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Stress-strain-strength and creep characteristics of a geotextile

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Title:
Stress-strain-strength and creep characteristics of a geotextile
Creator:
Takriti, Omar Salah
Place of Publication:
Denver, CO
Publisher:
University of Colorado Denver
Publication Date:
Language:
English
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ix, 95 leaves : illustrations ; 29 cm

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Subjects / Keywords:
Geotextiles -- Testing ( lcsh )
Strength of materials ( lcsh )
Geotextiles -- Testing ( fast )
Strength of materials ( fast )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Bibliography:
Includes bibliographical references (leaves 51-52).
Thesis:
Submitted in partial fulfillment of the requirements for the degree of Master of Science, Department of Civil Engineering
Statement of Responsibility:
by Omar Salah Takriti.

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|University of Colorado Denver
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|Auraria Library
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All applicable rights reserved by the source institution and holding location.
Resource Identifier:
17998017 ( OCLC )
ocm17998017
Classification:
LD1190.E53 1986m .T34 ( lcc )

Full Text
STRESS-STRAIN-STRENGTH AND CREEP
CHARACTERISTICS OF A GEOTEXTILE
by
Omar Salah Takriti
B.S., University of Colorado at Denver, 1985
M.S., University of Colorado at Denver, 1986
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado at Denver in partial fulfillment
of the requirements for the degree of
Master of Science
Department of Civil Engineering


This thesis for the Master of Science degree by
Omar Salah Takriti
has been approved for the
Department of
Civil Engineering
by
Andreas S. Vlahinos
Date


Ill
Takriti, Omar Salah (M.S., Civil Engineering)
Stress-Strain-Strength and Creep Characteristics of a Geotextile
Thesis directed by Professor Tzong Wu
The application of geotextiles to permanent structures
requires that geotextiles be sufficiently stable to permit
acceptable performance of the structure throughout its design life.
However, there are many uncertainties concerning the long-term
reliability of geotextiles, particularly their resistance to
sustained loading. Field experience of geotextile-reinforced
structures indicates that in certain cases the effectiveness of
geotextiles as reinforcement appears to decrease with time; in
others, however, the effect of creep is negligible. Knowledge of
the long-term behavior of geotextiles is essential for safe and
economic design of geotextile-reinforced earth structures.
A study was undertaken to investigate the stress-strain and
creep behaviors of a non-woven, needle-punched, polyester
geotextile, called Trevira 1127. A total of eight short-term
stress-strain tests (all these tests were repeated to check for test
repeatability) and seven creep tests were performed using test
devices designed at the University of Colorado at Denver. The tests
were conducted with the geotextile in isolation as well as in the
confinement of soils of variable overburden pressures (8.36 psi,
10 psi, and 16.53 psi), soil densities (107 pcf and 110 pcf), soil
types(#30 Ottawa and Monterey No. 0/30 sands), and geotextile
specimen sizes (3 inches wide by 1.5 inches long and 3 inches wide
by 1 inch long samples).


iv
It was found that stress-strain and creep tests on the
geotextile should be performed in the confinement of the soil type
to be used in the field. The geotextile exhibited very different
behavior in-isolation and in the confinement of soil. The stress-
strain-creep characteristics of the geotextile was significantly
different in the confinement of the two sands prepared at the same
density.
A regression analysis procedure was presented to show how
the creep test results can be extrapolated beyond the test period.


CONTENTS
CHAPTER
I. INTRODUCTION................................................ 1
1.1 Objectives of the Study................................ 2
1.2 Method of Approach..................................... 3
II. SHORT-TERM STRESS STRAIN BEHAVIOR
OF THE GEOTEXTILE........................................... 5
2.1 Background............................................. 5
2.2 The Test Materials..................................... 5
2.3 The Test Apparatus..................................... 8
2.4 Stress Strain Tests of the Geotextile.............. 10
2.5 Results and Discussion of Results................... 14
III. CREEP BEHAVIOR OF THE GEOTEXTILE........................... 21
3.1 Background............................................ 21
3.2 Creep Test Apparatus.................................. 21
3.3 In-Isolation Creep Tests.............................. 23
3.4 In-Soil Creep Tests................................... 25
3.5 Results and Discussion of Results................... 26
IV. PREDICTING CREEP BEHAVIOR OF THE GEOTEXTILE
BEYOND THE TEST PERIOD..................................... 36
4.1 Background............................................ 36
4.2 Regression Analysis of the Test Results............. 37
4.3 Predictions
42


vi
CHAPTER
V. SUMMARY AND CONCLUSIONS................................... 48
5.1 Summary.............................................. 48
5.2 Conclusions.......................................... 48
BIBLIOGRAPHY...................................................... 51
APPENDIX.........................*............................. 53
A. SHORT-TERM STRESS STRAIN TEST DATA..................... 53
B. LONG-TERM CREEP TEST DATA................................ 64
C-I. NEWTON-RAPHSON METHOD..................................... 85
C-II. LEAST SQUARES FIT (NON-LINEAR REGRESSION)................ 86
C-III. EXAMPLE CALCULATION....................................... 88
C-IV. EXAMPLE ON THE DETERMINATION
OF THE GOODNESS OF THE FIT............................ 91
C-V. FORTRAN PROGRAM........................................... 93


Vll
TABLES
Table
1. Typical Physical Properties of Trevira 1127.................. 6
2. Physical Properties of #30 Ottawa Sand
and Monterey No. 0/30 Sand............................. 7
3. Stress-Strain Test Conditions on the
Geotextile............................................ 13
4. Creep Potential of the Geotextile........................... 24
5. In-Isolation Creep Test Conditions.......................... 24
6. In-Soil Creep Test Conditions............................... 26
7. Results of the Regression Analysis.......................... 43
8. Determination of the Goodness of the Fits................... 44
9. Predicted Time-Dependant Strains of the Geotextile...... 45


Vlll
FIGURES
Figure
1. Short-Term Stress-Strain Test Apparatus..................... 9
2. Friction Resistance Between the Metal
Clamp and (a) #30 Ottawa Sand (b) Monterey
No. 0/30 Sand.............................................. 11
3. Load vs. Displacement Relationship for
the Geotextile Alone in Two Directions..................... 15
4. Load vs. Displacement Relationship
for the Geotextile Under Three Different
Overburden Pressures....................................... 16
5. Load vs. Displacement Relationship for
the Geotextile Confined in Two Different
Soil Densities............................................. 17
6. Load vs. Displacement Relationship for
the Geotextile Confined in Two Different
Soil Types................................................. 18
7. Load vs. Displacement Relationship for
the Geotextile With Two Different
Specimen Sizes............................................. 20
8. Side View of the Creep Testing Apparatus................... 22
9. Strain vs. Time Relationship for
the Geotextile In-Isolation at a Load
of 16.5 lbs................................................ 27
10. Strain vs. Time Relationship for
the Geotextile In-Isolation at a Load
of 42.9 lbs................................................ 28
11. Comparison Between In-Isolation
(Unconfined) and In-Soil (Confined)
Geotextile with the Same Strain
Level (3.8%)
30


Figure
IX
12. Strain vs. Time Relationship for
the Geotextile Confined In-Soil
at a Load of 57.0 lbs. (3.8% Strain)..................... 31
13. Strain vs. Time Relationship for
the Geotextile Confined In-Soil
at a Load of 79.0 lbs. (13% Strain)...................... 32
14. Strain vs. Time Relationship for
the Geotextile Confined In-Soil
at a Load of 69.0 lbs. (3.8% Strain)..................... 34
15. Strain vs. Time Relationship for
the Geotextile Confined In-Soil
at a Load of 93.0 lbs. (13% Strain)...................... 35
16. Predicted Strain vs. Time for the
Geotextile Confined in #30 Ottawa
Sand for Tests; (a) Cl, and (b) C2....................... 46
17. Predicted Strain vs. Time for the
Geotextile Confined in Monterey
No. 0/30 Sand for Tests; (a) C3,
and (b) C4............................................... 47


CHAPTER I
INTRODUCTION
Soil is inherently strong in compression, but weak in
tension. The concept of reinforcing an earth fill by incorporating
materials which posses a much higher tensile strength than soil, and
the capacity to bond with soil through friction has recently begun
to gain popularity in the United States. Among various materials
which have been used for earth reinforcement, geotextiles have
demonstrated great potential in many highway applications. In
general, geotextiles are more economical, more easily handled and
constructed, and stronger in resisting corrosion and bacterial
action than many traditional materials including metals.
The application of geotextiles to permanent structures
requires that geotextiles be sufficiently stable to permit
acceptable performance of the structure throughout its design life.
However, there are many uncertainties concerning the long-term
reliability of geotextiles, particularly their resistance to
sustained loading. Field experience of geotextile-reinforced
structures indicates that in certain cases the effectiveness of
geotextiles as reinforcement appears to decrease with time; in
others, however, the effect of creep is negligible. Knowledge of
the long-term behavior of geotextiles is essential for safe and
economic design of geotextile-reinforced earth structures.


2
There is little published information on the creep
characteristics of geotextiles in typical geotechnical environments.
Some studies have been carried out to determine the creep behavior
of both fibers (Finnigan, 1977) and fabrics (Van Leeuwen, 1977;
Haliburton et al., 1978; Shrestha and Bell, 1982), but they have not
included the effects of reinforcement-soil interaction. It is
important to recognize that geotextiles tested in isolation may
exhibit significantly different behavior than geotextiles tested in
the confinement of soils. The suitability of geotextiles as
reinforcement in permanent structures depends on the relative rates
of plastic yielding and strength increase of the subsoil versus the
rates of creep in the reinforcement. If the soils consolidate and
gain strength faster than the corresponding creep in the reinforce-
ment, it is conceivable that the effect of creep may be effectively
neutralized. On the other hand, if the soils do not consolidate and
gain strength, such as in the case of reinforced sands for retaining
walls, creep deformations under high loads could be very significant
(Holtz et al., 1982).
1.1 Objectives of the Study
The objectives of this study are twofold. The first
objective is to investigate the short-term stress-strain-strength
characteristics of a geotextile in the confinement of soils under
typical geotechnical environments. The second objective is to
conduct preliminary investigation on the creep behavior of the
geotextile, in isolation as well as in the confinement of soils.


3
It is clearly impractical to carry out controlled creep
tests for the same time period as the life time of geotextile-
reinforced earth structures (some researchers are estimating that
they may have design life expectancies well beyond 50 years). The
results obtained by the preliminary study can be incorporated in an
analytical model for predicting creep behavior beyond the test time
period.
1.2 Method of Approach
The stress-strain-strength characteristics of a geotextile
are dependent upon such factors as soil confinement (geotextile
alone versus in the confinement of soil), soil type, soil density,
overburden pressure, as well as the age and moisture content of the
geotextile. In this study, an apparatus devised at the University
of Colorado at Denver by Wu and his associates was used to
investigate the stress-strain-strength characteristics of a non-
woven, needle-punched, polyester geotextile, Trevira 1127. Both in-
isolation and in-soil tests were conducted. For the in-soil tests,
two different soils were used. The soil density and overburden
pressure were varied.
Investigation of the creep behavior was carried out by an
apparatus also devised by Wu and his associates at the University of
Colorado at Denver. The tests were performed with geotextile alone
and with the geotextile confined in two different soils subject to
two sustained loads. The sustained loads used in the tests were
determined by the results of the corresponding in-soil short-term
tests.


4
A regression analysis procedure was presented to demonstrate
how the creep test results can be used for predicting the creep
behavior beyond the test period.


CHAPTER II
SHORT-TERM STRESS-STRAIN BEHAVIOR OF THE GEOTEXTILE
2.1 Background
A total of eight short-term stress-strain tests (all these
tests were repeated to check for test repeatability) were conducted
in this study, including two in-isolation (geotextile only) tests
and six in-soil tests.
Short-term stress-strain tests were performed for two
purposes: (1) to compare with the results of the long-term tests in
order to assess the effect of time on the geotextile properties, and
(2) to establish the loading levels for the corresponding long-term
tests. Short-term stress-strain tests were performed using the
materials described in section 2.2 and using the apparatus and the
procedures described in section 2.3. In addition, two friction
tests were conducted on the metal clamp alone confined in-soil.
2.2 The Test Materials
The geotextile used in this investigation was a non-woven,
needle-punched, polyester geotextile called Trevira 1127, manufact-
ured by Hoechst Fibers Industries. The material has been used in
roadways, drainage systems, pond liners, rail beds, and retaining
walls, including the Glenwood Canyon Test Wall.
Table 1 shows some typical physical properties of the
geotextile provided by the manufacturer. It is to be noted that


TABLE 1
TYPICAL PHYSICAL PROPERTIES OF TREVIRA 1127
Fabric Weight (oz/yd2) 8
Thickness (mils) (ASTMD-1777) 125
Grab Strength (lb, M*/C) (ASTMD-1682) 260/225
Grab Elongation (%), (M/C)(ASTMD-1682) 85/ 90
Trapezoid Tear Strength (lb, M/C)(ASTMD-1117) 100/ 95
Puncture Strength 5/16" (lb)(ASTMD-751) 125
Mullen Burst Strength (psi)(ASTMD-3786) 380
Vertical Water Flow (gal/min/ft2)(HFI Test) 280
EOS (CW-02215) 70-100
Std. Roll Widths (ft.) 12.5, 14.5
and 16.0
Std. Roll Length (ft.) 300 and
1000
M = Machine Direction
C = Cross-Machine Direction


among those properties are the strength and elongation character-
istics. These properties were obtained by ASTM procedures in which
the geotextile was tested in-isolation.
Two types of soils were used in this investigation, (1) #30
Ottawa sand, and (2) Monterey No. 0/30 sand. Table 2 shows the
physical properties of Ottawa and Monterey sands used in this study.
Both sands were prepared at a density of 107 pcf.
TABLE 2
PHYSICAL PROPERTIES OF #30 OTTAWA
SAND AND MONTEREY NO. 0/30 SAND
#30 Monterey
Sand Type Ottawa No. 0/30
Unified Soil
Classification SP SP
Specific Gravity 2.65 2.65
Particle Size
D50 (mm) 0.50 0.45
Cc* 1.21 1.00
cu** 1.43 1.60
Dry Unit Weight
7 maximum (Pcf) 112.19 105.80
7 minimum (Pcf) 97.52 91.70
(^3q)2/(^60 x D10) ** Cu = D6 o/^10


8
2.3 The Test Apparatus
The short-term stress-strain tests were conducted by using a
test apparatus designed at the University of Colorado at Denver
(Siel et al., 1986). The apparatus consisted of a test box, shown
in Figure 1, which was designed to be used with a Wykeham Farrance
direct shear loading frame. The test box was constructed of alum-
inum with a steel top loading cap. The test box was designed with a
metal clamp to affix one end of the geotextile to the test box, and
a slot on the opposite side through which a movable clamp extended
to securely grab the other end of the geotextile sample. The test
box was designed so that the geotextile sample was entirely within
the test box and subject to the overburden pressure throughout the
test. The interior dimensions of the test box were 6.5 inches by
4.75 inches by 2.5 inches deep. The top loading cap was 6.5 inches
by 4.75 inches to distribute the normal load uniformly over the soil
material contained in the text box.
Four short-term stress-strain tests were conducted using a
4.0 inches long by 1.0 inch wide sheet metal clamp, including two
friction tests. The sheet metal clamp was glued to the geotextile
from one end and welded to a metal wire from the other end. The
wire was connected to the direct shear machine, and the clamp was
entirely inside the test box. The test box was used for both types
of stress-strain tests, unconfined (in-isolation) and confined (in-
soil) tests.


9
N Top Loading Cap
Figure 1 Short-Term Stress-Strain
Test Apparatus


10
2.4 Stress-Strain Tests of the Geotextile
A total of eight short-term stress-strain tests (all these
tests were repeated to check for test repeatability) were performed
on the Trevira 1127 geotextile. Two different sizes of the geo-
textile sample were used: 3 inches wide by 1.5 inches long and 3
inches wide by 1 inch long. These wide and short sample shapes were
chosen for two reasons: (1) to avoid significant necking of the
sample during the test, and (2) to minimize side friction by placing
the geotextile sufficiently far from the side walls of the test box.
In conducting the tests, one end of the geotextile was
secured between two thin sheet metals using epoxy resin and harden-
er. With the 3 inches wide by 1 inch long geotextile sample, 4
inches by 1 inch long metal clamp was used. The metal clamp was
entirely confined in the soil throughout the tests so that the geo-
textile would be kept in the confinement of soil and be subjected to
uniform straining across its width.
It should be noted that the applied forces in the tests were
partially resisted by the frictional resistance between the confin-
ing soil and the sheet metal clamp. As may be seen from Figure 2,
the frictional resistance can be very significant. The friction
angles between the 4 inches wide by 1 inch long metal clamp confined
in #30 Ottawa and Monterey No. 0/30 sands were 17.8 and 20.5,
respectively. Consequently, to obtain stress-strain-strength
relations of the geotextile, the forces must be corrected by
subtracting from them the frictional resistance.


11
0.2 0.4 0.6 0.8 1.0
Displacement (in.)
(a)
0.2 0.4 0.6 0.8 1.0
Displacement (in.)
(b)
Figure 2 Friction Resistance Between
the Sheet Metal Clamp and
(a) #30 Ottawa Sand
(b) Monnterey No. 0/30 Sand


12
The stress-strain tests were performed at a constant strain
rate of 4.72% per minute or a deformation rate of 1.2 mm per minute
for the 3 inches wide by 1 inch long geotextile samples, and at a
constant strain rate of 3.15% per minute or a deformation rate of
1.2 mm per minute for the 3 inches wide by 1.5 inches long geo-
textile samples. The short-term stress-strain tests were continued
to 100% strain. In the field, geotextiles are rarely strained more
than 20%. The strain rates used by other researchers were somewhat
lower. El-Fermaoui and Nowatzki (1982) conducted in-soil tests at
2.5% strain per minute, and McGown et al., (1982) carried out in-
soil tests at 2% strain per minute.
Four overburden pressures were used: 8.36 psi, 10 psi, 16.53
psi, and 0 psi (unconfined or in-isolation). The stress-strain test
conditions are summarized in Table 3. For purposes of convenience,
a three-letter symbol was used to designate the tests. The first
letter represents the soil type: "0" = Ottawa sand, "M" = Monterey
sand, and "I" = in-isolation, no soil confinement. For the in-soil
tests, the second letter indicates the overburden pressure : "L" =
8.36 psi, "M" = 10 psi, and "H" = 16.53 psi; while for in-isolation
tests indicates the sample direction: "M" = machine direction, and
"C" = cross machine direction. The sample size is shown by the
third letter: "S" = 3 inches by 1 inch (width X length), and "L" = 3
inches by 1.5 inches.
The two short-term stress strain tests, OMS and MMS, were
performed using a smaller clamp of 4 inches wide by 1 inch long
instead of the bigger clamp (4 inches wide by 4.5 inches long) which


13
Test
Symbol
OLL
OML
OHL
IML
OMS
ICL
OLL*
MMS
TABLE 3
STRESS-STRAIN TEST CONDITIONS ON THE GEOTEXTILE
Soil Type Overburden Pressure (psi) Soil Density (pcf) Geotextile Direction Geotextile Size (in.)
#30 Ottawa Sand 8.36 107 Machine 3 x 1.5
#30 Ottawa Sand 10.0 107 Machine 3x1.5
#30 Ottawa Sand 16.53 107 Machine 3x1.5
0 Machine 3 x 1.5
#30 Ottawa Sand 10.0 107 Machine 3x1
0 Cross- Machine 3 x 1.5
#30 Ottawa Sand 8.36 110 Machine 3 x 1.5
Monterey No. 0/30 10.0 107 Machine 3x1
Sand
* Same as OLL except soil density


14
was used in all of the other stress-strain tests. This was done
because the smaller clamp would entirely be confined in the test box
during the test. Therefore, the uncertainty in determining the
frictional resistance of the clamp and the soil was avoided.
2.5 Results and Discussion of Results
Short-term stress strain test data are presented in
Appendix A.
Two tests were conducted on the geotextile in-isolation
(Figure 3). Although the geotextile appeared to be isotropic, it
demonstrated higher stiffness and strength in the cross-machine
direction than in the machine direction.
Figure 4 shows the effect of the overburden pressure on the
stress-strain-strength relations of the geotextile. The three tests
shown in the figure had the same soil type, soil density, sample
direction, and sample dimensions, the only variable was the over-
burden pressure. It may be seen that the higher the overburden
pressure, the higher the strength of the geotextile. The stiffness
of the geotextile was not significantly affected by the overburden
pressure, at least for the pressure range used in this study.
Figure 5 shows the stress-strain relationship for the
geotextile confined in Ottawa sand prepared in otherwise identical
conditions except soil density. Again, the effect on the geotextile
stiffness was not significant, although under the slightly higher
density the geotextile did exhibit higher strength.
The effect of soil type was depicted in Figure 6. It is
seen that the geotextile stress-strain-strength characteristics are


15
0.3 0.6 0.9 1.2 1.5
Displacement (in.)
Figure 3 Load vs. Displacement Relationship for
the Geotextile Alone in Two Directions


16
T3
(0
o
0.3 0.6 0.9 1.2 1.5
Displacement (in.)
Figure 4 Load vs. Displacement Relationship for
the Geotextile Under Three Different
Overburden Pressures.


Load (lb.
17
0.3 0.6 0.9 1.2 1.5
Displacement (in.)
Figure 5 Load vs. Displacement Relationship for
In-Soil Geotextile Confined in Two
Different Soil Densities


Load (lb.
18'
0.2 0.4 0.6 0.8 1.0
Displacement (in.)
Figure 6 Load vs. Displacement Relationship
for the Geotextile Confined in Two
Different Soil Types


19
very different for the two soils which were prepared at the same
density. This is an indication that stress-strain-strength tests of
the geotextile should be performed in the confinement of the soil to
be used in the field.
It is to be noted that the stress-strain relations of the
geotextile is also affected by the size of the geotextile sample, as
shown in Figure 7. The smaller specimen size exhibited higher
stiffness and strength than the larger specimen size. This
observation appeared to agree with the findings of McGown et al.,
(1982) which indicated that needle-punched geotextiles were most
critically affected by the shape and size of the test specimen.


Load (lb.
20
0.2 0.4 0.6 0.8 1.0
Displacement (in.)
Figure 7 Load vs. Displacement Relationship
for the Geotextile With Two
Different Specimen Sizes


CHAPTER III
CREEP BEHAVIOR OF THE GEOTEXTILE
3.1 Background
All polymeric materials exhibit time dependant behavior
(Bonaparte et al. 1985). Creep is defined herein as the tendency
of a material to undergo time dependant elongation under application
of a constant dead load static stress. Generally speaking,
geotextiles polyester have a higher creep resistance than
geotextiles polypropylene. However, a heavy polypropylene may
provide good creep resistance if design loads are low compared to
the geotextile strength (Christopher and Holtz, 1985).
In order to conduct long-term creep tests, a new test
apparatus was designed and two identical test setups were
manufactured. The test apparatus allow for creep tests to be
performed in isolation as well as in the confinement of soil subject
to different overburden pressures. A total of three in-isolation
tests and four in-soil tests were performed.
3.2 Creep Test Apparatus
Creep tests were performed using an apparatus designed at
the University of Colorado at Denver. The test setup is illustrated
in Figure 8. The dimensions of the test box were identical to those
used in the short-term test box. The geotextile specimen was held


7 Movable Metal Clamp
8 Test Box
9 Metal Wi re
10 Pul ley
11 Ball Bearing
12 Hanger
13 Hanger
Figure 8 Side View of the Creep Testing Apparatus
hO
TO


23
inside the box on one end by a fixed clamp, and was glued on the
other end to a movable sheet metal clamp. The movable metal clamp
was welded to a metal wire which was connected to a loading
mechanism that was applied by dead weight in a hanger system. To
apply the overburden pressure to the soil-geotextile system, a lever
arm was employed. The lever arm was connected to another dead
weight and a hanger system. The lever arm had a ratio of 5 to 1;
therefore, whatever load was put on the hanger was multiplied by 5
and divided by the area of the top load cap to obtain the desired
overburden pressure.
3.3 In-Isolation Creep Tests.
Christopher and Holtz (1985) recommended a method for
assessing creep potential of geotextiles in their report to the
Federal Highway Administration. The method suggested that the
geotextile be tested in isolation for 36 hours or longer. They
defined the percent creep (pc) as:
percent creep =
amount of time-dependant elongation
amount of initial elongation
(3.1)
where the initial elongation is the amount of elongation occurred
immediately after the application of the static load. Table 4 shows
a quantitative measure of the creep potential in terms of percent
creep of a geotextile.
Three in-isolation creep tests were conducted on the Trevira
1127 geotextile. The static dead loads used in the tests were 16.5
lb, 42.9 lb, and 20.3 lb, which corresponded to 3.8%, 13%, and


24
TABLE 4
CREEP POTENTIAL OF THE GEOTEXTILE*
Percent Creep
0 - 25
25 - 50
50 100
> 100
* Christopher and Holtz (1985)
Creep Potential
Nil
Low
Moderate
High
3.8% strains, respectively, in the corresponding uniaxial stress -
strain tests of the geotextile (Figure 6). Table 5 summarizes the
test conditions of the three in-isolation tests.
TABLE 5
IN-ISOLATION CREEP TEST CONDITIONS
Test Symbol Dead Load (lb.) Corresponding Strain Level (%) Geotextile Sample Size (in.)
11 16.5 3.8 3 x 1.5
12 42.9 13.0 3 x 1.5
13 20.3 3.8 3x1


25
3.4 In-Soil Creep Tests
In-soil creep tests were performed using the materials and
the apparatus described in sections 2.2 and 3.2, respectively. Two
types of soils were used, #30 Ottawa sand and Monterey No. 0/30
sand. Both sands were prepared at a density of 107 pcf. The dead
load was maintained for a duration of approximately 45 days.
ASTM recommended that tests to be carried out at 21 + 2C
(70 + 4F) for geotextile testing. This temperature is higher than
the in-ground temperature for most applications in the United
States. Since polymer strength increases as temperature decreases,
use of the prescribed test temperature is generally conservative
(Bonaparte et al., 1985). If the reinforcement was exposed to
temperatures well above 21C (70F), a substantial reduction in
reinforcement tensile stiffness and strength may occur. At the
other temperature extreme, very cold temperatures result in
diminished material ductility and a reduction in elongation to break
(Bonaparte et al., 1985).
Reductions in reinforcing material strength due to
construction should also be considered in the design analysis.
These reductions could be determined by testing reinforcing
materials that have been subjected to the placement and construction
procedure. For example, compaction of blast rock against a
geotextile can induce damage that reduces the material tensile
stiffness and strength. In contrast, compaction of beach sand is
expected to have little effect on the material properties (Bonaparte
et al., 1985).


26
In this study, temperature and site damage effects were not
investigated. However, the test temperatures were recorded as test
progresses (typically 75F). Table 6 shows the test conditions of
the in-soil tests. All geotextile samples were 3 inches wide by 1
inch long.
TABLE 6
IN-SOIL CREEP TEST CONDITIONS
Soil Dead Corresponding
Test Sand Density Load Strain Levels
Symbol Type (pcf) (lbs) (%)
Cl Ottawa 107 57.0 3.8
C2 Ottawa 107 79.0 13
C3 Monterey 107 69.0 3.8
C4 Monterey 107 93.0 13
3.5 Results and Discussion of Results
Long-term creep test data are presented in Appendix B.
The plot of strain (in arithmetic scale) versus time (in
logarithmic scale) is designated as "creep curve" in this study.
Figures 9 and 10 show the creep curves of the geotextile
alone with two sustained loads (tests II and 12 in Table 5). As
may be expected, the higher the sustained load the larger the creep
strains. The shape of the creep curves are significantly different.
At the lower load level, the strain rate increases with time; while
at the higher load level, the strain rate is nearly constant.


Strain (%)
Time (min.)
Figure 9 Strain vs. Time Relationship for the Geotextile
In-Isolation at a Load of 16.5 lb.
ro


Strain (%)
Time (min.)
Figure 10 Strain vs. Time Relationship for the Geotextile
In-Isolation at a Load of 42.9 lb. ^
oo


29
It is to be noted that tests II, 12, and 13 resulted in a
percent creep (PC) of 1.03%, 1.05%, and 1.12%, respectively.
According to Christopher and Holtz (1985), the creep potential of
the Trevira 1127 geotextile is nil (see Table 4).
The effect of soil confinement on the creep behavior of the
geotextile is depicted in Figure 11, which shows a comparison
between the creep curves of Test 13 (in-isolation) and Test Cl (in-
soil) A substantial reduction in the strain was observed when the
geotextile was confined in-soil. McGown et al., (1982) explained
that this reduction had two components: a reduction in initial
strains and a reduction in creep strains. Following this
explanation, the creep strain in the confinement of soil is
significantly lower than the in-isolation condition, and so as the
initial strain. It should be noted that the creep strain rate is
enormously higher when the geotextile is tested in-isolation, thus
gives a distorted picture of the creep behavior.
Figures 12 and 13 show the creep curves of the geotextile
tested in the confinement of soil with two sustained loads (Tests Cl
and C2). Again, the strains are higher at the higher load levels.
The creep strain rate was nearly constant until about 100 hours
after the tests were initiated. It is of interest to note that the
shapes of the curves, unlike the in-isolation tests, are very
similar. This reaffirms the fact that creep behavior of the
geotextile must be obtained by testing the geotextile in the
confinement of soil.


Strain (X)
Time (min.)
Figure 11 Comparison Between In-Isolation (Unconfined)
and In-Soil (Confined) Geotextile with the
Same Strain Level (3.8%)


0.1
10
10
10
3
Time (hours)
Figure 12 Strain vs. Time Relationship for the Geotextile
Confined In-Soil at a Load of 57.0 lb. (3.8% Strain)


Strain (%)
8.8
8. A
8.0
7-6
0.1
10
10
10-
Time (hours)
Figure 13 Strain vs. Time Relationship for the Geotextile
' Confined In-Soil at a Load of 79.0 lb. (13% Strain)
ro


33
Figures 14 and 15 show the creep curves of the geotextile
tested in the confinement of Monterey No. 0/30 sand with two
sustained loads (Tests C3 and C4). Again, the strains were higher
at higher load levels. One can see that the shapes of the curves
are similar (as was the case for Tests Cl and C2). However, in
Tests C3 and C4, the initial strains were much higher, and the creep
strains were lower than Tests Cl and C2. This is another indication
that the geotextile must be confined in the same soil type as in the
field.


Strain (%)
Time (hours)
Figure 14 Strain vs. Time Relationship for the Geotextile
Confined In-Soil at a Load of 69.0 lb. (3.8% Strain)


Strain (S)
Time (hours)
Figure 15 Strain vs. Time Relationship for the Geotextile
Confined In-Soil at a Load of 93.0 lb. (13% Strain)
OJ
VJl


CHAPTER IV
PREDICTING CREEP BEHAVIOR OF THE GEOTEXTILE
BEYOND THE TEST PERIOD
4.1 Background
Prediction is the ultimate practical aim of engineering
analysis. The purpose of experimentation is to make it possible for
the researcher to infer, from the results of the present sample, new
conclusions about other future samples and behaviors.
Where substantial error is associated with data, polynomial
extrapolation is inappropriate and may yield unsatisfactory results
when used to predict future values. Experimental data are often of
this type (Chapra and Canale, 1985). A more appropriate strategy
for such case is to derive an approximating function that will fit
the shape or general trend of the data without necessarily matching
the individual points.
Because it was not possible to investigate the creep
behavior of the geotextile in an existing foundation (in the field)
for its design life, which could be some fifty years, the capability
of predicting geotextile behavior beyond the test period is mandate
for investigating the creep behavior.


37
This chapter shows how the test results can be used for
predicting the creep behavior of the geotextile, using a functional
curve by means of a nonlinear least squares regression analysis.
4.2 Regression Analysis of the Test Results
Mitchell (1976) described the creep rate behavior of a wide
variety of soils using the following equation:
m
e = Ae
qD
(H
(4.1)
where,
A, a, D,
fci
t
= creep rate
m experimentally obtained constants
= reference unit of time
= elapsed time
A minimum of two creep tests are needed to obtain the values
of A, a, D, and m. By integrating the above expression, a general
relationship between strain e and time t can be obtained. Taking
£ = e1, at t = 1 and tx 1, then
A aD f l-m I , .
e = £x + e t 1 (m ^ 1) (4.2)
and,
£ £x + AeQ^ Lnt (m = 1, t = 1) (4.3)
The value of m is the slope of the log £ vs. log (tx/t) curve. It
was found that, from the test data, m was smaller than 1.
Therefore, equation (4.2) was used in this study.


38
The following explains how to obtain a functional fit of
equation (4.2) to the data points obtained experimentally from the
in-soil long-term creep tests.
Since the values of constants A, a, and D could not be
determined independently, the term AeaP was considered as one
constant in this investigation. Rearranging equation (4.2) gives
e
AeaD ] f Ae^ ]
1-m J + [ 1-m J
t1 -m
(4.4)
This is of the form
y = A + Bxk
where,
A = i
AeaP
1-m
(4.5)
B
AeaP
1-m
k = 1-m
The problem at hand is to obtain the values of A, B, and k
for a set of data points (x^, y^) through nonlinear regression
analysis. The following demonstrates how this can be done:
Step 1: An initial estimate of the values of A, B, and k is
needed. These values can be estimated as follows:


39
(i) Take three widely separated points that seem to
be representative of the data : (x3, y3), (x2, y2),
and (x3, y3). (ii) Assume a value for kn, say 0.5.
(iii) Use Newton-Raphson method to find a value for
kn+i by a procedure described in Appendix C-I.
Repeat until successive values of kn+1 do not change
by more than a very small value, say 10'6. Once a
suitable value of k is found by the Newton-Raphson
method, then solve for B:
thus, estimated values of A, B, and k were obtained.
Step 2. Use least squares fit (nonlinear regression) to find
values of A and B using the estimated k (See
Appendix C-II). This is a nonlinear system which
can be solved by iteration.
Step 3. With the new values of A and B found in Step 2, use
(4.6)
and then for A:
(4.7)
Newton-Raphson method (using estimated k) as
follows:
(i) F(k) = nA + B 2x Eyi
(4.8)


40
(ii) F'(k) = BSxi Lnxi (4.9)
Step 4. (iii) kn+1=kn-|^|L (4.10) (iv) Repeat until | kn+1 kn | < a small number say 10"4; then return to Step 2 and solve for a new set of A and B using the least squares fit with kn+1 as the estimated k. Repeat steps 2 and 3 until successive values of A, B, and k are satisfactory close. For instance, until on successive trips through steps 2 and 3 the values do not change by more than 10'6.
Step 5. Having obtained A, B, and k,
and,
1 m = k, or m = 1-k (4.11)
also,
AeaD ? B (4.12) 1 -m
Finally, AeaD T* A e, = = e1 B = A 1 1-m 1


41
therefore,
<4 = A + B (4.13)
Substituting back in equation (4.2) the values of ex, B, and
k yield an expression to fit the data points obtained from the in-
soil long-term creep tests.
Once the expression is found, a question of how good this
expression is to fit the data points arises. To answer this
question, one may return to the original data and determine the sum
of the squares around the mean for the dependant variable (in this
case, e). This sum is called the total sum of the squares St. This
is the amount of spread in the dependant variable that exists prior
to regression. After performing the regression described earlier in
this section, one can compute the sum of the squares of the
residuals around the regression line. This sum is denoted by Sr,
which represents the spread that remains after regression. The
difference between St and Sr quantifies the improvement or error
reduction due to the functional representation. If the difference
is normalized to the total error one can obtain the coefficient of
determination r2 as follows:
r
2
(4.14)
Taking the square root of the coefficient of determination one gets
the correlation coefficient r. For a good fit, r2 has to be as
close to 1 as possible. If r2 = 0 the functional fit is no good
(Chapra and Canale, 1985).


42
It is also important to calculate the total standard
deviation Sy, and the standard error of estimate Sx/y which can be
calculated by the following formulas:
and,
Sx/y = /§*
(4.15)
(4.16)
Where, n is the number of data points.
If Sx/y < Sy, then the regression model has "merit" (works).
4.3 Predictions
The values of the constants e.
Ae
aD
-1 1-m
for each of the four in-soil long-term tests,
and m were calculated
and tabulated in
Table 7.
The total standard deviation, the standard error of
estimate, the coefficient of determination, and the correlation
coefficient were calculated for each in-soil long-term creep test
and tabulated in Table 8 (See Appendix C-IV for an example of
calculation).
aD
By inserting the values in of e1 , > and m i-n equation
(4.2), one can obtain an expression for the creep behavior of the
geotextile beyond the test period. Table 9 shows the predicted
time-dependant strains in 10, 20, 30, 40, and 50 years for the four
tests. Figures 16 and 17 show a graphical presentation of the
predicted time-dependant strains for the four tests.


43
TABLE 7
RESULTS OF THE REGRESSION ANALYSIS
Test Symbol Soil Type Strain Level (%) ei (in. ) AeaD 1-m (xlCT 5 ) m
Cl #30 Ottawa Sand 3.8 0.0488 11.80 0.670
C2 #30 Ottawa Sand 13.0 0.0765 0.225 0.253
C3 Monterey 0/30 Sand 3.8 0.1656 1.87 0.541
C4 Monterey 0/30 Sand 13.0 0.2031 78.7 0.807


44
TABLE 8
DETERMINATION OF THE GOODNESS OF THE FITS
Test r2
Symbol i%}_ (xlO'5)
Cl 97.6 4.1506
C2 98.6 14.20
C3 94.1 1.898
C4 96.5 7.618
Sr (xlO-7) sy sx/y
9.925 0.00148 0.000235
19.61 0.00273 0.000330
11.20 0.000996 0.000249
26.30 0.00200 0.000382


TABLE 9
PREDICTED TIME-DEPENDANT STRAINS OF THE GEOTEXTILE
Creep Strain (%)
Test Svmbol 10 Years 20 Years
Cl 0.0681 0.0731
C2 0.2439 0.3431
C3 0.1882 0.1966
C4 0.2179 0.2202
30 40 50
Years Years Years
0.0766 0.0794 0.0817
0.4266 0.5012 0.5700
0.2030 0.2082 0.2128
0.2216 0.2227 0.2236


Strain (%)
46
0 10 20 30 40 50
Time (Years)
(a)
0 10 20 30 40 50
Time (Years)
(b)
Predicted Creep Strain vs. Time for the
Geotextile Confined in #30 Ottawa Sand
for Tests; (a) Cl, and (b) C2
Figure 16


Strain (%) Strain (%)
47
0 10 20 30 40 50
Time (Years)
(a)
0 10 20 30 40 50
Time (Years)
(b)
Predicted Creep Strain vs Time for the
Geotextile Confined in Monterey No. 0/30
Sand for Tests: (a) C3, and (b) C4
Figure 17


CHAPTER V
SUMMARY AND CONCLUSIONS
5.1 Summary
A study was undertaken to investigate the stress-strain and
creep behaviors of a non-woven, needle-punched, polyester
geotextile, called Trevira 1127. A total of eight short-term
stress-strain tests (all these tests were repeated to check for test
repeatability) and seven creep tests were performed using test
devices designed at the University of Colorado at Denver. The tests
were conducted with the geotextile in isolation as well as in the
confinement of soils of variable overburden pressures, soil
densities, soil types, and geotextile specimen sizes. The creep
behavior of the geotextile was investigated using #30 Ottawa and
Monterey No. 0/30 sands. The long-term creep tests were performed
under two sustained loads which corresponded to strain levels of
3.8% and 13%.
A regression analysis procedure was presented to show how
the creep test results can be extrapolated beyond the test period.
5.2 Conclusions
Based on the results of the study, the following conclusions
on the stress-strain-strength relations and creep behavior of the
geotextile are advanced.


49
1. The geotextile stress-strain-strength
characteristics were very different in the
confinement of #30 Ottawa sand and Monterey No. 0/30
sand prepared at the same density. This is an
indication that stress-strain-strength tests of
geotextile should be performed in the confinement of
the soil to be used in the field.
2. The stiffness of the geotextile was not
significantly affected by the overburden pressure,
at least for the pressure range used in this study.
3. In conducting the tests, the frictional resistance
between the confining soil and the sheet metal clamp
was found to be very significant and should be
accommodated for correct interpretation of the
stress-strain-strength relations of the geotextile.
4. The geotextile specimen size was found to have
modest effect on the stress-strain-strength
characteristics of the geotextile.
5. The in-isolation creep tests on the geotextile
demonstrated that the higher the sustained load the
larger the creep strains. The shape of the creep
curves were significantly different; at the lower
load level, the strain rate increased with time;
while at the higher load level, the strain rate was
nearly constant.


50
6. The creep strain in the confinement of soil was
significantly lower than the in-isolation condition,
and so as the initial strain. The creep strain rate
was enormously higher when the geotextile was tested
in isolation.
7. The creep tests conducted on the geotextile confined
in #30 Ottawa sand showed that the creep strains
were higher at higher load level. However, the
creep strain rate was nearly constant until about
100 hours after the tests were initiated.
8. The shapes of the in-soil creep curves obtained at
different load levels, unlike the in-isolation creep
curves, were very similar. This indicated that in-
isolation creep tests may give a distorted picture
of the creep behavior.
9. Creep tests on the geotextile confined in Monterey
No. 0/30 sand showed much higher initial strains and
lower creep strains than the case where the
geotextile was confined in #30 Ottawa sand. This
reaffirms that the geotextile must be tested
confined in the same soil type used in the field.
10. A nonlinear regression analysis procedure may be
used to show how the creep test results can be
extrapolated to describe the creep behavior of the
geotextile beyond the test period.


BIBLIOGRAPHY
Bonaparte, R., R.D. Holtz, and J.P. Giroud, "Soil Reinforcement
Design Using Geotextiles and Geogrids," Symposium, ASTM Committee
D-35 on Geotextiles and Related Products, June 1985, pp. 13-14.
Chapra, S.C., and R.P. Canale, "Numerical Methods for Engineers,"
McGraw-Hill Book Company, 1985, pp. 286-294.
Christopher, B. and R.D. Holtz, "Geotextile Engineering Manual,"
Course Text, Prepared for Federal Highway Administration, National
Highway Institute, Washington, D.C., 1985.
El-Fermaoui, A., and E. Nowatzki, "Effect of Confining Pressure on
Performance of Geotextiles in Soils," Second International
Conference on Geotextiles, Las Vegas, Nevada, Vol. 3, 1982,
pp. 799-804.
Finnigan, J.A., "The Creep Behavior of High Tenacity Yarns and
Fabrics Used in Civil Engineering Applications," Proceedings of
the International Conference on the Use of Fabrics in Geotechnics,
Ecole Nationale des Ponts et Chaussees, Paris, Vol II, April 1977.
Haliburton, T.A., C.C. Anglin, and J.D. Lawmaster, "Testing of
Geotechnical Fabric for Use as Reinforcement," Geotechnical
Testing Journal, ASTM, Vol. 1, December 1978.
Holtz, R.D., W.R. Tobin, and W.W. Burke," Creep Characteristics and
Stress-Strain Behavior of a Geotextile Reinforced Sand,"
Proceedings of the Second International Conference on geotextiles,
Las Vegas, Nevada, August, 1982.
McGown, A., K.Z. Andrawes, and M.H. Kabir, "Load-Extension Testing
of Geotextiles Confiend In-Soil," Second Interntional Conference
on Geotextiles, Las Vegas, Nevada, Vol. 3, 1982, pp. 783-798
Mitchell, J.K., "Fundamentals of Soil Behavior," John Wiley & Sons,
Inc., 1976, pp. 329-331.
Shrestha, S.C. and J.R. Bell, "Creep Behavior of Geotextiles Under
Sustained Loads," Proceedings of the Second International
Conference on Geotextiles, Las Vegas, Nevada, August 1982.


52
Seil, B.D., "An Investigation of the Effectiveness of Tensile
Reinforcement in Strengthening An Embankment Over Soft
Foundation," Master's Thesis in Science, Civil Engineering
Department, University of Colorado at Denver, April 1986.
Van Leeuwen, J.H., "New Methods of Determining the Stress-Strain
Behavior of Woven and Non-Woven Fabrics in the Laboratory and in
Practice," Proceedings of the International Conference on the Use
of Fabrics in Geotechnics, Ecole Nationale des Ponts et Chausses,
Paris, Vol. II, April 1977.


APPENDIX A
SHORT-TERM STRESS STRAIN
TEST DATA


SHORT-TERM STRESS-STRAIN TESTS
Test No.:
OLL
Soil Density: iDl-O pC.fi-
Sample Size: 3 y 1**0 IH
Date of Testing: fa-17-36
Soil Type: *30 OWam Sflnj
Overburden Pressure: g-36 psi
Sample Direction: Machine
Displacement (in.) Load fibs.1
0.10 34. £
0.20 bo.k
0.30 8i-3
0.40 . 105-3
0.50 12 5.2
0.60
0.70 u-l
0.80 isdM
0.90 im
1.00 ZM
1.10 UM
1.20 ZtfM
1.30
1.40 zbsn
1.50 zerf.l


SHORT-TERM STRESS-STRAIN TESTS
Test No.: C^l^A l_______ Soil Type: 30 0\^CUM SClf\d
Soil Density: 1 Q~7Q P0(* Overburden Pressure: jQ p$|
Sample Size: 3 X LS \r>, Sample Direction: H6.
Date of Testing:
Displacement fin.) Load fibs.)
0.10 3\^
0.20 bZ-b
0.30 0.40 10 b.D
0.50 - \zQ.3
0.60 lM'Z-2
0.70 IU1
0.80 I8B5
0.90 ZbU,
1.00 ziZ'S
1.10 ZZ&'b
1.20
1.30 znA
1.40 2.1 n
1.50


SHORT-TERM STRESS-STRAIN TESTS
Test No.:

Soil Density: I 07.0 PC A
Sample Size: 3X1-5 IH
Date of Testing: b-ZVS1
Soil Type: &30 0ffo.6c)fl ZTirvl
Overburden Pressure:
Sample Direction: M Displacement (in.) Load (lbs.1
0.10 £3.Z.
0.20 49.5
0.30 17$
0.40 450
0.50 im
0.60 m.z
0.70 163.1
0.80
0.90 \H 2
1.00 Z/45?
1.10 ms
1.20 Z537
1.30 273-1
1.40 Z79.5
1.50 Z74.0


SHORT-TERM STRESS-STRAIN TESTS
Test No. : \_______
Soil Density: _____
Sample Size: 3)(I'S i W
Date of Testing: (p-9- Q6?
Soil Type: rn /60lq~(~^n
Overburden Pressure: Q
Sample Direction: Mac^\r\e
Displacement' fin.) Load fibs.1
0.10 14.1
0.20 35.1
0.30 bo, 5
0.40 57.1
0.50 ///-Z
0.60 1363
0.70 15ZA
0.80 \10,D .
0.90 1913
1.00 zcRo
1.10 223 A
1.20 23
1.30
1.40 Z43-0
1.50 23 52>


58
SHORT-TERM STRESS-STRAIN TESTS
Test No.: QM 5
Soil Density: \Ol.0
Sample Size: 3*\ \/\,
Date of Testing: 7-23?
Soil Type:'£30 OHltJa
Overburden Pressure: \Q
Sample Direction: M Qj}r\
Displacement Load
fin. > fibs.)
0.10 32-0
0.20 36.0
0.30 85.0
0.40 ill-0
0.50 130 d
0.60
0.70 170.0
0.80 l?0.0
0.90 7CR5
1.00 ZZi.O
1.10
1.20
1.30
1.40
1.50


59
SHORT-TERM STRESS-STRAIN TESTS
Test No.:
LC L
Soil Density: _______
Sample Size: '3)0x5 llrv
Date of Testing: 1 1-8(f
Soil Type: J-Tl- 150__________
Overburden Pressure: 0______
Sample Direction: Gass MMm
Displacement fin.) Load fibs.)
0.10 18- 5
0.20 453
0.30 78 M
0.40 1084
0.50 '(425
0.60- - n>.=,
0.70 Mo
0:80 z/84
0.90 zqxo
1.00 is&.o
1.10 Zl2'0
1.20 280.0
1.30 Z&>.0
1.40 245.5
1150 Z37.0


60
SHORT-TERM STRESS-STRAIN TESTS
Test No.:
£>Ll_
Soil Density: [ if). PC-C-
Sample Size: ^ 0 ( H.
Date of Testing: 7 I 3
Soil Type: 3oQlkzuxi
Overburden Pressure: 8'3fcpsi
Sample Direction:
Displacement (in.) Load (lbs.)
0.10 54.o
0.20 Mo.
0.30 (01.0
0.40 IZ&-0
0.50 /S7.5
0.60 1 (a(pO
0.70 182-0
0.80 \40.5
0.90 2215
1.00 Zitf-b
1.10 2P>Z-o
1.20 3CO.O
1.30 590.0
1.40 zefi.o
1.50 Z2b0


SHORT-TERM STRESS-STRAIN TESTS
Test No.:
MM 5
Soil Density: \0~l.0
Sample Size: lr\.
Date of Testing: Q-2-3~ 8£
Soil Type: VkrfWj ^ISO ^
Overburden Pressure: o PS(
Sample Direction: VWcVi \ C\?.
Displacement fin.) Load fibs.)
0.10 1
0.20 . 33,0
0.30 5^D
0.40 83*0
0.50 M2,0
0.60 M8.0
0.70
0.80 Z2Q.0
0.90 2SZ-0
1.00 Z7J-0
1.10
1.20
1.30
1.40
1.50


SHORT-TERM STRESS-STRAIN TESTS
Test No.: Z.S 'Inchon
Soil Density: /07.0 Pc{~
Sample Size: ______~________
Date of Testing: 9-12.-86
Soil Type: #30 OHd^Od
Overburden Pressure: jO \pSI
Sample Direction: ____
Displacement Load
(in.) (lbs.1
0.10 411
0.20 47.0
0.30 52,-0
0.40 of-D
0.50 49.0
0.60 510
0.70 E>U
0.80 5LU
0.90 4M
1.00 49.o
1.10
1.20
1.3 0
1.40
1.50


63
SHORT-TERM STRESS-STRAIN TESTS
Test No.:
32. PncWon
Soil
Type:
Soil Density: (D7*0 PC-C- Overburden Pressure: P$~I
Sample Size:
Sample Direction:
Date of Testing: 7-^/ 3b
Displacement Load
fin.) fibs.)
0.10 bZ'0
0.20 b*>.0
0.30 b3-S
0.40 6Z-S
0.50 (o!' 3
0.60 &>-s
0.70
0.80 (oS'\
0.90 M.o
1.00 Q-z
1.10
1.20
1.30
1.40
1.50


APPENDIX B
LONG-TERM CREEP TEST DATA


CREEP TESTS
65
Test No.: ri _ Soil Type: _______________
Soil Density: ______ Overburden Pressure: O
Sample Size: 3x7.5 iYI. Sample Direction: N\dsh\
Strain: _____?<, Dead Load: _______un.c, /h<;
Test Type: Un7oKOrT
Date Time fT) AT (hours) Temp. (F) Humidity Elong. fin.)
6-Z0-g£ lfo:30 0.00 \bl o.\zs O
|(b: 45 OXs 0\ZS8
17: QO 0.50 OAZ I7sd J.O OM&ij
!8:5t> DAZbZ
IQ'30 3-0 3.127/
ZD'30 4.0 - - 0.1 Z72
21:30 5.0 . 0.1273
21:00 5-5 - - o.\zi4
(p-21-567 ns 0JZ19
I2:0o (9.5 - O.XSQ
Z0:0o Z1S \237
02>:00 .3lS o.u9z









CREEP TESTS
Test No.: X2.________ Soil Type: ___________________
Soil Density: .______ Overburden Pressure: O
Sample Size: yl.S fr\. Sample Direction: Mnchmi.
Strain: ______l*/a Dead Load: _______42. / b ^.
Test Type: ^hX4a\QL-H0l0
Date Time m AT fhours) Temp. fF) Humidity Elong. (in.)
6-ZO-86 l(b:00 acoiby 0-267S-
lb: ir ais A 2 osO 0.Z^^5
17,& 1.0 O-ZRSS
(8: do z.o
l9: Oo 3.0 0.2371
Zb'&o '^1.0 o.zvi
.Zl:00 SO 0.2991
ZZ:0O 6.0 0.2993
k-zi-Sb O^/rOO loi.O 0.3oo0
)2:Q0 ZO'O 03038
20:09 ?g.o
OZ>:(£ 3S0 0.2027

*







67
CREEP TESTS
Test No.: X 3__________ Soil Type: __________~____________
Soil Density: ______ Overburden Pressure: Q
Sample Size: 3y l s'n. Sample Direction: MflY.infn-g.
Strain: ________3. ft % Dead Load: _________5~7. Q lb A .
Test Type: In.
Date Time m AT (hours) Temp. (F.) Humidity Elong. (in.)
9-/4-tb &:0Q QCOlfal Q.osro
D: |T CLZS aosQ9
13:30 0.50 - o.osqt?
ll:CO uo O.ObQZ
1 XOO 2'0 (XObo^
/SiOO so 0.0 bO^
l(Q:00 4o O.obof
11:00 5.0 &.0(?O(a
13 too 6.0 OMO(o
9 -if- 36 Z4;0J P*0 0.66o9
08'.00 2U' O.Ofc/0
1^:00 23'0 0.00/2.
Z4c0 34 0 Q0(pIlI


t






CREEP TESTS
Test No.: C 1__________ Soil Type: Ck-bluJa
Soil Density: pT.^ Overburden Pressure: Z-iQ.pti'
Sample Size: | fry Sample Direction: M(UC h
Strain: ____3 & ?o_____ Dead Load: ___________^7.0 fb.<;
Test Type: -Term
Date Time (T) AT (hours) Temp. (F) Humidity Elong. (in.)
7-ZV-S6 IZ'.OO 0.01 0.088$
D.Olhl , 0.048 0
6.0S0 ' o.o^ae-
O.l 00 qomq8
GZ00 00489
0.300 0.0^0
0.400 o.cM^o
0.500 0,0491
0,bCD oscw9l
07100 ooq9|
0.B00 oo49l
0.9 00 OMQl
N:C0 0 0.0891
z-Q 0.0491
lfo-0) 3.0 40491
- 17.- 06 4.0 O.o<44l
IS: CD 5,0 0.0491
l^'CO . 6.0 0.0898
£30:00 TO 0.0499
2\;bQ 8.0 0.049$


CREEP TESTS
Test No.: ConV.
Soil Density: ___
Sample Size: ____
Strain: _________
Test Type: _______
Soil Type: __________
Overburden Pressure:
Sample Direction: ___
Dead Load:
Date Time (T) AT (hours) Temp* fF) Humidity Elong. (in.)
ZZxCb 70 o.oq%
25:00 |0.0 0497
7- zr-& Z4;0o ItO 0.0498
1:00 1<3S 0,049 g
Z:0o /3>o o.o498
53 co l(k0 (00999
/2.-C0 Z3~0 0.0SO0
I'TJo-Qk ?'J0 SIS O.OSDl
(1:00 530 0.0502
1-Z1-&0 14:30 '12-5 Q(&3
Z^OO 7 9.0 0.0So4
8:00 9 Id 0.050^1
7-2?-8t l:30 ms 00505
I3:0 1700 0.0510
l9:CO I2&.D 0,05/1
Z4:C0 121-0 0.05/ /
7-30-8* AG) l 19: CD ISD.0 Q 05//5
7-51-8b 15: CO 108-0 77 5? O-OSIIS
19:00 174-0 3/ 59 0.03>II5


CREEP TESTS
Test No.: Conk
Soil Density: ____
Sample Size: _____
Strain: __________
Test Type: _______
Soil Type: __________
Overburden Pressure:
Sample Direction:____
Dead Load: ______
Date Time (T) AT fhours) Temp. fF) Humidity Elong. (in.)
ZB: CO 179.0 74 $9 0.0SI/5
8-1-8b ii-.oo l9o.O 8( s\ 6.0S/IS
Z 2:00 cOGD 0 78 0,051/ 5
£>-z-8& 11:00 c3|0-o &Z (ol 0*051/5
<31:00 820.0 7s (o\ O.OS 12J>
S-b-Sb IB: 0O 237.0 82- b 1 0,05/2-
Z4zoo> Z97.0 73 (oh 00512.
f-4-8C, 10: (I) ZS-7.0 77 (o\ 805/3
ZCkoo 201.0 7r bO OO513
8-7-3t> 9:00 ZTQ.0 7*? S1 0.05/35
Iftoo Z87.0 8Z> 59 305/35
8-6- 8 6 IO:CO 30>.?> 86 6o 0.05135
1(3:00 312-0 85 (ol 0.05/35
8-1-81 I3:0i> 832- 89 59 OO5/34
Zftoo 3 90.0 ai 60 QOS/34
8-8-86 Z0; 04 3o9-0 sr s-S Qos i9
8-%%. Za.0o 388-0 77 r9 00315
B-10-96 30:0 0 912-8 89 (o! 005/4
8-11-84 (OzOO 932-0 78 6>0 905/7
8-12-86 (b:CX) 9&.o S3 (=>z_ Qo 5/8


CREEP TESTS
Test No.: Con\r.
Soil Density: ____
Sample Size:
Strain: __________
Test Type: _______
Soil Type: __________
Overburden Pressure:
Sample Direction: ___
Dead Load:
Date Time fT) AT fhours) Temp . rF) Humidity Elong. fin.)
8-B-86 70- tx> 499.0 a<3 60 905/9
ZO: CO 3.o 9o 58 Ao 519
3-IS.gfe 33:00 527*0 90 59 .05Z/
8-lb-8& Zi>iOQ 556.0 Q(o 58 0-65Z3
8-17-86 ( 8-18-86 I7.-Q0 6o/*Q 31 0.0525
8-19-86 78-. CO 623.0 88 6/' 0.05Z6
8-70-86 Z0, oO (352-0 89. (oi 00521
8-22.-86 (9; CD <019.0 74 (oQ Q0S78
8-Z9-86 Z&oo 798-0 0/ 5% 0.0 529
8-23-86 70:00 899-0 73 00 33^
8-31-96 ' 818-0 7X £3 0053/
7_r-8£ /ZCD U023.0 gr ho 4&S3Z
9-7-96 j&'OO ' I,d80 63 b ? A0S33




1



CREEP TESTS
Test No.: C£
Soil Density: ' /D7.0'pC-f~
Sample Size: | fn
Strain: \~^c[q________
Test Type: -~T>.rm
Soil Type: ^30
Overburden Pressure: IQ p$i'
Sample Direction: MnTfM'rte.
Dead Load: ________ 7<^.Q |,bC.
Date Time fT) AT (hours) Temp. (F) Humidity Elong. (in.)
7-19-% b 12:00 0.01 0,075.
qoife7 0.076
0.050 0,0763
O.IO0 0016S
O.TjOO 0,0767
0.2£0 0076?
'O.^cw . o.oiog
OSoo 0.0768
O.boo OC768
CQ0> oo76gr
OSOo qo769
dploo o.oltfs
13:00 1.00 0.016%
I9-.00 20 007695"
IS-:0<3 ' 3.0 0,077/
lb:0d 4o - 4077/r
17:0d 3.0 A 077 2
(9:00 (oJO 0.0112.
iQ.-OO 10 0.0172f
10,00 8.0 0.07725'


73
CREEP TESTS
Test No.: Cof\Vi________ Soil Type: ___________
Soil Density: ___________ Overburden Pressure:
Sample Size: ____________ Sample Direction:
Strain: _____________. Dead Load: _________
Test Type: ______________
Date Time m AT (hours) Temp. (F) Humidity Elong. ( in.)
Z h Oo 9-0 9D773
22:00 (0.0 0.0773
2l:oo 11.0 O0773r
2-4:00 Iz-o 6.07725
7-30-86 10:00 ZZ.0 0.077 4
IB'^o 20.V 0.0774
7-1L81? I4;00 SOM 11 58 0.0115
19:0) 3^0 8>\ 59 00118
24:00 6o.o -J -O S9 Q0777
8-1-36 l:0O 10.0 81 59 60777
70: 00 SD-o 18 s? 0.0178
8-Z-86 S'OO 90. o 79 <6/ O.0H8
\8'00 (OQo 18 0,077 9
8-3-86 \6;< iz>. 8^ ^:Oo i30.o 18 6/ 0.0I8I
3-4-86 (&0d NO.O 77 61 0.01Q2S
Z0:C0 (So.o 7 S'' 60 0,0184
9;(P lb 1-0 79 (qO 00786,
W:0o 170,0 82> 59 00189
<8~6-S6 10:00 177o, 0 36 To 0079


74
Test No. ____
Soil Density:
Sample Size:
Strain: _____
Test Type:
Cor^r,
CREEP TESTS
_ Soil Type: ___________
_ Overburden Pressure:
_ Sample Direction: ____
Dead Load:
Date Time m AT (hours) Temp. fF) Humidity Elong. fin.)
I6:qq 192.0 88 61 <3 019Z
6-i- a*. feoo ZIZ-0 68 59 6. 0795
ZO:0Q 220.0 81 60 9 0793
8-8-21, 2.0:00 249.0 85 58 0.0798
IQ-.QO zbQ-o 75- 72 o.oso
8-lo-gc, 30:06 29 2-0 64 <61 0 080 3
8-li-afe (P'CO 3/2-0 IB 60 O.05D5
8-iz-db l(o:0D 33S.0 S3. 6>2 O.0Q6]
8-11-8 ( 70:00 5£>9.o 86 60 ooQ(o
8-14-94 ZO-oo 398-0 90 68 9C8I2.
8-1S-96 70:00 4/2-0 Qo 6? o.oQlcj
3-I6-8& ZO'.Ob 7760 86? 69 0.0814
3-17-96 lb; CO 5-18-84 \7;00 48/- 81 60 90S 18
8-MJS4 Zo:OD 50g.O 38 6| 0.08ZO
8-20- 94 7C:0D 5?2-0 84 b\ 0082.4
S-ZZ-80 | [: Q 0 5/9-0 79 60 OpQ 21
3-24-2G ZO'.oO 422.0 81 09 44330
8-28-84 ZD: CD 729 73 66 0.0830
g-2J-8fc 27-: oo 199 A 75- 63> 0.0890


CREEP TESTS
Test No.: Coni.
Soil Density: ___
Sample Size: ____
Strain: _________
Test Type: ______
Soil Type: __________
Overburden Pressure:
Sample Direction: ___
Dead Load:
Date Time (T) AT (hours) Temp. (F) Humidity Elong. (in.)
12:00 908 81 60 <3.o89 y
ZO;00 1,036 12- 0.0951
9-/2-Si / 6;00 1,080 (oQ lob 0.oS5l



















CREEP TESTS
Test No.: C3 Soil Type: MOf^D 5W
Soil Density: \Dl.Q Overburden Pressure: |Q p^\'
Sample Size: 3 X \ ~ m Sample Direction: MnC hm.?
Strain: 3.3 % ~ Dead Load: (nQ.q Ihv
Test Type: Ln^-^Tgjnrn~
Date Time fT) AT (hours) Temp. (F) Humidity Elong. ( in.)
?-2fc-8£ / 7; 4S" O.Ol 73 y*/ 0. (fos
O,0lb7 78 S-4 o.ifcs
O.OSo 73 £8 OJG5
O.ioo 73 s4r 0.1 (=57
0.2-00 78 54 0.165,8
0.300 78 s4 o.lfeSg
OM00 73 s4 0.1659
0.500 10 54 O.I&59
Qfc ft) 18 £ 0.700 79 54 o,\b6
o.Qco 78 54 CX\(ok
O80O 78 54 Qlfet
(S'-HZ f.o 77 £9 A166
|9:45" 2.0 ' 77 (cO O.IGG
ao.-'/r 3.0 77 55 Qlbk
z/:4r 4.0 77 S3 O (U
7Z:q5 3>.0 77 55
22,: 45 ko 77 S8
9-21-86 17; 45 70.0 7/ 5b
ZZ-.4S 2 f.o do 56 0,\b62_


CREEP TESTS
Test No.: 63 rrH
Soil Density: ____
Sample Size: _____
Strain: __________.
Test Type: _______
Soil Type: __________
Overburden Pressure:
Sample Direction: ___
Dead Load:
Date Time fT) AT (hours) Temp. fF) Humidity Elong. (in.)
9-Z8-86 3-45 30 0 1& 53 0 Ikfez
/3-'*4s 90,0 7/ J>S 0,1 (£3
18 4s 950 7o 58 . Qlt43
-Z3-AS EOJO 7S S3 0(664
9- Z9-% 4 W 945 60.0 79 37
, i 1945 700 38 57 OIOW
?-30_ 8b 10:95 85o 79. SS 0.\ - ZO;95 95.0 15 58 O.UjbS"
lO-l-Sb 945 io8-o 00 5b 0,1(0667
2/45 120.0 74 61 0, lfc>66
10-7.-86 9:45 I3Z-0 a/ 5=9 o.\(dn
ZZ.45 450 78 38 OMcTSl
/0.3-86 |0.4S> 1570 Sz 37 0.1667
'845 /85o eo 38 Q 1
tO-H-M) 945 170.0 83 36 31 (0I08
2l:P m 80 36 O.[(do%
lOS-% 11-45 \%.o as S3 OACztJj
ZZ45 707.0 79 S7 0\lU9
(0~6-Q& //:# Z/9.75 86 5S Q 1


CREEP TESTS
Test No.: ____
Soil Density:
Sample Size:
Strain: ______
Test Type: ___
Conk
Soil Type: __________
Overburden Pressure:
Sample Direction: ___
Dead Load:
Date Time (T) AT (hours) Temp. fF) Humidity Elong. (in.)
/o_7_B b 10; 00 Zlz-o % sV o>7
m-bb tO;Qb Zbb.O 85 53 0.1871
IOJj-Qk (0:00 z 10-10-60 10:00 314.0 go SJo a 1 biz
(O-U-Qb /O:0O 338.6 7? 5b 0.167Z
IOJZ-8i> 11:0) 363-0 78 51 8/873
0-13-26 10: CD S&A 8z 5S~ Q1873
/O-iM-gfo 10:00 Hio.o 8*7 59 0. Ib77
IOr-15-St (2:00 7i6.o 86 S3 0.1 (619
\0-\(e-8(o 12:00 %0l 89 54 0.1877
to-17-3b 11:00 <465-0 80 56 0.1677
IO-I8-SI6 II :0b .5)7.0 7? (O 1 o/6?r
|0-fl-8fc ID; 00 520.0 So 6Z 0.1878
IO-ZO-SG 10:60 5SiO 83 S3 0./676
|0-2l-8fe (0: CO 578-0 78 J5>b 0.1677
10-TZ-Q(o ( 0;00 (jbT-'O 93 0.1617
'0-22^86 /0;di 62 b. 0 81 si d. \m
I0-24-8C, 12:00 652-0 S3 50 a ibid
(O-ZC-gb 10 >00 674-0 7? 6( 0.1678
(0-2b-9b 11:06 699.0 so 58 0.167?


CREEP TESTS
Test No. _____
Soil Density:
Sample Size:
Strain: ______
Test Type: ___
ConV-.
Soil Type: __________
Overburden Pressure:
Sample Direction: ___
Dead Load:
Date Time fT) AT (hours) Temp. (F) Humidity Elong. (in.)
IO.Z7.86 10;00 123-0 85" rr 0.1 (ol9
10-28-86 lO:00 7 10.29-36 10:00 771.0 Q>(o ro OMc&Z.
I0-3D-& 10:00 7910 53 o.iegz
i i (0:00 9(9.0 85 S\3 0.1<83
11-1-80 10:00 843-0 li 74 Q1L83
11-2-80 (0:00 861.0 79 r9 0.1 (oQ9
11-3-86 10:00 891.0 71 1 D.I&84
i t-4-fo (0:00 9 Ho ib bz 0. i68r
it-7-86 10:00 Q3U . 75 58 omi
1 1-b-8& (0:00 103.0 80 19 0. \(o%6
11-7.86 (O.'OS 987.0 81 5b 0.I68 6
il -8- 26 10:00 (011.0 8 0 Ol I&8G
11-9-86 10:00 1037-0 78 sy ojosi
11-/0-86 (0:00 \05i0 77 19 0- IbQl







CREEP TESTS
Test No.: C4 Soil Type: NfonWeY 0/30 6W
Soil Density: 101-ft pCJr Overburden Pressure: IQ ps\
Sample Size: 3X1 in Sample Direction: Mac
Strain: 1 3 7o_____ Dead Load: ________ q
Test Type: Lnwg -Tbrm
Date Time m AT (hours) Temp. (F) Humidity Elong. (in.)
9-24-86 (9,00 O.Ol 75 54 O.zoz
O.CAbl 18 59 P.TOZ
0.050 18 54 OZ035
QIOD 75 si O.ZO38
O-ZOq 72 sd 0.2033
O.3CD 7£ - ^4 AZ039
O.cf 00 79 59 azW
A SCO 7(9 59 0.Z 0.600' 78 59 O.ZcW
onov 73 s4 o.ioi
0.900 73 3? o.zo4
0.1CD 7§ ^0 0.204
19:00 l JO 11 55 o.zo4z
ZQ'.OO zo 11 Q2jdM3
2 UO 3-0 77 55 O.TtWS
Z£:Q0 4.0 77 53 0.2047
73:00 5.0 77 55 4Zo4&
^:C0 6.0 77 58 D.Tofl
9-Z7-86 18:00 zoo 7/ 53 O.Z039
Z3.-0D ZSIo 90 5b 0.7055


81
Test No.: Co>oV.
Soil Density: ___
Sample Size: ____
Strain: _________
Test Type: ______
CREEP TESTS
_ Soil Type: ___________
_ Overburden Pressure:
_ Sample Direction: ____
Dead Load:
Date Time m AT (hours) Temp. fF) Humidity Elong. (in.)
9-12-% 4: CO 3ao Id 53 dtps 6
IA:0O 40. o 1\ 53 0.7057
- 19:0(3 45 o 58 0.7058
24:00 50.0 75" 53 42059
9-23-St 5:0t> 55.0 73 56 OruToO
10:00 00.0 77 37 O.ZffcO
20:00 70.0 18 s 9-30-<% 11:03 Qb.o 79 55 0.7062
Z 1:00 i5.o 75 58 O.ZDlo3
ID-i-db 10:00 /OS.O 83 5(o O.TDbS
Zl:00 mo 74 5\ Q2D64
IO-Z-86 IQOO 1320 81 s Z3;bb 145.0 78 38 0.7065
10-5-86 11:00 1520 <92. ^7 Qt064?
14:03 165.0 80 3£> 0.7067
10-9-80 l0:00 170.0 85 0.7O fe8
ZZ:00 idz-o 80 55 07369
0-5-86 17:00 l%.0 85 53 Qzo(?9
25:00 ZOIC) 78 57 8 ZO70
(O-Mfc 11:00 z\t.o 56 53 Q Z010


CREEP TESTS
Test No.: ConV^ _ Soil Type: _________
Soil Density: _________ Overburden Pressure:
Sample Size: __________ Sample Direction:
Strain: _______________ Dead Load: __________
Test Type: ____________
Date Time (T) AT (hours) Temp. fF) Humidity Elong. (in.)
10-1-86 13 00 Z42-0 5>b 0.7O11
ID-8-8C 10: 03 Ztio-D &s £3 0.2072
M-db IO:CO 290,0 S3 0.2073
10-10-86 |0:CO 319.0 SO J3(a O.2073
10-11-80 1Q:C0 338-0 79 E>(o Q 2074
tO-iz-66 (Uco o 78 si 0 Z07r
lO-K-Sb |O:0D 3S6,o 82 S3 o.zo7r
laui-SL 10:06 4(0.0 84 59 0.2076
IQ. 15- 8b 12:03 4 38.o 86 53 0.2077
/0_/£>-$& 12: CD 4b0.o 8>4 0.2078
10-17-96 1 \i00 483-0 80 56 QZ013
(0-18-80 11 '.QD 3o7.o 79 0/ 07.071
10.-00 233,0 So 102}-8 6 lD:CO S64.0 83 35 Q208I
(0.21-86 I0; 0D £73-0 73 3 (o-lz-80 lO;QD 602-0 83 0.2002
(0-tZ-8Q 10:CO Colb'O 9' -£>7 o.z33
(o.24M IZ:C0 6520 ^3>3 lo0 0.2033
10-28-86 10:0b 67^0 71 &>| 0.203c/
10-21,-26 li-.flo 3 - sa Ozo<3r


CREEP TESTS
Test No.: ____
Soil Density:
Sample Size:
Strain: ______
Test Type: _

Soil Type: __________
Overburden Pressure:
Sample Direction: ___
Dead Load:
Date Time (T) AT (hours) Temp. (F) Humidity Elong. (in.)
lO;Q0 723.0 £7 77 0.2086
I0-2B-S& (0:00 7<-(7.0 83 7( Q208C,
ID.73-8& 10:00 771.0 BCp 70 0.2081
10-36-86 (0:00 79fo 93 73 0.2088
/0-3I-86 10:00 8(9.0 8S~ 78 Qzo88
H-i-80 16:06 8 JI-7.-8& (Q:0d 3&7.0 79 S~4 O.TJtfff
11-3 - to.-00 831.0 77 (ol o.zo9 0
d-4-86 10:00 qis-.o l(o 6?Z -azoH(
a-r-Sb 10: Od 939.0 77 S8 0.269 2
n-Q>-26 10:00 963-0 8o sr? o. zo93
N-7-8& [0:06 98>7.o 81 76 0.2093
1L 8-S& 10.'00 lOu.o 83 79 0.7o?y
11-9-86 lO.'fc I08S.O 18 yr 0.20?y
H-IO.% (0;OO tos9.o IT QZfift"







APPENDIX C
C-I NEWTON-RAPHSON METHOD
C-II LEAST SQUARES FIT
C-III EXAMPLE ON THE NONLINEAR REGRESSION ANALYSIS
C-IV EXAMPLE ON THE DETERMINATION OF THE
GOODNESS OF THE FIT
C-V FORTRAN PROGRAM


85
C-I NEWTON-RAPHSON METHOD
1. Take three widely seperated points that seem to be
representative of the data, then
2. yx = A + Bx1
. _ k
y2 = A + Bx2
. k
y3 = A + Bx3
Solution of this gives an estimate
yi - y2 _ k = B(X! k x2)
y2 - y3 = B(x2 k x3) -
yi - y?, k xi - k x2 *
y2 - y3 k x2 * k x3
Eliminate A
Eliminate B
4. Assume
F(k) = (x^ x2)(y2 y3)
- (*2 x3 )(yi y2)
and,
F'(k) (x^ Ln x: x2 Ln x2) (y2 y3)
1c 1c
- (x2 Ln x2 x3 Ln x3) (yx y2)
5. Let k0 =0.5 (if this does not work, try other values)
k = k F^n)
Kn+i Kn F'(kn)
kn+i kn
< 106 ,
or so


86
C-II LEAST SQUARES FIT
(NON-LINEAR REGRESSION)
n
Let P(A, B, k)

A + Bx^ -
i-1
To find the minimum we set
|£ 0 ; |£ 0 ; and |E 0
and solve:
n
8T
8A
- 2
A + Bx^ -
- 0
3P
3B
hL 2
i-1
n
i-1
A + Bx^ y^_
Xi = 0
n
3P
3k
or,
- 2
A + Bx^ y^
Bx^ Lnx^ = 0
i-1
nA + B

yi
k + B' v 2k \ k
xi ) xi - 2 xi yi
k Lnx^ + B) 2k T Y k
xi x^ Lnx^ = ) x^
Xi yi LnXi
This again, is a nonlinear system which can be solved only
by iteration.


Use,
87
k + B V 2k \ k
xi / xi ii r\- h** t-**
k Lnx 2k Y k
xi + B ) X£ Lnx^ = y 1 xi
To find A and B solve the above two equations with two
unknowns A and B.


88
C-III EXAMPLE ON THE NON LINEAR REGRESSION ANALYSIS
First, we need some kind of estimate of the value of A, B,
k. These can be estimated as follows:
1. Choose 3 widely seperated points that seem to be
representative of the data:
(x1; Yl) = (10, 0.0489)
(x2, y2) (400, 0.04936)
(x3, y3) (64800, 0.0533)
2. Assume k 0.75
F(k) = (10-75 400-75)(0.04936 0.0533)
- (400-75 6480075)(0.0489 0.04936)
= -1.5
F'(k) (10-75 x Ln(10) 400-75 x Ln(400))
x (0.04936 0.0533)
- (400-75 x Ln(400) 64800-75 x Ln(64800))
x (0.0489 0.04936) -18.3917
3. Calculate the new value of k
kn = k F(k)/F'(k)
kn = 0.75 (-1.5/-18.3917) 0.6684
4. Repeat until | kn k | < 10"6 or so
5. After 10 iteration we get,
k 0.3985
6. Least squares regression
E xi = 558.7763
2k
S xi 29247.8413
S Xixyi = 28.8889


89
S yi = 1.0073
Xx'X LnXi = 5304.4218
9k
S Xi x Lnxi = 299081.5330
S x^ x x Lnx£ = 275.3729
7. Solving the two equations with the unknowns A and B:
558.7763 x A + 29247.8413 x B = 28.8889
5304.421 x A + 299081.5330 x B 275.3729
yields, A = 0.04893
B = 0.00005285
8. Check for k again,
F(k) (20)(0.04893) + (0.00005285)(558.7763) 1.0073
= 0.00083
F'(k) = (0.00005285)(5304.4218) = 0.2803
kn = 0.3985 0.00083/0.2803 = 0.3956
Go back to find another estimated k
9. Using k = 0.3956
Ex- = 543.3119
o\r
S 27531.4263
E x- x yi = 28.0862
S X£ X Lnxi 5152.3052
9k
E x^ x Lnxi = 281362.1796
£ x^ x yi x Lnxi = 267.4541
yields, A = 0.0489
B = 0.00005497


90
10. Check for k:
F(k) = (20)(0.0489) + (0.00005497)(543.3119) 1.0073
- 0.000566
F'(k) = (0.00005497)(5152.3052) 0.2832
kn = 0.3956 (0.00056/0.2832) = 0.3946
| kn k | = 0.001 "good enough"
.-. k = 0.3955 = 1 m
- A + B = 0.0489 + 0.00005497 0.0489
yields,
e = 0.0489 + 0.00005497 (t0-3955 1)


91
C-IV EXAMPLE ON THE DETERMINATION
OF THE GOODNESS OF THE FIT
Yi (Observed) Y (Calculated) (Yi ( - Y)2 Sr (Yi - Y)2 sr
0.0486 0.0488 3.12 X 106 4 X 10'8
0.0488 0.0488 2.45 X 10'6 0
0.0488 0.0489 2.45 X 106 1 X 10'8
0.0490 0.0489 1.86 X 10'6 1 X 10'8
0.0491 0.0490 1.60 X 10'6 1 X 10'8
0.0491 0.0490 1.60 X 10'6 1 X 10'8
0.0491 0.0490 1.60 X 10'6 1 X 10'8
0.0492 0.0493 1.36 X 10'6 1 X 10'8
0.0497 0.0494 4.42 X 10'7 9 X 108
0.0500 0.0496 1.33 X 107 1 .6 X 10'7
0.0502 0.0499 2.72 X 10'8 9 X 10'8
0.0505 0.0504 1.82 X 108 1 X 10'8
0.0511 0.0506 5.40 X 107 2 .5 X 107
0.0511 0.0508 5.40 X 10'7 9 X 10'8
0.05115 0.0510 6.16 X 107 2 .25 . X 10'8
0.05135 0.0514 9.70 X 10'7 2 .5 X 10'9
0.0516 0.0517 1.53 X 10'6 1 X 10'8
0.0525 0.0522 4.56 X 10'6 9 X 108
0.0531 0.0529 7.48 X 10'6 4 X 108
0.0533 0.0531 8.61 X 106 4 X 108