SySTEM

l§
Cu.

i
ll
\

'\.-‘\
\xi 7:
U

x
5)

F
N

I
I

$RE QQOT-
1968

-S OF
h
S
’fiLBO PEDRO COBP'

1w...
1.2.
by v“ Mu
s1 ;i “W -u.
. A: «\U I ,-

C33:
’38
fifl33f

AW?

*3.

‘7
Nu 7- an.
I

‘

k3 "t‘LlE.
2‘: 1:: fl

:‘1‘
U

 
 
 

r'aamrr._~_;.“8hj-w

L I B R A R Y
Michigan (Pate
University

 
  
 
  

mews

 

This is to certify that the

thesis entitled

On the Mechanics of the Root Soil- System

presented by

A. P. Cobra

has been accepted towards fulfillment

of the requirements for

Ph.D. degree in Agricultural
Engineering

MW

Major professor
Date 5" jg ' é 1‘

0-169

 

 

WWI W] 1mm Miflfl'lflfl

31293 01095 9306

1 W242?

91:3? l 7 793’!)

 

 

ABSTRACT
ON THE MECHANICS OF THE ROOT—SOIL SYSTEM

by Anivaldo Pedro Cobra

Several studies have been made to determine the up-

rooting force of crop plants. These studies do not,

however, contain any information related to the soil

characteristics and of the stress distribution and strength

of the root—soil composite.
A knowledge of the root—soil relationship would be

of importance for the crop scientist, the soil scientist,

and the agricultural engineer. It may become possible to

determine the best positioning of soil in relation to the

plants and to select strains to obtain better anchorage

of the crop plants. Also, by learning about the inter-

active behavior of the root-soil composite, the prediction
of failures of vegetated s10pes and the endurance of

vegetated linings of earth dams and canals can be further

improved.
The objective of this work is to obtain background

data for the study of root~soil relationships from an

engineering standpoint.
For this study, sorghum was planted in the field in

a loamy fine sand soil. When the plants had nearly reached

their full size they were subjected to an uprooting force

Anivaldo Pedro Cobra

Measurements of force and displace-

applied to the stems.
The dry weight

ment at the base of the plant were made.

of stem samples and the stem bundle diameter at the base

of the plant were measured. Soil moisture content, bulk

density, and penetration values were determined. The
weight, shape, and dimensions of the pulled out root-soil
bulb and the remaining undisturbed crater were recorded.

In order to determine the stress and strain distri—

bution and the strengthening effect of the root on the

soil, underground and top surface failure patterns of the

field plants were filmed for some tests.
Studies of the root system were made for plants

grown in boxes in a greenhouse. Root angle and root

length were determined by directly tracing the roots.

These roots were sampled and tested for tensile strength.

The measurements made at rupture were: force, strain,

diameter, the distance from the attaching point to the
fractured section and the position of the fracture with
respect to the clamping Jaws.

From the field experiments it was found that the

maximum pulling force required to pull the plant was

considerably greater than the weight of the bulb or the

soil weight of the crater. The maximum pulling force was

reasonably well correlated with the respective displacement
at the base of the plant, the soil moisture content, the

weight of the root—soil bulb, the dry weight of a 2-inch

Anivaldo Pedro Cobra

sample of stems and the volume of the crater. Also a

reasonable correlation was found between the displace—

ment at the base of the plant and the depth of the

crater.
From the studies of the root system it was found

that the number and the length of roots varied with the

angle measured from the soil surface. The greater

number of roots and the longer roots were found at angles

of 60 to 80 degrees.

The tensile tests showed that the strength of short

roots was proportional to a linear dimension of the cross

section, while that of long roots exhibited an additional

proportionality to the square of the same dimension. In

general, the further away from the attaching point of the

root the tension specimens were taken, the weaker these

specimens were found to be. Finally, short roots exhibited
lower average strength than long roots. This difference

in strength is probably due to biological differences in

the two types of root.
The observations of failure patterns showed that

the underground rupture of the root-soil composite started
at the centerline of the plant at the bottom of the future

crater, when the pulling force was close to its maximum

value. The failure surface developed from the centerline

laterally outward to a polar angle of about 60 degrees
Then it assumed the shape

and slightly concave upward.
The

Of a typical Rankine pattern, up to the soil surface.

Anivaldo Pedro Cobra

soil surface failure cracks indicated that the least
strength of the composite is in the direction perpen-

dicular to a plane containing the centerline of the

plant. The maximum strength of the root-soil composite

was found to be in the direction of the roots, or in a

polar—spherical direction.
An attempt was made to develop constitutive

equations which would enable the evaluation of the

strengthening effect of roots on the soil, in terms of

a strengthening factor.

Approved M W

Major Professor

Approved (kn! @411

Department Chairman

 

 

ON THE MECHANICS OF THE ROOT—SOIL SYSTEM

By

Anivaldo Pedro Cobra

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Agricultural Engineering

1968

ACKNOWLEDGMENT

I express my gratitude to Dr. Sverker P. E. Persson
for his advice and assistance given during this work.

Acknowledgment also goes to the "Escola Superior de
Agricultura Luiz de Queiroz " University of Sao Paulo,
Brazil and to The Rockefeller Foundation which provided
for my stay in this country.

I would also like to thank Mr. Glenn Bowditch, of
the University of New South Wales, Australia, for his
assistance in the preparation of equipment and the carrying

out of experiments.

To my wife and five children I am deeply grateful.

ii

TABLE OF CONTENTS

Page
ACKNOWLEDGMENTS . . . . . . . . . . . . ii
LIST OF FIGURES . . . . . . . . . . . . iv
LIST OF TABLES . . . . . . . . . . . . viii
CHAPTER
I. INTRODUCTION 1
2. THE UPROOTING FORCE 4
2.1 Review of Literature A
2. 2 Field Procedure and Equipment 6
2. 3 Results and Discussion 16
3. THE ROOT SYSTEM, DESCRIPTION AND STRENGTH. 47
3.1 Description of the Root System in
the Literature . . . . . . . . A7
3.2 Procedure for Determining Tensile
Strength of Roots . . . . . . . 51
3.3 Results and Discussion . . . . . 56
A. STRESS DISTRIBUTION . . . . . . . . 81
4.1 Introduction. . . . 81
4.2 Theory of the Mechanics of the
Root- Soil System . . . . . . 8A
“.3 Observed Failures . . . . . . . 120
5. RECOMMENDATIONS FOR FURTHER WORK. . . . 143
6. SUMMARY OF RESULTS . . . . . . . . 145
REFERENCES. . . . . . . . . . . . . . 147

iii

LIST OF FIGURES

Figure Page

2.2.1 A general view of pulling device and
measuring instrument . . . . . . . 9

2.2.2 Typical arrangement of the load cell,
traction Jaws, and spike of the displace-
ment bar with LVDT. . . . . . . . 9

2.2.3 Typical penetration curve (from eXperiment
number 10) . . . . . . . . . . 12

2.3.1 Typical shape and dimensions of a pulled
out root-soil bulb (load centrally

applied) . . . . . . . 17
2.3.2 The effect of force misalignment or non-

verticality of stems as affecting the

final shape of the root-soil bulb. . . 18
2.3.3 (A), (B), and (C) Crater profiles from

tests 21-26 . . . . . . . . . 2O
2.3.“ Typical force versus displacement curve

for an integral plant. . . . . . . 27
2.3.5 Typical force versus displacement curve

for a sectioned plant. . . . . . . 29
2.3.6 Maximum pulling force versus soil moisture

content . . . . . . . . . . . 32
2-3.7 Maximum pulling force versus displacement

at base of plant . . . . . . . . 33
2-3.8 Maximum pulling force versus weight of

root-soil bulb plus weight of Jaws . . 3A
2.3.9 Maximum pulling force versus average

diameter of stems at base of plant . . 36
2-3.10 Maximum pulling force versus dry weight

of a 2—inch sample of stems. . . . . 37
2.3.11 Displacement at base of plant versus

average diameter of stem bundle at the 39

base of the plant

iv

Figure

2.3.12

.10

.12

EUGUULULAJUU
NWUOUUUULA)

.11'

Weight of root—soil bulb plus weight of
jaws versus soil bulk density

Maximum pulling force versus volume of
crater given in pounds of water and
cubic feet

Volume of crater in pounds of water and

cubic feet versus soil moisture content.

Volume of crater in pounds of water and
cubic feet versus weight of root-soil
bulb plus weight of jaws.

Diagram showing how the dimensions and
root angle were obtained by direct
tracing the roots

Typical force vs deformation curves from
root tensile tests.

Root angle vs root original length, with
transition zone included. . .

Diameter of fracture vs root original
length. . .

Force vs diameter of fracture.
Stress vs. diameter of fracture

F/nd vs diameter of fracture for short
roots

F/nd vs diameter of fracture for long
roots . .

F/nd vs root original length
Modulus vs root original length
Diameter of fracture vs dipoint
FOrce vs dipoint

F/nd vs dipoint . . .

Free body diagram of root embedded in the

soil

Axial tangential stress (r) versus dis—
placement(j;. . . . . .

Page

A0

A2

AA

A6

53

59

62

6A
66
67

69

70
73
75
77
78
79

88

9A

Figure Page

A.2.3 Residual force (F ), displacement (j) and
the axial tangefitial stress (T) as
functions of the radial coordinate (p) . 96

A.2.A The displacement at failure surface is
maximum for G = O, and minimum for

e = H/2 . . . . . . . . . . . 107
A.2.5 The static system of the soil composite . 110
A.2.6 Equilibrium diagram: XFZ = O. . . . . 112
A.2.7 Isostrength curves OR = constant. . . . 115
A.2.8 The strengthening effect of roots on

failure surface. . . . . . . . . 118
A.3.1 Sectioned wall at zero load . . . . . 122
A.3.2 Failure occurred first at the centerline . 122
A.3.3 Rankine pattern is well outlined here . . 12A
A.3.A Tertiary crack and tension crack at soil

surface are outlined . . . . . . . 12A

A.3.5 Tension crack and tertiary crack at soil
surface is now quite visible . . . . 125

A.3.6 Observe the compression zone and an
unfractured root which did not attain

the effective length . . . . . . . 125
“-3.7 Forces acting on the root-soil bulb. . . 127
A.3.8 The disruption of the bulb is outlined

based on surface tension crack . . . 129
“-3.9 A close-up of the compression zone . . . 129
A.3.1O Final stage of rupture prior to bulb

disruption . . . . . . . . 130
A.3.1l A close up of root in the process of

reaching the effective length . . . . 130
“-3.12 Observe that the roots are all fractured

at the failure surface . . . 132
“-3.13 Underground failure with x-y recorder in l

the filming, at zero load . . . . . 33
”o3.lA x—y recorder in the field of filming . . 133

vi

Figure
A.3.15

Crack appeared at .85 of F max (F =
2A7 lbs) . . . . . . . .ma¥

C a k t .
r c pa tern at 97 of Fmax

Pulling force vs displacement curve of the
specimen illustrated by figures A. 2. 13
to 17 and 19.. . . .

Crack pattern when force has declined to
.70 of Fmax

Note bulb disruption about the compression
plane, in final stage of rupture

Shows the symmetry of the cracks in the
initial stage of rupture.

Shows that symmetry persisted until the
final stage of rupture . . .

The disruption of the bulb leads to an
asymmetric appearance. . . .

No symmetry can be visualized by observing
the pulled out bulb .

Soil surface cracks

vii

Page

13A

13A

135

136

136

138

138

139

139
1A0

LIST OF TABLES

Major soil characteristics.

Variables measured in the field eXperi—
ments

Results of tensile tests and direct
tracing of short roots

Results of tensile tests and direct
tracing of long roots.

Rupture strength parameter F/Hd in
pounds per inch.

viii

Page

1A

57

58

7A

I. INTRODUCTION

During the growth of a crOp it is important that the
stability of the aerial part of the plants be maintained
in order to secure a full development of the product and
to allow an efficient performance of the machinery
involved in the production process.

The stability of a plant in the field is affected
not only by the weight of the plant itself, but also by
such horizontal forces as wind load (or similar horizontal
loads). Under such loads, the plant sometimes becomes
unstable and lodging occurs. This lodging may be due
either to failure of the anchoring system or to failure
of the aerial part. There is no standard definition for
lodging; but it seems to be commonplace in works appearing
after Hall (193A) to consider as "lodged" any plant
leaning more than A5O from the vertical, including both
root lodging and stalk breakage.

A knowledge of the strength relationships between
root and soil is necessary in order to interpret the
factors affecting the underground failure of the plant.
These relationships are very complex due to the nature of
the materials involved. Therefore, for an engineering
approach of the problem it was decided that a simple type

of loading, such as an uprooting force, would permit a

preliminary assessment of the important parameters for
plant anchoring.

The objective of this research is to find background
data to study the strength relationships between soil and

root using as an example sudangrass (Sorghum vulgarerar.

 

Sudanense,Hitch.), subjected to an uprooting force. The

 

ultimate goal, however, is to detect the important
parameters regulating the strength of the root-soil compos-
ite, so that they can be assessed and used to predict
failure of the root-soil system of other crops of economi-
cal importance, such as sugar cane or corn.

The original intention was to study these relation-
ships for sugar cane. However, due to ecological diffi-
culties presented to the growth of sugar cane in this area,
it was decided that the work could be done with sorghum,
because of its similarity in the root system, and the size
of the plant which would facilitate the eXperiments.

To fulfill the objectives, sorghum plants were
planted in field conditions and subjected to a vertical
pull. A continuous record of force versus displacement
at the base of the plant were made. Soil and plant
characteristics were determined as a basis for
further correlations.

The establishment of the mechanical relationships
between root and soil may become important in the

ascertainment of factors which contribute to the full

development of a crop. This knowledge can be used in
many phases involved in the process of crop improvement
and production.

It will enable the breeder to select varieties whose
root configuration will be adequate to perform the desired
anchoring function, or a configuration that will offer a
high resistance to uprooting. This statement is also
applicable to the selection of grasses used to line canals,
SIOpes, etc.

It will indicate to the agronomist and soil scientist
how to position and shape the soil at the soil surface to
impart a better anchorage to the plant. This will allow a
more advantageous use of certain varieties. Resistance to
wind forces could be ascertained and crop lodging could
be prevented or minimized by providing better mechanical
anchorage.

In the design of harvesting equipment it will furnish
relations that will allow the determination of the magni—
tude and mode of the uprooting force. In the cases where
small plants are taken out of the ground to be re-planted,
critical force values can be determined as to least affect

the root system.

2. THE UPROOTING FORCE

2.1 Review of Literature

 

Holbert and Koehler (192A) working with corn found a
relationship between root anchorage and lodging, such that
when the mean pulling resistance of a group of plants de—
creased, the percentage of leaning plants increased (plants
leaning 300 or more). Also it was determined that for
plants of good strain (which exhibited greater pulling
resistance) the number of main and lateral roots was higher
than that presented by plants susceptible to disease.

Wilson (1930) reported that in the absence of brace
roots corn lodged badly. However, the secondary roots and
plant height were not related to lodging. In the field,
the diameter of the stem of the lowest internode showed
no relation with lodging.

Hall (193A), working with corn under natural rain-
fall conditions found that in most cases the force required
to pull the plant from the soil was negatively correlated
to lodging. A similar relationship was found for force
and disease. He also reported that no relationship existed
between lodging and ear height, cross section or ear weight.
Hall used a mechanical device for obtaining the force
required to pull the stalks over to an angle of A50,

keeping the stalk rigid from the first internode to the

point of attachment of the load, by fastening the stalk

to a piece of wood.

Dillewijn (1952) reported that it is generally
recognized that lodging exerts a harmful effect on sugar

yield of sugar cane, but exact figures as to the losses

involved are scarce. For pot eXperiments made by Borden,

an average loss of sugar of 25 per cent was reported to

be due to poorer juice quality of lodged plants. He also

reported that according to Honig lodging is associated with
starch formation in the concave side of the stem.

Newman e§_a1. (1952) reported that stalk breakage
caused more loss of corn and reduction of quality than root
lodging. It was reported that root lodging generally oc—

curred only before the corn is ripe and if the ground is

soft.
Nelson (1958), in his work with field corn reported

that

"significant relationships were shown between
lodging and the mechanical force needed to break
the standing stalk or the third internode, the
diameter of the third internode, the height of
the ear, and the yield of grain. The best single
measurement for determining the lodging potential
was the force needed to break the third internode.
In combination, the best two measurements were
ear height and the force needed to break the

standing stalk."

Nelson also used mechanical devices to record the force
required to pull the stalks over to an angle of A50 and

the force to break the stalk at the third internode.

In the works reported here there has been no consid-
eration given to root distribution as affected by factors

such as soil bulk density, availability of nutrients and

water, and seasonal variations. When an uprooting force

was applied, no effect of soil moisture content was
specifically determined, no measure of soil strength

given, nor was root strength determined.

2.2 Field Procedure and Equipment
The field experiments were made in a plot of the

Soil Science experimental farm of Michigan State University,

on a loamy fine sand soil. Some of the major characteris-

tics of the soil can be seen in Table 2.1.

TABLE 2.l--Major soil characteristics.

Soil: Spinks--loamy fine sand

Mechanical Analysis**
Density 2.62
fine graV91 1'36% Bulk density 1.51*
coarse sand 3.66% TOtal p?rosity 39.90%*
medium sand 7.73% (air pyc)
Non-cap.porosity *
fine sand 50.30% (air pyc.) 10'00%

very fine sand 20.63% Upper plast.limit 19.90%
6 Lower plast.limit —
silt and clay l .32% Moisture equiv. 15.80%

M.C. at 60 cm tension 20.AO%

*Corresponding values.

**Silt and clay content was calculated by subtraction.

On June 15, 1967, after the field had been plowed
and harrowed, three to five seeds of sorghum per hill were
manually planted in hills spaced five feet between rows
and four feet in the row. This spacing was eXpected to
avoid major interferences of root systems.
A starting fertilization on the basis of 12.5 lb.
of nitrogen per acre was applied. After the plants reached
a height of 12-15 inches, a side dressing was applied with
100 1b. of nitrogen, 25 lb. of P205 and 75 1b. of K20 per
acre.
On July 5 the experimental plot was cultivated
between rows with a front-mounted cultivator and handhoed
in the rows. On August 5 a second cultivation was made
similar to the first. After September 15 a mower was
used whenever needed to control weeds and to minimize
disturbance to the soil. Nevertheless, it was noticed
during the eXperiments that weed roots were present, in
some cases interfering with the results, as was apparent
in one of the sectioned plants.
For the pulling experiments a pulling device was
built and instrumented. The pulling device consisted of a
12 V dc compound electric motor (3800 rpm) with a worm-
gear box for speed reduction. A screw, attached to the gear
box output shaft drove a nut welded inside a square tube.
This vertically driven tube was prevented from rotating and

guided by a square opening in the outer housing tube. The

8

displacement rate obtained was approximately 2 to 2.A
inches per minute, reSpectively for loaded and unloaded
conditions. The housing tube supported the whole device
and was loosely bolted to a tripod. Footings were provided
for the tripod to minimize sinkage of the system. Figures
2.2.1 and 2.2.2 show respectively a general View of the
pulling device and a closeup giving the typical placement
of load cell, traction jaws and displacement bar with the
linear variable differential transformer (LVDT). The
pulling force was applied to the plant by two traction
jaws made of L-shaped steel bars with metal lath welded
to their inner faces. The addition of this metal lath
imparted no major injury to the stem. The pressure
against the stems was produced by equally tightening
the wing nuts holding the two bars together. No slip
problem was eXperienced provided the wing nuts were
adequately tightened.

The tripod was located over the plant with the
telesc0ping tube aligned with the center of the plant.
A load cell was connected between the traction jaws and
the telescoping tube including a universal joint to elim-
inate side pull. The force was measured using a Day-

tronic 250 1b. load cell with a 300 C/6l transducer-plug-

in amplifier combination.

.993 and: Hen psoEoomHQme one. .Ho .ucoESHpmcfl
8.33m paw nmean cofipomnp .Haoo pmoa on» mQHnSmon new moi/mp wcflnasa
.Ho ucosowsmshm Havana. .m.m.m onswfim .Ho 33$ Hmsocow .4. .H.m.m onzwfim

 

used to sense the lifting of the base of the plant. The
spike was pushed into the base of the plant. The dis-
placement was measured by a Schaevitz HR 2000 LVDT (i 1
inch linear range), located at midpoint of the bar. The
output was demodulated and amplified by a Daytronic 300 C
transducer amplifier with a modified type 60 plug-in unit.

A 750 watt, 60 Hz generator was used to provide
power for the equipment in the field. Adequate grounding
was provided to minimize noise.

A force versus displacement curve was recorded from
the two transducer amplifier outputs on a Moseley Autograf
x-y recorder, model 135. Figures 2.3.A and 2.3.5 in Section
2.3.A show typical force vs. diSplacement graphs for inte-
gral and sectioned pullings, respectively.

The diameter of the plant stem bundle in its natural
state was measured at its base before pulling. Then the
stems were cut at 20 inches above the soil surface and a
stem sample two inches long was collected for later drying
and weighing. The traction jaws were then attached to the
stems in such a way to cause minimum disturbance to the
plant.

Soil moisture content, bulk density and penetrometer

readings were determined for most of the pullings. One

undisturbed soil sample and two or three penetrometer

readings were taken for each test, at a radius of about

20 inches from the plant.

readings in some stony spots. A plow sole was detected
at a depth of approximately 8 inches whose effects will
be commented on later.

Observations as to shape and dimensions of the root-
soil bulbs were made after they had been pulled, with the
intention of using their shape as representative of the
failure surface and their dimensions as possible parameters
to be compared with the pulling force. Average values of
the dimensions are given in Figure 2.3.1.

When pulling the plant, observations were made as
to the development of surface cracks. This was facilitated
by "powdering" the area around the plant with industrial
plaster. The develOpment of these cracks was filmed during
some tests. A series of photographs from the film are
shown in Section A.3, where the cracks are described as
they took place.

The deve1Opment of the failure surface below the soil

surface was also observed and filmed for some eXperiments

(called sectioned tests). For these tests two

180
160

1A0

120
100

Penetration Force
(Pounds)
EO‘xCI)
000

R)
C)

 

 

l2

 

 

 

 

 

Depth (in)

10

ll

12

Figure 2.2.3——Typica1 penetration curve(from

experiment numberlO).

13

sectors of 90° each, meeting at the center of the plant

were opened symmetrically in the soil. The sides of the
sectors were first cut with a trowel and then carefully

the rest of the soil was removed. The depth of these
sectioned walls at plant center was always greater than

10 inches to avoid a possible effect of the bottom of the
section upon the failure surface. Following a smoothing-

up of the sectioned wall, a grid pattern was applied to it
by powdering industrial plaster through a grid with 0.75
inch mesh. To allow filming of the trace of the failure
surface, a shallow trench was made perpendicular to the
sectioned wall to be filmed. The failure surface develOp—
ment could then be observed and filmed. A series of photo-
graphs showing the shape and location of the failure surface
with respect to the plant are given in Section A.3. Some of
the filming was done with the x-y recorder in the field of
view to allow a comparison between development of cracks

and the magnitude of the pulling force. Thus, two types

of pulling tests were made, namely: sectioned, which has

just been described, and integral where no sectors had

been cut in the ground. Table 2.2 shows the data obtained

in the field for all integral and sectioned tests.
As the experiment developed it was noticed that if
no extraneous roots or other materials were present, a

distinct undisturbed crater surface could be found by

carefully removing the disturbed soil of the crater after

the bulb had been removed. This was done and the crater

.mpa 0.0 n 300 go acmflozxa .wumop 0000auomm oumofipcfi wI 20H: mucosa: ucoEHLmme:

 

1A

 

H.0 mm 0.0m 00 m.m 0.m0 0H 0m.H 0.0H 00.H mam 0m
0.5 0m 0.0m 0m 0.m 0.m0 2a 00.H 0.:H 0m.0 mam mm
3.0 mm 0.00 mm 0.: 0.0% 3 ms; 73 00.0 mam am
0.0 Hm 0.m: ms m.m 0.0m 4H ma.H 0.NH 00.0 mam mm
0.0 . Hm m.0: 00 m.0 0.40 NH .m.H 0.0H mH.H mmm mm
N.N mm m. m m0 0.m 0.ma 0H 02.H m.HH 00.0 0mm Hm
I I I mm I 0.00 NH 00.H :.HH 00.H How mIom
I I I 00 0.m 0.0: 0H H~.H H.fia 00.0 0mm ma
I I I 00 I 03.5 i 004 T: 00.0 000 W?
m.~ am I 00 n.m 0.00 m 00.H 0.:H 0H.H amm 5H
I I I 00H I m.w 0H ms.a :.MH m0.H mma mI0H
0.0 ma I 00 0.m 0.00 0 00.a H.mH H0.0 0am ma
I I I 00 I m.nm 0H 02.H w.afi 00.0 02H mIaa
0.0 cm I 00 0% T: 0H :4 0.: 004 mam ma
I I I OHH I m.ma ma 00.H m.ma 00.0 mmm mImH
I I I oma I 0.3m ma ms.H H.md mm.0 mmH mIHH
I I I 00 06 0.0.0 .: mmé mi: 0.7a mam OH
I I I I I m.wz mH N0.H a.» .zm.0 mmm m
I I I I I t... ma 3... 0.0a 00.0 00m. 0.0
I I I I I 0.3 a... 004 m0 No.0 SN «mi.
I I I I I m.we m mm.fi m.0 No.0 mmm 0
I I I I I m.mm ma 0m.a H.n 0m.a mam m
I I I I I m.me Ha ma.fl 0.0 00.0 mam :
I I I I I 0.00 0H mm.fi 0.0 m0.0 Hmm m
I I I I I 0.ma 0M 00.H m.~ 00.0 0mm m
I I I I I I 0H 0m.fi m.0 0H.H 00m 0
U
SE; 3: 2: 3d Asset: _ 3.... 2: 3C
Acfiv Acfiv . z : hero . . . hngzz
stucco oomassm HHom. WMpMWW mewwom ucmam 00 ”smmyu tanenw \mEdbmv wmwwmoma Axmemv Axmemv acmEHpoaxm
as .8095 as 0398 .00 defies. Iosascea team as seen 0.- 8.1.0.. sewn t5 DECS «tow a... as doses
00 £0000 uo Lmqumwm mo pmuoemwn . I: ; arafimx n00 xfism 0L0 -firo .omaawaa Eseflxmz

 

.mpcmEHsoaxm pawaw on» Ca oopsmmwe moanmfinm>IIm.m mqm<H

15

profile, volume, diameter at soil surface and depth at
the center were measured using the following order and
procedure:

A.—-Crater profile and depth at center: the
disturbed soil was removed and a pantograph was used to
reproduce (trace) the crater profile (N—S, E—W). A
diagram with height and dimensions are given in Figure
2.3.3;

B.——Crater diameter: three measurements were made
(N-S, E-W, NW—SE) for each of nine experiments, and the
average used as a representative value of crater diameter;

C.-—Crater volume: the crater was lined with a thin
sheet of plastic. The weight of water required to fill
the volume displaced by the root-soil mass was determined.

The values for crater volume, average diameter and
depth are given in Table 2.2.

An attempt was made to estimate the amount of roots
remaining in the soil below the crater, but all the methods
which were considered seemed unreliable.

In order to ascertain the performance of the pulling
device and the instrumentation, several trial tests were made
in the field. These tests are numbered from 1 thru 9 in
Table 2.2. The first preliminary experiments on integral
plants were carried out on October 7, in order to observe
what other variables should be measured besides pulling

force, displacement at base of plant, soil moisture content

16

and bulk density,weight of dry stem and weight of the bulb.
Experiments number 7 and 8 were performed with sectioned
plants on October 8, to verify the symmetry response of
the root—soil system with respect to pulling force. Ex—
periments number 10 to 20 were performed on October 1A,
and other variables such as diameter of stem bundle at
base of plant, penetrometer reading and shape and dimen-
sions of the pulled bulb were collected. For these exper-
iments a series of randomly located integral and sectioned
plants were pulled in order to further ascertain the
symmetry response. During these experiments the importance
of the crater parameters was noticed and some preliminary
observations were made. On October 25, experiments 21 to
26 were made in order to observe and determine parameters
of the crater. On October 27, the first snowfall took
place in the region, resulting in stem breakage, thus

preventing further tests.

2.3 Results and Discussion

 

2.3.1 Root-Soil Bulb

From the observations made of the conformation and
dimensions of the root-soil bulbs that were pulled up with
the plants, it was possible to reproduce a diagram that
is shown in Figure 2.3.1. The values in the diagram
represent averages of three measurements for each dimen-

sion for five bulbs of integral plants. In Figure 2.3.1,

17

the line EH indicates a circular conical band consistently
showing the greatest number of roots projecting out of

the root—soil bulb. Though the angle 5_g§§ could not be
determined accurately, its value as calculated varied
from 18 to 32 degrees with an average of 28 degrees.
However, the shape and dimensions of the pulled out root-
soil bulb was considerably altered during the detachment
from the soil. This was chiefly due to the tension
cracks developed in the soil surface and the falling-off
of the soil sustained by the root mesh during the pulling

action. This matter will be elaborated on in Section A.3.

 

50': 6.5 in.
ER = 3.5 in.
d§'= 3.5 in.
ahi= 7.3 in.
53': 7.3 in.
3g": 10.3.in.
e? = 12.9 in.

i 0 = 28°

. E’ = 38°

Figure 2. 3. l—-Typical shape and dimensions of a pulled
out root- soil bulb (load centrally applied)

18

In some cases it was found that the bulb was un-
symmetrical. The main source of this seemed to be a
misalignment of the pulling force on the plant caused
by the positioning of the tripod. After this was first
observed the operation was more carefully performed.
Nevertheless, in some plants it was noticed that the stems
for some reason did not grow perpendicularly to the soil
surface. Whenever a misalignment took place, some diffi—
culties were experienced in measuring the diSplacement at
the base of the plant. This was due to a bending moment
introduced at that point, which caused a slight movement
lengthwise of the aluminum bar used to sense the displace-
ment. The movement of the bar affected the positioning
of the LVDT thus somewhat affecting the measurement. The
effect of this bending moment was noticeable in the final
shape of the bulb. A diagram based on these observations
is given in Figure 2.3.2. If the diagram of Figure 2.3.2

is compared with that of Figure 2.3.1, this effect is quite

‘.
I

\

Figure 2.3.2—-The effect of force misalignment or non-
verticality of stems as affecting the final shape of the
root-soil bulb.

19

evident. As it might be expected, the shape of the crater
also became altered. This was quite evident as observed
for eXperiments 26 and 23 where the effect can be seen

through the profiles given in Figure 2.3.3.

2.3.2 The Crater

 

As earlier mentioned the crater was defined as the
hole in the ground after all disturbed soil had been removed.
Observations of crater profile and depth were graphically
made for experiments 21 to 26. These can be seen in the
diagrams of Figures 2.3.3 (A), (B), and (C). The center
of the crater, as shown in these figures corresponds
to the vertical line through the center of the plant, as
it was located prior to pulling. The depth of the crater
was measured to the line representing the surrounding
surface of the soil. The difference in height that two
profiles of the same crater might present, is mainly due
to the unevenness of the soil surface close to the crater.
In these figures it can be noticed that at least one of
the profiles of each crater presents a similar configura—
tion with the others. Despite careful finger-tracing
of the bottom of the crater when removing the disturbed
soil, difficulties were encountered in some cases in
distinguishing clearly the undisturbed surface. Ac-

cording to the observations, the factors causing these

20

Figure 2.3.3——(A), (B), and (C)-—Crater profiles
from tests 21—26. Broken lines indicate the soil
surface and the vertical axis of the plant.

21

W

#21 (a)

 

      

r_-_..--________---
t
I
I
l
l
I
I
I
I
I

—-——_‘¢—.---—-—~_—u—Di—

   

‘
lllllltl-

 

j inch

I, ‘

2+

 

04;,

Scale

(A)

3‘... '—

 

22

 

5inch

 

Scale

(B)

23

 

01 2 3A Sinch

 

Scale

(C)

2A

diffiCUltieS were: mesh of extraneous roots (weeds);

in some tests, the high moisture of the soil which inter—
fered with the feel of the undisturbed surface; the effect
of secondary failure surfaces which remained adhered to

the bottom of the crater strongly enough to be felt as a
part of it. This latter effect will be better understood

when the failure patterns are described in Section

A.3.
In general, the non—homogeneity of the root—soil

system affected the tracing of the crater bottom, and con-

sequently that of the failure surface.

2.3.3 Effect of Sectioning
In Table 2.2 the experiment numbers followed by a —S

indicate tests with sectioned plants. For the cases of

experiments 7 and 8, they were the first trials with
sectioned plants and since the sides of the sectors were
not cut as to meet at the center of the plant, their

results should be considered with reservations.

A statistical analysis was made to find out whether

the mean value of maximum force for sectioned plants was

equal to one—half that of the integral plants. For this

analysis the maximum force values from the following

eXperiments, reduced by the weight of the jaws (6.7 lb),

were used: 11, 12, 1A, l6, l8 and 20 for sectioned plants

(XS) and 10, 13, 15, 17, 19 and 21 for integral (xi).

The number of observations per group was i s

 

25

“ tn. was to be tested at a sig—

The basic hypothesis “5

nificance level of 0.05.
An F-test was used to compare the variances of the
samples under the hypothesis as = of’ The value of F

was:

'0)
03R)

= 1A.53

’11
u
m
va

A comparison to F (.025, 5, 5) = 7.15 implied that one

could be 95% confident that the variances were different.
(A more appropriate hypothesis had probably been as =

%Oi.) Therefore the approximate t—test to be used to

compare the sample means was

s i = 1.592

 

2.571 indicated that there

The critical value t (.05, 5)

was little evidence that the mean value of the maximum
force for sectioned plants was not equal to one—half the
mean value of the maximum force for integral plants. This
justified our assumption of undisturbed response of the
root—soil system with respect to the value of the maximum
Pulling force for sectioned plants.

A similar analysis was made for the weight of the

root—soil bulb of sectioned plants, as compared to

 

26

one—half of that of the integral plants. Since in this

case the variances of the sample means were regarded

equal by an F test, an exact t test was used, considering

 

 

 

 

_ _ ; = _ -
V (XS 2 i) V (XS) + %V(Xi) and
V (XS) = V (Xi)’ then
V (x - l4T) — 1 25 0-2-
s 2 i x
where 0% is a variance common to both means. Thus,
it — ax. 53 + 38
_ S l 2 _ s i
t - and S - n + n. _ 2
s l
/<2><1.25>s2
n
t = 0.0567 and t (.05, 10) = 2.228

which indicates that there is little evidence that the
mean value of the weight of the root-soil bulb for

sectioned plants differs from one-half that of the

integral plants.
An analysis of the displacement at maximum pulling

force showed that there was no evidence of a difference

between sectioned and integral plants.

213.A Force and Displacement

The graph of force versus diSplacement in Figure

2-3.A shows that for integral plants a fairly linear

27

 

.pcmaa Hmnwopcfi :0 Mom o>nso quEoomaamHU mzmno> 00000 H00HQ>BII:.m.m madmam
ACHV unmam mo 0000 um ucosoomaamflo

0.m 0.5 0.0 0.m 0.: 0.m 0.m 0.H

'
h i
1 r I. . . .

300 + eaam so .03

 

I OOH

 

I 00m

 

 

I 00m

 

 

(sqt) aoaog

28

relationship applies up to a point close to the maximum
force. Beyond this assumed straight line, the system
begins to yield with an increase in the rate of dis—
placement, resulting in a curved shape of the graph.
Around the point of the maximum force the curved path

of the graph is characterized by sudden Jumps of the
recording pen, which suggest the successive breaking of
roots. During the tests this Jerk of the recording pen
would take place accompanied by an audible breaking sound
coming from the ground. The successive, instead of
simultaneous breaking, of roots will be explained later
in Section “.3 with reference to the effective root length.
In some cases these sudden Jumps are more noticeable as
can be seen in Figure 2.3.5 for a sectioned plant. As to
the initial section of this curve, it is also seen that
the curved shape became more evident with sectioned
plants. Also, by comparing the straight line portions
with the values of the maximum forces of the two typical
curves, it is seen that the proportional limit is smaller
for sectioned plants. A reasonable explanation of this
effect may be found by considering the viscoelastic nature
of the soil and that of the roots. The interaction be—
tween soil and root under the natural geometry seems to
lead the behavior of the composite to a "quasi—elastic"
response and to a closer value of the maximum force, which

can be seen from the curve of the integral plants. It

29

0.m

.pcmaa Umsoa
.pomw w pom m>p30 pcmsmomaowfio mamnm> bosom Hmofiozelnm.m.m opsmam

AQHV unwam mo mmmm um pomsmomfimmfio
o N 0.0 o.m 0.: o.m

m b
q u
1 -

0.N

 

b
1

3m0 + Dasm mo.93

J.

0.ooa

.4 com

..oom

 

(ng) eoJog

30

seems that by cutting the sectors this "quasi-elastic"
behavior of the composite is considerably reduced.

At the end of the test the curves indicate only
the weight of the bulb plus that of the Jaws. Typical
values are shown in Figures 2.3.4 and 2.3.5.

Simple correlation and regression analysis were
made using Michigan Agricultural Experiment Station
(1967) Stat Series Routines. The correlated variables
which presented a significant partial correlation co-
efficient, were plotted. The pertinent partial corre-
lation coefficient and regression equation obtained are
given at respective graphs. In addition, certain
variables were plotted despite a rather low partial
correlation coefficient, to give an idea of the varia-
tions eXperienced.

Two sets of tests from the data given in Table 2.2
were analyzed separately as follows: experiments number
10, 13, 15, l7, l9, and 21 to 26, were used for the
analysis of all the variables listed, except crater
values; the analysis of the data of experiments 21 to
26 included also the crater parameters, and these results
and discussion will be presented later in this section.
As mentioned earlier tests 1 thru 9 were preliminary

tests. Their values were not statistically analyzed.

31

A plot of force* versus soil moisture content is
shown in Figure 2.3.6. A large variation is apparent and
no specific conclusion can be drawn from the plot. It is
noticed, however, there is a tendency to a decrease in the
value of the force with increasing soil moisture content.

Very low partial correlation coefficients were
found for force or displacement with respect ot pene—
trometer reading. The same was true for displacement
or penetration value versus soil moisture content.

The force was found to be positively related to
displacement, weight of bulb, dry weight of a 2-inch
sample of stems and diameter of stem bundle at the
base of the plant.

The maximum force versus correSponding displace-
ment are shown in Figure 2.3.7. This behavior was
expected, if the root system size is taken into
account. However, the partial correlation coefficient
was rather low for this relationship.

Figure 2.3.8 shows a plot of force versus weight
of root-soil bulb. During the experiments it was

noticed that the shape and the dimensions of the bulb

 

*Further use of the terms force and displacement
(in this chapter) will mean the maximum pulling force
and the respective displacement at the base of the
plant, unless otherwise stated.

Maximum Pulling Force (lbs)

32

 

350 v
(9
(9
3H0 %
330 at G
(D G
C9
320 4% a
(9
(9
(9
Q
310 h/Vs 4. a 4 f + a a 4. a

 

ll l2 13 14 15 l6 17 18 19

Soil Moisture Content (%)

Figure 2.3.6-~Maximum pulling force versus soil moisture
content.

Maximum Pulling Force (lbs)

33

 

350 T
G)
3M0 “ Q
330 “
320 r
310 i G

 

a 4‘ L 4 4A A— ; k A
f ' U I 1 I

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2

 

Displacement at Base of Plant (in)

Figure 2.3.7—-Maximum pulling force versus displace—
ment at base of plant. Regression equation:
Y = 291 + 36 X; pcc = .ASO.

Maximum Pulling Force (lbs)

34

350 f

340

330

320

 

310

 

EM .

40 50 60 70 80
Weight of Bulb + Jaws (lbs)

Figure 2.3.8--Maximum pulling force versus weight of root-
soil bulb plus weight of Jaws. Regression equation:
Y = 293 + .52 X; pcc = .611.

35

did not represent that of the underground failure
surface as was assumed in the beginning of this section.
However, the analysis of the data shows that the force
is reasonably correlated with the weight of the bulb.
This suggests that the weight of the root-soil bulb is
to some extent representative of the root development,
despite the detachment of soil which takes place

during the pulling process. The large constant term
and the low ratio indicate that the pulling force is
mainly determined by other factors than the bulb
weight.

A positive relationship was found for the force
as compared with the diameter of the stem bundle at the
base of the plant. A plot of this relationship, the
regression equation and partial correlation coeffici-
enuzare given in Figure 2.3.9. Again the large constant
term indicates only a partial influence of plant
size or a nonlinear relationship. The diameter of the
stem bundle and the dry weight of a 2—inch sample of
stems were expected to indicate the size of the plant.
A plot and the partial correlation coefficient of

force versus dry weight of 2-inch of stems are shown

in Figure 2.3.10.

Maximum Pulling Force (lbs)

36

O .
35 f a

340 «-

330 “

320

 

310

 

 

2.5 3.0 3.5 4.0 4.5
Diameter of Stems at Base of Plant (in)

Figure 2.3.9--Maximum pulling force versus average
diameter of stems at base of plant. Regression
.564.

equation: Y = 243 + 22 X; pcc =

Maximum Pulling Force (lbs)

 

 

37
350T
G)
O
3uo..
330" ®
(9 G
320« Q o
G)
Q
G
310 ..
’7’
[M 3 4 ‘fi 4fi -.L— J. k ;_ 4
9 10 11 12 13 14 15 16 17

Dry Weight of 2-inch of Stems (grams)

Figure 2.3.lO—-Maximum pulling force versus dry weight
of a 2—inch sample of stems. pcc = .A46.

38

As to displacement and diameter of stem bundle at

the base of the plant, a plot and partial correlation coef—

ficient is given in Figure 2.3.11. Part of the variation

shown by the plotting may be attributed to a misalignment
of the pulling force and consequent movement of the dis—
placement sensing bar, as previously mentioned.

The effect of soil bulk density upon the weight of the

bulb can be seen in Figure 2.3.12. An increase in soil bulk

density caused a decrease in the weight of bulb. Although
the change in bulk density was small and not artificially
induced, this fact may suggest some impeding effect of the
soil bulk density upon the root and plant development.
Other reasons for the relationship also probably exist, as
will be mentioned in Section 3.1.

A partial correlation coefficient of -.ul2 was deter-
mined for the weight of 2—inch samples of stems versus the
diameter of the stem bundle at the base of the plant. This
suggests the possibility of the latter to be used as a
parameter of plant size, since it is a rather simple

measurement.
Since bulb size did not seem to be the main factor

influencing the force, crater size was determined in the

last set of experiments. In order to detect how the crater

depth, diameter and volume behaved with respect to other
variables, a correlation and a regression analysis were made

for experiments 21 to 26, including the crater measurements.

)

Displacement at Base of Plant (in

39

O
O\

 

2.5 3. U.O 4.5
Diameter of Stems at Base of Plant (in)

01»
w
U1

Figure 2.3.1l--Displacement at base of plant versus
average diameter of stem bundle at the base of the

plant. pcc = .597.

Weight of Bulb + Jaw (lbs)

40

BOT

 

 

 

G
0
70"
6O .-
50"
140 .. G) 0
r—vv # 4 we ‘r 4
1.4 1.5 1.6 1 7 1 8
Soil Bulk Density
(grams/cm )

Figure 2.3.12—~Weight of root-soil bulb plus weight of
Jaws versus soil bulk density. Regression equation:

Y = 177 - 76 X; pcc =-.543.

41

A partial correlation coefficient of 0.735 was found
for force versus crater volume. A plot and regression
equation are given in Figure 2.3.13. From the regression
equation it is seen that the tendency is to have an in-
crease in maximum force as the volume of the crater
increases. The increase is less than the increase in
crater soil weight but there is a large constant term.
The total soil weight in the crater is considerably less
than the maximum pulling force. This indicates that soil
weight is not a main part of the pulling force, and that
root strength, tension and shear stress in the soil con-
tribute to the anchoring of the plant. The reasons for
the increase in the force may be due to an interaction with
the soil moisture content, which is discussed later, or
there may be a variation in the development of the root
system of the plant.

It is reasonable to assume that a larger root
system would require a higher force, if other variables
remain constant. In Figure 2.3.8, which is a plot of
force versus weight of bulb, it was seen that the force
increased as the weight of bulb increased. If it is
assumed that the weight of the bulb is an indicative
parameter of the root system size, it seems reasonable to
attribute the relationship between force and crater
volume as found in Figure 2.3.13 to a larger root system
of the plant. Bulb weight and crater volume were clearly

correlated as shown later in Figure 2.3.15.

42

.mmw. u com mx 5:. + mam u w umHm>Huomammp .mpm
“Loam: mo mUCSOQ go mEpmp CH ooQ cum cofiumsvo cofimmohmmm .pmmm oflozo paw pope:

mo mvcdoa :fi Cm>flw Leanne no mESHo> mamum> moeom mafiaasa ESEmezllmH.m.m ohswfim

mESHo> pmpmpo

 

mp0 NH.H :Q.H mm. mm. ow. me. am. mm.
0N3 MO mo...” ON. mo 00 mm Om m: 0: mm
T v + « ll 1. a |w
.N
..oam
G

..0mm

 

 

-iomm

(sqI) aoaog Butttnd mnmtxew

43

Figure 2.3.1” shows a plot of crater volume versus
soil moisture content. The variations are of such magni-
tude that no conclusions can be drawn with regard to this
relationship. It seems reasonable to visualize a tendency
of decreasing crater volume with increasing soil moisture
content.

A possible relationship which was not contradicted
by the experiment might be found considering the tensile
strength of the soil and its adherence to the roots. Con—
sidering the roots as a reinforcing medium adhered to the
soil, the bonding force between them is likely to decrease
with an increase in the soil water content. In a fully
saturated soil mass, the pulling force would be limited to
that of sliding the roots out of the medium. No root fail-
ure would be likely to occur if the tensile strength of the
roots were greater than that imposed by the reSpective
sliding force. Theoretically, a soil in such a state would
leave a very small crater volume since it is reasonable to
assume that when the adherence is zero the roots could be
pulled out with a minimum disturbance of the soil. As the
moisture content of the soil decreases, the root-soil ad-
herence increases and so does the resisting sliding force
between the root and soil. If the soil moisture is decreas-
ed beyond a certain value where the bonding force between
all the roots and the soil is equal to or larger than

the pulling force, the system is likely to fail at a

44

 

 

 

70 T «1.12
O
65 .L ‘71.04
8
(\l
34
O
a)
,o
H 0
g 55 v -r .88
3. o
O
>
$4
0)
4‘3 50 1‘ + 80
(‘3 0 °
145 1‘- 6) 4' .72
’40 14 .514
G
35 Lv/ —L‘_ + 5 f #— %—— i f
11 12 13 1“ 15 16 17 18 19

Soil Moisture Content (%)

Figure 2.3.lA-—Volume of crater in pounds of water and

cubic feet versus soil moisture content.

Crater Volume (ft3)

U5

surface where its tensile strength equals that imposed by
the pulling force as transmitted through the roots to the
soil inside the failure surface. Thus, the volume of the
crater will be dictated by this failure surface and, within
limits, the greater the adherence between root and soil,
the larger will be the crater volume expected to become,
because:

A. The better the bonding between root and
soil, the more efficient the reinforcing
effect;

B. The better the reinforcing effect, the fail-
ure is likely to occur deeper because the
reinforcement at the crown is quite sub-
stantial and tends to decrease with depth;

C. The deeper the failure (the crater depth) the
larger the volume of the crater, if the
profile maintains a reasonably constant shape
as was shown earlier in this section.

The weight of the bulb showed a positive correlation

with the volume of the crater. Figure 2.3.15 shows a
plot, regression equation and partial correlation coeffic-
ient. The low constant value and the high correlation
coefficient suggest that the bulb weight may be considered

a good indicator of crater volume.

Crater Volume (lbs of H20)

46

 

 

 

 

70 1
‘71.12
c
55 ..
1.04
60 w
96;
ii
(I)
E
55 -- .88 :3
$4
0)
.1.)
CU
$4
0
50 s .80
“5 " .72
L10 ‘r- .614
o
35 __x¢ . 4 r = .56
50 60 7O 80

Weight of Bulb (lbs)

Figure 2.3.15-—Volume of crater in pounds of water and

cubic feet versus weight of root-soil bulb plus

weight of Jaws. Regression equation and pcc in terms

Of'pounds of water are, respectively: Y = 4.0 +

.76 X; pcc = .809.

3. THE ROOT SYSTEM, DESCRIPTION

AND STRENGTH

3.1 Description of the Root System
in the Literature

 

 

It is clear from the literature that the study of
the root system has been neglected in favor of that of the
aerial part. The reason is probably the difficulties
encountered with this type of research. The root system
is hidden in the soil mass which is characterized as a
heterogeneous medium, represented by stones and hard pan,
differences in soil moisture, in soil structure, and in
chemical composition. Therefore, great variations in root
development have to be expected since the roots are eXposed
to these heterogeneous and ever—changing conditions of
growth. This fact also explains to a great extent the
contradictory results found in experiments performed
in this area of study.

Weaver (1926) states that "roots have a form and
structure remarkedly well adapted to perform their function
of anchorage; and of absorption, conduction and storage of
water, nutrients, and elaborated foods." This was demon-
strated by experiments with corn in soils of very similar
physical and chemical composition. The crops were grown

under different amounts of irrigation and root development

47

48

and distribution were markedly different. In the fully
irrigated soil, where both water and nutrients were plenti-
ful, the roots were almost all in the upper one foot and
nearly parallel with the surface soil. In fact the bulk
of them was in the surface 6 inches of soil. As to the
root habits of sorghum, Weaver summarizes that
"though varying somewhat in the different varieties,
is very similar to that of corn. The roots are
finer and more fibrous, and often have twice as many
branches as those of corn in a similar stage of
development. The early superficial rooting habit
is marked, plants only in the 6- to 8—leaf stage
having a lateral spread of 3 feet, with a network
of roots extending even to the soil surface,
although the entire root system may be confined
to the surface 1.6 feet of soil. Later in the
develOpment, the roots penetrate the deeper soils,
working levels of 3 to 4 feet being common and
maximum depths of 4.5 to 6 feet frequent."

References such as that of Miller (1916) still con-
stitute a very good source of quantitative information for
the study of the root system. Data are given as to the
extent of the root system in four stages of growth, number
of secondary roots per unit of length of primary roots,
and soil moisture content and depth of root penetration.
Photographs presented by Miller on his work with sorghum
showed that a large portion of the roots were distributed
in a conically shaped area, symmetrical about the plant
vertical axis. This was observed when the plants were at
the 13th week of growth,xnaturing seed, and at a height of
about 5 feet. Under these conditions most roots reached

3 to 4 feet to the side and 5 to 6 feet below the plant

center.

49

DillewiJn (1952) reports on investigations done in
sugar cane. Lee et al. found that in irrigated cane,
generally more than 50 per cent of the roots (by weight)
occurred in the topmost 8 inches of soil, and this per—
centage decreased markedly in the deeper layers. The
vertical distribution of roots changed with the age of the
plants, and the percentage of roots at different levels
attained a maximum at 4 months after planting. Kamerling
worked with roots in soils with poor physical character-
istics. In such soil, the root tip was often damaged
resulting in the formation of lateral roots. When the
tips of the latter also became damaged, they too started to
branch. Thus the roots in a compacted soil remained rela—
tively short and much-branched as compared to longer and
little-branched in a physically good soil.

The mechanical properties of the soil influence those
of the root-soil composite in two ways: directly as an
element of the composite, and indirectly by its influence
on the root system development. It is clear from the
review of literature related to physicochemical properties
of soil affecting root growth that an interaction of soil
density, particle shape and size distribution, aeration
and moisture content are major factors influencing the
mechanical impedance and growth characteristics of roots.
This was particularly evident for seedling roots, in works
of Gill and Miller (1956), Wiersum (1957) and Tackett and

Pearson (1964), and for adult roots in works of Bertrand

50

and Kohnke (1957) and Scott and Erickson (1964). Wiersum
states that,

"Attention is drawn to the fact that it is

usually difficult to be certain of the impor—

tance of mechanical resistance in the field,

in account of the close similarity of its

effect with those of excess water and insuffi—

cient aeration."
Gill and Bolt (1955), reporting on Pfeffer's studies of
the root growth pressures, state that due to the "plastic”
properties of the root its path through the soil will
generally be along the line of least resistance. R00 (1966)
states that the absence of any significant root growth in
and through the plow pan is caused not by insufficient
aeration but by mechanical obstruction to the roots. Letey
g£_al. (1961) working with snap dragons found support for
the idea that the effect of aeration is dependent on the
stage of plant growth. Stoltzy gt_al. (1961) established a
range of oxygen diffusion rates at which root initiation
was reduced or stOpped. Williamson (1964) working with
grain sorghum, soybeans, cabbage, sweet corn, and dwarf
field corn, found that under extremely poor aeration the
yields of those crops were reduced by 25, 35, 40, 65 and
75 per cent, respectively.

Spencer (1940) made a comparative study of the

seasonal development of the corn root system of hybrids
and inbred lines. He reports that marked differences

were noted among the strains in regard to number, dry

weight, and total length of main roots of the crown root

51

system. The single-cross hybrids exceeded the inbred
lines in dry weight of roots, dry weight of tops,
diameter of main roots, length of roots, resistance to
vertical pull, diameter of culm and plant height. With—
in all strains the force required to pull a corn plant
from the ground was most closely correlated with dry weight
of the crown roots. However, it was not made clear whether
this dry weight of crown roots was obtained from the pulled
bulb or from the whole root system. It was also stated
that no data were available to test the differences in
seasonal root develOpment as a criterion of the ability of
a plant to resist lodging, but the problem was considered
of sufficient importance to deserve further study.
Pavlychenko (1937) published a good review of
literature of the methods used in the study of root
systems. In addition to his own soil-block washing
method, he described eleven different ways used by pre-
vious investigators. It seems, however, that the direct
tracing of roots is the method which yields the most
consistent results.

3.2 Procedure for Determining Tensile
Strength of Roots

 

 

On June 22, 1967, sorghum seeds were planted in
three wooden boxes with dimensions 48 inches long, 24
inches wide, and 18 inches deep, filled with soil from

the experimental plot. Two hills with 3 to 5 seeds per

52

hill were planted on the center line of each box,

and were located about 15 inches from the ends.

These boxes were left outdoors and the plants
received the same fertilization schedule used for
field plants, plus additional nitrogen equivalent to
the starting dosage, since they presented symptoms of
nitrogen deficiency. Nevertheless their development
was subnormal, and of the original six plants only
three survived. On October 20 the boxes were trans-
ferred to the greenhouse and at the time tests were
made only one plant had recovered, but it still did
not present an aerial development similar to that of

the maJority of the field plants.

On December 22 root samples were collected ac-
cording to the following procedure. Two sectors A and
B of 30° angle each were marked on the soil surface. The
sides of sector A were cut with a troweL,and two thin
sheets of metal were placed in the cuts. The roots in
this sector were directly traced by use of brushes
and small hooks, and values such as angle formed
with the surface line, original length and the quarter

of the sector angle in which the roots were positioned were

53

determined for each root. The roots were not classified
as main or secondary roots for this tracing. They were
viewed as elements of a given root system which had a
reinforcing action upon the soil. The root angle was

calculated from measurements obtained according to Figure

 

 

 

3.2.1.
- b
a = Sin a
a = root angle
L = root original

length

 

Figure 3.2.l—-Diagram showing how the dimensions and root
angle were obtained by direct tracing the roots.

It was later realized that little meaning could be attrib-
uted to the quarter—location in the sector, since many
roots were developed so tortuously that they entered all
four quarters of the sector. The roots were then cut
loose at the point where they were attached to the crown
("the attaching point"), and numbered in the order they
were found. This same procedure was used in collecting
root samples for sector B. Roots numbered from 1 to 9

were sampled in sector A and 10 to 26 in sector B. Some

54

support roots of very short length were considered vertical
(90° angle), despite a slight inclination of some of them.

The roots thus numbered and positioned were taken to
the laboratory in boxes covered with soil to avoid drying.
Within 6 to 7 hours they were tested for tensile strength
in an Instron testing machine, model TM, using a tension-
compression load cell model DR.

Trial tests using other roots were previously made
to determine the pressure of the traction Jaws which would
cause a minimum of stress concentration. Tests were made
both with and without cushioning material. These tests,
however, did not furnish consistent results, but they
indicated that the pressure should have a value of 10 to
15 psi as a minimum value to avoid slipping with a bare
Jaw.

The sample roots were consistently positioned in the
center of the traction Jaws and in such a way that the end
toward the plant center was always held by the top Jaw.

The velocity of the cross head of the Instron testing
machine was 2 inches per minute, which was about the same
as that given by the pulling device in the field. The
gage length was one inch for most of the tests, being
changed to 0.7 inch for roots of original length smaller
than 2 inches. More than one specimen was tested for the
same root whenever the original length permitted such a
procedure. Based on this characteristic the roots were

called "long roots" or "short roots."

55

A force versus deformation graph was recorded up
to the rupture point. The velocity of the recording paper
was also 2.0 inches per minute in order to record actual
deformation of the specimen (Figure 3.3.1).

The diameter of the fractured roots were measured
at the section of rupture using a Bausch and Lomb stereo—
microscope and a scale graduated in hundredths of an inch.
Measurements were also made of the distance from the
attaching point (see above) to the section of rupture.
This distance was called "dipoint."

Record was kept of the point where the fracture
occurred as related to the traction Jaws. A rupture at
the bottom Jaw was coded "B" and one at the top Jaw "T".
Similarly if the position of the fracture occurred at the
midpoint from the Jaws, it was coded "C"; and if at a
certain distance from the Jaws, e.g., .1 inch "B" or "T".
The number of roots breaking at the bottom Jaw was very
large. This fact was expected since the root tissue is
made of younger cells at the greater distances from the
attaching point.

For long roots the first specimen closest to
the attaching point was coded, e.g., as 20-1, the
second as 20-2 and so forth as presented in Table
3.2. The dipoint was also measured at the end of the test
for each root, by assembling all the specimens tested into

the whole root, and taking measurements from the attaching

56

point to the respective sections of rupture. The third

specimen of root 19 was discarded because of bruises.

Tables 3.1 and 3.2 show the experimental data
obtained for the study of the root system, for the short
and the long roots respectively. The data in Table 3.2
are more useful for studying the variations within one
root, as indicated by the changes of characteristics as
functions of the dipoint. The values in Table 3.1 plus
the values of the first specimens in Table 3.2 are most

useful for comparisons between roots.

3.3 Results and Discussion

 

The data were analyzed to obtain a partial
correlation coefficient for the variables of interest
and a regression equation. This was respectively done
by a BASTAT and a LEAST SQUARES routine programmed for
the computer of Michigan State University by Michigan
Agricultural Experiment Station (1967). Roots number 6,
10 and 14 in Table 3.1 were not tested since they were

too short to be clamped by the traction Jaws.

A typical force and deformation curve as obtained
from the Instron recorder is given in Figure 3.3.1. For
this root and most of the others, it was evident in the

force versus deformation curve that a straight line portion

57

 

comma

 

omem waooo. mac. m.H o.m as m. m om.o om
m.oa ooom coma omooo. mmo. m.s m.m 3; ON. m om.o mm
m.mm ocean oosm 028. one. m.H m.. so OH. m os.m em
m.sa some cash moose. mmo. m.H m.m as as. m as.” mm
o.m comm om: Wazoo. meo. A.H o.s Q; as. m.ca H. om.” mm
0.:H ooom omHH omfioo. omo. 2.0 m.. we 2H. 9 om.m ma
s.wm ocean comm Hsooo. cmo. m.m m.m so om. m os.m ma
m.mm comma oeom Heooo. cmo. H.m o.m as mm. m om.m ma
.I I I I I I 0.4 00 I I I :H
a.HH oomom ommm mfiooo. mac. m.m 3.3 as as. m om.o ma
I . I I I I I Q.H as I I I OH

m.ma oooza omom amooo. omo. m.m o.m am am. m em.o m

I I I I I I r.fl am I I I. o

a.am oomoa osmm mmaoo. One. 3.3 r.H an ma. m oa.a m

o.m comma omHH omooo. amo.. m.H o.m om so. a om.o m

m.0H ooam cam momoo. omo. Q.H m.fl mm as. m oa.= m

m.aH oomHH oaafl emaoo. omo. o.m o.m 3m OH. m mm.~ a

c mm. mm . . c z, . u hmw J was _
A wnmmv mw<\m0 mwxmw ,mfiww mev pmmwaao AMMW A mwov e. eawwwq otzpowwm Mwwv uwmmmz
msasvoz mmmpum wwu< mhsuompa hemmed waned. .c 00 cofipfimom mopom
mo amusemfia Hmcamfinc pcom opsuazm
poem

 

.prOL phozm go mcfiomau

uompfio Ucm

mums» oHHmzo» ho muasmomIIH.m mqm<e

58

 

 

c A comHH cHoH Hmccc. cmc. m.m o.HH JH 3H. m cm.o c.Hm
o.oH cccmm omsm HHcco. ch. o.e m.HH me co. m mo.c m.Hm
o.oH ooamH comm HHooo. oHo. s.: m.HH me om. m.:H a. Hw.o m.am
m.c ooze omcH Hmccc. cmc. c.H m.HH ms cm. a mm.c H.Hm
m.mH ccoom oocm Hsccc. omo. H.r ”.IH as cH. e oc.H c.cm
o.mm ocmoH comm Hsccc. cmo. c.e ,.mH so Hm. c Hc.m m.cm
w.mm oomcm cmsm Heccc. cmo. n.. c.mH as mH. e mc.m m.cm
m.mm ccmom cscm Hscoc. cmo. H.c s.c on mm. m cc.m m.mm
I I. I I I I I I I I I . H
m.mm cccmH cmcm Haccc. cmc. c.s e.s ma aH. m mH.m m.mH
s.mm occmH comm Hscco. cmo. n.m o.m me so. m c~.m H.cH
o.mH oommH ozom mcoco. mmc. o.: m.c on 2H. 0 HH.H m.sH
c.=m compo cmHm Hsccc. omc. A.H “.0 cs 3H. m cm.m H.~H
H.mH ccmmm cams HHccc. ch. u.e :.cH so wH. e cm.o m.mH
m.oH ocqom ommm HHooc. ch. c.m o.oH cm mu. m 20.0 m.mH
c.mm ccmcm omcm moocc. cHo. ..u c.oH 30 AH. m ss.c H.mH
N.mH ccscH cmmH Hmccc. nmc. n.a ..cH mo AH. m cc.H m.HH
0.ma oooaa ooam H5000. omo. 2.: ;.0H m1 ma. 9 02.H m.HH
o.Hm ooHeH comm Hsocc. cmc. c.w o.cH mm H. m oc.m H.HH
e.gm oommm cmom mmocc. cmc. c.m a.» HH mm. a.cH mm. Hm.H m.m
m.mc ccwmm cesm Hmocc. omo. ..m m.e on :m. m me.m H.o
m.cH cosmH omem coccc. cnc. r.c c.c mm mm. m cm.H m.»
c.mm ocmmH chm Hscco. cmc. c.H c.o um cu. m mm.m H.~
c.mm comom coca mcccc. an,. 3.3 a.m r4 cH. m mo.m m.=
m.~m ocmmm omom Heocc. owc. H.a m.c ms oH. m cm.m H.=
mcfi\nav AHmav AHmav Auch ACHV HzHV Ann“ Ammmammwa A00 mcmfim AQHV
c4 r . I . Hi. . . . . Hoossz
o.\m A \mv A<\av Hay 1c” HoncoHl cgc;.. Awe cHsecm opcccccu Hav Boom
unannoz wmmaum mmgq manpowem cwswmw caucm mo coHunom mopom
ho hometh . .m poem mpspazm

HcCHuHHQ

.uuoon whoa no w:flcmnu pcmpfin 0cm munch mHchop uo wpazmwmIIm.m mqm<9

59

 

 

 

 

 

 

 

41[
3‘?
”I;
.0
H
m 2..
O
S.
0
EL.
1.
a II
—.N J If ,.
O l 2 3

Deformation (in.)

Figure 3.3.l—-Typical force vs deformation curves
from root tensile tests: a) root number 15; b)
root number 7.2, and c) root number 25.

60

consistently appeared up to a value of .4 to .6 of

the force of rupture, indicating a Hookean behavior. Once
past the linear limit the rate of increase in deformation
is larger until the point of failure is reached, without
an evident bio—yielding point. A rather brittle failure
took place which indicates a possible behavior of the
material, or suggests the occurrence of stress concentra-
tions at the Jaws.

The values for strain were obtained from the force
versus deformation curves by measuring the deformation at the
point of rupture and dividing this value by the gage length.
Since the root presents a natural tortuosity, its real
initial length was greater than the gage length established
by the Jaws. This introduced an inaccuracy in the measure—
ment of strain since it is calculated from the gage length
established by the testing machine. Therefore, the values
calculated for strain are likely to be higher than the
real values if the root had been naturally straight at the
beginning of the testing. This effect is more evident for
roots of larger diameter in which the force required for
this straightening up of the root affects the initial
shape of the force—deformation curve. The ratio between
this idle displacement due to root tortuosity and the
displacement at rupture, varied from .1 to .5, respectively
for roots of smaller and larger diameter.

The region of the root attachment to the plant was a

transition zone of stems and roots. This zone was estimated

61

to be-a semiusphere with a radius of 1.5 to 2.5 inches
and centered at the intersection between plant center-
line and soil surface. A plot of root angle vs. length
is given in Figure 3.3.2. If the two sectors A and B
are added it can be seen that most of the roots were
found at an angle ranging from 30 to 80 degrees from
the surface line. The greatest number of roots were
located at an angle from 60 to 80 degrees. This indi—
cates a reasonable qualitative agreement with the
photographic evidence given by Miller from his study

of other varieties of sorghum.

The area of rupture was calculated from the
diameter measured at the section of rupture, assuming
a circular cross section. The stress was calculated
as the ratio of the force of rupture to this area.
The strength of the root at the point of rupture, which
was called "modulus," was calculated as the ratio of

the stress to the strain at rupture point.

Average diameter and standard deviation were
calculated for short and long roots and the values

are, respectively:

Short Root Long Root
(in) (in)
Diameter 0.038 0.0239

Standard Deviation 0.020 0.0073

frI-rI\

I I. Kari

 

 

Depth (in)

I E of plant

soil surface

 

4 6 8 10 12 14(in) Root Length

 

 

 

 

 

T . 00
O
0 Thloo
e 1‘
\
\
\ Y
‘ 4
a. \\ N200
\\
\ \
JI- ‘ \
10 _ ‘ \ a short roots
, , x,‘\ + long roots
\ \ -—- transition ‘~30°
12 J I ‘\ zone
I
“‘V \\
14 - I Jr ‘I IL \— ‘3 1
80° 70° 60° 50° 40°
90° Root Angle (a)

Figure 3.3.2——Root angle vs root original length, with
transition zone included.

Root Angle (a)

63

The rather high value for the standard deviation of short
roots may be attributed to the comparatively small number
of observations and to the fact that among these short
roots there were in reality two different types of roots,
one of them being similar to the long roots. The other
was the bracing roots, which have a larger diameter, are
more aqueous and less fibrous, as was noticed during the
experiments. This was confirmed by further studies of
the types of roots and by literature. Weaver (1926)
reports work done by Eyick, with a Folger variety of
sorghum, in which it was found to have a great resemblance
of the root system with that of corn, "although the
fibrous growth of roots near the surface was much less
prominent." From Figure 3.3.2 it is seen that the less
fibrous roots are located in the topmost 4 inches of soil.
Figure 3.3.3 shows a plot of the diameter of
fracture for the first specimen (the base diameter) vs.
root original length. This plot, and all the others
involving root original length were made with the
respective values found in Table 3.1 and those of the

first specimens of long roots from Table 3.2. It is seen

that the spread of values in base diameter for short roots

was much larger than that of long roots. This explains the

64

.czonm mam whoop mcoa pom mcoEHoQO
pmpfim haco .npwcoH Hmcfiwfipo poop m> mthompw mo LmumEmHQIIm.m.m mhzmflm

HeHV sowecq HmcHwHto pccm
NH HH cH c c a o m a m m H

 

 

 

 

 

 

1 IIIIII XI.III.IIIIIIIIIA
_
. n T G
u x x “ ..omo.
_ .
. .
Fl IIIII XII! IIIIIIIII *L.» GO 0
o
o
o ..o:o.
o
O o
..0©o.
whoop MCOH x
mpoop who 0
am e
a ..cmc.

(ut) aanqoeag Jo Jeqametq

65

rather high standard deviation found for short roots.
It suggests also that in the study of root strength at
least two types of roots have to be considered.

A plot of force* vs. diameter of short and long
roots, seen in Figure 3.3.4 shows that for both cases
the trend was for an increase in force as the diameter
of rupture increases. The regression equations and
partial correlation coefficients (pcc) were: Y = .63 +
37.5 X and 0.584 for short roots; and Y = .44 + 89.0 X
and 0.734 for long roots. Thus, the force increased with
diameter at a higher rate for long roots.

Figure 3.3.5 shows a plot of failure stress vs.
diameter. As might be eXpected, the stress decreased
with an increase in diameter. It decreased at a greater
rate for long roots. The respective regression equations
and partial correlation coefficients for short and long
roots were: Y = 3,820 - 4.17 x 104 X and pcc = -.633;

Y = 7,700 - 15.6 x 10L4 X and pcc = -.590. The fact that
the stress is not constant with diameter, but shows a
negative relationship, implies that the rupture force is
not proportional only to the area but also to a linear
dimension of the cross section.

The circumference was chosen as a linear dimension

Of the cross section due to consideration of the

L

*From now on, in this chapter, whenever it is referred

t0,force, diameter, stress, strain, modulus and strength,
correspond to parameters taken at the rupture point,
unless otherwise stated.

66

QJMNO
n cod 0cm x 0.00 + ::.I n w "whoop wcoa pom mzmm. u cud 0cm x m.>m +
o. u w "whoop uponm pom ”meduomhm mo pmmemHU m> monomllc.m.m mmswfim

ACHV chapompm no HmumEmHQ
000. 000. 050. 000. omo. 0:0. 0m0. omo. 0H0.

b P F b P I D
‘ I3 ‘ 1 1 ‘ ‘ (I

 

whoop mcoa x N. 00am.»
whoop uponm o 0 \\.I
I. H
d
o
J
O
a
‘V N O
.J
H
n
d
n17
m
I m a
T.-
o.
S

 

67

.00m.| n 000
0:0 x 00H x 0.ma I 000.0 u w muooe wcoq .mm0.I n cod 0:0 x 0H x 0H.:
I 0N0 m u w muoom uponm .mHSuompmmo LoumEmHU m> mmmppmllm.m.m meswwm

ACHV endpomnm mo HopoEmHQ

000. 000. 000. 000. 0m0. 0:0. 0m0. 0m0. 0H0.

F I I I P h
1 I

I F
d 1 Id I 11 ‘1 1

000a
000m
000m

: 000:

x / .. oocm
/../ I 0000

 

Q
x

I 0000

mpoon wcoa x 4 0000

mpOOh ugh—”05m Q

 

. 0000

(red) eanqdng JO sseJQS

68

biological nature of the root (Esau, 1966). Figures

3.3-5 and 3.3.7' show plots of’"surface strength" F/nd
vs. diameter for short and long roots. The regression
equation and partial correlation coefficients for short

and long roots were, respectively:

Y = 18.5 - 28 X; pcc = — .060 and
Y = 13.1 + 360 X; pcc = .309.
The low value of pcc = - .060 for short roots indicated

that there was a negligible correlation between F/nd and
diameter. Therefore, it might be assumed that the lepe

of the regression line was zero for short roots. ThUS,

Fs = Clwd
where
FS = rupture force for short roots, lbs;
C1 = 17.4 lbs;
d = rupture diameter, inch.

In the case of long roots, a t—test was used to verify

whether the lepe equals zero. The hypotheses were:

H : lepe = 0 and H : lepe # 0. The values obtained for
o a

t calculated and critical were: ltl = 4.82 and t (.05, 22)

= 2.074, respectively, which indicates that there is

evidence to reJect the null hypothesis. Therefore, in

69

.000.I u 000 .mpoon uposm n00 meduomnm mo HmmeMHU m> 0:\mII0.m.m mmswam

AQHV ohsuomnm mo LomemfiQ

000. 000. 000. 000. 0m0. 0:0. 0M0.

- r - b n L b
I1 1 d 1 II 1 d

0m0. 0H0.

D b
1 ‘1

 

0H

0m

0m

0:

(ut/sqt) pu/eoaoa

70

.000. u ccc 008 x com + H.0H u H

”mpOOH MCOH nou.mn:uompm.fio 00008000 m> 0=\mII0.m.m madman

AGHV caduomnm mo nmpmewam

 

0m0. 0N0. 0H0.
.X
X
X 1K
1x
m a
I\
IIIIIIIII
-\
x \
x I\I 1X
“MIMI
.* x
x X
x X
X

; 0H

0m

. 0m

I 0:

 

(HI/sat) pn/SOJOJ

71

the case of long roots the effect of the area can not
be neglected, and the relationship between force and

diameter can be written as:

= 2
where

F = rupture force for long roots, lbs.
C = 13.1 lbs/in
C4 = 1440 lbs/in2

d = diameter of fractured section of the root,
inch.

So far it has been seen that from a strength stand-
point there were at least two types of roots, short and
long, and their average diameter and standard deviation
were calculated and given above. The tests indicated
that the force of rupture for short roots was mainly
related to the perimeter rather than the area which
might be due to their biological constitution. This
was not the case for long roots, for which it was seen
that the force of rupture was also related to a square
dimension of the cross section.

It was earlier shown that diameter and root length

were used to identify two groups of roots and that there

were different relationships between rupture force and

diameter for these two groups. These observations

72

should be reflected in a comparison of force and root
length. A plot of surface strength F/nd versus root
original length is shown in Figure 3.3.8. For this

plot the COrresponding values were taken from Table

3.1 and from the first specimen of Table 3.2. The
values were arranged in Table 3.3 for easier comparison.
The average values of F/nd and of standard deviations

for short and long roots were, respectively:

Short Roots Long Roots
(lb/in) (lb/in)
Surface Strength 17.4 30.1
Standard Deviation 9.3 9-8

From the plot it could be seen that all long roots

had an F/nd value higher than the majority of the short

roots. Despite the large values of the standard

deviations, this confirmed that different rupture strength

values should be considered for short and long roots.
Figure 3.3.9 shows a plot of modulus versus root

original length. Average values of modulus and standard

deviations for short and long roots were, respectively:

Short Roots Long Roots
(psi) (psi)
Modulus 13,000 24,000

Standard Deviation 5,800 12,800

.prcmfi Hmcfimfiho poop m> 0=\mII0.m.m mhswflm

HcHV 000080 HconHsc cccm

 

NH Ha 0H m 0 0 0 m 0 m m
Amcmefiomam pmaam Aacov _
whoop msoa + "
mecca phonm o .
_
_ 0 O
. o
_ O 0
_
6
. o moo
_
_
_
H3 _
7. + .
If _
IT _
+ _
+ _
+ u 0
_ o
_
.
_
_
_
.f _ 0
_
_
.
_
_

.0H

0m

0c:

 

(at/gqt) pu/ aOJOJ

74

TABLE 3.3——Rupture strength parameter F/nd in pounds
per inch.

 

 

 

Short __¥ Long roots (F/nd)
roots 1st 2nd 3rd 4th
(F/Hd) specimen specimen specimen specimen
14.2 27.5 28.9 12.2 15.5
16.3 25.0 19.8 13.1 7.9
9.0 43.2 27.7 25.6 -
31.1 21.9 15.8 16.6 —
13.8 22.6 16.8 - -
11.4 24.0 15.0 - -
38.3 28.7 22.4 _ _
28.7 38.3 25.8 - -
14.0 9.2* 16.0 - -
8.0 — - ‘ ‘
14.5 - - ' ‘
23.8 - - ' ‘
10.2 — - ‘ '
10.6 — - ‘ _

X(average)

17.4 28.9 21.0 16.9 11.7
S(standard

deviation)

9.3 7.8 5.5 6-1 -

 

—-‘

*This value was not considered in the analysis.

Amcmeflomdm wmhflm

75

NH HH 0H

00:00
whoop mcoa +

muoop phozm o

Hch ecmocq HcchHsc 0000

0

.300200 Hmcfiwfipo poop m> weasvozII0.m.m mpswfim

0

b
4

n

F

a

0

V
I!

Ln

—— _——‘>

-----—-——--——————--———-----G~—-

«(Y3

a»
17-

 

0000a

0000m

0000M

0000:

0000m

OI x :sd) snInpow

(a

76

Here, again, high values of the standard deviations were
found, but there does appear to be differences between short
and long roots, the longer roots being less elastic. A
modulus based on the perimeter of the root might have been
more representative of its elasticity than a modulus based
on the area as it was defined.

Referring to the geometrical variations occurring
along a root, it is seen from a plot of diameter vs.
dipoint, Figure 3.3.10, that there may have been a slight
decrease in diameter as the dipoint increased. However,
the regression analysis showed that this influence was not
significant.

A plot of force vs. dipoint (Figure 3.3.11) showed
that the force decreased as the dipoint increased. The
regression equation and partial correlation coefficient
obtained were Y = 2.49 - .18 X and pcc = -.488. The t
test showed that the correlation was significantly differ-
ent from zero for all tests of long roots where the absolute
value of the partial correlation coefficient was equal or
greater than 0.440. For this case there was a significant
change in force with dipoint which could be caused either
by the conical shape or by a change in strength of the

root with dipoint, or both.
The ratio F/nd is plotted vs. dipoint in Figure
3-3.l2, and a significant negative relationship was ob-

served as indicated by the regression equation and partial

correlation coefficient: Y = 29.80 - .18 X and p00 = -.509.

Diameter of Fracture (in)

77

.030 T X X x: x x xx x x

X

x
X K
x

.020 x x x

X X X

x

.010 "

 

 

l 2 3 4 5 6 7 8
Dipoint(in)

Figure 3.3.lO--Diameter offkecturevs dipoint.

.000.I I coo one x 0H. I 00.0 I » .ccHocHo m> conchIHH.m.m cscmHm

Hch coHooHo
0H 0 0

3

78

4F

 

(gqt) aanqdng 30 90208

Force/TId (lbs/in)

79

 

+
40:-
*
30"
* +
\\+ ‘I'
+
+ + g\\\\ r
r ~ +
§
20 \...\
$ + .x
+ ‘t\\‘
r
*
10" +
4.

 

1 2 3 4 5 6 7 8 9

Dipoint (in)

Figure 3.3.12-—F/nd vs dipoint.
Y = 29.80 - 1,8 X and pcc = —.509.

 

80

Since an increase in dipoint caused a significant decrease
in value of F/nd, which was considered the most important
strength parameter of rupture, it may be stated that the
root strength decreased as we departed from the attaching

point toward the root tip.

4. STRESS DISTRIBUTION

4.1 Introduction

 

In this chapter a theoretical approach will be pre-
sented which describes the uprooting force applied to a
root-soil composite. For this study several approaches
were considered as to their feasibility, advantages and
disadvantages.

Kaul (1965) reports that the inclusion of roots was
found to increase the shear, tensile and compressive
strength of soil. At first it was thought that the problem
might be regarded as a reinforced medium, similar to
reinforced concrete. The qualitative nature of the strength
of concrete could be compared with that of the soil, but
obJections might be given to regarding the roots as similar
to steel bars. A preliminary study of the research done
on reinforced concrete indicated that little attention had
been given to configurations of reinforcement similar to
the root system. This approach was therefore abandoned.

Rosen (1964) studying the mechanics of composite
strengthening states that when a fracture criterion is
desired, an understanding of the average stress—strain
response is no longer sufficient, and consideration must
be given to internal irregularities in the state of stress.

He presents a solution to these problems for failure of a

81

82

fibrous composite under uniaxial compressive and tensile
load. The study is based upon consideration of-the phe—
nomena that occur subsequent to an initial internal frac-
ture and when the strength of brittle fibers are defined
by a statistical distribution function. Despite the dif-
ferent geometry between the root system and that of the
reinforcing fibers, the solution could probably be applied
to the mechanics of the root system later on when its
statistical distribution function is better known. Rosen,
in his work, defines the effective length of a fiber
embedded in a matrix and presents a solution for the inter-
face shear stress.

Maclaughlin (1966) working with matrices of fiber-
reinforced material models was able to obtain photoelastic
values for maximum shear stresses developed in the surround-
ing of the embedded fibers subJected to tensile forces.

The models were made by casting a birefringent epoxy resin
around variously arranged steel strips. The peak stresses
resulting from a gradually tapered fiber was found to be
slightly higher than that from a square—ended fiber. A
round—ended fiber produced a peak stress which was slightly
lower than that of the square-ended fibers. Peak stresses
resulting from two square—ended fibers butted closely
together were considerably higher and decreased with in-
creasing gap. It made little difference whether the gap
was Open, simulating a void resulting from a broken fiber,

or filled with matrix material.

 

83

The use of a photoelastic approach for the study of
the root system was considered, since it was learned in a
work reported by Richards Jr. and Mark (1966) that Moreno
§g_§1., in Spain, had used gelatin models to study rein—
forced concrete, using rubber bands as the reinforcing
element. A complete review of literature was made of the
use of gelatin models for photoelastic analysis. This
study included prOportioning of gelatin mixes, moulding
process, and calibration methods for testing for quantita-
tive results. Several trials were made in COOperation with
the Botany and Physiology Department of Michigan State
University, in an attempt to germinate sorghum seeds in an
Agar gelatin medium. The seedlings were able to germinate
and it was noticed that the growth of roots was affected
by the proportions of the gelatin mix. Difficulties were
encountered in obtaining a translucency of the medium which
permitted a good view in the polarisc0pe. The necessity
soon became apparent of controlling certain critical factors
whose effects might invalidate the results completely.
These factors were: friction between gelatin mix and the
wall of the model; a minimum thickness of the model to
transparency and plain strain state; and the calibration of
the model root-gelatin.

It is known that one of the approaches used in the
determination of the soil bearing capacity and for sta—

bility calculations of the soil-foundation system, is

84

based on studies of failure conditions. This method
requires knowledge of how the failure in the foundation-
supporting soil takes place. It was therefore decided to
observe the cracks taking place underground and at the
surface of a root—soil composite subJected to a pulling
force. These observations proved valuable in the descrip-
tion of the failure surface. Therefore the phenomena were
filmed and the results will be reported in the following
sections of this chapter.

4.2 Theory of the Mechanics of the
Root-Soil System

 

The root—soil system may be considered as being a
reinforced composite with the following specific charac—
teristics:

a. the roots are mainly distributed in a conical

pattern;

b. this distribution is non—uniform both with
regard to the apex angle of this cone and
also circumferentially;

c. the roots present geometrical and histological
variations;

d. there is a transition zone encompassing the
attaching point with a high density of rein—
forcement (roots);

e. the soil is an anisotropic medium with low

tensile strength;

85

f. the bonding between root and soil is

altered by the soil moisture content.

Forces applied to a plant are counteracted by two
principal factors, the weight of the soil, plant and roots,
and the forces due to the strength of the composite. It
was seen that the value of the maximum force that could be
applied to the plant was by far greater than the weight of
the plant plus the root—soil bulb and also greater than
the weight of the soil in the crater.

Therefore, this indicates that the root-soil composite
presents a certain tensile strength. The soil itself pre—
sents a low tensile strength and it shall be considered
mainly as a bonding matrix. The roots, compared to the
soil, have a rather high tensile strength and in this
analysis they will be regarded as if they were the main
resisting element. The test results seemed to indicate
that the material may be assumed to be Hookean up to about
one half of the value of the maximum force.

The theory for a simplified root—soil system can be
attempted upon the assumptions that:

a. the center of the root distribution cone is

the intersection of the vertical centerline
of the plant and the soil surface line;

b. the root system has rotational symmetry around

the vertical plant axis. The distribution is

defined as a function of the cone apex angle;

86

c. the roots are cylindrical in shape but their
strength decreases as the distance from the
attaching point increases;

d. the transition zone close to the center of
the plant base is a hemisphere;

e. only the portion of the pulling force created
by the composite strength will be considered.
The influence of soil weight will be neglected;

f. the composite behaves as a Hookean body, up to
a proportional limit or "yield strength" of the
composite;

g. the changes occurring in soil moisture are
assumed small and the friction and adhesion
between root and soil are constant;

h. the actual behavior properties of the roots
are assumed to follow the assumptions of the

theory of elasticity.

Other assumptions will be specified at the appropriate
time in the analysis of the root—soil system.

4.2.1 The Bond Between Main
Roots and Soil Composite

An uprooting force applied to a plant reaches the
main root through their attaching point. From the main
root this force is transferred to the surrounding com—

posite made up of soil, branch roots and root hairs, by

bond or shear forces along the main roots.

87

The free body diagram of Figure 4.2.1 shows a segment
of root embedded in the soil. The radial coordinate be
defines that point of the root beyond which it remains

stationary when subJected to a force F The root seg-

t'
ment from the origin (0) to po defines a central zone
within which the physical phenomena are considered unde—
termined, and where it is assumed that the root-soil system

behaves as a solid body.

From the free body diagram it can be written

s r
or
p O
—[ dFr = J dFS (4.5)
Do Do
Also,
0
Ft — Fr — J dFS (4.6)
0o
where
Ft = total force applied to the attaching

point of the root [Ft = (Fr)p=OO];

"£1
ll

residual force eXperienced by the root at

a section under consideration;

"111
II

total tangential force in the axial direc—

tion at the root—soil interface.

88

Figure 4.2.l--Free body diagram of root embedded in the soil.

89

The factors influencing the root soil bond are:
adhesion, root-soil friction and pressures exerted on the
roots from the outside. A possible interaction among these
factors is to be considered. The presence of branch roots
and root hairs alters this behavior further, due to an
increase in bonding area and a shearing of these elements
during the relative displacement between root and soil.
The attracting force of adhesion is determined by two
factors: the actual strength of attraction of a unit area
of bonding and the actual area of the attracting bonds.
Outside pressures applied to the root surface influence
both of these quantities, so that evaluation of these re—
sults is difficult (Gill and Vanden Berg, 1966). There-
fore, it is assumed here that the tangential stress (I)
acting in the axial direction of the root encompasses the
influence of all the factors contributing to the transfer
of forces between root and soil.

Thus, the elementary axial tangential force (dFS)

develOped at the root—soil interface is given by

dFS = 2erdp (4.7)
where

r = root radius;

T = axial tangential stress on the periphery

of the root;

9 = radial coordinate of the root element.

90

Therefore, the axial tangential force can be eXpressed as

0
FS = 28 I rT do (4.8)
Do

and from equation (4.6) the residual force is given by

0
Fr = Ft - 2w J rt dp (4.9)
Do
The conditions under which an axial tangential
stress I exists are dictated by the factors discussed
above, and also by the relative displacement (J) between

root and soil. Thus, I can be eXpressed in a general

form as

T = f (J) (4.10)

When subJecting the root to a force, different dis—
placements of a given point at the interface will be
experienced by the soil and the root due to differences
in imposed stresses and in "elastic" properties. Thus,
there will be a relative displacement (J) at the point of

the root—soil interface which may be expressed as
J: S — S (8.11)

where

91

root displacement, and

(D
II

(II
II

soil displacement.

Consider the diagram of Figure 4.2.1. The elongation
of an elementary section do in terms of the property of the

material may be expressed as

F
2W r Er

where

dp = elongation of the elementary section do;
E = surface modulus of elasticity of the

root with dimensions force/length.

If the displacement Sr is assumed to be zero at
radius pe the displacement of any root segment in the

negative direction of p could be written as
De
s = I do (4.13)

Substituting the value of 8p found in equation (4.12)

into equation (4.13) it becomes

 

0e F
_ l r
8r — 2n 1 r E dp (“-1”)
p r

92

If it is now assumed that the displacement of the
soil is negligible as compared with that of the root, then

equation (4.11) can be written as

 

p F
. _ _ 1 e r
J " Sr, " 2.”. 1p 1" E dp (8.15)
r

The earlier definition of the radius pe now implies

that for

From equation (4.9)

(Fr) o=oe = 0 (4.16)

It is proper at this point to define the effective
length of a root as the radius pe because from this radius
outward the root does not experience any residual force.

The definition of the effective radius pe could be
expanded to mean the radius beyond which SP = $3.
Thus, from equations (4.6) and (4.9) it can be

written that
0e
F = 2n J r1 dp. (4.17)

r
D

It should be made clear that the shear stress func-

tion I = f(j), given by equation (4.10), has to be

93

determined eXperimentally. A typical shear stress-
displacement diagram obtained from a direct shear apparatus
for highly cemented and dried soils or hard, clean sands
is given in Figure 4.2.2, curve 1. The reinforcement
effect of the roots in the soil may be of the nature of
curve 2. A higher value of Tmax. for the composite curve
may be Justified by the fact that the penetrating action
of the roots and their diametral growth cause a higher
degree of compaction at the root-soil interface. From
shear tests of soils it is also known that the shear
strength increases during shear for confined specimens.
If the movement of the root takes place under small
changes in volume it is likely that this also imposes a
"confinement" onto the process, and the shear stress is
increased. The value of Tmax. for soil alone takes place
over a shorter displacement change, whereas that for the
root-soil system is thought to persist for a greater change
in displacement (J). This may be Justified by considering
that before the maJority of branch roots and or root hairs
have failed, longer displacements are to be expected as
compared to the displacements for soil alone. At high
values of the displacement (J) the value of the axial
tangential stress would be reduced to root-soil friction.
Based on equations (4.9), (4.10), (4.15) and curve
2 of Figure 4.2.2, a theoretical attempt can be made to

describe the general nature of variables such as the

 

94

 

 

 

 

 

 

 

 

-__- _...__T-.. ______ .1
/ I
/ 2 i
I 1
i
l
l l
|

0»

I fl
I
I
l

J .

o o J

Figure 4.2.2--Axial tangential stress ( T) versus dis—
placement (J). Curve 1 is a typical curve for soil.
Curve 2 may represent the reinforcement effect of roots.
The broken line represents the assumed linear model.

95

residual force Fr)’ the axial tangential stress (I) and
the relative displacement (J) as functions of the radial

coordinate (p) of the root element (Figure 4.2.3).

Since it has been found that (Fr)p=p = 0, there
e
are two values known for Fr, namely: (Fr)p = Ft and
(Fr)p = O. The displacement J equals zero at p = pe

and has its maximum at Q: p0. Consider equation (4.9).
If (T) is assumed positive a decreasing tendency is to be
eXpected for Fr with increasing 0. For small values of p,
high values for J can further be expected. From curve 2
of Figure 4.2.2 it is seen that at high values of J, the
axial tangential stress (I) is constant but small. Thus,
the curve of Fr in Figure 4.2.3 is expected to present a
slightly negative slope for points between 00 and pl.

For points beyond 01’ the J values are assumed to be less
than J6 in Figure 4.2.2. This means that the T values
are higher and therefore the decrease in Fr is faster.

From pl to p the value of Fr will decrease until it

e
becomes zero at pe.

If the assumed values for Fr are introduced in
equation (4.15), it shows that the basic assumptions
regarding the displacement J are reasonably correct.

A mathematical derivation can be found for the

curves of Figure 4.2.3 by considering equations (4.9),

(4.10) and (4.15).

Fr3J:T

 

 

 

 

 

 

Figure 4. 2. 3—-Residual force (Fr ), displacement (J) and
the axial tangential stress (T)r as functions of the
radial coordinate (o). The broken line represents the
values of T as given by the assumed linear model.

97

 

0
Fr = Ft - I 2wr1dp (u 9)
Do
I = f (3) (4.10)
0e F
. _ 1 r
J - E? J P E 90 (8.15)
D r

Taking derivatives of equations (4.9) and (4.15)

with respect to I) gives

dFr
d—_ = - 2TTI’T (4.18)
p
and
. F
91 = _ ___£__
do 2WP Br (“’19)

The negative sign in equation (4.19) is due to the order

of the limits of integration that are used. The second

derivative of J is then

d j = _ l P (4.20)

Substituting the value of dFr/dp from equation (4.18) into

equation (4.20), gives

98

T
E (4.21)
I”

and the general equation can be written as
9—1 — IELII - o (4.22)
r

In order to solve equation (4.22), f (J) must be
known. Assume T = f (J) to be represented by the simpli—
fied model given by the broken lines shown in Figure 4.2.2.
For reasons mentioned earlier, it is assumed that the
values for J and T given below will apply in the regions

of p in Figure 4.2.3, as follows:

 

 

o J T = f (J)
' 0
Do to p1 > J5
' K
91 to 02 J5 to J2
. . a
02 to De J2 to 0 J

The solution will be made considering the three regions for

0 indicated above separately.

For the portion pO to pl, equation (4.22) becomes
d—1 = o (4.23)
2

Integrating gives

99

d

5% = Cl (4.24)
and

J = Clo + C2 (4.25)

Using equation (4.19) and (4.24) gives

F F
_ ___£__ = c = _ ___2__
2flr E l 2nr E
r r

because at p = p

0
Fr = Ft (14.26)
and
Ft (4 2)
J = - 2wr Er p + C2 ° 7

C = . ____t__ (4.28)

and therefore

t _ (4.29)
J _ 35 + an Er (pl 0)

100

A = = ' -
180 when p p0, J (J)po, and from equation (4.29)

Ft
00 J5 + 2wr Br (01 — DO) (“-30)

For the portion pl to 02 equation (4.22) becomes

(1 ' K
'_3% = E_ (4.31)
r

9.1 = __

dp Er p + C4 (4.32)
and

3= 5%- 02 + C4 0 + G5 (4.33)

From equations (4.19) and (4.32)

_F___=_I:
2 r Er Br

0 + C4 (4.34)

and

"IJ
ll

_ 2nr K p — 28 r Erc4 (“-35)

But when p = pl, F = Ft and from equation (4.35)

 

\
.v

101

F
1 t
4 - - E; (28 r + K pl)

Thus, equation (4.35) can be written as

Fr = Ft - 2w K r (p - pl)

Combining equations (4.36) and (4.33)

 

 

F Kp
_ K 2 t 1
3 ‘ 2 E p (2nr E + E ) p + C5
1” 1° 1”

By applying the boundary conditions
J = J2 at p = 02; and J = 35 at o = °1’

equation (4.38) becomes

F Kp
K 2 t l

J = __—_ p _ (—————— + ———) p + C

2 2 Br 2 2nr Er Er 2

and
K02 F

J = —-—--—1 - — t p + C

5 2 Er 2nr Er 1 5

Equations (4.39) and (4.40) can be combined to

—K F

(4.36)

(4.37)

(4.38)

(4.39)

(4.40)

t .-
35 - 32=[§—§; (01 ‘ 92) ‘ 2F?‘E;J (81 82)

(4.41)

L ILA-i i'

 

102

For the portion 92 to oe equation (4.22) becomes

 

 

2. .
Q_% _ %1 = o (4.42)
do r
Let a/Er = A A solution of equation (4.42) is
J = c7 ec8 0 (4.43)

therefore,

- o
2.1 = C8 .
do C7C8 e (4 44)
and
2. 2 c D
g—J- = c c e 8 (4.45)
do 7 8

Substituting the values of equations (4.45) and (4 43)

into equation (4.42) results in

_ i A (4.46)

J = C e + ClO e_Ap (4.47)

.110

_ = 0
When o = w, J = 0, and C10 e - 0. Therefore, 09

and equation (4.47) is

 

llmfi—l‘ I

103

_ ~40
J ‘ C10 e (4.48)
When o - o2, J J2, and
c = J er2 (u 4
10 2 ~ 9)
Thus equation (4.48) can be written as
. . -A -
J = J2 e (0 92) (4.50)
Then,
g1 = _ . -A(o - o )
do AJ2 e 2
and using equation (4.19)
F = 2nr E A J e'Mp ’ 82) (4.51)
r r 2

From equation (4.37) Fr is found to be at o = p2

= _ K - )
(Fr)p2 Ft 2n r (02 pi

and from equation (4.51)

(Fr)o2 = 28 r Er A J2

which gives

 

104

Ft = 2m [K (92 - 01) + Er A J2] (4.52)

In summary, the following equations apply:

 

_ t ( - )
.j 35 + 2 r Er pl 0 (Ll-29)

pl can be found from equations (4.30) and (4.52)

F = F (4.26)

 

 

For 01 i o 1 92
F K o
= K 2 t 1
J 2 Br 0 - (2FF—E; + E;—_) O + CS (4.38)
CS can be derived from equation (4.41)
Fr = Ft - 2an (p - 01) (4.37)
for

 

J =12 e“A (II - pg) (“-50)

p2 is found from equation (4.53)

2
A - a/Er

 

105

_ -A -
Fr - 2nr Er A J2 e (o 02) (4.51)

For the solution the following equations are available:

 

Ft = 2nr [K (o2 — pl) + Er A 32] (4.52)

35 - I, = [K (22E; pl) + 2;;31 (p, - 81)
(4.53)

(I)p0 = 35 + Ig; (02 - pl) + A J21 (pl - oo)
(4.54)

These equations contain only three unknowns (Ft’
p1 and o2) and can therefore be solved. It can be seen

that under the assumptions made for these calculations Ft

will have a fixed value determined by o2 - ol which in its

turn is a function of the soil and root properties. ol
will be a function of (J)po. An increase in (J)po will
mean an increase in p1 and therefore in oe but no change
in Ft’ unless the soil prOperties change with o. If

the applied force is less than Ft as determined by equa-

tion (4.52), (J)p will be less than J5 and the solution
0
has to be changed correspondingly.

Based on these equations, the curves for Fr and J

in Figure 4.2.3 can be derived.

"3

 

106

4.2.2 The Displacement of
the Attaching Point

 

An analysis of the displacement of the attaching
point of the root may be attempted on the assumption that
the root is affected by the displacement only between the
plant and be, and that it remains basically straight over
this length.

From Figure 4.2.3 it can be shown that the displace-

ment of the sttaching point of the root is given by ‘

 

AL \/ (L + d cos 0 )2 + (d sin 0 )2 - L (4.55)

 

where

AL

elongation of a root at the attaching
point;
L = root length between po and pe;

vertical displacement at the base of

GI
ll

plant (or of the attaching point);
e = angle that a root makes with the vertical
axis of the plant.
By assuming AL/L a small number and neglecting the
second order term in AL/L, equation (4.55) becomes

2

- d . 6
AL - 2 L + d cos 0 (4 5 )

Equation (4.56) shows that AL is a linear function of

cos 0. If the ratio d/L is assumed to have a low

107

 

 

Horizontal Boundary
d cos 9 ‘ ° y Surface

 

 

+y

   

Figure 4.2.4-—The displacement at failure surface is
maximum for 8: 0, and minimum for 0 = n/2.

108

value and 0 < H/2, then
AL = d cos 6 (4.57)

From equation (4.55) it can be shown that the elonga-
tion of a root at the attaching point is maximum at 0 = 0 1
and minimum at 0 = H/2.
4.2.3 Stress Distribution
in the Soil Composite

The soil composite is regarded in this discussion is

composed of soil, branch roots and root hairs excluding

 

the main roots. Then, the reinforcing action of the root
elements of the composite can be assumed to be of such a
nature and order that the displacements of the root elements
and the pure soil will be the same.

From the analysis of Section 4.2.2 it was seen that
the transfer of forces from root to soil acquires signifi-
cant magnitudes for a radius equal or larger than o1.

Thus, it may be inferred that for the analysis of stress

distribution in the soil the values of radius p of main

interest are those from pl to oe and beyond. Furthermore,

01 and pe define points which may be assumed to be
relatively close as compared with the whole length of the
root.

An assumption which has been proposed by Boussinesq

(1885) and used by Jumikis (1962) and which is qualitatively

109

in agreement with the Boussinesq stress distribution is

that the displacement of a point in the soil is given by

(4.58)

m
R
‘O|I—’

The displacement (s) is assumed to apply equally for
reinforcing roots and surrounding soil; g may further be
assumed to be prOportional to the displacement (AL) of
the attaching point.

From equations (4.57) and (4.58) the displacement
(s) of a point N (o, 0) in Figure 4.2.5 can be eXpressed

8.8

S = C dpcos 8 (4 59)

 

where

constant of proportionality, with dimensions

0
II

of length.

Now compare the point N in Figure 4.2.5 With a point
M (p + do, 0) in the same direction of o. The displace-

ment at point M is given by equation (4.59) as

= C d cosgg (4.60)
1 o + do

The strain of the composite element of the length

do is

3 '-

 

I’ mfg—19'.-
I
l

 

 

110
’F
Horizontal Boundary
(b) j? Surface
ll'N“ 0(X) +y
6 I I
' / /
l o / ’
/ /
/ /
/ x
. | /
\\ / / /
0‘.~___fl, _ /
l M
\\\ //

0 = polar stress

Figure 4.2.5-—The static system of the soil composite.

 

 

111

_ l _ C d cos 0
E - do - (14.61)

2
(3 +odp

 

Considering that do is small compared to o,

C d cos 0

2
D

 

(4.62)

At this point an average stress 0 may be defined

R
on the basis of the total force in the radial direction
and the cross—sectional area of the composite element,
including both roots and soil. Based on previous assump-

tions of linear stress-strain relationship it might be

written that

B C d C08 8 (“.63)

where

o = polar tensile stress in the root-soil
composite;
B = constant of proportionality, with
dimensions force per unit area. B
is normally a function of 0 and o.
From the equilibrium diagram of Figure 4.2.6, the

forces acting in the z-direction are given by

112

 

fis‘ty

 
     

principal
polar stress

Figure 4.2.6—-Equilibrium diagram: ZFZ = O.

 

 

113

A
F = I OR cos 0 dA

where

dA

28R ode, but R = o sin 0, so

dA 2-IIp2 sin 8 d0

Thus, equation (4.64) can be written as

00 2
F = 2n J o o sin 0 cos 0 d0

(4.64)

(4.65)

where 00 is the limit for force transmitting elements,

00 s w/2

Substituting the value of GR from equation (4.63)

into equation (4.65) and assuming B and C constant for

6 s 80,

00 2
F = 2W8 C d I sin 0 cos 0 d0

0

or after integration, as
e 00
l 3
I 0 sin 0 cos20 d8 = - j COS 0

%‘(l " 005360)

(4.66)

114

3 F
2 (l - cos3 0°)

 

Substituting the value of equation (4.67) into equation
(4.63),

3 F cos 8 (4 68)
2"02 (l - cos3 00)

Figure 4.2.7 illustrates equation (4.68).

Summarizing, it can be said that the transfer of
forces from roots to the soil is characterized by distinct
values of the radial coordinate o. For values from oO to ol
the force transfer is not significant, and the stresses are
taken up by the root. From ol to oe the transfer of force
to the soil is effective and the stresses are then shared
by root and soil. The region ol to oe may be considered
as a probable region of failure. The strength of the com—
posite in this region will be influenced by the imper—
fections that the root-soil composite might present. Thus,
it would be difficult to characterize exactly how the
composite fails because of the dependence of the strain
distribution between its elements. From oe to w the

stresses are taken up entirely by the reinforced soil and

decrease.

115

////

 

 

60 degrees

raj
II

321 lbs

Figure 4.2.7--Isostrength curves OR = constant.

116

4.2.4 The Failure Strength of
the Root—Soil Composite

The observations made of the underground failure and
those presented in Section 2.3.2 provide elements for
estimating the strengthening effect of the roots on the
soil.

The strength of the composite is given by that of
the soil plus a reinforcing effect introduced by the roots.
This additional strength can be described by a reinforcing
factor, which depends upon the distribution of the roots
with the radial coordinate o and the angle 0.

It was seen from the direct tracing experiment of
roots and from the plot of Figure 3.3.2 that the greatest

number of main roots were found at an angle (a) from the

soil surface between 60 and 80 degrees. Also, for values

of (a) less than 30 degrees, the number of roots declines

to practically zero. The branch roots and root hairs may

be assumed to be distributed in approximately the same man-

ner as the main roots. From the profiles of craters given

in Figure 2.3.3 (A), (B) and (C), it can be seen that the
"flat" bottom portion of the crater is involved by an

angle (0) of about 50 degrees. For values of 0 of 50
degrees and above, the failure surface attains a typical

Rankine pattern, due to reasons which will be discussed

later in this chapter.

 

 

117

Therefore, the reinforcement effect of the root upon
the soil as reflected by the actual failure surface, will
be considered for values 0 S 0 S 50 degrees.

In Figure 4.2.8, the isostrength curve OR = const.,
from equation (4.68), would represent the surface of
incipient failure of the non—reinforced soil. The shape
of the actual failure surface of the composite is taken
from the tests (Figure 2.3.2 (C) N-S profile of eXperiment
25). It is assumed that this surface represents the locus
of points of equal strength of the composite, neglecting
the fact that the failure surface develops gradually with
decreasing force and decreasing active area. Since the
length of roots near the centerline are rather short, it
will be assumed that the strength of the composite is
equal to that of the not reinforced soil at 0 = 0. Thus,
in Figure 4.2.8 the isostrength curves should coincide
at the point (A) where they intersect the centerline of the

plant.

The strengthening effect is assumed to be expressed

by the factor

2 - —-2— (4.69)

where

 

 

 

 

 

[Case 2

Figure 4.2.8—-The strengthening effect of roots on failure
surface; case 1 is the surface failure of soil along; case
2 is the failure surface of the composite [N-S profile of
eXp. 25, Figure 2.3.3 (C)].

 

 

119

K = strengthening factor of roots on soil;

01 = stress at radius 1 for composite caused by F2;
2
01 = stress at radius 1 for soil alone caused by Fl;
1
02 = stress at radius 2 for composite caused by F2;
2
F2 = force necessary to cause failure of
composite;
Fl = force necessary to cause failure of non—

reinforced soil.

Thus, from equation (4.68) it can be written that for a

constant 0

2 fl 2
F2 ‘ C1 °1 °1 ’ C1 02 D2
2 2
and
F1 = Cl °1 pl
1
where

and o2 = radii of points on the failure
surface of the composite and
soil alone, respectively, for

a given direction 6.

 

120

For both F1 in case 1 and F2 in case 2 the stresses reach
the critical value SR in point A. SR is the rupture
strength of the composite independent of the angle 8 and
the radius o. SR applies outside the failure surface.
The same stress applies for all points on the curve of
case 1, for the pure soil, and for all points on curve of

case 2 for the reinforced soil, respectively. Thus,

and

0
NM

(4.70)

:74
II
D
FJN

If values of K versus 0 (for O S 0 5 50) were
plotted, the overall effect of root strengthening can be

estimated.

4.3 Observed Failures
As mentioned earlier in Sections 2.2 and 4.1, a film
was made of the underground and tOp surface cracks, in
order to learn more about the failure pattern. For the
underground failure the sectors were Opened as described
in Section 2.3. The photographs to be presented were
selected from a 200 foot film, and were considered to be

most representative of the respective phenomena.

121

Reservations should be made as to the use of the
word "surface" in the descriptions of the underground and
the top surface cracks that will follow. Actually what
was observed in the underground and in the soil surface
represent failure surface traces in a vertical and in a

horizontal plane, respectively.

4.3.1 Underground Failure

 

The filming was made on October 1, and the pictures
from 4.3.1 to 4.3.12 represent one specimen.

Figure 4.3.1 shows the sectioned wall at zero load.
The print of the squares in the photograph correspond to
a square of 0.75 inch actual size. The centerline of the
plant is on the left of the reader. At a point 8 squares
to the right and 12 squares below the surface (8, 12) on
the sectioned wall a discolored region is seen which
represents a nonhomogeneity of the composite. Its effect
on the failure surface will be noted later.

When the maximum pulling force is reached, a crack
appears immediately below the point ofapplication of the
force (plant centerline) at a depth of about 7 inches
(0, 9), (Figure 4.3.2). It indicates the region where
the failure of the composite begins. This fact may be
explained with reference to the stress distribution dis-
cussed in Section 4.2.3 where it can be seen that for a

given distance from the center of the plant the stress

The depth where it will

will have a maximum at 0 — 0.

 

Figure 4.3.1--Sectioned wall at zero load.
Centerline of plant on the reader's left, at
the end of grid. Grid lines are .75 inch apart.

 

Figure 4.3.2-—Failure occurred first at the
centerline.

123

take place depends on the size and of the length of the
roots.

As the pulling continues, the cracks extend toward
the right and upwards, as can be seen in Figure 4.3.3.
Here it is visible that the master crack is already out-
lined and normally characterized by larger displacements.
However, secondary cracks appear above the master crack
and within what will later be the fractured bulb. This
is quite evident in Figure 4.3.4. In this figure the
effects of the nonhomogeneity of the composite are noticed
by the deviations eXperienced by the master crack. As
stated earlier, this effect and that of the hard pan layer
can affect considerably the shape of the bottom of the
crater. Notice that the secondary cracks are quite
evident and so is the deflection of the composite, as
indicated by the deflection of the grid lines.

Figure 4.3.4 also shows a tension crack outlined at
a point (5,0) at the soil surface. The forming of the
tension cracks is due to less reinforcement at the soil
surface, and the fact that the soil is characterized by a
low tensile strength. The tension cracks play an obvious
role in the disruption of the soil bulb as will be seen
later.

Figure 4.3.5 shows the tension and secondary cracks
The forming of the latter is related

now quite evident.

to the effective length of the roots. Effective length

has earlier been defined as the radius (be) where the main

gwrm: '.E" in ' 72'7“

124

 

Figure 4.3.3-—Rankine pattern is well outlined
here. Note the master and the secondary cracks.

 

Figure 4.3.4—-Tertiary crack and tension crack
at soil surface are outlined.

125

 

Figure 4.3.5-—Tension crack and tertiary crack
at soil surface is now quite visible. Note
effect of non homogeneity on failure surface.

 

Figure 4.3.6——Observe the compression zone and
an unfractured root which did not attain the
effective length.

126

part of the pulling force has been transferred to the soil.
Beyond the effective length the root serves only as rein-
forcement of the soil and is normally subJected to a small
fraction of its strength. The master crack indicates the
average effective length of the root system at a particular
point when stress at this point has reached rupture values.
The secondary cracks appear below and above the master
crack, due to variations in effective length of individual
roots.

Referring back to Figure 4.3.3 note that the master
crack makes an angle of about 45 degrees with the horizontal
in its outer part. Note, also, that the secondary cracks
follow the same pattern, and that a tertiary crack appears
at about 3 inches above the secondary and behaves likewise.
This pattern may indicate slip lines representing shear
failure in the material. If the development of this pattern
is followed through the sequences of Figures 4.3.1 to 4.3.6
and 4.3.8, it may be concluded that as the composite de-
flects upwards a compression takes place out to the right
from a hypothetical nearly vertical plane located about 4
to 5 inches from the centerline, at the height of the first
crack. To the right of this plane it appears that a
pressure ksbuilt up which is responsible for this pattern
of slip lines (Rankine passive failure). The occurrence
of this compression zone may be attributed to a wedging
caused by the pulling force and the upward movement of the

composite, as shown in Figure 4.3.7. In this diagram P

am 0‘ Luis" :x-‘h‘

 

127

1 {Q of plant

soil surface

 

 

Figure 4.3.7-—Forces acting on the root—soil
bulb.

 

 

 

128

represents the part of the pulling force F that has been
transmitted by the root to the force transfer zone gdgl,
at the bottom of the future disturbed soil. F minus P
equals the weight of the material above gdgL. P creates
stresses in the boundry 3g which have the horizontal com-

ponent P The action of P may be considered a passive

1' 1
pressure on the element acb because the weight of the

soil is of small magnitude compared with P Bond forces

1'
acting in the direction of the surface represented on the

trace b3 counteract P and their action originates a com—

1
pression zone whichtxxxxmxssalient at the corner b, as
shown in the extreme right of Figure 4.3.8 and in the
close-up of Figure 4.3.9. In the sectioned tests, the

soil in that region, at a certain stress, would flake off
from the vertical wall. This is not shown in this sequence
of pictures, but was consistently observed and registered
in other sectioned tests as in Figure 4.3.19. In later
stages of the pulling, the soil in the bulb is subJected

to bending due to the weight of the soil and the strength
of the bond along the edge of the future crater. This
bending causes tension cracks at the soil surface closer

to the plant and accentuates the compression in the area
of the future crater rim, as mentioned earlier. The
tension crack will determine the size of the future root-
soil bulb, as is apparent in Figure 4.3.10.

Referring back to Figure 4.3.6, 4.3.8, and the close-

up of Figure 4.3.11, it is seen that there is a root which

Mona-“Pannlir [I45 ‘IJN‘I... -1. T I. ’1?!

129

 

Figure 4.3.8--The disruption in the bulb is
outlined based on surface tension crack.

 

Figure 4.3.9——A close up of the compression
zone.

130

 

Figure 4.3.10—-Final stage of rupture prior
to bulb disruption.

 

Figure 4.3.ll--A close up of root in the
process of reaching the effective length.

131

did not experience rupture and is still being stretched,
despite the large relative displacement at that point.
This may be used as a typical example of what was meant
by effective length. This particular root due to its
positioning in the composite (and maybe partly due to the
sectioning of the composite) did not attain an effective
length until the master crack had opened wider than for
the maJority of roots, and therefore did not contribute
with its strength in the failure process. Note, however,
in Figure 4.3.12 that in the open crack of the failure,
there are practically no root ends proJecting beyond the
fractured bulb. This indicates that they fractured with
the composite as a unit. The only root ends which appear
are those related to the non-homogeneity of the composite
and to a region of smaller displacement where some of the
local roots were not stretched enough to be effective.

In order to relate the magnitude of the pulling force
to the underground failure pattern, a test was filmed with
the x-y recorder in the field of view. The sequence of
figures from 4.3.13 to 17 shows the development of the
cracks related to the value of the pulling force. It is
reCOgnized here how inaccurate this relation might be if
based only on the photographs given. But it was possible
to reproduce this relation to a reasonable degree of
accuracy by comparing the proJection of the film and the

curve which is given in Figure 4.3.18. Figure 4.3.18 shows

 

132

 

”
A

Figure 4.3.12——Observe that the roots are all
fractured at the failure surface.

4

133

.Uo>oE won Cod wcflcgoooh mmcHEHfiw mo
vacflm 00p 20 pocgoowg zlxllza.m.: mhstm

.Umoa Ohms pm
.wcHEHHm mo Uaoflm 600 CH Lovhooog zIx
spas ogsaHmm ccsosmhochIImH.m.z mhsmfim

 

134

.00 00.

pm Choppmg xomsoII0H.m.: ohsmflm

Mo m0.

me
.Amoa arm u 00 x06 0
pm copmodam xompOIImH.m.: ohswflm

 

135

ail-34111 (lad... I

. I. . ab”. 1.1.0!
...I. as.ur....‘l

 

.sH co mH.m.0 mcscwHomoo
>Hm>Hpomdwme .UCOQmmhhoo M on m Sosm mpcfiom .mH 020 0H on ma m 0 mos: Hm

II . . magma
mp UmpmnomSHHH coefioon can mo m>H30 pCmEmodemHU m> mogom mCflHHSm 0H m 0 .m

ACHV pcmam mo mmmm pm pcoEoodemHQ
0 0 m 0 m m H m

V IF
4 q

.4.
«I»
.

 

8 n b
I q d a

sea + oHco so .03

L.00..”

——-----~---—4

——-———~—-—--—¢~—_-—

‘.

———-—-———---—-—-—--q

(sqt) ooaog

o LIOQN

 

136

 

.mMSHQSg mo owmum
Hmcflm CH .ocde scammmsdEoo 60p pdoom
QOHpQSHmHv case opOZIImH.m.: ohswflm

 

m
.x as cs. 60 ccsHHocc cos
oohom cons Choppmm xomMOIINH.m.: ohswfim

 

137

the points a, b, c, d and e which correSpond respectively
to pictures 4.3.13 to 17. This experiment was listed as
number 7 in Table 2.2. Figure 4.3.13 shows the system at
zero load and 4.3.14 is right after the recording pen had
moved. In Figure 4.3.15 the value of the force was about
.85 of the maximum value when the cracks were first
detected, indicating that failure had started taking place.

Figure 4.3.16 shows the pattern at about maximum force

- .. 3.231597!“

[.97 of F max' (F max = 247 lbs)]. In Figure 4.2.17 the

, ~._- wan-ml

force had already declined to about .70 of F max.

 

Figure 4.3.19 shows the final stage of the rupture.

rmz-Wm F}. -. . ,
I

The separation of the outer part from the bulb is now
quite clear, and so is the Rankine pattern portion of the
failure surface. Note, also, that the white grid has
disappeared at the compression zone, from which the soil
broke loose due to that stress.

Two tests were made in order to verify if the under-
ground failure would occur symmetrically in the composite.
A relatively high degree of symmetry was found present up
to the final stages of the rupture process, as can be
seen in Figures 4.3.20 and 4.3.21. However, this was
changed in the final stages of the process, as indicated

by Figures 4.3.22 and 4.3.23.

4.3.2 Soil Surface Cracks

 

The sequences of photographs 4.3.23(a) to (d) show

the pattern of surface cracks, recorded on October 14.

   

Figure 4.3.20—~Shows the symmetry of the
cracks in the initial stage of rupture.

 

Figure 4.3.2l——Shows that symmetry persisted
until the final stage of rupture.

 

Figure 4.3.22——The disruption of the bulb
leads to an assymmetric appearance.

 

Figure 4.3.23—-No symmetry can be visualized
by observing the pulled out bulb.

140

.echocsto oHso op sOHso one

. . 0000 one

vmmw mMNmmm Hmvas ocmdpmhu szmoHo 03000 A00 mmzwvw>M0Whmoco HmecohomE:oHHo w

0 H .0 H00 .mHMm 0 xomho pthm 600 A00 "0&0mwo momMHMMoMHo HprconmESosMw
. . _ It. .. . . 0 II . .

.. I..\... .... , «A. at.mr\l . v. D . . H m 3N M 3 WLHSanH

     

     
   

 

141

Figure 4.3.24 (a) and (b) show, respectively, the system
when the first crack appeared in the field of filming
and a more advanced stage, where the radial cracks are
leading. From the latter photographs one cannot precisely
tell whether the radial or the circumferential crack ap—
peared first. However, from observations during the tests
and by considering Figures 4.3.24(a) and (d), it may be
concluded that the radial cracks appeared first. The
appearance of the radial crack first may be attributed as
an effect of the geometry of the root system. When the
radial cracks appeared, they indicated that the strength
of the composite perpendicular to their direction had
been exceeded. Actually, the "umbrella" nature of the
root-geometry, suggested that the strength of the composite
in a direction perpendicular to the radial cracks was
expected to be of a relatively low magnitude.

The pictures of Figure 4.3.24(a) to (d) show a
chronological sequence of the surface cracks leading to
a final stage of the disruption process. From observations
made in other tests, it was noticed that these cracks
were significantly visible only after the maximum pulling
force had passed its peak.

The circumferential crack corresponded to the
tension cracks that appeared for the underground observa—
tions. The fact that they appeared later can be explained

also by the rather "anisotropic" nature of the composite,

142

having a "polar" root geometry. By "polar" root-geometry
is meant the fact that the root radiated from the attach-
ing point not necessarily radially, but polarly. This
geometry of the reinforcement characterized the composite
as a typically "polar" resistant medium, i.e., the
greatest strength was in the direction of the roots.
However, the ascertainment of an overall "anisotrOpic"
behavior of the root-soil composite requires other tech-

niques in the experiments.

5. RECOMMENDATIONS FOR FURTHER WORK

Based on the observations and results obtained in

this study, the following future investigations are recom-

mended:

1.

A series of experiments with single roots in the soil,
to determine the force and the displacement distribu-
tion between the root and the soil for an increasing
load, and to verify the derivations made in Section

4.2.1. This should be studied at different soil con-

ditions such as different moisture content and
different degree of compaction, considering the influ—
ence both (a) at the time of the testing and (b) during
the growth period up to the time of testing.

The distribution in space of roots with regard to
length, number, diameter, and strength properties.
Changes of the distribution of roots in space with
plant growth.

Studies of possible time dependent effects with regard
to roots and the composite (visco-elastic behavior).
To investigate other measures for the plant size and
the root system size, as for instance the dry weight

of the roots in the root-soil bulb.

An attempt should be made to utilize a photoelastic

approach by use of gelatin models.

143

 

‘
. 10-4):Lm“

I :1“ 21““.3-“1

7.

144

A mechanics for the root-soil system snould be further
developed, as to determine the desirable root distri-
bution from a strength standpoint and how it can be
achieved by controlling nutrients, moisture, and the
degree of compaction of the soil.

Further studies of the failure process including

film techniques.

Verify the results also for plants presenting

pronounced tap roots.

 

.. 11.3

 

 

 

 

lm’. ; A

 

 

6. SUMMARY OF RESULTS

The results obtained from the field tests of up-
rooting force show that the penetrometer reading did not
correlate or affect significantly the maximum pulling
force or the respective displacement at the base of the
plant. The soil characteristics which may influence the
maximum pulling force and the respective displacement at
base of the plant were the soil moisture content and the
bulk density. The bulk density may have affected the plant
development. The plant characteristic best correlated to
the variation of the maximum pulling force and the respec-
tive displacement at the base of the plant was the diameter
of the stem bundle at the plant base. The weight of the
root-soil bulb which may be considered as a root-soil
characteristic also was correlated to the maximum pulling
force. The crater volume and the weight of the root-soil
bulb were related and they may represent two comparable
measures of root system size.

Under the pulling force the root-soil composite seems
to behave as a Hookean body up to value of the displace—
ments at the base of plant which corresponded to about 0.5
of the recorded maximum pulling force. This behavior was
altered for sectioned tests, and a more non linear behavior
was noticed at lower values of the displacements at the

base of plant and maximum pulling force.

145

 

 

 

 

146

From the studies of the root system it was seen that
there were two types of roots, namely: short roots, with
a larger diameter and lower strength, and long roots with
smaller diameter and higher strength. Also, the strength
for short roots is mainly related to a linear dimension
(circumference) of the cross-section, whereas that for long
roots was also related to a square of that dimension (area). ’
For long roots the strength decreased slightly from the [
attaching point toward the root tip. The tapering of 5
long roots seemed to be negligible.

The observations of the underground failure indicated

A‘

 

that it started at the plant centerline and propagaged
outwards until a Rankine failure pattern was noticed from
the bottom failure to the soil surface. The initial failure
took place at a value of the pulling force slightly below
the maximum pulling force and then developed under a sym-
metrical pattern, which may be altered by nonhomogeneity

of the composite.

The top surface cracks seem to indicate that the
highest strength of the composite is in a direction along
the roots. The radial cracks leading the circumferential
ones are indicative of the existence of a plane of least

strength. This plane is vertical and contains the plant

centerline.

 

 

f
.
ii!
. “.02....st _—

 

REFERENCES

Bertrand, A. R. and H. Kohnke. (1957). Subsoil conditions
and their effects on oxygen supply and the growth of
roots. Soil Science Society of America Proceedings.
21:135-140.

Boussinesq, J. V. (1885). Application des Potentiels a
L'Etude de L'Equilibre et de Mouvement des Solides
Elastiques. Paris: Gauthier-Villars. 721 pp.

DillewiJn, C. Van. (1952). Botany of Sugar Cane. The
Chronica Botanica Co., Waltham, Mass., USA. 371 pp.

Esau, K. (1966).. Anatomy of Seed Plants. John Wiley
and Sons, Inc., New York, USA. 376 pp.

Gill, W. R. and G. H. Bolt. (1955). Pfeffer's studies
of the root growth pressures exerted by plants.
Agronomy Journal. 47:166-168.

Gill, W. R. and R. D. Miller. (1956). A method for
study of influence of mechanical impedance and
aeration on the growth of seedling roots. Soil
Science Society of America Proceedings. 20:154-157.

Gill, W. R. and G. E. Vanden Berg. (1966). Soil Dynamics
in Tillage and Traction. United States Department
of Agricultrue, Agricultural Research Service,
Agriculture Handbook No. 316. ‘511 pp.

Hall, D. M. (1934). The relationship between certain
morphological characters and lodging in corn.
Minn. Agr. EXpt. Sta. Tech. Bul. 103. 31 pp.

Holbert, R. Jr., and B. Koehler. (1924). ‘Anchorage and
extent of corn root systems.‘ Journal of Agricul-
tural Research 27:71-78. . '

Jumikis, Alfreds R. (1962). Soil Mechanics. D. Van
Nostrand Co., Inc., Princeton, New Jersey, USA.

791 pp.

Kaul, R. N. (1965). The influence of certain mechanical

prOperties of an uncompacted soil. Unpublished Ph.D.

Thesis, North Carolina State University, Raleigh.

147

- .-- _4.‘~.;‘;H.T-"'J

 

 

 

 

Letey, J., O. R. Lunt, L. H. Stoltzy, and T. E.
Szuszkiew. (1961). Plant growth, water use and
nutritional response to rhizosphere differentials
of oxygen concentration. Soil Science Society of
America Proceedings. 25:183-189.

MacLaughlin, T. F. (1966). Effect of fiber geometry
in fiber-reinforced composite materials. Experi-
mental Mechanics 6:481—492.

Michigan Agricultural Experiment Station (1967). STAT
Series Description. Michigan State University,
Computer Laboratory Library, No. 5 and 7.

Miller, E. C. (1916). Comparative study of the root
systems and leaf areas of corn and sorghums.
Journal of Agricultural Research 6:311-332.

Nelson, C. E. (1958). Lodging of field corn as affected
by cultivation, plant population, nitrogen ferti—
lizer and irrigation treatment. Production
Research Report No. 16, ARS, USDA, 16 pp.

Newman, J. E., S. R. Miles and P. L. Crane. (1952).
Performance of private and open—pedigree corn
hybrids in Indiana. Indiana Agricultural Experi-
ment Station, Circular 380, 23 pp.

Pavlychenko, T. K. (1937). The soil-block washing
method in quantitative root study. Canadian
Journal of Research Sec. 0, 15:33-57.

Richards, R. Jr., and R. Mark. (1966). Gelatin models
for photoelastic analysis of gravity structures.
EXperimental Mechanics 6:30-38.

Roo, H. C. (1966). Root training by plastic tubes III:
Soil aeration appraised by tube-grown plants.
Agronomy Journal 58:483—492.

Rosen, B. W. (1964). Mechanics of Composite Strengthen—
ing. Chapter 3, pp. 37-75. in Fiber Composite
Materials. American Society for Metals, Metals
Park, Ohio, USA. 245 pp.

Scott, T. W. and A. E. Erickson. (1964). Effect of
aeration and mechanical impedance on the root

development of alfalfa, sugar beets and tomatoes.
Agronomy Journal 56:575—576.

148

 

 

 

uu-‘k‘ - ~

 

Spencer, J. T. (1940). A comparative study of the
seasonal root development of some inbred lines and
hybrids of maize. Journal of Agricultural Research
61:521-538.

Stoltzy, L. H., J. Letey, T. E. Szuszkiewicz and 0. R.
Lunt. (1961). Root growth and diffusion rates as
functions of oxygen concentration. Soil Science
Society of America Proceedings 25:463-467.

Tackett, J. L. and R. W. Pearson. (1964). Oxygen
requirements of cotton seedlings roots for pene-
tration of compacted soil cores. Soil Science
Society of America Proceedings 28:600-605.

Weaver, John E. (1926). Root Development of Field
CrOp. McGraw-Hill Book Co., Inc., New York, USA.

291 ppo

Wiersum, L. K. (1957). The relationship of the size
and structural rigidity of pores to their penetra-
tion by roots. Plant and Soil 9:75-85.

Williamson, R. E. (1964). The effect of root aeration
on plant growth. Soil Science Society of America

Proceedings 28:86—90.

Wilson, H. K. (1930). Plant characters as indices in
relation to the ability of corn strains to with-
stand lodging. Journal cf American Society of Agron—

omy. 22:453—458.

149

 

 

 

"I1444111414ES