Performance of Geopier Foundations during
Simulated Seismic Tests at South Temple Bridge
on Interstate 15, Salt Lake City Utah
Interim Report
By
Evert C. Lawton, Ph.D., P.E.
Associate Professor
University of Utah
Department of Civil & Environmental Engineering
122 South Central Campus Drive, Suite 104
Salt Lake City, Utah 84112-0561
June 1999
Report No. UUCVEEN 99-06
FORWARD
The study described in this report was part of a combined program of structural and
geotechnical engineering research that was conducted at the I-15 Bridge over South
Temple site in Salt Lake City, Utah. The primary purposes of the geotechnical research
were to perform full-scale simulated seismic tests on existing bridge bents in which the
behavior of pile foundations supporting the existing bridge, as well as geopier
foundations support the structural reaction frame, were studied. This interim report
describes preliminary results and conclusions obtained to date regarding the performance
of the geopier foundations supporting the structural reaction frame footings. Results and
conclusions determined regarding the existing bridge pile foundations will be presented
in a separate report.
The geotechnical research was funded the Utah Department of Transportation, the
Federal Highway Administration, the National Science Foundation, Geopier Foundation
Company Inc., and the University of Utah. This support is gratefully acknowledged.
i
ACKNOWLEDGMENTS
The author is grateful to Wasatch Constructors for allowing these tests to be conducted.
Without their permission and cooperation, this research could not have been undertaken.
UDOT, FHWA, NSF, Geopier Foundation Company Inc., and the University of Utah
provided funding for this project. ConeTec performed the cone penetration testing at no
cost to the project. Dywidag Systems International USA provided the threaded uplift
bars at their cost.
The UDOT Research Division was critical to the success of this research. In particular,
Mr. Sam Musser and Dr. Steven Bartlett conducted oversight and management duties,
acted as liaisons with personnel from Wasatch Constructors, and provided helpful
suggestions throughout the full-scale testing.
Special thanks go to my colleagues at the University of Utah. Dr. Scott Merry was
instrumental in providing expertise related to the instrumentation and data acquisition.
Mr. Chang- Lin Hsu was the primary student who assisted with the work and was vital to
the project. Other students who worked on the project included Mr. David Plehn, Mr.
Robert Haight, and Mr. Ed Pezeshki. Dr. Chris Pantelides and Dr. Lawrence Reaveley
were responsible for the structural portion of this research. Without the extensive
communication and cooperation shown between the structural and geotechnical
personnel, these tests could not have been conducted in the short amount of time
available.
Woodward-Clyde and Terracon provided significant information regarding the properties
of the soils in the I-15 corridor. This material was especially helpful in understanding the
potential problems at the site.
Geopier Foundation Company NW provided engineering and supervisory personnel at no
cost to the project. Particular thanks are due John Martin Sr., John Martin Jr., and James
Johnson for donating their time to this project.
Many other people also contributed to the project, and their assistance is gratefully
acknowledged.
ii
TABLE OF CONTENTS
TOPIC
PAGE
FORWARD.......................................................................................................................................i
ACKNOWLEDGMENTS................................................................................................................ii
INTRODUCTION ...........................................................................................................................1
PRELIMINARY UPLIFT TESTS ON SINGLE GEOPIERS .........................................................5
FULL-SCALE GEOTECHNICAL SIMULATED SEISMIC TESTS ..........................................10
Induced Vertical Compressive Stresses ...................................................................................11
Footing contact stresses during compressive loading ........................................................11
Distribution of induced vertical stress within geopiers......................................................18
Displacements of Reaction Frame Footings.............................................................................21
Horizontal displacements ...................................................................................................21
Vertical displacements .......................................................................................................31
CONCLUSIONS............................................................................................................................34
REFERENCES...............................................................................................................................36
INTRODUCTION
During May and June of 1998, geotechnical testing was conducted in conjunction with
structural testing on a section of the existing northbound I-15 bridge over South Temple
in Salt Lake City, Utah. The tests were performed after the northbound bridge had been
taken out of service, northbound traffic was diverted to the existing southbound bridge,
and the remainder of the northbound bridge had been demolished (see Figs. 1 and 2).
The section of the bridge that was tested consisted of two bents and the deck and girders
spanning the two bents. Cyclic lateral loads were applied to the bent caps to simulate
seismic shaking during an earthquake.
Three separate tests were conducted. A schematic elevation view of the testing setup is
shown in Fig. 3. The anticipated maximum lateral load to be applied to the bent caps
during testing was 400 kips, as indicated in Fig. 3. During the actual testing a maximum
lateral load of 490 kips was applied. The cyclic lateral loads were applied to the bent
caps using a hydraulic actuator attached to a steel reaction frame. The reaction frame was
founded on two reinforced concrete footings, which were newly constructed for this
research project. Each footing was 24.5 ft long, 8.25 ft wide, and 3.75 ft thick and was
supported by a geopier foundation system consisting of 10 uplift piers (see Fig. 4).
Figure 1. Looking Southward over the Project Site.
1
Figure 2. Looking Northeastward at the Two Bents Tested.
Figure 3. Schematic Representation of Test Setup and Design Loads.
2
8'-3"
4'-3"
2'-0"
2'-0"
2'-0"
REACTION FRAME FOOTING
24'-6"
6'-0"
4'-3"
36 in. dia. Geopier with four
#7 Dywidag bars attached to
1/2" thick, 34" dia. steel uplift
plate (Typical)
2'-0"
4'-3"
6'-0"
Anchor for Reaction Frame
Figure 4. Footing Dimensions and Locations of Geopiers and Frame Supports.
The forces generated by the reaction frame on top of the supporting footings during the
cyclic pushing and pulling on a bent cap are illustrated in Figure 3 for the anticipated
maximum lateral pushing/pulling force of 400 kips on the bent cap. During pushing on
the bent, a 500-kips compressive force was produced on the exterior footing with a 500kips uplift force produced on the interior footing. During pulling the same magnitude of
vertical forces were produced, with uplift on the exterior footing and compression on the
interior footing. The 400 kips horizontal force was carried by the two footings as a unit
because the footings were tied together by the rigid reaction frame. During the tests the
two reaction frame footings were founded on the ground surface, so the resistance to the
lateral loads was produced by shearing along the footing-soil interface, as well as by
pushing of the uplift bars on the geopiers. This horizontal force couple produced an
3
overturning moment on each footing, with a moment arm equal to or greater than the
thickness of the footing.
The first structural test was conducted on May 23, 1998 on the southern bent, which was
in the “as-is” condition. This bent was subjected to gradually increasing cyclic lateral
loads on the cap starting at 40 kips and increasing to 375 kips, which was the maximum
lateral load the bent could carry and hence the bent “failed”. The second structural test
was performed on June 6, 1998 on the northern bent, which had been previously wrapped
with carbon fiber composites around the joints where the three columns intersect the cap.
The purpose of this test was to determine the effectiveness of carbon fiber composites in
providing additional strength and ductility if installed prior to an earthquake. During the
test, this bent was able to carry a maximum lateral load of 490 kips with a substantial
increase in ductility. The third structural test was conducted on June 27, 1998 on the
southern bent. This bent, which was failed in the first test, was wrapped with carbon
fiber composites prior to this testing. The purpose of this test was to determine if carbon
fiber composites can be used to restore a bridge to service once the bents have failed
during an earthquake. In the third test, the wrapped bent was able to carry a maximum
load of 430 kips, which was a substantial increase compared to the unreinforced case.
The wrapped bent was also much more ductile than the unreinforced bent.
An analysis of the piles indicated that the piles might fail laterally during these tests. To
prevent this from occurring during the three structural tests described above, the pile caps
were tied structurally to the reaction frame footings to limit the amount of lateral
movement. Following the second and third structural tests, the lateral bracing systems
were disconnected so that the pile caps and the reaction frame footings would move
without artificial restraint. Geotechnical tests were then conducted in which the bent was
pushed in a cyclic manner similar to that used for the structural tests.
The geopier foundation system is one of the few soil improvement methods that can
safely carry significant lateral and uplift forces. Details on the method of installation of
geopiers and their behavior under compressive and uplift loads can be found in Lawton
and Fox (1994) and Lawton et al. (1994). The method of installation consists of opening
holes in the ground by augering or excavation, and filling the cavities with highly
densified granular material via a specially designed tamper using high energy, low
frequency impact procedures. Where large lateral and uplift capacities are needed, a steel
plate is inserted at the bottom of each hole prior to construction, with threaded steel bars
attached to the plate near its perimeter. The bars are extended past the tops of the
geopiers into a footing and become bonded to the footing when the concrete is placed.
Uplift and passive resistance are mobilized in a geopier when the footing moves, pulling
on the bars, which mobilizes passive (bearing) resistance as the plate at the bottom is
pulled upward. Additional lateral resistance is also generated by the high shearing
resistance along the footing-geopier interfaces at the bearing level, compared to the
shearing resistance provided by the matrix soil, and by uplift bars being pushed into the
geopier material.
4
One of the primary purposes of the geotechnical portions of the tests on the bridge bents
was to verify under full-scale conditions the mechanisms by which geopier foundations
resist lateral, compressive, and uplift loads. Furthermore, it was desired to determine if
geopier foundations can be used successfully to support structures in regions of high
seismic potential. The primary technical discussions in this paper relate to the
performance of the geopier foundations supporting the structural reaction frames during
the two geotechnical tests.
PRELIMINARY UPLIFT TESTS ON SINGLE GEOPIERS
Prior to installing the geopiers used to support the reaction frame foundations, a series of
five uplift tests was conducted on single geopiers of the same nominal diameter (3 ft)
with heights 3, 6, 9, 12, and 15 ft. The primary purposes of these tests were to determine
the influence of height of the geopier on uplift capacity and to verify the uplift capacity of
a 15-ft tall geopier, which was the preliminary design height. The uplift resistance of
each geopier was provided by a 34-in. diameter by 0.5-in. thick A-36 steel plate located
directly beneath the compacted geopier material. Four No. 7 Grade 60 threaded bars
extended through 1 1/16-in. diameter holes near the perimeter of each plates, upward
along the perimeter of the compacted geopier material, and above the top of the geopier.
Each threaded bar was attached to the uplift plate by a nut below the plate and a nut
above the plate. A reaction system consisting of steel beams and short compression-only
geopiers, along with a hydraulic jack, was used to pull upward on the four threaded
reinforcing bars.
The soils at the site consisted primarily of Lake Bonnevile deposits. Most of the soils
within the upper 30 ft were low plasticity silty clays and clayey silts (CL, ML), although
there were some zones of highly plastic clays. Interbedded within these cohesive
materials were layers of sand. Profiles of tip resistance, side resistance, and friction ratio
to a depth of 15 ft obtained from cone penetration tests at the location of the uplift tests
on single geopiers are shown in Fig. 5. These profiles are reasonably typical for the site,
including the location of the foundations for the reaction frame. The upper 6 to 18 in.
consisted of a slightly cohesive clayey silt of low-to-moderate stiffness that at some
locations was highly contaminated with petroleum.
Underlying this was an
approximately 5-ft thick layer of very soft silty clay, which was underlain by a 2 ft thick
layer of sand. The material underlying this upper layer of sand consisted primarily of
moderately stiff silty clays and clayey silts but contained two layers of sand – a very thin
layer at a depth of about 10 ft and a 1.5-ft thick layer at depths from about 12.5 to 14 ft.
The groundwater table was located at depths ranging from about 4 to 7 ft below the
ground surface.
During each test the Dywidag bars were pulled upward at an approximately constant rate
by hand-pumping of the hydraulic jack. With the exception of the 12-ft tall geopier, each
geopier was loaded in uplift until peak failure occurred. Peak failure occurred when the
generated uplift force reached a maximum value and then either remained constant or
decreased with continued pulling on the bars. During the test on the 12-ft tall geopier,
which was the first test conducted, the bottom nut came loose from one of the bars and
5
the bar pulled loose from the plate. The test was stopped at this point and the load was
removed. The loading system was then rearranged so that only two opposite bars were
pulled upward. The test was restarted and continued until it was noticed that one of the
reaction beams was bending significantly. Peak failure had not occurred when the test
was stopped.
Depth below Ground Surface, z (ft)
CPT 9
0
50 100 150 200
0 1 2 3 4 5 6
0.0 0.5 1.0 1.5 2.0 2.5
0
0
0
-5
-5
-5
-10
-10
-10
-15
-15
-15
0
50 100 150 200
Tip Resistance, qc (ksf)
0.0 0.5 1.0 1.5 2.0 2.5
Sleeve Friction, fs (ksf)
0 1 2 3 4 5 6
Friction Ratio, f R (%)
Figure 5. Cone Penetration Test Profiles at
Location of Uplift Tests on Single Geopiers.
During the tests as failure was beginning, approximately circular cracks and radial cracks
began to appear at the ground surface and grew in size as the failure process continued to
occur. The circular cracks represented the base of an inverted, truncated conical failure
zone that began at the perimeter of the uplift plate at the bottom of the geopier and
continued to the ground surface. The relationships of peak pullout force and diameter of
the base of the failure cone versus the height of the geopier are shown in Figures 6 and 7.
The peak pullout force increased from 22 to 175 kips as the height of the geopier
increased from 3 to 15 ft, with a concomitant increase in the average diameter of the base
of the failure cone from 6.0 to 17.3 ft.
6
0
20
200
180
180
160
160
140
140
120
120
100
100
2
4
6
8
10
12
14
16
18
80
80
NOT FAILED
60
60
40
40
20
20
0
0
2
4
6
8
10
12
14
16
18
0
20
Height of Geopier, H (ft)
Figure 6. Peak Pullout Force as a Function of Height
of the Geopier from Uplift Tests on Single Geopiers.
Diameter of Base of Pullout "Cone" (ft)
Peak Pullout Force, T (kips)
200
3
4
5
6
7
8
9
10
11
12
13
14
15
20
20
18
18
16
16
14
14
12
12
10
10
8
8
6
6
4
4
2
2
0
3
4
5
6
7
8
9
10
11
12
13
14
15
Height of Geopier, H (ft)
Figure 7. Diameter of Base of Failure Cone as a Function of
Height of the Geopier from Uplift Tests on Single Geopiers.
7
0
The uplift resistance of a single geopier or a group of geopiers consists of three
components: (1) the shearing resistance of the soil, (2) the effective weight of soil within
the pullout zone, and (3) the self weight of the anchor(s). The effective weight of soil
within the pullout zone for the single 15-ft tall geopier was estimated by assuming that
the shape of the failure zone was the frustum of a right circular cone (see Fig. 8); the
groundwater table was 4 ft below the ground surface; the unit weights of the matrix soil
and geopier above the groundwater table were 95 and 135 pcf respectively; and the
buoyant unit weights of the matrix soil and geopier below the groundwater table were 33
and 75 pcf respectively. The calculated value for the effective weight of the soil and
geopier within the pullout zone was 98 kips. Ignoring the self weight of the anchor,
which was negligible compared to the other components, the estimated uplift capacity
provided by shearing resistance of the soil was 77 kips.
17.3'
15'
MATRIX SOIL
PERIMETER OF PULLOUT ZONE
GEOPIER
3'
VERTICAL CROSS-SECTION
PERIMETER OF PULLOUT ZONE
AT GROUND SURFACE
GEOPIER
3'
17.3'
PLAN VIEW
Figure 8. Schematic Illustration of Assumed
Pullout Zone for Single Geopier
8
Analyses of the group effects on each of the two components of soil resistance were then
performed and group efficiency factors for each component were calculated. The
assumed shape of the group pullout zone is a prismatoid, as illustrated in Fig. 9. The
group efficiency factor for effective weight of the soil within the pullout zone was
calculated as the effective weight of the soil divided by the effective weight of soil for ten
single pullout zones, which yielded a value of 0.46. The group efficiency factor for the
shearing resistance of the soil was calculated as the ratio of the surface area of the group
pullout zone on which the shearing occurred divided by the surface area of ten single
pullout zones, which produced a value of 0.28. The peak uplift capacity for the group of
ten geopiers supporting each reaction frame footing was then calculated as follows:
Tug = n(Egs Tuss + Egw Tusw) ............................................................................................... (1)
Where Tug = peak uplift capacity of the group
n = number of geopiers in the group
Egs = group efficiency factor for shearing resistance of the soil
Egw = group efficiency factor for effective weight of soil and geopiers within
pullout zone
Tuss = peak uplift capacity for a single geopier based on shearing resistance
Tusw = peak uplift capacity for a single geopier based on effective weight
Inserting the appropriate values for the terms in Eq. 1 gives
Tug = 10[(0.28)(77) + (0.46)(98)] = 666 kips
Approximately 32% of the peak uplift capacity is from shearing resistance of the soil
along the surface of the pullout zone, while 68% is from the effective weight of the soil
and geopiers within the pullout zone.
The design uplift force induced on each footing by pushing or pulling on the bent cap was
500 kips. The dead load acting on each footing was about 100 kips, giving a net design
soil uplift force of 400 kips. Thus, the estimated factor of safety for the net design uplift
force was 666 / 400 = 1.7.
9
21.55'
MATRIX SOIL
PERIMETER OF PULLOUT ZONE
GEOPIERS
GEOPIERS
7.25'
VERTICAL CROSS-SECTION THROUGH WIDTH
7.25'
23.50'
37.80'
PERIMETER OF PULLOUT ZONE AT TOP
PERIMETER OF PULLOUT ZONE AT BOTTOM
21.55'
PLAN VIEW
Figure 9. Schematic Illustration of Assumed Pullout
Zone for Group of Geopiers Supporting Footing
FULL-SCALE GEOTECHNICAL SIMULATED SEISMIC TESTS
Procedures used during both geotechnical tests and the results from both tests are similar,
so the discussions in this paper will be restricted to the second geotechnical test. The
loads were applied to the bridge bent by alternately pushing and pulling on the cap in
10
cycles of gradually increasing horizontal displacement. In the second test, the cap was
first pushed then pulled laterally a maximum distance of 1 in. and then this same
displacement pattern was repeated. This procedure was repeated for maximum
displacements of 2 through 8 in. in increments of 1 in. The cap was then pushed a
maximum distance of 9 in. and then pulled back to zero displacement and this pattern was
repeated for a second cycle. This procedure was then used for maximum displacements
of 10, 11, and 12 in. This modified procedure at maximum displaces of 9 in. and higher
was necessitated by limitations on the stroke of the actuator and stretching of the
prestressing strands used to pull back on the cap. The horizontal displacements of the cap
as a function of elapsed time are shown in Fig. 10(a). It is important to note that the
displacement of the bent cap was measured from its original location prior to the start of
the test.
Shown in Fig. 10(b) is the measured lateral force on the bent cap versus elapsed time. It
can be seen that the magnitude of the lateral forces at the same level of displacement for
the pushing and pulling portions of the same cycle were not the same. For example,
during the second push-pull cycle at a maximum displacement of 8 in., the force at the
maximum displacement during the push cycle was 235 kips, while the force at the same
maximum displacement during the pull cycle was 355 kips. These disparities are likely
related to permanent damage done to the superstructure of the bent and during the
structural test and also during the geotechnical test, as well as net movements of the pile
caps during the testing.
INDUCED VERTICAL COMPRESSIVE STRESSES
Footing Contact Stresses during Compressive Loading
A geopier foundation is a composite system consisting of stiff, strong, cylindrical
inclusions within a matrix of weaker, more compressible native soil. A rigid footing
carrying a centric, vertical load will settle uniformly on any stable bearing system. For a
rigid footing settling uniformly on a geopier foundation system, stress-deformation
compatibility dictates that the induced contact stresses on the stiffer geopiers be greater
than the stresses induced on the more compressible matrix soil. Using subgrade reaction
theory (Terzaghi 1955), Lawton et al. (1994) have shown that the following equations
apply for the contact stresses induced by a rigid footing on the supporting geopiers and
matrix soil:
Rs
.................................................................................................... (2)
Ra ( Rs − 1) + 1
∆q g = ∆q ⋅
∆q m = ∆q ⋅
∆q g
1
=
...................................................................................... (3)
R a ( R s − 1) + 1
Rs
where ∆qg = induced contact stress on geopiers
∆qm = induced contact stress on matrix soil
11
∆q = average induced contact stress
Ra = area replacement ratio = Ag / A
Rs = subgrade modulus ratio = k g / km
kg = subgrade modulus of geopiers = ∆qg / S
km = subgrade modulus of matrix soil = ∆qm / S
S = average settlement of the rigid footing
Four pressure plates were placed on top of the geopiers and matrix soil to measure
induced contact stresses during the tests. Three pressure plates were placed on top of
selected geopiers and one pressure plate was placed on top of the matrix soil at the
locations shown in Fig. 11. A photograph showing the pressure plates is provided in Fig.
12 after the forms and the bottom flexural reinforcing steel for the footing had been
placed. The concrete for the footings was poured directly on top of the pressure plates.
Measured stresses for the four pressure plates are shown in Fig. 13 for the first push cycle
at a maximum displacement of 8 in. It is obvious from this figure that the induced
stresses on the geopiers were substantially greater than the induced stresses on the matrix
soil. At the peak of the push cycle, which occurred at an elapsed time of 73.3 min., the
measured induced stresses in the pressure plates on top of the geopiers were 35.4, 26.4,
and 30.0 psi for pressure plates 9, 10, and 11, respectively. The corresponding induced
stress on top of the matrix soil as measured by pressure plate 7 was 0.77 psi. One method
of assessing the reasonableness of these measured stresses was obtained by the following
procedure:
1. One estimate of the total applied vertical force at the peak of the push cycle was
obtained from the measured stresses by assuming the load to be centric and
multiplying the measured stresses by the appropriate contact area. This assumption
results in assumed stresses of 35.4 psi on the two center geopiers, 26.4 psi on the four
intermediate geopiers, and 30.0 psi on the four corner geopiers. Using the nominal
diameter of the geopiers (36 in.) to calculate the contact areas for the geopiers gives
an estimated total force of 302 kips carried by the geopiers. Similarly, assuming the
stress on the matrix soil to be 0.77 psi at all locations and multiplying this stress by
the area of matrix soil (total footing area minus area of ten geopiers) gives an
estimated total force of 15 kips carried by the matrix soil. Thus, the total estimated
force induced on the footing by the pushing is 317 kips using this method.
2. A second estimate was obtained by multiplying the measured lateral force applied to
the bent cap (235.0 kips) by the appropriate multiplication factor of 1.25 obtained
from static analysis of the reaction frame assuming the supports are hinged. This
method gives an estimated vertical force of 294 kips.
3. Comparing the two predicted values shows that method one gives a value 8% greater
than method two. Therefore, it appears that the measured values of induced stress are
reasonable.
12
Lateral Displacement of Bent Cap (in.)
0
20
40
60
80
100
120
Positive (+) is to the east
Negative (-) is to the west
12
10
12
10
8
8
6
6
4
4
2
2
0
0
-2
-2
-4
-4
-6
-6
-8
-8
0
20
40
60
80
100
120
Elapsed Time (min.)
Lateral Force on Bent Cap (kips)
(a)
0
20
40
60
80
100
120
400
400
Positive (+) is push, negative (-) is pull
300
300
200
200
100
100
0
0
-100
-100
-200
-200
-300
-300
-400
-400
0
20
40
60
80
100
120
Elapsed Time (min.)
(b)
Figure 10. (a) Lateral Displacement of Bent Cap and (b) Lateral Force on Bent
Cap versus Elapsed Time During Second Geotechnical Test on June 27, 1998.
13
V2
V3
WESTERN REACTION
FRAME FOOTING
BENT 5
H1
PIC23,24
PP7
PIEZ5
PP9
N
H4
PPs 6, B9, B8, B10, B7
AT DEPTHS OF 3, 6, 9, 12, 15'
PP10
PIEZ6
PP11
V5
STRAIN GAGES ON
TOP FLEXURAL STEEL
Figure 11. Major Instrumentation in and beneath Western Reaction Frame Footing.
14
Figure 12. Photograph Looking Southward at Western Reaction Frame Footing
after Placement of Bottom Flexural Steel. Four Pressure Plates Used to
Measure Contact Stress Can be Seen on the Right Side and Middle of Footing.
Induced Contact Stress, ∆q (psi)
71
40
30
72
73
74
75
PP 9 - Center Geopier
PP 10 - Tweener Geopier
PP 11 - Outer Geopier
PP 7 - Matrix Soil
Average ∆q
40
30
20
20
10
10
0
0
71
72
73
74
75
Elapsed Time (min.)
Figure 13. Measure Induced Contact Stresses on Geopiers and Matrix Soil.
15
A number of actual conditions vary from those assumed above. As will be shown in a
subsequent section, the applied loads were eccentric. There was some significant rotation
of the top of the western footing from east to west, which would result in lower stresses
on the geopiers on the east side of the footing as compared to the measured stresses on
the geopiers on the west side of the footing. In addition, there was some small rotation
from south to north, which would have generated slightly higher stresses on the geopiers
on the northern side of the footing than the comparable geopiers on the southern side.
The actual diameters of the geopiers were somewhat larger than the nominal diameter
owing to pushing of the geopier material laterally into the adjacent matrix soil during
construction of the geopiers. These factors offset each other to some extent with respect
to the estimated vertical load, so that the measured values of stress still appear to be
reasonable.
Stress Concentration Ratio, ∆qg /∆qm
The measured induced stresses yield stress concentration ratios (∆q g/∆qm) of 46, 34, and
39 for pressure plates 9, 10, and 11 compared to pressure plate 7. The stress
concentration ratios versus time are shown in Fig. 14 for the main part of the push cycle.
The values at the beginning and end of the cycle are not shown because they were erratic
owing to inaccuracies in measuring ∆qm at very low stress levels. It can be seen in Fig.
14 that the stress concentration ratios range from approximately 25 to 45.
72.0
72.5
73.0
73.5
74.0
50
50
40
40
30
30
20
20
PP9 to PP7
PP10 to PP7
PP11 to PP7
10
0
72.0
72.5
73.0
10
73.5
0
74.0
Elapsed Time (min.)
Figure 14. Contact Stress Concentration Ratios.
Also shown in Fig. 13 is average induced contact stress versus time. Values of ∆q were
calculated as the applied vertical stresses divided by the area of the footing. To
determine if Eqs. 2 and 3 can be used to provide reasonable estimates of ∆qg and ∆qm,
calculations were performed using the data shown in Fig. 13. The area replacement ratio
16
Stress Concentration Ratio, ∆qg /∆q
is calculated as the area of ten 3-ft diameter geopiers divided by the area of the footing,
which gives Ra = 0.350. If it is assumed that the settlement of the footing at the location
of all four pressure plates was about the same, which is reasonably correct, then the stress
concentration ratios are approximately equal to the subgrade modulus ratio, Rs. Thus, a
reasonable range for Rs is 25 to 45. From Eq. 2 it is found that the calculated values of
∆qg /∆q are not very sensitive to Rs, with ∆qg /∆q varying from 2.65 for Rs = 25 to 2.74
for Rs = 45. Values of ∆qg /∆q determined from the test data are plotted versus time in
Fig. 15 for the main portion of the push cycle (same time range as for stress concentration
ratios in Fig. 14). Although the values of ∆qg /∆q shown in Fig. 15 vary from 1.0 to 3.5,
the variation is much less (2.6 to 3.5) over the time period of 73.0 to 73.7 minutes, which
is also the period for which the values of ∆qg /∆qm are nearly constant for each pressure
plate. The average value of ∆qg /∆q = 2.7 calculated from Eq. 2 is within the range of
measured values (2.6 to 3.5) for the time period for which the data seems most consistent.
Therefore, it appears that Eq. 2 can be used to provide a reasonable estimate of ∆qg if Rs
is known or can be reliably estimated.
72.0
4
72.5
73.0
73.5
74.0
4
3
3
2
2
PP9
PP10
PP11
1
0
72.0
72.5
73.0
73.5
1
0
74.0
Elapsed Time (min.)
Figure 15. Values of ∆qg /∆q Determined from Measured Data.
Estimates of ∆qm /∆q using Eq. 3 are fairly sensitive to the value of Rs, varying from 0.11
to 0.06 for Rs = 25 to 45. Values determined from measured data range from 0.04 to
0.08, with values between 0.07 and 0.08 for the time period 73.0 to 73.7 min. Therefore,
it appears that Eq. 3 can be used to give reasonable estimates of ∆qm. It should be also
noted that since the matrix soil carries so little stress compared to that carried by the
geopiers, the estimate of settlement for a geopier foundation system generally does not
depend significantly on the estimated magnitude of ∆qm.
17
Distribution of Induced Vertical Stress within Geopiers
Within the central geopier of the western footing that had pressure plate PP9 on top, five
additional plates (PP6, PPB9, PPB8, PPB10, PPB7) were placed at depth intervals of 3 ft
within the geopier (at depths of 3, 6, 9, 12, and 15 ft below the top of the geopier, see
Figs. 11 and 16). These pressure plates, along with the plate on top, were located so as to
provide information on the distribution of vertical stress within that geopier.
Unfortunately, PPB7 – which was placed on the top of the uplift plate - was damaged
during installation of the geopier and no data was obtained from this pressure plate. The
other four pressure plates functioned properly throughout the test.
FOOTING
PP9
5 SPA. @ 3' = 15'
PP6
CENTER GEOPIER
PPB9
PPB8
PPB10
PPB7
Figure 16. Locations of Pressure Plates with Depth within Center Geopier.
18
Induced Comp. Vert. Stress, ∆σv (psi)
The measured induced compressive vertical stress for these pressure plates are plotted in
Fig. 17 for the first push-pull cycle at a maximum displacement of the bent cap of 8 in.
During the push cycle, which applied a compressive vertical force to this footing, ∆σv
was greatest at the top of the geopier and decreased with increasing depth within the
geopier. During the pull cycle, uplift forces were induced on the footing and the loads
were transferred to the geopiers by the uplift plates at the bottoms of the geopiers. Thus,
the plates located near the bottom of the geopier had the largest induced compressive
stresses, and the induced stressed decreased with increasing distance above the bottom of
the geopier.
71
72
73
74
75
40
76
77
78
79
∆σ v, PP-9, Top of Geopier
∆σ v, PP-B7, 3' below Top of Geopier
∆σ v, PP-B10, 6' below Top of Geopier
∆σ v, PP-B8, 9' below Top of Geopier
∆σ v, PP-B9, 12' below Top of Geopier
30
80
40
30
20
20
10
10
0
0
71
72
73
74
75
76
77
78
79
80
Elapsed Time (min.)
Figure 17. Induced Compressive Stress at Various Depths within a
Central Geopier of the West Reaction Frame Footing during the
First Push-Pull Cycle at a Maximum Bent Cap Displacement of 8 in.
The results for the push cycle (induced compressive force on footing) are shown in
normalized fashion in Fig. 18 for the first push cycle at maximum displacements of the
bent caps of 8, 10, and 12 in. The normalized results are nearly the same for all three
push cycles and show that the induced compressive stresses dissipate quickly with depth
within the geopier. For example, the induced stress reaches a level of 10% of the stress at
the top of the geopier at a depth of about 10 ft, which is 3.3 times the diameter of the
geopier and 1.2 times the width of the footing.
19
Normalized Depth below Top of Geopier, z/d g
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0
0
-1
-1
Best-Fit Line through Experimental Data
for Induced Stresses within Geopiers
-2
-2
Lateral Displacement of Bent Cap = 12 in.
Lateral Displacement of Bent Cap = 10 in.
Lateral Displacement of Bent Cap = 8 in.
-3
-3
Theoretical Induced Stresses for Homogeneous Soil
-4
-4
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Normalized Induced Vertical Stress, ∆σv(z)/∆σv(z=0)
Figure 18. Normalized Induced Compressive Stress as a Function of Normalized
Depth within the Geopier for a Central Geopier of the Western Footing during the
First Push Cycle at Maximum Displacements of the Bent Cap of 8, 10, and 12 in.
Also shown in Fig. 18 are the theoretical induced stresses as a function of depth at the
same location within the footprint of the footing for the case where there is no
reinforcement (without geopiers). This theoretical relationship was determined using a
Boussinesq-type analysis, which assumes that the induced contact stress is uniform
(footing is perfectly flexible) and the soil is homogeneous. Although these assumptions
are not strictly valid (the footing is quite rigid and the soil is inhomogeneous), this
method provides an approximate but reasonable method of estimating the induced
stresses that would occur without geopiers. It was also assumed that ∆qg / ∆q = 3.0,
which represents an average value at the peak displacements as shown in Fig. 15.
Comparing the measured stresses induced on the geopiers and the estimated stresses
without geopiers, it can be seen that at depths less than about 2d g the stresses induced on
the geopiers are greater than the case without geopiers. This is expected at shallow
depths because of the stress concentration on the stiffer geopiers, as discussed previously.
At depths greater than about 2d g, however, the stresses induced on the geopiers are less
than for the case without geopiers. This reduction in stress at greater depth likely results
from a greater lateral distribution of the induced load produced by the increased stiffness
of the geopier foundation system, similar to what occurs when a stiff base course is
placed over a compressible subgrade soil in a pavement system. These results suggest
that for geopier foundation systems with depths greater than about 2dg, the stresses
induced in the underlying native soil would be less than would occur without the geopier
system. Hence, in addition to reducing the settlement that occurs within the geopier
20
zone, it is likely that a geopier foundation system also reduces the settlement that occurs
below the reinforced zone.
DISPLACEMENTS OF REACTION FRAME FOOTINGS
Horizontal Displacements
The structural reaction frame tied the two footings together so that they moved laterally
as a unit. This was verified during the testing by placing a displacement transducer
between the two footings to monitor differential lateral movement. The data showed that
the differential movement between the two footings was negligible at all times during the
test.
The footings were founded on the ground surface and thus were not embedded.
Therefore, the only two mechanisms available for resisting lateral loads were shearing
resistance along the bottom of the footing and passive resistance from the uplift bars
being pushed into the geopier material.
The lateral displacements of the footing versus elapsed time during the test are shown in
Fig. 19. Inspection of the peak displacements for each set of load cycles at the same
displacement level of the bent cap shows some interesting results. During each set of two
push cycles, there was little net displacement after the second push compared to the first
push except for the last two cycles where a small net displacement to the west occurred.
In contrast, during the pull cycles, some noticeable net displacement to the east occurred
on the second push compared to the first push for every cycle except the first two. As
shown in Fig. 10(b), the peak forces for each set of two push or pull cycles were
essentially the same. The reason for this difference in force-displacement behavior
between the push and pull cycles is not known. At the final time where the force was
zero (elapsed time of 116.3 min.), there was a net displacement of about 0.9 in. to the
east.
The relationship between lateral force and lateral displacement of the footings for the
entire test are shown in Fig. 20. A maximum displacement of 1.8 in. occurred during the
push cycles at a force of 305 kips. For the pull cycles, a maximum displacement of 1.6
in. occurred at a force of 355 kips. Considering that the total dead load acting on both
footings was only about 200 kips (weights of the two footings, reaction frame, and
actuator) and that the footings were not embedded, these maximum displacements are
quite small. Furthermore, these results show that geopier foundations are ductile and can
sustain large deformations – such as those generated by earthquakes – without significant
damage, thereby maintaining post-earthquake serviceability.
21
Lateral Displacement of Footings (in.)
0
20
40
60
80
100
120
2
2
1
1
0
0
-1
-1
Positive (+) is to the east
Negative (-) is to the west
-2
-2
0
20
40
60
80
100
120
Elapsed Time (min.)
Figure 19. Lateral Displacement of Footings versus Elapsed Time.
Lateral Force on Footings (kips)
-2
-1
0
1
2
400
400
300
300
200
200
100
100
0
0
-100
-100
-200
-200
-300
-300
-400
-400
-2
-1
0
1
2
Lateral Displacement of Footings (in.)
Figure 20. Lateral Force versus Lateral Displacement of Footings.
22
The force-displacement curves in Fig. 20 show an interesting trend at high displacements
or lateral loads – the stiffness of the geopier foundation system increases significantly
with increasing displacement or force. An analysis of the lateral capacity of the geopier
foundation systems shows that for applied lateral forces of about 80 kips or more, the
factor of safety against sliding failure reached a minimum limiting value greater than one.
Thus, regardless of the lateral load applied, sliding failure would not have occurred
unless the displacements were so large that some of the contact area between the footing
in compression and the tops of the geopiers was lost. This unusual characteristic can be
explained as follows:
1. Footings bearing on geopier foundation systems have high lateral sliding capacities
owing to the effect of vertical stress concentration. A high percentage of the total
vertical load is carried by the geopiers, which have much higher shearing strength
than the matrix soil. For example, in the previous section it was shown that at the
peak of the first push cycle at a bent cap displacement of 8 in., the geopiers carried
about 95% of the total generated vertical load (302 out of 317 kips) even though they
occupied only 35% of the total contact area. The general equation for the maximum
lateral resistance of a footing bearing on a geopier foundation system developed by
shearing resistance along the base only (Rhs, ignoring passive resistance from the
uplift bars) is as follows:
Rhs = Vg tan φ g + Vm tan φ m + Am cm .......................................................................... (4)
Where
Vg = total compressive vertical force acting on geopiers = qg Ag
Vm = total vertical force acting on matrix soil = qm Am
Ag = area of geopiers beneath footing
Am = area of matrix soil beneath footing
2. During pushing of the bent, the vertical force acting on each footing was 1.25 times
the lateral force, with the vertical force on one footing compressive and the other
footing in uplift. The dead load acting on each footing was approximately 100 kips,
so that for lateral forces less than 80 kips, the total vertical force (dead load plus load
generated by pushing or pulling) on each footing was compressive with the total on
both footings equal to 200 kips. For example, a lateral force of 40 kips would
produce an uplift force of 50 kips and a total force of 50 kips in compression on one
footing and would produce a compressive force of 50 kips and a total force of 150
kips on the other footing. The total vertical force on both footings would be 50 + 150
= 200 kips in compression.
For lateral loads greater than 80 kips, the uplift force on one footing would be greater
than the dead load so that the footing would be lifted above the ground surface,
thereby providing no resistance to sliding except for passive resistance from the uplift
bars being pulled into the geopiers. The compressive force generated on the other
footing would be equal to 1.25 times the lateral force. Therefore, the total
23
compressive force on both footings available to resist sliding would be 1.25 times the
lateral force plus 100 kips dead load, which is more than 200 kips. For example, a
lateral force of 100 kips would pull one footing above the ground surface and
generate a compressive force of 125 kips on the other footing. Therefore, the total
compressive force on that footing would be 100 kips dead load plus 125 kips
generated by the lateral force, for a total of 225 kips.
3. Equations will be developed to illustrate the factor of safety against sliding failure
using appropriate strength parameters. Values of the Mohr-Coulomb strength
parameters for the geopiers and the matrix soil are needed for these analyses.
Measured values of friction angles for geopiers from full-scale direct shear tests have
ranged from 48 to 53°. The results of a cone penetration test performed within the
interior of a reaction geopier at about 10 in. from the perimeter are shown in Fig. 21.
The reaction geopier was approximately 9-ft tall. The upper 2.5 ft of the reaction
geopier consisted of a well-graded gravelly sand that met UDOT’s requirements for
base course material. The lower portion of the reaction geopier consisted of an opengraded cobbly material varying in nominal size from 2 to 4 in. Estimates of the
effective friction angle for the two zones of the geopier will be obtained from the
relationships developed by Robertson and Campanella (1983) shown in Fig. 22. The
assumed unit weights of the geopier above and below the groundwater table are 135
pcf and 75 pcf, respectively. The groundwater table was at a depth of about 4 ft
below the ground surface at the time the cone penetration tests were conducted.
Estimate of φ′g in Upper Portion of Geopier (0 to 2.5 ft)
Average value of qc = 287 ksf = 13.7 MPa
Average value of σ’v0 = (1.25 ft)(135 lb/ft 3 ) = 169 psf = 8.1 kPa
From Fig. 22: φ′g ≈ 50° (extrapolating above the line representing φ′ = 48°)
Estimate of φ′g in Lower Portion of Geopier (2.5 to 9 ft)
Average value of qc = 245 ksf = 11.7 MPa
Average value of σ’v0 above GWT (2.5 to 4 ft) = (3.25)(135) = 439 psf
Average value of σ’v0 below GWT (4 to 9 ft) = (4)(135) + (2.5)(75) = 728 psf
Average value of σ’v0 for lower portion (4 to 9 ft) = [(1.5)(439) + (5)(728)] / 6.5
= 661 psf = 31.6 kPa
From Fig. 22: φ′g ≈ 47°
The estimated values of φ′g for both the upper and lower zones are consistent with the
values obtained from full-scale direct shear tests on other geopiers (φ′g = 48 to 53°).
24
Depth below Top of Geopier (ft)
0
50 100 150 200 250 300 350 400 450 500
0
0
-5
-5
-10
-10
-15
0
-15
50 100 150 200 250 300 350 400 450 500
Tip Resistance, qc (ksf)
Figure 21. CPT Tip Resistance versus Depth within a Reaction Geopier at the Site.
25
UPPER GEOPIER
LOWER GEOPIER
Figure 22. Correlation between Peak Effective Friction Angle and CPT qc
for Uncemented Quartz Sands (from Robertson and Campanella 1983).
26
Preliminary tests indicate that the silty clay at the bearing level of the footings was
overconsolidated with a preconsolidation pressure of about 720 psf. In the
overconsolidated range, the peak strength parameters of the matrix soil were φ m ≈ 26°
and cm ≈ 210 psf. In the normally consolidated range, peak values were φ m ≈ 38° and
cm ≈ 0. The value of lateral force on the footings that would produce normal
consolidation of the matrix soil at the bearing level is calculated as follows:
For one footing: Ag = 10(π/4*32 ) = 70.7 ft 2 , Am = (8.25)(24.5) – 70.7 = 131.4 ft 2
Vm required to produce normal consolidation = (0.720)(131.4) = 94.6 kips
Total vertical footing force required to produce normal consolidation = 94.6 / 0.05 =
1,890 kips
Let H = lateral force on bent cap = lateral force carried by both footings combined.
H required to produce 1,660 kips on footing in compression = (1,890 – 100) / 1.25 =
1,430 kips.
For H ≤ 80 kips
V = 200 kips, Vg = (0.95)(200) = 190 kips, Vm = (0.05)(200) = 10 kips
From Eq. 4:
Rhs = 190 tan 50° + 10 tan 26° + (0.21)(2)(131.4) = 226 + 5 +55 = 286 kips
Considering only sliding resistance at the bearing level, the factor of safety against
sliding was
FSsliding = Rhs / H.......................................................................................................... (4)
The factor of safety against sliding varied from infinity at H = 0 to a value of 3.6 at H
= 80 kips.
For H > 80 kips
∆V = ± 1.25 H ⇒ V = VDL + ∆V = 100 ± 1.25H
Vg = 0.95V = 95 ± 1.1875H
Vm = 0.05V = 5 ± 0.0625H
Rhs = (95 + 1.1875H) tan 50° + (5 + 0.0625H) tan 26° + (0.21)(131.4) =
= 143 + 1.45H
FSsliding = (143 + 1.45H) / H
27
At a value of H just slightly greater than 80 kips, one footing was lifted in the air,
which reduced the frictional and adhesional sliding resistance for that footing to zero,
and the factor of safety against sliding dropped to 3.2. At the maximum value of H =
355 kips applied during the test, the estimated factor of safety was 1.9. It should be
noted that the lateral displacements of the footings may have dropped the strength of
the matrix soil into the residual range. However, even if the sliding resistance
provided by the matrix soil is completely ignored, the estimated factor of safety was
1.5. According to the equation for factor of safety, sliding failure could never have
occurred with the geopier foundations as the minimum value of factor of safety was
1.45 (or 1.42 if the contribution from the matrix soil is ignored). This analysis is
based on an assumption of full contact between the bottom of the footing and the
geopiers. Failure could have occurred, therefore, only at very high displacements (6
in. or more) where the trailing edge of the footing would have moved past the edge of
the geopiers so that only partial contact with those geopiers would have existed. The
estimated maximum lateral capacity of the same size footing without geopiers is 109
kips using the peak strength parameters of the silty clay.
Analyses was performed using the finite difference program COM624 (Reese et al. 1984)
to estimate the lateral resistance to sliding of the reaction frame footings developed by the
uplift bars being pulled or pushed into the geopier material. The following parameters
were used in these analyses:
φ g = friction angle of the geopier material = 50° for upper 4 ft and 47° for 4 to 15 ft
dw = depth to groundwater table from ground surface = 4 ft
γg = unit weight of the geopier material above the groundwater table = 135 pcf
γ’g = buoyant unit weight of the geopier material below the groundwater table = 75 pcf
nh = constant of horizontal subgrade reaction = 225 pci above groundwater table
= 125 pci below the groundwater table
db = diameter of the uplift bars = 0.875 in. (#7 bar)
Esteel = Young’s modulus for the steel uplift bars = 29,000 ksi
The values of nh used in the analysis were obtained from Reese et al. (1984) for dense
sand. The p-y curves for the geopier material were generated internally by the program
using the method developed by Reese et al. (1974) for sands.
Analyses using COM624 were performed for a single uplift bar. Predicted results of
lateral deflection versus depth for three values of horizontal force (H) are shown in Fig.
23. As the magnitude of the horizontal deflection or force increased, the deeper the zone
over which the horizontal passive resistance developed as the uplift bars moved into the
geopiers increased. For the three horizontal loads shown in Fig. 23, the height of this
zone of passive resistance increased from about 17 to 23 in. In addition, the greater the
horizontal load or deflections, the greater the amount of bending and movement of the
bar in the opposite direction to the applied load.
28
Depth within Geopier (in.)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0
0
10
10
20
20
H = 500 lb
H = 1,000 lb
H = 2,000 lb
30
40
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
30
1.8
2.0
40
Horizontal Deflection (in.)
Figure 23. Horizontal Deflection of a Single Uplift Bar at Three Values
of Horizontal Force Predicted from Analyses Using COM624.
The relationship between horizontal force and horizontal displacement at the top of one
uplift bar is shown in Fig. 24. As expected, the horizontal resisting force increases with
increasing horizontal displacement, but at a decreasing rate. A schematic illustration of
the uplift bars for each geopier, as well as their location within the geopiers, are shown in
Fig. 25. Owing to the large spacing between uplift bars in any geopier in comparison to
their diameter (s/d b = 21.83 / 0.875 ≈ 25), there was no significant influence on any bar
from adjacent bars. Therefore, to obtain the total resistance provided by all the bars in
both footings (4 bars per geopier x 10 geopiers per footing x 2 footings = 80 bars), the
values of lateral force for one bar were multiplied by 80, with the results shown in Fig.
26. The nominal clearance from the outer edge of the uplift bars to the perimeter of the
geopier was 6.56 in., which should have allowed full development of passive resistance
within the geopier itself (no resistance provided by the matrix soil). However, a
conservative lower bound for the passive resistance provided by the uplift bars would be
to assume that the 40 bars close to the perimeter of the geopiers for any direction of
lateral movement produced no lateral resistance. This relationship is shown in Fig. 26.
The magnitude of resistance provided by the uplift bars increased with increased lateral
movement of the footings. For example, the maximum lateral force (355 kips) occurred
during this test at the peak of the first push cycle for a maximum displacement of the bent
cap of 8 in. The corresponding lateral displacement of the reaction frame footings was
1.58 in. At this value of displacement in Fig. 26, the estimated lateral resistance provided
29
by the uplift bars ranges from 74 kips (40 bars) to 148 kips (80 bars), which represents 21
to 42% of the total horizontal force.
Analyses were also conducted to determine what effect uplift of the footing above the
ground surface had on the lateral resistance provided by the uplift bars. At the level of
uplift displacements measured during the test, the effect on the lateral resistance was
small (less than 5%).
Horizontal Force (lb)
0.0
2500
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2500
2000
2000
1500
1500
1000
1000
500
0
0.0
500
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
0
2.0
Horizontal Displacement (in.)
Figure 24. Horizontal Force versus Horizontal Displacement at the Top
of One Uplift Bar as Predicted by Numerical Analyses Using COM624
Nominal Perimeter of Borehole
21.83"
6.56"
21.83"
11.35"
Directions of Movement
R18"
R21"
Uplift Bar (Typical)
Approx. Actual Perimeter of Geopier
Figure 25. Plan View of Spacing and Location of Uplift Bars within Geopiers.
30
Horizontal Force (kips)
0.0
200
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
180
2.0
200
180
160
160
80 Uplift Bars
140
140
120
120
100
100
80
80
60
60
40
40
40 Uplift Bars
20
0
0.0
20
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
0
2.0
Horizontal Displacement (in.)
Figure 26. Horizontal Force versus Horizontal Displacement at the
Ground Surface of Groups of Uplift Bars in Both Reaction Frame
Footings as Predicted by Numerical Analyses Using COM624.
Vertical Displacements
Three transducers were used to measure the vertical displacement of each reaction frame
footing. The vertical displacement transducers were placed in the northeast, northwest,
and southwest corners of each footing (see Fig. 11). The vertical displacements of the
western footing for the entire test are shown in Fig. 18 for the entire test. The peak
upward displacement of 0.82 in. occurred in the northwest corner of the footing at an
elapsed time of 76.1 min. under an uplift force of 444 kips. The other measured
displacements of the footing at that time were 0.56 in. in the southwest corner and 0.32
in. in the northeast corner. The maximum downward displacement of -0.42 in. occurred
in the northwest corner at an elapsed time of 110.0 min. The corresponding
displacements at the other locations were -0.41 in. in the southwest corner and -0.08 in. in
the northeast corner. The vertical displacements of the footing the last time the force was
zero (elapsed time of 116.3 min.) were –0.07 in. for the northwest corner, -0.02 in. for the
northeast corner, and –0.12 in. in the southwest corner.
To examine the features of the vertical displacements more closely, the results for the
first push-pull cycle at a maximum bent cap displacement of 8 in. are shown in Fig. 28.
The net displacements are calculated as the displacements from the original position of
the footing at the start of the cycle. Comparing the results for the displacements in the
northwest and northeast corners, it can be seen that rotation occurred in the direction of
the overturning moment for both the push and pull cycles. During the push cycle, the
lateral force on the footings was to the west and the vertical force was compressive. The
primary lateral resistance developed as shear along the footing base to the east, producing
an overturning moment that rotated the top of the footing from east to west. During the
31
pull cycle, the lateral force on the footings was to the east and the vertical force was
uplift. The primary lateral resistance developed as shear along the footing base to the
west, producing an overturning moment that rotated the top of the footing from west to
east. It can also be seen that there was some small transverse rotation during the push
cycle, with greater rotation during the pull cycle. This occurred throughout the test and
indicates that the direction of the pulling force was farther out of alignment with the bent
cap than the pushing force. The maximum settlement of the footing for this cycle was
-0.49 in. in the northwest corner under a compressive vertical force of 294 kips and an
overturning moment of at least 956 ft-kips. The maximum uplift was 0.58 in., also in the
northwest corner, under an uplift vertical force of 444 kips and an overturning moment of
at least 1,440 kips.
The relationship of induced vertical force versus net vertical displacement for this same
push-pull cycle is shown in Fig. 29. During both the compression and uplift cycles
starting from zero induced force, the geopier foundation system stiffens with increasing
displacement or force. This stiffening effect is more pronounced in compression than
uplift. Thus, the geopier system had a high factor of safety against failure at the peak
forces or displacements for both compression and uplift.
0
20
40
60
80
100
120
Vertical Displacement (in.)
1.0
1.0
Ch. 2 - NW Corner
Ch. 3 - NE Corner
Ch. 5 - SW Corner
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
0.0
-0.2
-0.2
-0.4
-0.6
Positive (+) indicates upward movement (uplift)
Negative (-) indicates downward movement (settlement)
0
20
40
60
80
-0.4
100
Elapsed Time (min.)
Figure 27. Vertical Displacements of the Western
Reaction Frame Footing for the Entire Test.
32
120
-0.6
Net Vertical Displacement (in.)
71
0.6
72
73
74
75
76
77
78
79
Ch. 2 - NW Corner
Ch. 3 - NE Corner
Ch. 5 - SW Corner
0.4
80
0.6
0.4
0.2
0.2
0.0
0.0
-0.2
-0.2
-0.4
-0.4
-0.6
71
72
73
74
75
76
77
78
79
-0.6
80
Elapsed Time (min.)
Induced Vertical Force, ∆V (kips)
Figure 28. Net Vertical Displacements of the Western Reaction Frame Footing
for the First Push-Pull Cycle at a Maximum Bent Cap Displacement of 8 in.
-0.6
500
-0.5 -0.4
-0.3 -0.2 -0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
500
400
400
300
300
200
200
100
100
0
0
-100
-100
-200
-200
-300
-300
-400
-400
-500
-0.6
-0.5 -0.4
-0.3 -0.2 -0.1
0.0
0.1
0.2
0.3
0.4
0.5
-500
0.6
Net Vertical Displacement (in.)
Figure 29. Induced Vertical Force versus Net Vertical Displacement
for First Push-Pull Cycle at Maximum Displacement of Bent Cap of 8 in.
33
CONCLUSIONS
The geopier foundations supporting the structural reaction frame in these full-scale
simulated seismic tests performed well. The foundations were subjected to large cyclic
lateral and uplift-compression loads, as well as significant overturning moments
produced by the horizontal forces. For the conditions of the tests – including large loads,
poor subsurface conditions, and no embedment of the foundations, the magnitude of the
maximum displacements and rotations were relatively small. Furthermore, the permanent
displacements at the end of the tests were small, indicating that geopier foundations are
ductile and can sustain large displacements – such as those generated by earthquakes –
without significant damage, thereby maintaining post-earthquake serviceability.
Specific major results and conclusions determined from the preliminary analyses of these
tests are summarized as follows:
1. The uplift capacity a geopier foundation system is derived from three sources: (a)
weight of the uplift plates and bars, (b) shearing resistance of soil along the surface of
the pullout zone, and (c) weight of soil and geopiers within the pullout zone. The
weight of the uplift plates and bars was insignificant in comparison to the other two
sources of pullout resistance in these tests. The peak pullout capacity of a single 15-ft
tall, 3-ft diameter geopier in poor subsoil conditions was 175 kips. Approximately 98
kips (56%) of the peak uplift resistance was provided by the effective weight of the
soil and geopiers within the pullout zone, and the soil along the surface of the pullout
zone contributed approximately 77 kips (44%) of the uplift capacity. For a group of
ten geopiers used to support one reaction frame footing, the peak pullout capacity was
estimated to be 666 kips. Approximately 32% of the group peak uplift capacity was
from shearing resistance of the soil along the surface of the pullout zone, while 68%
was from the effective weight of the soil and geopiers within the pullout zone.
2. Most of the vertical compressive load applied to the foundation system at the bearing
level was carried by the geopiers. For one loading cycle analyzed in detail, 95% of
the peak vertical compressive load was carried by the geopiers, while only 5% was
carried by the matrix soil. The footing contact stresses induced on the geopiers
ranged from about 25 to 45 times the contact stresses induced on the matrix soil.
3. Within the upper portions of the geopier foundation systems, the vertical compressive
stresses induced on the geopiers were greater than would have been induced without
the geopiers. However, the stresses induced on the geopiers within the lower portions
were less than would have been induced without geopiers. This reduction in stress at
depth likely results from a greater lateral distribution of the induced load produced by
the increased stiffness of the geopier foundation system, similar to what occurs when
a stiff base course is placed over a compressible subgrade soil in a pavement system.
Hence, in addition to reducing the settlement that occurs within the depth of the
geopier zone, it is likely that the geopier foundation systems also reduce the
settlement that occurs below the reinforced zone.
34
4. Equations developed previously (Lawton et al. 1994) for estimating the induced
contact stresses on the geopiers and matrix soil based on subgrade reaction theory
were found to provide reasonable estimates of the measured stresses.
5. During uplift of the foundations, the measured induced compressive stresses within
the instrumented geopier were greatest at the bottom and decreased with decreasing
depth. These results confirm that uplift loads are transmitted to the ground via the
uplift plates at the bottoms of the geopiers.
6. The geopier foundation system provided significant resistance to sliding from lateral
loads. This resistance was derived from two primary sources: (a) shearing resistance
along the geopier-footing interfaces, and (b) passive resistance generated by the uplift
bars pushing on the geopier material. Numerical analyses indicate that the portion of
lateral resistance provided by the uplift bars was between 21 and 42% of the peak
lateral force generated during the test.
7. A maximum lateral displacement of 1.8 in. occurred during the push cycles at a force
of 305 kips. For the pull cycles, a maximum displacement of 1.6 in. occurred at a
force of 355 kips. Considering that the total dead load acting on both footings was
only about 200 kips (weights of the two footings, reaction frame, and actuator) and
that the footings were not embedded, these maximum displacements are quite small.
8. The permanent displacements at the end of the test (force equal to zero) were small –
0.9 in. lateral displacement and less than 0.1 in. average vertical settlement.
35
REFERENCES
Lawton, E. C., and Fox, N. S. (1994). “Settlement of Structures Supported on Marginal or
Inadequate Soils Stiffened with Short Aggregate Piers.” Vertical and Horizontal
Deformations of Foundations and Embankments, ASCE Geotechnical Special
Publication No. 40, Vol. 2, pp. 962-974.
Lawton, E. C., Fox, N. S., and Handy, R. L. (1994). “Control of Settlement and Uplift of
Structures Using Short Aggregate Piers.” In-Situ Deep Soil Improvement, ASCE
Geotechnical Special Publication No. 45, K. M. Rollins, Ed., pp. 121-132.
Reese, L. C., Cooley, L. A., and Radhakrishnan, N. (1984). “Laterally Loaded Piles and
Computer Program COM624G.” Technical Report K-84-2, U.S. Army Corps of
Engineers, Waterways Experiment Station, Vicksburg, Mississippi.
Reese, L. C., Cox, W. R., and Koop, F. D. (1974). “Analysis of Laterally Loaded Piles in
Sand.” Proceedings of the 5th Annual Offshore Technology Conference, Paper No.
OTC 2080, Houston, Texas.
Robertson, P. K., and Campanella, R. E. (1983). “Interpretation of Cone Penetration
Tests. Part I: Sand.” Canadian Geotechnical Journal, Vol. 20, No. 4, November,
pp. 718-733.
Terzaghi, K. (1955). "Evaluation of Coefficients of Subgrade Reaction. " Geotechnique,
Vol. 5, No. 4, December, pp. 297-326.
36