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Evaluation of pier uplift in expansive soils

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Title:
Evaluation of pier uplift in expansive soils
Creator:
Westman, Erik C
Publication Date:
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English
Physical Description:
vi, 81 leaves : illustrations ; 29 cm

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Subjects / Keywords:
Soil-structure interaction ( lcsh )
Swelling soils ( lcsh )
Soil-structure interaction ( fast )
Swelling soils ( fast )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Bibliography:
Includes bibliographical references (leaves 80-81).
General Note:
Submitted in partial fulfillment of the requirements for the degree, Master of Science, Civil Engineering.
General Note:
Department of Civil Engineering
Statement of Responsibility:
by Erik C. Westman.

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Source Institution:
|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:
30839197 ( OCLC )
ocm30839197
Classification:
LD1190.E53 1993m .W47 ( lcc )

Full Text
EVALUATION OF PIER UPLIFT IN EXPANSIVE SOILS
by
Erik C. Westman
B. S., Colorado School of Mines, 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
Civil Engineering
1993


This thesis for the Master of Science
degree by
Erik C. Westman
has been approved for the
Department of
Civil Engineering
by
j
Date ^


Westman, Erik C. (M.S., Civil Engineering)
Evaluation of Pier Uplift in Expansive Soils
Thesis directed by Professor Nien-Yin Chang
ABSTRACT
Uplift from expansive soils continues to damage many
structures in the United States. One method of design to
decrease the damage is to found the structure on drilled
or driven piers. This method, however, is not fail-safe,
as the soil can swell laterally, squeezing the pier, and
vertically, lifting it out of the ground. A complete
understanding of the interaction between the expansive
soil and the pier is required.
Using the results of laboratory tests as input, a
suite of numerical models simulating pier uplift due to
swelling soils was completed; regression analysis of the
results produced an equation for pier uplift. 1-D swell
and triaxial compression laboratory tests were conducted
to provide swelling and strength properties of an
expansive soil. The coefficient of friction between the
expansive soil and pier materials (steel and concrete)
was determined by using the direct shear apparatus to
fail a composite of the two samples. The results of the
laboratory tests were used as input to the numerical
modeling series. A total of 729 numerical models were
iii


completed using the finite difference code, FLAC. This
code was chosen due to its abilities to model large
displacements and specify interface friction and
cohesion. Three separate values for each of the six
independent variables were varied. Regression analysis
of the results produced the following equation:
Y =
D117
e0.357S £1.61
^0.831 yO-760
c161
where Y = vertical displacement of pier
head (ft.),
S = swell pressure of expansive soil
(ksf),
T = thickness of expansive soil
(ft.),
D = depth to center of expansive soil
(ft.),
L = structural load applied to pier
head (ksf),
f, = interface friction between pier
and soil, and
C = cohesion of expansive soil (ksf).
The degree of fit is given by the square of correlation
iv


coefficient, r2 = 0.958. The results predicted by this
equation compared very well to results predicted by
Sahzin's theoretical model [17].
This abstract accurately represents the content of the
candidate's thesis. I recommc
Signed|
Nien-Yin Chang
v


Chapter
5. Simulation of Pier Uplift with Numerical Modeling 37
5.1 Design of Numerical Modeling ................... 37
5.1.1 Selection of Modeling Code.................... 37
5.1.2 Description of Modeled Parameters ............ 38
5.1.3 Description of Model............................ 38
5.1.4 Description of Failure Criteria .............. 44
5.2 Formulation of Functional Relation ............... 47
5.2.1 Description of Relation......................... 47
5.2.2 Development of Relation......................... 48
5.3 Statistical Analysis ............................. 53
5.4 Discussion of Results............................. 59
6. Conclusions and Recommendations for Future Research 67
Appendix
A. Results of Laboratory Tests ........................ 69
References............................................. 80
vii


CONTENTS
Chapter
1. Introduction ...................................... 1
1.1 Need for Research...................................1
1.2 Engineering Significance .......................... 1
1.3 Scope of Study......................................2
2. Theoretical Background ............................ 3
2.1 Pier Background.....................................3
2.2 Mechanics of Pier Uplift............................5
2.3 Analysis of Swell Potential ....................... 9
2.3.1 Molecular Structure ............................. 9
2.3.2 Laboratory Measurement of Swell Potential . 10
2.4 Analysis of Skin Friction......................... 11
2.4.1 Mechanics of Skin Friction...................... 11
2.4.2 Field Determinations of Skin Friction .... 13
2.4.2.1 Effective Stress Method .................... 14
2.4.2.2 Other Methods............................... 17
2.4.3 Design of Piles for Reduction of Skin Friction 19
3. Laboratory Soil Characterization ............... 22
3.1 Soil Used......................................... 22
3.2 1-D Swell........................................ 24
3.3 Atterberg Limits ................................. 27
3.4 Triaxial Compression ............................. 27
4. Laboratory Determination of Coefficient of Friction 32
vi


1. Introduction
1.1 Need for Research
Expansive soils are those which have the ability to
rapidly increase in volume with an increase in moisture
content. Frequently, these volume changes result in
substantial damage to property. It has been estimated
that the annual cost of damage in the United States is
more than double the cost of damage due to flooding,
hurricanes, tornadoes, and earthquakes combined [12],
1.2 Engineering Significance
Drilled and driven piers are fundamental methods of
foundational support. However, if these piers are not
adequately designed and constructed, drastic remedial
action may be necessary. An especially troublesome area
for construction is one in which expansive material is
present. When subjected to cycles of wetting and drying
this material can quickly change in volume causing much
damage. The soil can expand both horizontally,
"squeezing" the pier, and vertically, lifting it upward.
The readiness with which this is done is a function of
both the skin friction at the pile/soil interface, and
the swell pressure of the soil.
1


1.3 Scope of Study
In order to accurately assess the impact of a given
expansive soil/pier system, a proper understanding of the
soil, skin friction, and complete system interaction is
required. A study was initiated to simulate in situ
behavior of the system with numerical modeling. The input
parameters of strength and swelling properties of an
expansive soil and the interaction of the soil and pile
materials at their interface were determined from
laboratory tests. Background information on piers and
the mechanics of their uplift is presented as an
introduction to different methods of skin friction and
swell pressure analysis. An equation for pier head
uplift based on the regression analysis of the numerical
model results is presented and discussed.
2


2. Theoretical Background
An understanding of pier/soil interaction is
necessary before a simulation with numerical modeling.
Basic descriptions of pier performance and pier uplift
are critical to a proper comprehension, as well as proper
knowledge of swell potential and skin friction. The
analysis of swell pressure at the molecular and
laboratory scales is briefly discussed. A more
comprehensive discussion of skin friction analysis is
presented. Thorough understanding of these concepts is
necessary prior to attempts at preparing a prediction of
vertical displacement.
2.1 Pier Background
When used for construction purposes, piers are
usually designed to carry their load by transferring it
to material beneath them, around them, or a combination
of the two.
Piers which transfer their load to the rock or soil
beneath them are termed "end bearing" piers. Typically a
load from a fairly light structure, such as a house, may
be transferred to a sand or gravel layer. However, a
heavier structure, perhaps a multiple story office
building, will produce loads which must be transferred to
a much stiffer material, typically hard bedrock.
3


The bearing capacity of a material may be surmised
by a number of different methods, each with its own
advantages and limitations. Field tests such as load
tests, pressure meter tests, and standard penetration
tests may be conducted, but they are expensive and a
fairly large number of these ought to be run to ensure
accuracy of the results. Laboratory tests such as
triaxial and unconfined compression tests should also be
conducted to further verify results obtained in the
field. One of the most reliable methods, though not
always available, is the performance of existing
structures.
Piers may also bear their load by transferring it to
the soil and rock around them through skin friction. The
difficulty is in determining a value for skin friction.
Methods for doing this will be discussed in detail later.
Once values for end bearing and skin friction have
been determined, the pier may be designed. Chen [6]
assigns a typical value for the increase in both end
bearing and frictional capacity as three percent per foot
of pier length. He acknowledges though, that this cannot
continue indefinitely. Thus, in order for an accurate,
economical design to be obtained it is necessary for both
end bearing and skin friction pressures to be known.
While it is possible to obtain a fairly accurate value
4


for end bearing pressure, it is much more difficult to
readily predict a skin friction pressure. In order to
study this more closely, the mechanics of pier uplift
will be examined.
2.2 Mechanics of Pier Uplift
When a pier is loaded, two forces act on it; an
uplifting force and a withholding force (Fig. 1). The
uplifting force is due to the swelling pressure trying to
push the pile up, while the withholding force is a
function of the applied load and skin friction and acts
contrary to the uplifting force. Uplift occurs when the
magnitude of the uplifting force surpasses that of the
withholding force. Greater than allowable uplift results
in failure of the structure.
To analyze the uplifting force, the swell pressure
must be known. A reasonable value for this can typically
be obtained in the laboratory. The portion of the swell
pressure which translates into the uplifting force,
however, depends upon the value of skin friction between
the pier and the soil. Because this is not known, it is
difficult to obtain an accurate value for the uplifting
force.
The analysis of the withholding force follows the
same lines as that of the uplifting force. The
5


3.2
1-D Swell
The 1-D swell test is an accepted industry standard
for determining swell potential. Standard Bishop-type
consolidometers were used for the tests (Fig. 3).
Figure 3: Bishop-type Consolidometer used in One-
Dimensional Swell Tests
Samples were compacted by placing the cutting ring in the
bottom of a Proctor mold, adding 470.0 grams of soil (at
10 percent moisture), and compacting with 60 blows of a
Proctor hammer. After trimming, this resulted in a
sample with dry density of approximately 117 pcf. The
sample was placed in the consolidometer, a seating load
24


was applied, and the loading arm was leveled. Following
consolidation under a 1000 psf load, the sample was
inundated. Five 1-D swell tests were performed; four
maintaining volume constant within 0.025 percent, and one
under constant pressure. Consolidation tests were
initially performed on a steel sample so that the volume
change in the test equipment could be separated from that
of the sample. Side shear between the soil and the
cutting ring may have reduced the normal load felt by the
soil, however it is not accounted for in standard
practice. The results of four of the swell tests are
displayed as Figure 4; a test with initial dry density
much lower than the target is not shown. A moderate
swell potential with a clear relationship to dry unit
weight is defined. Swell pressures of 2, 5, and 10 ksf
will be used in the numerical modeling series.
Initially, two constant volume swell tests were
conducted. The results of these tests indicated a swell
pressure substantially less than that obtained by Colby.
Part of the difference was attributed to a lower dry
density. A second set of tests was conducted at a dry
density closer to that used by Colby. These tests also
resulted in a swell pressure less than that obtained by
Colby. As all aspects of sample preparation and test
execution closely matched those used by Colby, it was
25


Figure 4: Results of 1-D Swell Tests
26


ui.>
Figure 1: Uplifting and Withholding Forces Acting on Pier in Expansive Soil
6


withholding force may be defined as the sum of
thepressure applied to the top of the pier plus the
withholding force due to skin friction acting around the
circumference of the stable soil portion of the pier.
While the pressure is known, the skin friction is not;
however, much work has been done to predict its
distribution.
Much of the research done on skin friction, and more
precisely its distribution, has been carried out under
consolidating rather than swelling soil conditions.
However, it has been shown that whether pushing or
pulling the piles, very similar results are obtained
[2,16] .
Fellenius and Broms [9] conducted studies on precast
concrete piles driven through clay, silt, and sand. In
the initial phase of their studies no external load was
placed on the piles. Thus the only loading was that
caused by the consolidation of the clay layer. It was
found that over a five month period the load at the
bottom of the clay layer increased from the weight of the
pile above it to over 260 psf. This corresponds to an
additional load of about 30 tons at that point. Below
the clay layer, however, the skin friction switched from
negative to positive through the silt and clay. This
prevented the piles from settling as much as they would
7


have if they had been founded in the clay alone. The
skin friction was shown to be caused by the remolding of
the clay around the piles and subsequent reconsolidation.
It was shown that even though settlements were small,
large values for skin friction were obtained.
Keenan and Bozozuk [13] conducted tests on a group
of three closed tip, steel piles in a compressible silt
over six and a half years. It was found that although
the piles were placed at a distance of only four pile
diameters from each other, each pile acted as an
individual, there was no group effect. It was also found
that the downdrag load due to consolidation and skin
friction reached a maximum at a certain point, and then
tapered off to positive skin friction. This was also
found by Endo et al. [8] in their study on four different
types of steel pipe piles in clay. This point is termed
the neutral point and is defined as the point at which
the axial stress is a maximum. The axial stress was
shown to be approximately symmetrical about the neutral
point, which is located approximately three quarters of
the way down the pile, regardless of how the end was
supported.
8


2.3 Analysis of Swell Potential
2.3.1 Molecular Structure
The swell potential of a soil is a function of its
molecular structure which influences its specific surface
and affinity for water. All clays are made up of
crystals which are smaller than 1 micrometer. There are
two fundamental crystal sheets, tetrahedral (silica) and
octahedral (alumina). Clays are made by stacking these
sheets in different arrangements. Kaolinite is composed
of alternating silica and alumina sheets. Hydrogen bonds
hold the sheet together tightly, giving kaolinite a low
affinity for water and making it one of the most stable
clay minerals. Montmorillonite is made of repeating
layers of silica-alumina-silica sheets, with van der
Waal's forces acting between the silica sheets. Van der
Waal's forces are much weaker than hydrogen bonds,
consequently montmorillonite has a much higher affinity
for water. Illite has a structure similar to
montmorillonite, however a potassium atom bonds the
silica sheets together more tightly than the van der
Waals forces. The stronger bond results in a lower
attraction for water.
The specific surface of a mineral is defined as the
ratio of surface area to volume. Montmorillonite is a
9


much more platy- shaped mineral than illite or kaolinite,
giving it a greater specific surface. As specific
surface increases, a certain amount of water covers more
surface area. Therefore, more montmorillonite sheets get
covered with water than other clay minerals. This
greater amount of available water, combined with the
strong affinity for water, gives montmorillonite its high
swell potential.
2.3.2 Laboratory Measurement of Swell Potential
The one-dimensional consolidometer is typically used
to obtain laboratory measurements of swell potential. A
one-half inch high, two and one half inch diameter disk
of soil, undisturbed or remolded, is subjected to a
consolidation load equivalent to that expected in the
field, and inundated. Two avenues can then be followed,
constant volume or constant pressure. To perform the
constant volume test, the axial pressure on the sample is
increased at a rate which maintains the sample very
nearly at its initial height. The swell potential is
then the pressure at which swelling ceases. During the
constant pressure, or unrestrained, or free swell, test
no additional pressure is applied until swelling has
completed. The pressure required to then return the
sample to its initial height is considered to be the
10


swell pressure.
2.4 Analysis of Skin Friction
2.4.1 Mechanics of Skin Friction
Laboratory measurement of skin friction, and
subsequent correlation to field applications is not an
easy process. Interface friction reduces as the
relationship of the bodies changes from stationary
(static), to sliding (dynamic), to rolling. Friction is
comprised of two natures; mechanical and chemical. The
mechanical aspect of friction lies in the fact that the
roughnesses, or asperities, of the surfaces must either
deform or break as they grind against the opposing
surface. The chemical composition of the surfaces
dictates the degree to which surface adhesion enhances
friction. The laboratory measurement of friction is
affected by machine stiffness, available displacement,
and surface roughness. The correlation of lab
measurement to field application implicitly includes
potentially detrimental effects of scale. Given the
daunting task of relating- laboratory measurements to
field applications, an understanding of the mechanics
involved is required.
When two bodies are in contact, there exists an
11


apparent area of contact and a real area of contact. The
apparent area (A,) is defined by the dimensions of the
outer limits of contact between the objects. In the case
of the soil/pile interface, the apparent area is
calculated as:
A, = 2tt d 1,
where d = pile diameter,
ls= length of pile in contact
with expansive soil.
The real area of contact includes only those regions
where the bodies are actually contacting each other.
Determination of the real area is difficult, but it is
proportional to the normal force acting on the surfaces
and much less than the apparent area of contact. The
junction of the two surfaces in the real area takes one
of three categories: mated and correlated, unmated and
correlated, or unmated and uncorrelated (Fig. 2). The
a)
b)
c)
Figure 2: Junction of Two Surfaces, a) mated and
correlated, b) unmated and correlated, and c) unmated and
uncorrelated
12


pile/soil interface is of the third category, while
failure of the surrounding soil is of the first or
second.
Many factors affect friction between two surfaces.
Friction can be decreased by increasing pore pressure
between the surfaces or lubrication lowering adhesion.
The temperature of the surfaces affects the brittleness
or ductility of the materials, indirectly raising or
lowering friction. The amount of gouge between the
surfaces can either increase or decrease friction,
depending on the nature of the gouge. The longer the
surfaces are stationary the higher the static friction
will be due to creep-induced increase in real area,
asperity indentation, gouge compaction, displacement of
lubricants, chemical processes, and/or ionic bonding.
Upon initiation of sliding, asperities fracture, plow,
indent, and possibly melt due to increased temperature.
To properly simulate field conditions, a laboratory test
must be of adequate size and design to allow activation
of these factors.
2.4.2 Field Determination of Skin Friction
Many different methods have been proposed to
determine the magnitude of skin friction between a pile
and its surrounding material. It has been theorized that
13


both drained and undrained conditions should be
incorporated in the solution. Proposed solutions have
ranged from very simple to very complex. Despite the
vast range, a few types of solutions have been more
widely accepted. Most of these incorporate effective
stress, and will be herein examined more closely.
2.4.2.1 Effective Stress Method
Many authors have proposed defining skin friction as
some sort of ratio of the effective stress. Burland [5]
proposed a straight ratio with a single coefficient, B.
Others have proposed incorporating undrained shear
strength, earth pressure, effective friction angle and
other soil properties. Kraft et al. [14] reported on the
comparative performance of six different methods.
Flaate and Seines [10] undertook a study of skin
friction acting on driven piles. Driven piles in
Norwegian soft to medium clays were studied, and an
attempt was made to correlate observed side friction with
results from readily available laboratory testing.
Because average side friction may be determined by the
bearing capacity minus the total point resistance, it was
necessary to be able to determine bearing capacity in a
consistent manner. This was done by attributing a time
factor to the percentage of ultimate bearing capacity,
14


thus an average value for the side friction over the
entire pile could be found. A more precise method,
however, was desired. It was observed that pile driving
creates a disturbed zone around the pile with increased
horizontal stresses and excess pore water pressures. As
these dissipate, even a normally consolidated clay will
become overconsolidated due to long term creep. Thus a
drained condition occurs and instead of using an
undrained method of analysis, an effective stress method
was determined to be more accurate.
Bjerrum [4] proposed defining the skin friction as:
f, = Mt [ ( where /nt = coefficient for time rate
effects,
ah'= effective horizontal stress,
Dm = mobilization factor for frictional
resistance,
ae'= equivalent consolidation pressure.
This can be derived into a more useful form by first
assuming that the original ground stresses are restored
in the soil, that the equivalent consolidation pressure
is near the maximum pore pressure set up due to the
driving, and that the coefficient of mobilized friction
(Dm) depends on the pile length (L). This leads to:
15


f. = Ml Mt [ (K av' tg#e) + x(K + av' + 5 su) ]
where /xL = a function of pile length
K = earth pressure coefficient.
However, this equation stills fails to incorporate
typical laboratory testing results. It must therefore
further be assumed that the parameters K0 tg$, K0, and x
are related to plasticity index (PI). A further
simplification to this equation can be made by expressing
K for overconsolidated clays in terms of K0, for normally
consolidated clays, multiplied by the square root of the
overconsolidation ratio (OCR). Also, x is reduced thirty
percent due to time rate effects. This yields:
f, = Ml [( (0.3 0.001) PI VOCR ffv') + (0.008 PI su) ]
This expresses skin friction in terms of soil parameters
readily available from laboratory testing. However, it
may further be simplified by using an su / cr0'
relationship, assuming the values increase with a higher
plasticity index.
fs = Ml ( 0.3 0.5 ) VOCR CTV'
The pile length parameter Ml has been found to be
approximately:
Ml = (L+20) / (2L + 20)
Thus, the formula for skin friction given above is
applicable for both normally and overconsolidated clays,
16


and is apparently independent of pile material. The
results computed with this method were compared with
observed results from forty-four test piles in varying
conditions and found to be in good agreement.
2.4.2.2 Other Methods
As mentioned previously, many other methods have
been presented to determine the magnitude of skin
friction. In addition to other effective stress methods,
analyses including undrained shear strength and
elasticity have been proposed.
In their analysis of several effective stress
methods Kraft et al. [14] came to the following
conclusions by using regression analysis. For normally
consolidated clays, the X and 6 methods provided slightly
better results than the a method, while for
overconsolidated soils the a and X methods provided
reasonable correlation. However, their primary interest
was deep piles for off-shore oil platforms, therefore,
the results may not be as applicable for more common
geotechnical engineering practices.
A direct correlation with undrained shear strength
(su) has also been proposed by several authors. This is
based on the idea that the skin friction between cohesive
17


soils and the pile shaft cannot exceed the cohesion of
the soil. The cohesion of the soil is assumed to be
equal to the undrained shear strength. The formula is
typically as follows:
f, = a su
However, the same forty-four piles analyzed by Flaate and
Seines fared much more poorly using this method.
It has also been proposed [16] to use an analysis
based on elastic theory. It was believed that instead of
assuming slippage along the entire shaft, there would be
no slippage at the pile-soil interface. This method,
however, is actually used to calculate tension in a pile
directly, and not skin friction. Once a solution is
reached, limiting shear stresses may be incorporated to
accommodate pile-soil slippage.
Finally, Anderson et al. [1] proposed a method for
predicting shaft adhesion for both drilled and driven
piles in both normally and overconsolidated clays. It
was concluded that shaft adhesion could be expressed in
terms of effective vertical stress (av'), an earth
pressure coefficient (K,) and the drained residual angle
of shearing of the clay (S) as found in a laboratory ring
shear test:
a, = Ks crv' tanS
18


It was also concluded that the horizontal effective
stress lost during drilling was fully recovered with
time.
With such a wide ranging variety of methods
available, it should be possible to determine the most
applicable to a given situation. It should also be noted
that further research is needed to establish the validity
of some of these formulas in expanding rather than
consolidating soils.
2.4.3 Design of Piles for Reduction of Skin Friction
One of the most notable differences between
consolidating and swelling soils is the relative amount
of ease with which the skin friction can be reduced.
Bjerrum et al. [3] conducted extensive studies on
the reduction of skin friction in shrinking soils through
the use of enlarged pile tips and surface coatings. It
was found that if the coating remained intact, down drag
due to skin friction could be almost totally eliminated.
Electro-osmosis was also used, but with less reduction of
down drag. The conditions for electro-osmosis, a clayey
soil, were favorable.
Begemann [2] also worked with consolidating soils.
The project was a large dock for mammoth tankers. The
dock was to be supported by wide flange beam piles, which
19


would be subjected to repeated cycles of pulling and
driving. It was found that by overstressing the piles
the skin friction could be reduced by one-third.
A number of ideas have been proposed for the
swelling soil problem. It would be ideal if a void could
be formed between the pile and the soil such that there
would be no surficial contact whatsoever. However, were
this the case, water could easily flow down around the
pile to its base, thereby greatly increasing the length
of the zone of wetting and possibly causing the pile to
heave at its base. This would also greatly reduce the
load carrying capacity of the pile and little lateral
resistance would be available.
A belled pier could be used with a void around it,
and under ideal circumstances this would work, but the
additional cost of belled piers often makes them less
attractive.
Another interesting concept designed to deal with
swelling soils comes from San Antonio, Texas, where
highly expansive clays are found. A belled pier is
drilled through the unstable zone and well into stable
material. The pile consists of core concrete surrounded
by a mastic-coated pipe, which in turn is surrounded by
an annulus of concrete. When the unstable zone swells
horizontally and "squeezes" the pile and heaves
20


vertically, the outer annulus of concrete breaks in
tension, leaving a coated surface and the inner core
carrying the load. This is an excellent idea assuming
the pier can be sunk deep enough into stable material and
is not economically prohibitive.
21


3. Laboratory Soil Characterization
Laboratory tests, including 1-D swell, Atterberg
limits, and triaxial compression, were performed to
provide the strength and swelling properties of an
expansive soil as input for the numerical modeling. The
laboratory tests were performed at a dry density of
approximately 117 pcf, and a moisture content of
approximately 10 percent. These values were determined
by Colby [7] to simulate a highly compacted soil at a
moisture content near in situ conditions.
3.1 Soil Used
The soil used for the study was obtained from a
claystone bedrock (clay shale) in the Roxborough Village
Subdivision, Douglas County, Colorado, by Colby for his
research [7]. The material was reduced to minus #4 size
(less than 4.75 mm diameter) and stored in a sealed
bucket. The results of index property tests performed by
Colby are shown in Table 1. A change in the physical
properties of the soil was not expected, so none of the
index properties tests were performed at the initiation
of this study. The initial tests performed were the 1-D
swell tests.
22


Table 1
Results of Index Property Tests
Performed bv Colbv r 71
Test Results
Max. Dry Density (ASTM D698) 98.5 pcf
Max. Dry Density (ASTM D1557) 112.0 pcf
Optimum Moisture Content (ASTM D698) 22.8%
Optimum Moisture Content (ASTM D1557) 15.5%
Liquid Limit 68
Plasticity Index 49
Specific Gravity 2.76
Percent Passing No. 8 Sieve 100
Percent Passing No. 200 Sieve 98
Percent Finer than 5(i 73
Percent Finer than 2/i 60
USCS Designation CH
AASHTO Designation A-7-6 (54)
Activity (PI/% 2/z) 0.82
23


decided to perform Atterberg limits tests in an attempt
to determine whether the physical characteristics of the
soil had changed.
3.3 Atterberg Limits
Eight Atterberg limit tests were performed according
to ASTM 4318. Two tests were conducted initially, which
resulted in a plasticity index 17 points lower than that
obtained by Colby (PI = 32 vs. 59). Portions for six
additional tests were subsequently quartered from the
soil and sent to a soils testing laboratory. The average
plasticity index obtained for these tests split the
results obtained from the two prior sets of tests (avg.
PI = 40). The difference in plasticity index remains a
question; however, the parameters obtained from the
laboratory tests for the numerical models are assumed to
be valid for a typical expansive soil.
3.4 Triaxial Compression
It has been said that the study of geotechnical
engineering is solely comprised of three divisions each
starting with the letter !s'; seepage, swell (or
settlement), and strength. The scope of the triaxial
test deals with the last of those three, and more
specifically with the measurement of shear strength
27


parameters in terms of total and effective stresses.
This is done by applying a confining pressure all around
the sample, and maintaining it while increasing the axial
load until the sample fails. The theory behind this will
be discussed in general terms.
When a force acts on a body, it can be divided into
the sum of three forces acting in the x, y, and z
directions. The strongest of these three is termed the
major principal stress, ax. The weakest is termed the
minor principal stress, cr3, and the middle termed the
intermediate principal stress, a2. These three stresses
are mutually orthogonal and the planes in which they act
are termed principal planes. There are no shear stresses
on the principal planes.
In a triaxial test, the cylindrical specimen is
initially loaded with pressurized water surrounding it.
This pressure is denoted ct3 (=a2) and termed the cell
pressure. The axial and radial stresses are equal, so
there is no shear stress induced in the sample. At this
point the sample may or may not be allowed to
consolidate. When the test begins, a vertical load is
applied from outside the cell. This load may then be
divided by the corrected cross-sectional area and termed
the deviatoric stress. The deviatoric stress is defined
28


as the difference between a, and a3:
= P / Acorr = a, a3
As mentioned, the area used in calculating the deviatoric
stress is a corrected area which is a function of the
initial area and of axial and volumetric strain. Strain
is defined as the change in length or volume divided by
the initial length or volume.
Aco = A0 [ 1 ev ] / [ 1 e. ]
In conducting the test, a cylindrical sample is
placed within a cell. As mentioned, water fills the cell
and is placed under pressure (the cell pressure, a3 ) .
The deviatoric load is applied with a piston which
penetrates the top of the cell. A thin latex membrane
surrounds the sample to keep the cell water from
contacting the sample. Although this membrane is thin,
it can have an effect on the results of the test, and a
correction for its presence can be made if desired. This
correction can be obtained from graphs available in
laboratory manuals.
Strength parameters for the expansive soil were
obtained from a set of three triaxial compression tests.
The tests were performed under confining pressures of 15,
30, and 45 psi to simulate pressures at depths up to 50
feet. Samples were compacted by placing three lifts of
29


soil into a split-cylinder brass mold and compacting with
a carpenter's hammer and brass tamper. This resulted in
a two-inch diameter, four-inch high sample with dry
density of 117 pcf, and a moisture content of 10 percent.
Drained tests were selected to simulate field conditions;
however, drained tests dictate complete saturation, which
would have required many days to accomplish. It was,
therefore, decided to perform pseudo-drained tests by
allowing the sample to saturate and consolidate for 24
hours, then conducting the tests at very low strain
rates. By deforming the sample very slowly, no excess
pore pressure was developed, simulating a drained
condition. The desired end result of the triaxial shear
test is the shear strength of the soil. The link between
the normal stresses obtained with the triaxial test and
the desired shear stresses is the Mohr-Coulomb equation:
t = c + a tan $
The major and minor principal stresses at failure are
plotted along the x-axis and connected as two points
along the diameter of a circle, with the y-axis being
shear stress. Thus with procedures common to the use of
Mohr's circle, the shear -stress at failure can be
obtained. The triaxial compression tests conducted in
this manner resulted in an angle of internal friction of
23.3 degrees, and a value of 27 psi for cohesion, as
30


Shear Stress, psi
shown in Figure 5. These values were used in defining
the physical properties of the expansive soil in the
numerical models.
Figure 5: Results of Triaxial Compression Tests
31


4. Laboratory Determination of Coefficient of Friction
The coefficient of friction between the expansive
soil and pile material was determined for the numerical
modeling by using the direct shear apparatus (Fig. 6) to
Figure 6: Direct Shear Apparatus used to Determine
Interface Friction between Soil and Pier Material
fail a composite of two materials. The first material,
the lower half in the shear box, was pile material, steel
or concrete, the second, upper half, was soil. The soil
was prepared by placing the cutting square in the bottom
of a Proctor mold, adding 400 grams of soil at 10 percent
moisture content, and compacting with 60 blows of a
Proctor hammer. A dry density of approximately 117 pcf
32


was obtained. The concrete sample was fabricated of
approximately one part fine coal aggregate, two parts
water, and four parts cement. The use of fine coal as
the aggregate lowered the density of the sample, however
should not have significantly affected the frictional
characteristics. The roughness of the pile could have
been simulated with either a random surface, or a non-
random, grooved surface. The grooved surface was chosen
as it was quantifiable. The grooves were one-sixteenth
inch wide by one-sixteenth inch deep, on one-quarter inch
centers (Fig. 7). Three tests were conducted on each
pile sample, one parallel to the grooves, one
perpendicular to the grooves, and one on the side without
grooves.
Figure 7: Pier Material Sample used in Direct
Shear/Interface Friction Tests; Grooved Side Displayed
33


The composite samples were placed under a
consolidating load of 14,314 psf and inundated. This
load was applied as it simulates the swell pressure
developed by the expansive soil acting normal to the
pile. As with the 1-D swell tests, side shear between
the cutting ring and the soil was not accounted for.
After the samples had consolidated, shearing was
initiated at a rate of 10.37 mm per day. A slow strain
rate was used to simulate in situ vertical expansion of
the soil. Horizontal and vertical movements of the
apparatus, and displacement of the proving ring were
monitored with linearly-variable differential
transformers (LVDT's). The coefficient of friction (/i)
was calculated to be the lateral force (S) at which the
composite sample failed, divided by the consolidating
load (acting as the normal force (N) on the sample):
The smooth pier samples failed at the pile material:soil
interface; while the grooved samples sheared the soil,
leaving soil filling the grooves at the completion of the
tests.
The results of the tests are shown in Table 2. The
34


Table 2
Coefficient of Static Friction.
Determined with Direct Shear Test.
Cohesion (3888 psf subtracted from Sliding Force
MATERIAL Groove Orientation Normal Force (psf) Sliding Force (psf)
STEEL None 14,314 3,674 0.257
Parallel II 1,593 0.111
Perpen. II 1,765 0.123

CONCRETE None 14,314 10,830 0.757
Parallel II 7,510 0.525
Perpen. 1 4,271 0.298
35


sliding force was calculated by subtracting the value of
cohesion determined in the triaxial compression tests
from the shear force at which the sample failed. This
calculation gave the true sliding force, which was then
divided by the applied normal force to determine the
coefficient of static friction. The friction angle can
be known by calculating the inverse tangent of the
coefficient of static friction:
$ = tan'V
Based on the results of these laboratory tests, friction
angles between the expansive soil and the pier of 10, 20
and 30 degrees were used in the numerical models.
36


5. Simulation of Pier Uplift with Numerical Modeling
5.1 Design of Numerical Modeling
5.1.1 Selection of Modeling Code
An appropriate modeling code was required for the
numerical simulation of pier uplift. Requirements for
the code included: appropriate failure criterion for soil
mechanics, interface capabilities, and large displacement
capabilities. Based on these requirements, the explicit
finite difference code FLAC, developed by the Itasca
Consulting Group [11], was selected. With the
capabilities of FLAC, an improvement could be made on
existing closed-form, theoretical solutions.
The requirement of failure criterion suitable for
soil mechanics is self evident. Many numerical modeling
codes exist for structural or mechanical engineering, and
these often include Mohr-Coulomb failure criteria. These
codes are not, however, tailored for the specific
conditions encountered in soil mechanics, including high
plastic deformations.
The ability to simulate an interface within the
numerical model was also a requirement in the selection
of the code to be used. Recently, several finite element
codes have been marketed which allow a null zone to be
37


placed within the model, simulating an interface. These
codes, though, do not allow the parameters of cohesion,
friction, shear stiffness, and normal stiffness to be
specified for the model. FLAC allows these parameters to
be specified.
Large displacements were also desired as a feature
of the code as the modeling scheme included piers with
high displacements, simulating failure. Finite element
codes require matrix inversion which may become unstable
with large displacements, especially large displacements
in only one portion of the model. The finite difference
method calculates small, discrete time-steps instead of
implicitly solving for a static solution. This requires
greater amounts of computation, however uses less memory
and allows for large displacements within the model.
5.1.2 Description of Modeled Parameters
The models were set up to calculate displacement of
the pier head as a function of six independent
parameters. The parameters and the values used are
listed in Table 3.
5.1.3 Description of Model
The initial step in the modeling process was to
define the pier size, number of soil layers, and physical
38


Table 3
Modeled Parameters
Parameter Values
Depth to Center of Expansive Layer 5, 9, 13 feet
Thickness of Expansive Layer 2, 4, 6 feet
Structural Load Applied to Pier Head 3, 6.5, 10 ksf
Interface Friction 10, 20, 30 deg.
Cohesion of Interface 3, 4, 5 ksf
Swell Pressure of Soil 2, 5, 10 ksf
39


t
Pier
Figure 8: Pattern used for Numerical Models
40


properties. The model used is displayed as Figure 8, it
can be seen that three soil layers were included in the
model. The pier was assumed to be 16 feet long. The
axis of symmetry through the center of the pier was used
to cut the number of computations in half. The grid was
extended 25 feet laterally from the pier to ensure no
stress change occurred at the far edge of the model due
to the pier. The element sizes were kept constant in the
vertical direction, but successively increased by 1.5
times their width away from the pier. Four feet of soil
were placed beneath the pier. The physical properties of
the concrete and soil are listed in Table 4, and were
determined by the lab testing and literature. The
pier/soil model is in fact axisymmetric, however, this
was not available. Plane stress was available, and would
have been suitable for the pier, but not the soil mass.
The default of plane strain was used. The interface
between the pier and soil was assigned normal stiffness
and shear stiffness of 106 lbs/ft. The interface friction
along the length of the pier, and the cohesion of the
expansive layer, were varied according to Table 3.
The model was supported and loaded to simulate in
situ conditions as closely as possible. Roller supports
placed on the sides of the model allowed only upward
41


Table 4
Material Properties used in Numerical Models
Material Density (slugs/ft3) Shear Mod. (psf) Bulk Mod. (psf) Friction Cohesion (psf)
Concrete 4.5 248e6 282e6 N/A N/A
Upper Soil 3.42 3.88e5 7.94e5 20 3500
Expansive Soil 3.63 9.72e5 1.70e6 23.3 3888
Lower Soil 3.88 2.03e6 3.09e6 26 4500
42


movement of the pier and soil. The bottom of the model
was pinned. After application of the structural load to
the pier head, the model was allowed to equilibrate under
gravity loading. Equilibrium was assumed when both the
unbalanced force of the model and the y-velocity of the
pier approached zero, and the y-displacement of the pier
was constant. Following equilibration under gravity
loading, the simulated swelling load was applied.
Because no known codes exist which allow the
elements of the model to expand, and no constitutive
relationship for expansive soils has been established,
the expansive load had to be simulated. Initially, the
swelling load was applied by placing the expansive layer
in compression, then allowing it to expand. This nicely
simulated the expansion due to moisture increase,
however, did not allow significant displacement to occur.
Displacements of less than 10^ feet dissipated all of the
simulated expansive load. Subsequently, loading was
simulated by applying forces in the x- and y-directions.
The magnitudes of the forces were derived from Boussinesq
theory for point loads in linear elastic half-spaces
[15]. It was theorized that if the stress felt
throughout an unloaded half-space due to a point load
behaved as shown in Figure 9, then the stress felt at a
43


Figure 9: Stress in Unloaded Half Space due to Point Load
point due to a loaded half-space would behave similarly.
In other words, a load of 10,000 psf, for example, would
be felt fully adjacent to the load; however, only 2000
psf would be felt at a distance of approximately 2.5
radii. The horizontal swell pressures were assumed to be
equal to the vertical swell pressures. Therefore, forces
were placed at nodes according to Figure 10.
5.1.4 Description of Failure Criteria
A Mohr-Coulomb plastic failure criterion was used
for the soil mass, while an elastic, isotropic failure
was used for the pier. For the soil mass, the elastic
stresses are calculated then converted to principal
44


Figure 10: Example of Forces Applied to Simulate Swell Pressures
45


stresses and substituted into the yield surface equation:
/ = i
t 2C(i"sip)l
i sin<|> 1 sin
where C = cohesion
$ = friction angle
If f was greater than 0.0, no corrections were made,
was less than 0.0, plastic corrections are made such
conformity to the yield surface is maintained. The
pier was modeled with an elastic, isotropic failure
criterion which follows Hooke's Law in plane strain.
Stresses were calculated from strains as:
Ao = (A>|o)Aen + (K-^G)&ta
Aon = (AT-|c?)Ae11 + (ATt^Ae^
A Oj2 = Ao21 = 2GAe12
where K = bulk modulus
G = shear modulus
if f
that
46


and the incremental strain tensor is defined as:
1 du, du,
Ae = (- +-)Af
* 2 Sr/
where
u = displacement rate
At = time step [11].
5.2 Formulation of Functional Relation
5.2.1 Description of Relation
Analysis of the modeling results yielded the
equation:
.0.357S rl.61
Y =
2)1.17 £0.831 y0.760 £i.ei
where
Y = vertical displacement of pier head
(ft.),
S = swell pressure of expansive soil
(ksf),
T = thickness of expansive soil (ft.),
D = depth to center of expansive soil
(ft.),
L = structural load applied to pier head
47


(ksf),
f, = interface friction between pier and
soil, and
C = cohesion of expansive soil (ksf).
The degree of fit is given by the square of correlation
coefficient, r2 = 0.958. An r2 of 1.0 is indicative of a
perfect fit between the observed data and the results
predicted by the equation. The results obtained for the
modeling indicate a high degree of correlation. A graph
of the predicted versus calculated values is shown as
Figure 11.
5.2.2 Development of Relation
Simple regression was performed initially to
determine basic relationships between displacement and
each of the six independent variables. Regressions were
performed using linear, multiplicative, exponential, and
reciprocal models. From these initial results, it was
determined that the highest correlations were achieved
with an exponential relationship to swell pressure, a
multiplicative relationship to thickness and cohesion,
and a linear relationship to depth, structural load, and
interface friction.
48


obserued
Figure 11: Predicted versus Calculated Results of Numerical Tests (LOG Scale)
49


Following the simple regression analyses, a multiple
regression analysis was performed. The option of
including a constant in the analysis was rejected, as
that would yield the unrealistic result of a non-zero
displacement when all of the independent variables are
zero. This analysis resulted in a value for r2 of 0.399,
which is indicative of a moderate correlation. In
plotting the predicted versus observed results (Fig. 12)
it was determined that a more suitable fit might be
obtained by performing a multiple regression with the
natural log (log) of displacement as the dependant
variable. This analysis was performed and resulted in an
r2 of 0.920, a substantial improvement.
The results of the simple regression analyses were
then incorporated into the multiple regression analysis
with log displacement as the dependant variable. In
order to maintain the linearity of the depth, structural
load, and interface friction variables, a regression was
performed with the log of these parameters. This
regression resulted in an r2 of 0.954, a further
improvement. The simple regression analysis between
displacement and cohesion indicated a low correlation
regardless of model used; therefore, to maintain
consistency with the first three parameters, a regression
50


observed
Figure 12: Predicted versus Calculated Results of Numerical Tests (Linear Scale)
51


was performed including log cohesion. An r2 of 0.957 was
achieved with this regression. The independent parameter
of swell pressure was left unaltered as the simple
regression analysis indicated a best correlation with log
displacement. The simple regression analysis of the
final independent variable, thickness, indicated a
greatest correlation between displacement and thickness2.
Multiple regression analyses were conducted incorporating
both log thickness and log thickness2; the results were
nearly identical, and in reducing the eguation, identical
results were obtained. The final multiple regression,
therefore, was of the following form:
Dependant variable: log displacement
Independent variables: log depth
log thickness
log structural load
log interface friction
log cohesion
swell pressure.
This analysis resulted in an r2 of 0.958, and an equation
as follows:
j Y = ____________(0.3575) (1.611og7)_______
8 (1.171ogD) (0.8311ogL) (0.7601ogjx) (1.611ogC)
52


This equation can be reduced by taking the exponential
function of both sides, resulting in:
y = ____________(e 0.3575) (e1.61log^_________
^ff1.171ogD) ^0.831k>gl) ^0.760k>gji) ^1.611ogC)
which simplifies to the final equation of:
.0.357s
Y =
£)1.17 £0.831 y0.760 ^,1.61
If the multiple regression had included log thickness2,
instead of log thickness, the regression would have
yielded e2*0806108 T, which is equivalent to e161logT. Figures
11 and 12 display the observed results versus the
predicted results in both linear (Fig. 12) and log:log
space( Fig. 11). In linear space the results and the
best fit line are non-linear; while in log:log space they
are linear.
5.3 Statistical Analysis
A discussion of the multiple regression results will
provide greater insight into the results obtained. By
interpreting the analysis of variance, residuals,
53


probability plot, component effects plots, and confidence
interval, a more complete understanding will be achieved.
The analysis of variance (Table 5) provides
information on the amount of variability of both the
independent variable and the predicted result. The r2
value is a measure of how closely the observed values
match the regression line. An r2 of one is a perfect fit;
the r2 of 0.958 achieved for this model is very good. The
standard error of the estimate indicates the amount of
unexplained variability in the dependant variable; which
for this model is log 0.949, equal to 0.0523 ft. The
mean absolute error is the average error which can be
expected in a prediction. For this model, the mean
absolute error is log 0.740, equal to 0.301 feet. The
amount of useful input contributed by each independent
variable is inversely proportional to its significance
level. Each independent variable in the model has a
significance level of 0.00, indicating that each
independent variable is significantly contributing to the
regression.
54


Table 5
Analysis of Variance Results
Independent Variable Coefficient Standard error t-value Significance level
LOG Depth -1.167377 0.079276 -14.7255 0.0000
LOG Thick 1.612627 0.075177 21.4510 0.0000
Swell 0.356919 0.010538 33.8694 0.0000
LOG f, -0.760208 0.064928 -11.7085 0.0000
LOG Cohesion -1.611146 0.139577 -11.5430 0.0000
LOG SLoad -0.830706 0.067295 -12.3443 0.0000

Standard Error 0.949159
Mean Absolute Error 0.740498
R-squared 0.958253
R-squared (Adjusted for degrees of freedom) 0.957964
55


The plot of the residuals (Fig. 13) displays the
difference between the predicted value and the observed
value for each test. The cumulative sum of these
residuals is always equal to zero, and they should be
randomly scattered about the zero line. The residuals
are not randomly scattered about zero for the tests with
very little displacement (less than e^^l.Se'3 ft.),
indicating that the regression is not as accurate for
these tests.
The normal probability plot (Fig. 14) charts the
residuals versus a normal probability scale. It is an
indicator that the data input to the model are normally
distributed, i.e. that they follow a normal Gaussian
distribution. The residuals of this regression model
follow the line very closely, indicating normal
distribution.
The degree of dependance between variables is given
in the correlation matrix (Table 6). Displacement is
most dependant on swell pressure and thickness of the
expansive layer, and less dependant on depth of the
layer, structural load applied to the pier, interface
friction, and cohesion between the soil and the pier. It
can also be seen that none of theindependent variables
are highly interdependent.
56


Residuals
4.4
2.4
0.4
-1.6 -
-3.6
V
i % m m m 'ft $ I*.. 1 *r. V t \ ,1 i d f'< i % V S 1 a" VB*.
>d s. §:** a > V>. hr.?:----' a a r /;. .
w w 'i 1 a *
* 1
1 1 1
_L
-8.3
-6.3
-4.3 -2.3
Predicted
-0.3
1.7
Figure 13: Residual Plot
57


cunulatiue percent
Figure 14: Normal Probability Plot
58


The 95 percent confidence intervals for the
coefficient estimates are shown as Figure 15. The figure
shows that most of the results fall within the 95 percent
confidence limit. This means that one can claim with 95
percent confidence that the given coefficients accurately
match the test results, and that the coefficient of each
independent variable accurately contributes to the
regression model. These intervals could be expanded by
specifying a higher confidence level, or reduced by
specifying a lower level.
5.4 Discussion of Results
The results of the regression model can be made into
a practical design tool by incorporating into a factor of
safety determination and being compared to other models.
The factor of safety can be used to provide the
design engineer with a tool for determining the potential
of uplift. Factor of safety calculations are obtained by
dividing the ultimate, predicted displacement by the
allowable displacement. If the result is less than 1.0,
the system is unstable and displacements higher than
allowable can be expected. If the result is greater than
1.0, the system is stable and displacements less than
allowable can be expected; the larger the factor of
safety, the less chance of greater than allowable
59


Table 6
Correlation Matrix
LOG Y dis LOG Depth LOG Thick Swell LOG f, LOG Cohesion LOG S Load
LOG Y dis 1.0000 0.4803 -0.6236 -0.7832 0.3992 0.3945 0.4172
LOG Depth 0.4803 1.0000 -0.3888 -0.4182 -0.0805 -0.0916 0.0695
LOG Thick -0.6236 -0.3888 1.0000 0.4704 -0.3660 -0.3668 -0.3164
Swell -0.7832 -0.4182 0.4704 1.0000 -0.3678 -0.3658 -0.3532
LOG f, 0.3992 -0.0805 -0.3660 -0.3678 1.0000 -0.2112 -0.0051
LOG Cohesion 0.3945 -0.0916 -0.3668 -0.3658 -0.2112 1.0000 -0.0126
LOG 8 Load 0.4172 0.0695 -0.3164 -0.3532 -0.0051 -0.0126 1.0000
60


LOG V dis
Figure 15: 95% Confidence Intervals
61


displacements. The equation for the factor of safety is:
stable displacements
allowable uplift
unstable displacements
The results obtained with the regression analysis of
the numerical models can be compared to results obtained
with another model. Sazhin [17] introduced a model for
predicting pier uplift based on the work required from
the frictional forces to move the pier. The equation
proposed for a pier under similar conditions to the
numerical model (i.e. embedded in a non-swelling layer,
has a layer of soil over the swelling layer, and has a
structural load applied) is:
Y = 0.7(1-iU)A j *
where: Y = displacement of pier head (cm)
k = coefficient for pier type
(drilled=0.12 or driven=0.1),
1 = length of pier (m),
A,= rise of ground surface due to
62


swelling layer of thickness = 1,
ffst = frictional force of saturated
swelling soil (MPa),
u = perimeter of cross-section of pier
(m) ,
N = force preventing uplift (kN),
defined as N = P + fstul3
where P = structural load applied to
pier head (kN),
f = standard skin friction of
soil (MPa),
13 = length embedded in stable
soil (m),
s = coefficient for the effect of the top
stable layer (kN/m),
defined as:
s
ffl
where fp* = frictional force of top
stable layer (MPa), and
hp = thickness of top stable
layer (m).
63


By assigning values, incorporating S, T, D, L, f,, and C
of the numerical tests, and making the following
conversions, Sazhin's model can be compared to the
regression model of the numerical tests:
k = 0.12,
1 = 4.9 m,
A, = 0.95,
ffrt = fjS+C,
u = 1.82 m,
N = L+[ (0.65fsS) (1.82) (4.9-D-T/2) ] ,
where f = 0.65f,S and
13 = 4.9-D-T/2 ,
s
= 2
(0.65nS)(D-|)
(0.65(iS)(4.9)
where fp5t = 0.65f,S and
hp = D-T/2.
By converting the resulting displacements to feet, the
same units used for the numerical tests, the results of
the two models can be compared. Figure 16 shows that the
magnitude of displacement is very similar for the two
models; however, Sazhin's model displays a very uniform
64


magnitude of displacement. The fact that the two models
correlate well on displacement magnitude is not proof of
their correctness; however, it is an encouraging
indicator of the validity of the regression model and
approximate predicted magnitudes from either model.
65


Figure 16: Comparison of Displacement Magnitudes (Sazhin black circle; CU-Denver
- white sguare)
66


6. Conclusions and Recommendations for Future Research
Future research must be performed to more clearly
delineate the interaction of a pier and an expansive
soil. The numerical modeling performed in this study is
a step towards greater understanding of pier performance
in expansive soils; however, it does not offer a complete
solution to the problem. Further numerical modeling
could be performed to identify the effects of different
pier and soil properties, different pier lengths and
diameters, and a more accurate constitutive relation for
expansive soils. Further laboratory tests could be
performed to more precisely determine realistic interface
resistance parameters. Laboratory- and field-scale tests
must be conducted with properly instrumented piers placed
in compacted expansive soils to develop a greater
understanding of the stresses and displacements
associated with the system.
A suite of numerical models was completed to
simulate pier uplift due to expansive soil. The finite
difference code, FLAC, was used because of its abilities
to model large displacements and interfaces. The
parameters of structural load, interface friction, and
expansive soil depth, thickness, swell pressure, and
cohesion were varied. Results of laboratory tests were
used as input for physical properties. Multiple
67


regression analysis on the results provided the following
eguation for pier head uplift:
Y =
D117
e0.357S j\.6i
£0.831 y0.760 £,1.61
where Y
S
T
D
L
vertical displacement of pier head (ft.),
swell pressure of expansive soil (ksf),
thickness of expansive soil (ft.),
depth to center of expansive soil (ft.),
structural load applied to pier head
(ksf),
f, = interface friction between pier and soil,
and
C = cohesion of expansive soil (ksf).
The r2 obtained for the equation was 0.958, indicating a
very good fit to the numerical test results. The
displacements predicted by the equation correlated well
with those predicted by a theoretical model.
68


Appendix A
Results of Laboratory Tests
69


Grooves on Steel Sample
70


Figure A2
Results
of Interface Friction Test #2,
Shearing
Parallel
to Grooves
on
Steel Sample
71


Figure A3: Results of Interface Friction Test #3, Shearing Against Smooth Steel
Sample
72


m


Figure A4:
Grooves on
Results of Interface
Concrete Sample
Friction Test #4,
Shearing
Perpindicular
to
74


Concrete Sample
75


Figure A6: Results of Interface Friction Test #6, Shearing Against Smooth Concrete
Sample
76


NO. 340DR-1 DIETZGEN GRAPH PAPER
----------re y id pra wrrn-----
z
0
H f
< ;
CL *
a 9
l
U ?
)
TCAAN^I
Figure A7: Results of Triaxial Compression Test #1, 15
psi Confining Pressure
77


Figure A8: Results of Triaxial Compression Test #2, 30
psi Confining Pressure
78


Figure A9: Results of Triaxial Compression Test #3, 45
psi Confining Pressure
79


References
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80


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81