n Rate

ml hr.

14 Darcy 1s Coeff. Of Perm. K^x^an

sec

15

1 98.38 89.93 86.18 12.20 3.75 23.1 1.12 27.5 1.712 10.654 6.9 7.6 9.0 6.3

2 98.41 91.42 86.16 12.25 5.26 23.1 1.13 43.0 2.338 10.60 5.0 5.5 7.0 5.0

3 98.39 91.00 86.29 12.10 4.71 23.1 1.12 39.0 2.0 9.99 5.5 6.1 11.0 7.7

4 99.10 92.82 86.80 12.30 6.02 23.1 1.11 49.0 2.423 9.795 4.5 4.9 12.0 8.5

5 98.56 94.78 86.36 12.20 8.42 23.1 1.12 69.1 3.534 6.745 2.1 2.3 9.8 6.9

6 98.95 95.75 86.63 12.30 9.10 23.1 1.11 74.5 4.175 6.2 1.6 1.8 10.8 7.6

64. Table 15 Synthetic S o i l ; E f f e c t of S a t u r a t i o n (S) On I n t r i n s i c P e r m e a b i l i t y

Void R a t i o (e) = 1.26 - .01 i

1 Satura­t e d Wt.

2 Wt.After Drainage On Tension Table

3 Oven-Dry Wt.

4 To t a l Pore Vol.

1-3

5 Vo l . Cf Water A f t e r

Drainage

2-3

6 Vol . Of Sample Core

7 Void R a t i o (e)

4 6-4

8 % Satur­a t i o n (s)

5 4

9 A i r Pres­sure

P-p s i .

" 10 V o l . A i r Flowing

V ( l i t e r s )

11 I n t r i n ­s i c Permea­b i l i t y K xX&m 2

12 Coeff. Of Perm.

K xl0 5cm sec

13 Ave.

Perco­l a t i o n Rate

ml hr.

14 Darcy 1s Coeff. Of Perm. KwxlQ^cm

sec

15

1 99.65 91.96 86.75 12.90 5.33 23.1 1.260 41.3 1.903 12.00 7.0 7.7 11.5 8.1

2 102.36 95.96 89.51 12.85 6.45 23.1 1.254 50.2 1.906 10.15 5.9 6.5 10.5 7.5

3 98.75 93-00 85.85 12.90 7.15 23.1 1.261 55.4 2.410 11.19 5.1 5.6 8.3 5.9

4 104.30 100.37 91.35 12.95 9.02 23-1 1.270 69.6 3.300 10.68 3.6 3-9 9.5 6,6

5 99.97 97.05 87.05 12.92 10.00 23.1 1.265 77.3 3.744 8.30 2.5 2.7 10.0 7.2

6 101.18 98.62 88.29 12.89 10.33 23.1 1.259 80.1 3.633 6.48 2.0 2.2 9.5 6.7

Table 16 Synthetic S o i l ; E f f e c t of Sat u r a t i o n (s) On 'In t r i n s i c ' P e r m e a b i l i t y Void Ratio (e) =1.40- .01

\ • i , " ' i , \ i \ ~ i i 1

Satur­ated Wt.

2 Wt.After Drainage On • Tens i o n Table

3 Oven-Dry Wt.

4 • :• T o t a l Pore V o l .

1-3

5 V o l . Of Water A f t e r D r a i n ­age . 2-3

6 Vol.Of Sample Core

7 Void Ratio (e)

4 6-4

8 % Satur­a t i o n (s)

5 4

9 A i r Pres­sure P-

p s i .

10 V o l . A i r Flowing V

( l i t e r s )

11 I n t r i n ­s i c Permea­b i l i t y K'x]08cm

12 Coeff. Of Perm.

K xlC^cm sec

.13 Ave. Perco-l a t i on Rate

ml . hr.

14 Darcy 1s Coeff. Of Perm.

5 1^x10 cm

15

1 102.60 95.03 89.10 13.50 5.93 23.1 1.40 44.0 1.530 9.155 6.6 7.3 13-5 9.6 • •' ' _

2 101.47 95.29 88.02 13.45 7.27 23.1 1.39 54.1 •" 1.906 10.148 5.9 6.5 16.5 11.5

3 102.57 97.17 89.02 13-55 8.15 23.1 1.405 60.3 2.504 11.055 4.9 5-4 14.0 9.9

4 101.60 96.89 88.05 13.55 8.84 23.1 1.410 65.4 2.691 9.732 4.0 4.4 11.0 7.9

5 103.33 99.70 89.83 13.50 9.87 23.1 1.402 73.3 3.360 8.360 2.6 2.9 ' 15.5 10.9

6 103.91 100.55 90.43 13.48 10.12 23.1 1.399 75.2 3.225 7.360 2.5 2.8 1 5 + 10.7

Table 17 S y n t h e t i c S o i l ; E f f e c t of S a t u r a t i o n (S) On I n t r i n s i c Permeability-Void R a t i o (e) = 1.55 - ..01

1 Satura­ted Wt.

2 Wt.After Drainage On. Tension Table

3 Oven-Dry Wt.

4 Total Pore Vo.

1-3

5 Vol.Of Water A f t e r D r a i n ­age •

2-3

6 Vol.Of Sample Core

7 Void Ratio

• (e)

. 4 6 4"

8 • % Satur­a t i o n (s)

5-r i 4 .

9 A i r Press­ure

P-p s i .

10 V o l . A i r Flowing

V ( l i t e r s )

11 I n t r i n ­s i c

• Permea­b i l i t y K'xl08cm

12 Coeff. Of Perm.•

K xl0 5cm sec

13 Ave.

Perco­l a t i o n Rate •' ml

h r . "

14 Darcy*s Coeff. Of. Perm. for xlC^cm

s ec

15

1 101.18 94.36 87.13 •14.05 7.23 23.1 1.550 51.5 1.625 11.00 7.5 8.2 16" . 11.1

2 98 .54 91,81 84.54 14.00 7.27 23.1 1.540 52.0 1.875 12.3Q 7.3 8.0 20.0 14-3

3 103.93 98.11 89.83 14 .09 8.28 23.1 1.555 59.0 1.775 10.15 6.3 6.9 14.5 10.3

4 100.94 95.29 86.84 14.10 8.45 23.1 1.560 60.0 1.875 10-.20 6.0 .6.6 15.5 10.8

5 98.12 93-05 84.09 14.03 8.96 23,1 1.545 . 64.0 2.000 9.99 5.5 6.1 19.5 13.7

6 99.56 94.35 35.51 14.05 8.84 23.1 1.549 63.0 2.000 9.99 5.5 6.1 14.0 10.0

Table 18 Synthetic S o i l ; E f f e c t of Sa t u r a t i o n (S) On I n t r i n s i c Permeability-Void Ratio (e) = 1.67 - .01

1 . Satura­ted Wt.

2 Wt.After Drainage On : Tension Table

. 3 Oven-Dry Wt.

4 T o t a l Pore V o l .

1-3

• 5 Vo l . Of Water A f t e r . Drain-' age 2-3 ;

6 Vol.Of

' Sample Core

7 Void Ratio (e)

• 4* . .6-4 .

8 % Satur­a t i o n (3)

1 .4

.9 . A i r

Pres­sure P.

p s i .

10 V o l . A i r Flowing • V ( l i t e r s )

11 I n t r i n ­s i c Permea­b i l i t y K' xK)8cm2

12 Coeff. Of Perm.

KxX?cm sec

13 Ave. Perco­l a t i o n Rate ml . hr.'

14 Darcy 1s Coeff. of Perm. K xD 5cm w — sec

15

1 99.65 92.11 85.15. •14.50 6.96 23.1 1.68 48.0 1.5 12.3 9.1 • 10,0 16.5 11.7

2 102.36 95.73 87.96 14.40 7.77 23.1 1.66 54.1 • 1.71 • 12.45 8.0 • 8.8 20.0 14.0

3 98.75 92 .60 84 .30 14.45 8.30 23.1 1.665 57.-5' 1.663 10.717 7.1 7.8 14.5 10.1

4 104.30 99.23 •

89.86 14.44 9.37 23.I 1.67- 65.O 1.875 10.20 6.0 6.6 17.5 12.2

5 99.97 95.15 85.48 14.49 9 .70 23.1 1.675 67.1 - 2.00 9.99 ' 5-5 6.1 19.5 13.9

6 101.57 95 .61 87.15 14.42 8 . 4 6 23.1 1.663 58.8 1.712 10.654 6.9 ': 7.6 15.5 + 11.1

Table, 19; Alderwood Sandy Loam; R e l a t i o n s h i p Between C o e f f i c i e n t of P e r m e a b i l i t y Ka And Darcy 1s C o e f f i c i e n t of P e r m e a b i l i t y K w

Void Ration (e) K'a (at S = 0$) K a (a + S = 0$) K w ( a t S = 100$)

0.420 14.5 16 13.0

0.502 19-7 21.7 16.5 0.550 17.6 19.4 18 .1 0.59 20.1 22.1 17.1 0.62 20.9 23.0 17.5 0.67 22.1 24.3 19 .0

Table 20; Synthetic S o i l ; R e l a t i o n s h i p Between C o e f f i c i e n t of P e r m e a b i l i t y K a

And Darcy's C o e f f i c i e n t of P e r m e a b i l i t y K w.

Void Ratio (e) K'a (at S = 0$) K a ( a t S = 0$) K w ( a t S^= 100$)

1.04 7.9 8.7 7.0

1.12 10.0 11.0 7.0

1.26 12.4 13.6 9.2

1.40 14.0 15.4 10.1

1.55 16.8 18 .5 11-7

1.67 18.2 20.0 12.0

69

Cylinder frro^U a 5lts J 3 ^

I*, cms

1

"if,

T

si

<-7«

-A

O'S cm;

F,ig. 18 Modified Steinbrenner•a Apparatus

Cutting edge made of steel. Rest of

apparatus made of ordinary pipe metal.

I

70.

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