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RESISTANCE OF A DRILLED SHAFT FOOTING TO OVERTURNING LOADS,
MODEL TESTS AND CORRELATION WITH THEORY
By
Don L. Ivey,
Kenneth J. Koch
and
Carl F. Raba, Jr.
Research Report Number 105-2
Design of Footings for Minor Service Structures
Research Study Number 2-5-67-105
Sponsored by
The Texas Highway Department
in cooperation with the
Department of Transportation, Federal Highway
Administration,
Bureau of Public Roads
July, 1968
TEXAS TRANSPORTATION INSTITUTE
Texas A&M University
College Station, Texas
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ACKNOWLEDGEMENTS
This research was conducted under an interagency contract
between the Texas Transportation Institute and the Texas Highway
Department. It was sponsored jointly by the Texas Highway
Department and the Bureau of Public Roads. Liason was maintained
through Mr. D. L. Hawkins and Mr. H. D. Butler, contact
repre-sentatives for the Texas Highway Department, and through Mr.
Robert J. Prochaska of the Bureau of Public Roads.
The theory presented in Research Report 105-l was programmed for
the IBM 7094 for analysis of the footings in this study by Mr. Leon
E. Travis, III, and Mr. Kurt A. Schemher.
The opinions, findings, and conclusions expressed in this
publication are those of the authors and not necessarily those of
the Bureau of Public Roads.
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SYNOPSIS
Reported in this paper are the results of twenty-eight model
tests of drilled shaft footings subjected to overturning horizontal
loads. The models are geometrically similar but reduced by a factor
o.f six compared to the average size of footings used for mino·r
service structures in Texas. The soils investigated range from
cohesion-less sands, through soils with both cohesion and an angle
o.f shear resistance, to clay§ with no angle of shear resistance
when tested using the unconsolidated-undrained quick triaxial
compression test.
The results o.f the model footing tests are compared with the
theory developed in this study,1* It was found that the
conventional methods of predicting ultimate load were conservative
by as much as 500% for the cohesionless sands and by as little as
20% for the clays. The coefficients developed in the new
theoretical treat-ment are evaluated so that the ultimate loads on
this type of .footing in any given soil can be predicted.
*Refers to numbers in selected references.
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TABLE OF CONTENTS Pages
INTRODUCTION
_______________________________________________________ 7
EQUIPMENT AND INSTRUMENTATION _________________________________
7 General Loading System Load Measurement Rotation Measurement
PLACEMENT OF FOOTINGS AND SOIL CONDITIONS ____________________ 8
Easterwood Clay Trinity Clay Laho·ratory Sandy Clay Ottawa Sand
TESTING PROCEDURE
_________________________________________________ lo
TESTING RESULTS------------------------------------
----------------11 COMPARISON OF TEST RESULTS AND THEORY
_________________________ l3
SUMMARY
------------------------------------------------------------17
SELECTED REFERENCES _______________________________________________
l7
APPENDIX _ _:_ ___________________________ __:
____________________________ :___18
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NOTATION
c cohesion ( force/length2 ) • * cp angle of shear resistance
(degrees) . y unit weight, in place o·r w~t (force/length3 ).
y1 modified. unit weight of soil in the direction of the applied
load (force/ length3 ).
y 2 modified unit weight of soil in the direction opposite the
applied. load (force/ length3 ).
P horizontal load applied to footing at some distance H above
ground (force).
H height of horizontal load, P, above ground (length).
D depth of footing (length).
d footing diameter (length).
a depth to point of footing rotation (length).
K0 coefficient of earth pressure at rest (dimensionless) .
K1 coefficient of passive earth pressure applied to unit weight
term (dimension-less).
K2 coefficient of passive earth pressure applied to cohesion
term (dimensionless) .
K3 coefficient of active earth pressure (dimensionless) .
k unit weight coefficient (dimensionless) .
J 1 coefficient of shear stress, vertical footing surfaces
(dimensionless) .
J 2 coefficient o·f shear stress, footing bottom (dimensionless)
.
B earth pressure coefficient modifier (dimensionless) .
*The dimensions of the various symbols are given in parentheses
after each definition.
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Introduction The wide use of drilled shaft footings to
support
service structures necessary for the functioning of a highway
system has focused attention on the highly conservative design
procedures presently in use. The foundations of structures such as
signbo·ards, strain poles, and lighting poles should be designed
using fac-tors of safety consistent with the relative importance of
the particular structure.
As the next necessary step, after the development of a
theoretical treatment for this type of foundation, a series of
model tests was undertaken. The purpose of these tests was to
evaluate certain coefficients intro-duced in the theoretical
treatment and to establish the degree of precision to be expected
in predicting ultimate loads with the new theoretical treatment.
The footings tested ranged in diameter from 2 to 4 in., and in
depth from 10 to 12 in. Height of load application ranged
from 0 to 42 in. The soils in which footings were tested ranged
from a dry sand with no cohesion to a clay with no angle of shear
resistance. The soils are referred to in this way on the basis of
the unconsolidated-undrained quick triaxial compression test. This
type of test was used to determine the pertinent soil parameters
because it best simulated conditions of short term loading in the
field. It is recognized that the same soils tested in an-other way
would exhibit different properties. Eight tests of footings in
soils with both cohesion and . an angle of shear resistance are
reported.
This is the second of a series of papers to be writ-ten
concerned with the design of these footings. The first, Research
Report 105-1, reported in detail the theoretical development of the
load prediction equations which are compared with test data in this
paper.
Equipment and Instrumentation General
In o·rder to conduct these ·tests, it was necessary to develop
systems capable of ( 1) applying a horizontal force on the footing
at a uniform displacement rate and ( 2) measuring the load acting
on the footing· at known angles of rotation.
Loading System A mechanically driven loading machine
normally
used for compression testing was modified to apply the
overturning force to the footings. Figure 1 illustrates the loading
system used for these tests. The loading machine was run at a speed
of 0.05 inch per minute but the pulley system increased this speed
to 0.20 inch per minute at the footing.
Load Measurement
The load applied to the footing was measured by means of a
fo-rce transducer spliced into the cable ap-proximately 2 feet from
the footing. Because of the
PULLEY SYSTEM
DRIVE SYSTEM
CABLE
FORCE
VERTICAL DRIVE SHAFT
Figure 1. Loading system.
wide range of load developed, 3 transducers were used f
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Figure 3. Placement of ultrG!Violet lamps.
The output voltages from these strain gages were ampli-fied and
recorded on a visicorder, providing a continu-ous record of the
load on the footing.
Rotation Measurement The position of the footing at known loads
was
measured by recording the rotation of a metal pipe that was
attached to the top of each footing. The pipe was screwed onto a
%-inch diameter threaded rod extending from the top of the concrete
footings. The cable from the loading machine was connected to the
pipe by means of a clamp that permitted the height of pull to be
varied along the entire length of the pole.
Very small holes were drilled in the pipe on 5-inch centers
along a straight line on the upper three feet of the pipe. These
holes provided point sources of light from two ultraviolet lamps
mounted on a carriage that had been lowered into the pipe as shown
in Figures 2 and 3. As the footing was rotated, these light sources
developed lines of movement on light sensitive paper mounted on a
wooden panel adjacent to the pipe. The lights were turned on and
off at specific loads so that the position of all ten traces could
be related. A straight line was extrapolated through each series of
termination points to find the position of the footing at that
specific load. Because of the use of the light sensitive paper, it
was necessary to perform all the tests in the dark. When the light
sources were turned off, an external triggering device
simultaneously marked the visicorder load record to denote the load
at which the rotations were measured.
Placement of Footings and Soil Conditions
Easterwood Clay A series of tests was conducted in the shallow
sandy
clay located in the vicinity of Easterwood Airport, Col-lege
Station, Texas. This soil was chosen as a repre-sentative of soils
possessing both cohesion (c) and an angle o·f shear resistance (
cf>) , as determined by the unconsolidated-undrained quick
triaxial test. After the test site location was determined by means
of a series of auger borings, the area was leveled and prepared for
the installation of footings.
A detailed procedure was established in order to install the
footings as they would be placed in actual practice. Special hand
augers were designed and con-structed to drill the footing holes.
These augers were aligned and guided during the drilled operation
by a wooden template placed on top of the ground. The excavated
hole was a right circular cylinder. A heavily reinforced steel cage
was lowered into each hole which was subsequently filled with a
cement mortar made from Type III cement and 20-30 Ottawa sand. The
steel cage was vibrated with a portable vibrato·r to eliminate air
bubbles o-r voids on the foO
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powdered form in 25 lb. bags, and mixed with water in a counter
current mixer to obtain a water content of 18%. The soil was
classified as a CL material by the Unified Soil Classification
System.
A test bin was constructed in the Civil Engineering Department's
Soil Mechanics Laborato·ry to facilitate these tests. The bin, 17.5
in. tall and 27.5 in. wide, was separated into 3 equal parts, each
48 in. long. The bin had a metal liner surrounded by 6 inch~ of
concrete for rigidity. The clay was placed in 4, in. thick, loose
layers and- compacted with a pneumatic hammer as shown in Figure 4.
The bin was completely filled with the compacted soil. A constant
amount of compaction effort was applied to each layer in order to
develop uniformity of unit weight and shear strength.
After the compaction of each bin was completed, holes were
drilled and footings were installed as de-scribed in the Easterwood
Clay section. This is shown in Figure 5.
The entire bin was covered with a sheet of thin plastic to form
an airtight fit. This prevented the soil-water mixture from losing
moisture through evapora-tion. A minimum of 14 days was allowed to·
elapse befme the footings were tested to pro·vide sufficient time
for the mortar to· cure. The compacted soil also gained strength
through thixotropy3 during this time. Thixotropy can best be
described as a gain in strength with time at a constant
volume-water content condition. Remolded or compacted soils are
known to possess dis-
Figure 4. Compaction of clay m test bin.
Figure 5. Footing steel reinforcement before placement of
mvrta.r.
tinctive stress-strain characteristics.4•5•6 These soils will
undergo large deformations prior to mobilizing their full
strengths. However, if allowed to "age," they be-come stiffer and
more closely approach the stress-strain characteristics of an
undisturbed soil.
After the footings were tested, representative sam-ples were
()btained thmughout the depth of the footings in each bin.
Miniature samples were obtained with a thin-walled core cutter;
these samples were 1.425 in. in diameter and 3.0 in. long. The core
cutter was pushed by hand into the clay and then trimmed out with a
knife. The soil specimen was then extruded from the cutter, wrapped
in aluminum foil, and waxed to prevent mois-ture bss. Quick
triaxial compression tests were con-ducted on these specimens. The
results of these tests indicated the follo·wing physical and
engineering prop-erties; cohesion (c) = 3790 psf, angle (}f shear
resist-ance ( cf>) = 0, and unit weight in place ( y) _:_ 126
pd.
Laboratory Sandy Clay
The sandy clay encountered in the field tests at Easterwood
Airport was only representative ()f the high-er shear strength
range. Because of this, it was con-sidered necessary t(} conduct
additional tests in c- cf> soils with lower shear strengths in
order that the spec-trum might be better covered.
The Trinity clay that was described previously was mixed with a
locally available well-graded concrete sand in different pmportions
and at different water contents. The constituents of these batches
are shown in Table 1:
TABLE 1
In Place Water Unit
Test %Sand %Clay Content Weight Number by Weight by Weight (%)
(pcf)
L-1 67 33 11.9 123 L-2 33 67 16.4 126 L-3 67 33 9.8 132
PAGE NINE
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The same procedures were followed as stated previously to
compact the soil, to install and test the footings, and to sample
and test the sandy clay specimens.
The results of unconsolidated-undrained, quick tri-axial
compression tests are shown in Table 2:
Batch Number
L-1 L-2 L-3
Ottawa Sand
TABLE 2
Cohesion (psf)
749 1152 1411
Angle of Internal Friction
(degrees)
3.5 5.0
12.0
A series of c = 0 case tests was conducted in the laboratory
using 20-30 dry Ottawa sand. This material was selected as the test
media because of its commercial availability and wide use as a
standard research soil. The test apparatus consisted of a shallow
round bin rigidly attached to the testing frame. A series of tests
wa§ conducted to establish the range of void ratios that could be
achieved (loose to highly compacted) by dif-ferent methods of
placing the sand in the bin. These extreme conditions were
represented by void ratios of 0.51 and 0.62. It was found feasible
to achieve either of these extremes but very difficult to
consistently pro-
duce intermediate void ratios. By testing at these ex-tremes,
the effect of void ratios on the ultimate over-turning loads was
indicated.
In the preparation of these tests, the precast con-crete
footings were suspended in place and the sand was placed around
them. To achieve the loosest void ratio condition (e = 0.62), a
"raining" technique was used to place the sand around the footing
in the bin. The sand was placed in a bucket held approximately 3
in. above the surface and poured in place to a depth of 18 inches.
The densest condition ( e = 0.51) was obtained by placing the sand
in the bin in 6-in. lifts and using a combination of rodding and
vibration t
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·Test Results The results of the model footing are presented
in
Table 3. Both the maximum load resisted and the load resisted
after a rotation of 5o are given. In general, the maximum load
occurred at a ro,tation slightly greater than 5o, but there were a
few tests in the Ottawa sand where the maximum load occurred
slightly before the 5o rotation was achieved.
Graphs of load and rotation point versus rotation (angle of
deflection) are given for each test in the appendix. Typical test
graphs for the footing in dif-ferent materials are shown in Figures
7 through 10. In the tests in sands and clays, Figures 7 and 8, a
well defined peak load is reached. The footings in sand continue to
support about 70% of the peak load up to rotations of about 20o
while the footings in the clay with no angle of shear resistance
lose l()ad pmgressively after the peak is reached. The footings
tested in soils with both cohesi()n and an angle of shear
resistance had no well defined point of maximum resistance up to
rota-tions of about 20°, but were marked by a very rapid increase
in load with in.creased rotations up to a ro-ta-tion of about 5o,
with a rapid decrease in the slope of the load versus rotation
curve for rotations between 5o and 20°. Photographs of the
surrounding soil surface for typical tests are shown in Figures 11
through 13.
On the basis of these model tests the load corresponding to a
footing rotation of 5o was chosen t() use in corre-lating the
theory with test data.
40 40
5 5
30 30
/r· """ 25 /-""
\" i 25
0 20 « 0 .J
15
10
0
0.0
I
\ ~ 0.5
1.0 0
'
'· I'·.._ ·- -'-·-
TEST NO. 3 TYPE OF SOIL 5 AND VOID RATIO : 0.513 SIZE OF FOOTING
4A x 12" HE GHT OF 246 I PULL ;
o-"--o -~ /"-----
10 15 20
0 20 « 0 .J
15
10
5
0
0.0
I\
"·------
TEST NO. 4 TYPE OF SOIL : SAND VOID RATIO : 0.613
-~
SIZE OF FOOTING : 4,~ lt 12" HEIGHT OF PULL : 24
~ 0.5 -.,/ -·-·--·--...../ r-----1.0
0 I 10 15 20
ANGLE OF OEFLECTION, deorees
Figure 7. Typical tests in Ottawa Sand.
TABLE 3. RESULTS OF MODEL FOOTING TESTS
Description of Tests Results of Tests Soil Parameters Size of
Max.
Footing, Height Load, De fl. Load, P Pt. of c 'Y Tes.t d X D, of
Pull, Pmax @ Pmax, @ 5o, Rotation
Number Type of Soil Inches H, Inches Lbs. De g. Lbs. @ 5°, a/D
PSF De g. PCF
1 Ottawa Sand 4 X 12* 24 28.3 6° 30' 28.1 0.74 37 109 2 Ottawa
Sand 4 X 12 24 34.0 2° 30' 29.0 0.60 37 109 3 Ottawa Sand 4 X 12 24
28.1 4° 30' 28.0 0.55 37 109 4 Ottawa Sand 4 X 12 24 29.7 3° 10'
28.3 0.62 37 109 5 Ottawa Sand 4 X 10 20 20.0 37 109 6 Ottawa Sand
4 X 12 24 33.0 4° 00' 31.0 0.55 37 109 7 Ottawa Sand 4 X 12 24 26.1
3° 40' 25.6 0.63 37 109 8 Ottawa Sand 4 X 12 24 9.3 0.64 32 102 9
Ottawa Sand 4 X 12 24 14.3 0.65 32 102
10 Ottawa Sand 4 X 10 20 22.0 3° 30' 20.8 0.63 37 109 11 Ottawa
Sand 4 X 10 20 18.5 2° 50' 16.6 0.62 37 109 12 Ottawa Sand 4 X 10
10 33.5 4° 20' 33.3 0.60 37 109 13 Ottawa Sand 3 X 12 24 22.0 4°
50' 22.0 0.67 37 109 14 Ottawa Sand 3 X 12 12 48.0 4° 40' 48.0 0.58
37 109 15 Ottawa Sand 2 X 12 24 22.3 0.70 37 109 16 Ottawa Sand 4 X
12 12 52.0 4° 10' 51.3 0.63 37 109 17 Ottawa Sand 4 X 12 0 115.0 4°
10' 113.0 0.69 37 109
E-1 Easterwood Clay 4 X 10 20 498.0 7° 40' 488.0 0.46 2810 9 133
E-2 Easterwood Clay 4 X 12 42 410.0 9° 00' 385.0 0.53 2810 9 133
E-3 Easterwood Clay 4 X 12 24 500.0 0 .. 54 2810 9 133 E-4
Easterwood Clay 4 X 12 12 615.0 0.64 2'810 9 133 E-5 Easterwood
Clay 3 X 12 24 352.0 7° 30' 340.0 0.63 2810 9 133 C-1 Trinity Clay
4 X 10 20 246.0 4° 30' 245.0 0.56 3790 126 C-2 Trinity Clay 4 X 12
24 357.0 6° 20' 348.0 0.68 3790 126 C-3 Trinity Clay 3 X 12 24
290.0 3° 20' 273.0 0.66 3790 126 L-1 33% Trinity Clay 4 X 12 24
120.0 0.73 794 3.5 123
67% Concrete Sand L-2 67% Trinity Clay 4 X 12 24 164.0 0.59 1152
5 126
33% Concrete Sand L-3 33% Trinity Clay 4 X 12 24 238.0 0.63 1411
12 132
67% Concrete Sand
*4-inch diameter X 12-inch depth.
PAGE ELEVEN
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40 0
350 --
I
30 o~
0 r·~.""' 0 I
I '·""' -·, 25
150 "-...
100
0
0
0.0
i
TEST NO. C 1 TYPE OF SOIL : TRINITY CLAY MOISTURE CONTENT : 18%
51 ZE OF FOOTING : f x 10" HEIGHT OF PULL 20
I ··---~ 0.5 ~/r 1.0
0 10 15 20
40 0
I
I .. '\ "'-350
0 I -~ .. , 25 0
I 0 I
150
I 10 0
0
0
0.0
~ 0.5
1.0 0
"
I
TEST NO. C ~ TYPE OF SOIL - TRINITY CLAY MOISTURF CONTENT : 18%
SIZE OF FOOTING . 4: x 12.• HEIGHT OF PULL 24
··-.____,_ ,_./ 10 15 20
ANGLE OF DEFLECTION , degrees
Figure 8. Typical tests in Trinity Clay.
30 0
I I i ! I
i I I --- I 0
I ! I I I I I
25
200
... I ,, . 0
~r· T I I ~1~
0 I 0 15
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Figure 11. Test of footing m Ottawa Sand. Figure 13. Test of
footing m Trinity Clay.
Figure 12. Test of footing m Easterwood Clay. Figure 13a. Test
se·t up at Easterwood.
Comparison of Test Results With Theory In developing a
correlation between the new theo·ry
and the model tests reported in this paper, it was neces-sary to
determine the influence of the various coeffi-cients introduced in
Research Report 105-l and to determine the optimum value of these
coefficients.
As discussed in 105-l, it was necessary to intro-duce a
modifying factor for the Rankine coefficients of passive and active
earth pressure. This factor was designated B., and was applied as
follows.
K1 Kv B tan2 ( 45° + t ) Kz = 2B tan ( 45° + f) KA = B tan2 (
45° t)
An additional coefficient was dictated by analysis of the model
tests in Ottawa sands. It was found that predicted values of the
footing rotation point were con-siderably lower than those values
observed in the tests. Study of this problem indicated that the
soil surround-ing the footing was developing higher passive
stresses in the direction of the applied load (above the rotation
point) and lower soil stresses opposite in direction to the applied
load (below the rotation point) than the unmodified theory
indicated.
It was surmised that the shearing stresses, acting downward on
the soil in front of the advancing face of the footing above the
rotation point, produced a slightly greater confining pressure on
this soil than would be indicated by the weight of the soil alone.
Similarly, the upward shearing stresses on the soil behind the
footing below the rotation point act to reduce the effective
PAGE THIRTEEN
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confining pressure. This change in confining pressure was
accounted fo·r by a mod.ification of the effective unit weight of
the soil in the following way.
Y1 y (1 + k tan cf>) Y2 y (1 k tan cf>)
Where:
Y1 Modified unit weight of soil in the direc-tion of the applied
load.
Y2 Modified unit weight of soil in the direc-tion opposite the
applied load.
k Unit weight coefficient.
Other coefficients introduced or used in Research Report 105-1
were:
J 1 Coefficient of shear stress, vertical foot-ing surfaces.
J 2 Coefficient of shear stress, footing bottom. K0 Coefficient
of earth pressure at rest.
The influence of these coefficients on the predicted load and
the point o.f rotation was determined by allow-ing each to vary
while the others were held constant. Typical sets of curves
developed in this manner are shown in Figures 14, 15, and 16.
Figure 14, representing a cohesionless material such as the dry
Ottawa sand, shows that two coefficients have
0.6
,: ;~
(5 0.7 '" 4! ()
~= . ., 1-, ..... () c: b 0.6 ()
>· 0: ,. o. OJ
" 0.5
60
40
,; ·< "' .J ·~ (/) 20 WID 1-..J !,!I OQ. w a: Cl.
0
B
k 1 Ko
A'-... ' h
:e.~
""'----
LEGEND•
-fi rl----'
~ .._""'-.
~ -~
B -X
J, -· h-0
X/
K0 -0 k -A
/"
-·-~== !=O=- c -·- -·--/
0
0.3
0.1
/ /
X:
0.5
0.3
l<
4 0.7
0.5
6 0.9
0.7
8
0.9
Figure 14. Coefficient sensitivity, c=O psf, cf>=37", H=2
ft., D=1 ft., d=0.33 ft.
PAGE FOURTEEN
a high influence on the theo-retical solution. The unit weight
coefficient, k, has a high degree of influence on the predicted
position of the point of rotation. The earth pressure coefficient
modifier, B, has a great ·influence on the predicted load.
In Figures 15 and 16, which represent soils with co-hesion only
and soils with both cohesion and an angle of shear resistance,
respectively, the great influence of B is again shown, while k is
no longer very influential.
A study of coefficient sensitivity charts and compari-son of
predicted and observed loads indicated that all coefficients except
B could be held constant for the range of soils tested in this
program. The values set for these coefficients are:
Jl J2 = 0.7 Ko = 0.5 k = 0.5
It was found that the value o.f B necessary to suc-cessfully
predict ultimate loads varied with the soil parameters of cohesion
(c) and angle of internal friction ( cf>) . The average values
of B indicated by the tests on Ottawa sand, Easterwood clay,
laboratory clay-sand mixtures, and Trinity clay were used to
develop a pre-diction equation for B. This equation was determined
from the function of cf> used in the theoretical solution and a
linear model in terms of c. This prediction equa-tion is given and
presented in graphical form in Figure 17.
0.7
->-'" z 5 Q.
z 0.6 0 r:: "' >-,_; ~~
~-r-o~ "'~-1!:1 ~ -I
o- _,.__ _,._
oc >-:r: 0.5 1- . Q. w 0
0.4 LEGEND:
1000
X
/ 600
0 s ..J
0(/) wm 1-..J
600 !
-
0.7
z 5'
0.6 .. z 0 j:: ~ «,_: bU. "'~ 0 0.5 f-:I: f-a.
"' 0 800
600
0 400 =20
=15
,j,: 10
,. =5
lj>=O
0 1000 2000 3000 4000
COHESION, c, lbs/ft 2
8 EQUATION
B =0.0000673 c + 10.25 ton+ 2.686 ton (45 + 12)
- 2.141 ton 2 ·(45 + .p/2)
5000
Figure 17. So.Zution for earth pressure coefficient
modifier.
TABLE 4. COMPARISON OF TEST RESULTS WITH THEORY, COHESIVE
SOILS
(1) (2) (3) (4) (5) Test No. Load at Predicted Loads
Rotation Conven- New Test Load to of 5° tiona! Theoryl
Predicted
(1) Theory7 (3) Load Ratios
lbs. (2) lbs. (1)/(2) (1)/(3) lbs.
E-1 488 200 459 2.44 1.06 E-2 385 179 337 2.15 1.14 E-3 500 241
535 2.07 .935 E-4 615 337 871 1.82 .706 E-5 340 181 384 1.88 .885
C-1 245 230 300 1.07 .817 C-2 348 276 344 1.26 1.01 C-3 273 207 241
1.32 1.13 L-1 120 63 92 1.90 1.30 L-2 164 93 154 1.76 1.06 L-3 238
128 324 1.86 .735
Using these coefficients in the theo·retical solution r:esulted
in the comparison of predicted loads and test loads shown in Tables
4 and 5. Also included in these tables are values of loads
predicted using the old theory.
In column ( 4) o.f Tables 4 and 5 the ratio of each test load to
the corresponding load predicted by the conventional theory7 is
tabulated. The test loads vary from an average o-f 20% higher than
predicted loads for the Trinity clay, to about 500% higher for the
Ottawa sand. For all 28 tests (seven different soil con-ditions)
the test values average 4.09 times greater than the loads predicted
by the conventional theory. Thus, the test loads are about 300%
higher than the predicted loads.
Tables 4 and 5 also present a comparison between the test loads
and the new theory in column ( 5) . The
·ratio of test loads to predicted loads shown in column ( 5) are
about the same for each different type of soil.
Two rather low values of this ratio ( .410 and .630) are given
by tests S8 and S9. These weTe tests in Ottaw~ sand which was in a
very loose condition. Ap-parently, the new theory gives a rather
poor estimate of the ultimate load for footings in a very loose
sandy soil. Fortunately, this is not often a condition of practical
importance.
Another test which correlated poorly was SIS. This was an
extremely slender footing, with a ratio of footing width to depth
of 0.167. The test load was 50% higher than the predicted load, an
error on the conservative side.
. The average value of the test load to· predicted load ratio
was 0.912 for all footings tested. The new theory thus predicted
loads that averaged 10% higher than the test loads.
The reliability of the theory with variation in the 1/:eometry
of the footing tests (i.e. variation in H/D and d/D) is shown by
Figures 18 through 20. Of the 20 test points compared to
theoretical curves in these fig-ures, only three show considerable
divergence from the theoretical curves. The test point at a value
o.f H/D of 1.0 in Figure 18 is about 30% low and the first and
third points in Figure 20 are 18% high and 13% low, respectively.
With these possible exceptions, the test data points closely
followed the theoretical curves.
PAGE FIFTEEN
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TABLE 5. COMPARISON OF TEST RESULTS WITH THEORY, OTTAWA SAND
(1) (2) (3) (4) (5) Test No. Load at Predicted Loads
Rotation Conventional New Test Load to Predicted Load Ratios of
5° Theory7 Theoryl (1) (2) (3) (1)/(2) (1)/(3) lbs. lbs. lbs.
S1 28.1 5.47 32.5 5.14 .865 S2 29.0 5.47 32.5 5.30 .892 S3 28.0
5.47 32.5 5.12 .862 S4 28.3 5.47 32.5 5.17 .871 S5 20.0 3.79 23.9
5.28 .837 S6 31.0 5.47 32.5 5.67 .954 S7 25.6 3.47 32.5 4.68 .788
S8 9.3 3.83 22.7 2.43 .410 S9 14.3 3.83 22.7 3.73 .630 S10 20.8
3.79 23.9 5.49 .870 S11 16.6 3.79 23.9 4.38 .695 S12 33.3 5.30 38.2
6.28 .872 S13 22.0 4.11 23.3 5.35 .944 S14 48.0 .5.74 50.8 8.36
.945 S15 22.3 2.75 14.9 8.11 1.50 S16 51.3 7.64 52.5 6.71 .977 S17
113.0 14.7 134.0 7.69 .843
Average 4.09 .912 .
Range 1.07-8.36 .410-1.50
c.v. 55% 23%
900
/ /'
,/
~ . o''· R HID= 2. ?,;)? l'i!>l'· v2. ~
0/ .~
/ ~
600
300
~ a:-0 0 ., "-0
z 0 ;:: g
900 a: !;( 0
"' 9 600
0.1 0.0 0.2. 0.4 0.5 0.3 diD
FOOTING DIAMETER TO DEPTH RATIO
~THEORETICAL ~ TESTS
~ "-.,
f' . ~-----~-- --. 300
150
HID=2
i--9.--1-o--
D. ~'hr:!.:.-- ~· ---_o-~ -
100
50 ,; CD ...J
a: :;, "- 0 0
z 0 ;:: 4 ,__ 0 a: 1- 150
"' 0 "' 0 ...J
100
0.0 0.1 0.2. 0.3 0.4 0. 5 diD
FOOTING DIAMETER TO DEPTH RATIO
~ THEORETICAL ~ TESTS
~ ~ diD =0.33
~. ~---- t---o-.
50
0 2. 3. 4 0
HID 0 I 5
5 0 2 3 4
HID HEIGHT OF LOAD TO FOOTING DEPTH RATIO HEIGHT OF LOAD TO
FOOTING DEPTH RATIO
Figure 18. Easterwood Clay tests. Figure 19. Ottawa Sand
tests.
PAGE SIXTEEN
-
500
;' ~THEORETICAL 1/ iTESTS - I
HID= 2 {:;/ / I/ .
~~ / o'< '< ,. . ?0 '
,; 400 m ...1
cC 0 "
"' lL 0 300 z 0 i= i'! 0 a: 1- 200 "'
0/
/'/~
~ ~/ ••
0
"' 0 ...1
100
0 0.1 0.2 0.3 0.4 0.5
d/0 FOOTING DIAMETER TO DEP.TH RATIO
Figure 20. Trinity Clwy tests.
Summary The purpose of the model tests reported in this
paper was to determine if the theory developed in Re-search
Report 105-1 could be successfully used to predict the ultimate
lateral loads which could be resisted by drilled shaft
footings.
The various coefficients involved in the the()retical solution
have been evaluated by correlation of the theory with the model
tests. Based ()n this correlation the theory can predict, with
reasonable accuracy, the ulti-
mate loads on footing models in soils ranging from cohesionless
sand to clays.
The indication given by these model tests is that the
conventional design techniques for service structure footings are
extremely conservative, and that existing footings are overdesigned
by a large margin.
The next step in determining the value of the new theory can
predict, with reasonable accuracy, the ulti-ings are presently
under construction as part of Research Study 2-5-66-105.
Selected References l. lvey, Don L., "The()ry, Resistance of a
Drill~d Shaft
Footing to Overturning Loads," Research Report No. 105-1, Texas
Transportation Institute, August, 1967.
2. Lambe, William T., Soil Testing for Engineers, John Wiley
& Sons, Inc., 1951.
3. Taylor, Donald W., Fundumentals of Soil Mechanics, John Wiley
& Sons, Inc., 1948.
4. Seed, H. B. and Chan, C. K., "Thixotropic Charac-teristics of
Compacted Clay," Proceedings, ASCE, Vol. 83, S.M. 4, November,
1957.
5. Mitchell, J. K., "Fundamental Aspects of Thixotropy in
Soils," Proceedings, ASCE, Vol. 86, S.M. 3, June, 1960.
6. Moretto, 0., "Effects o-f Natural Hardening on the Unconfined
Compression Strength o·f Remolded Clays," Second International
Conference on Soil Me-chanics and Foundation Engineering,
Rotterdam, Vol. 1, 1948.
7. lvey, Don L., and Hawkins, Leon, "Signboard Fo()t-ings to
Resist Wind Loads,'' Civil Engineering, De-cember, 1966, p. 34.
PAGE SEVENTEEN
-
Appendix
40
5
30
/' f--·" . ...._ 5 /
0 2.0
-
0
-
PAGE TWENTY
70 0
50
400
-
70 0
60 0
50 0
40
a3o .. 0 .J
0
0
I
/" ~ /
-.'\
700
60 0
I
50 0
\ v' 0 .
/
/"
/ o I
40
20 ol----- 20 0
10 0
0
0.0
~ 0.5
1.0 0
'
TEST NO. E I TYPE OF SOIL : EASTERWOOD CLAY MOISTURE CONTENT :
17.5•!.- 19°/. SIZE OF FOOTING : 4,." x 10" HEIGHT OF PULL 20
f\ .. , /-.. ---.......v
10 15 20
10 0
0
0.0
~ 0.5
1.0 0
.
TEST NO. E •2 TYPE OF SOIL : EASTERWOOD CLAY MOISTURE CONTENT :
17.5% - 19•!. SIZE OF FOOTING : 4• x 12." HEIGHT 0 F P 42." ULL
~. v'. t---:7
10 15 20
ANGLE OF DEFLECTION , degroos
400 35 0
350 30 0
30 0 ,r-•, ,. 1\
-\ 250 o-zo
~I < "' 0 I
25
20
,.-;:/
-·\ .,. 0'
of ~-~ .J . I
20 0
10 0
0
0.0
\ 1--r-.
TEST NO. E !5 TYPE OF SOIL : EASTERWOOD CLAY MOISTURE CONTENT •
17.5%-19% SIZE OF FOOTING • 3" x 12• HEIGHT OF Dl'L ' ...
51'7"---· -~ 0. 1.0
0 10 15 20
ANGLE OF DEFLECTION, dooreoo
15 0
10 0
5 0
0
0.0
0 ..
~ ")
-TEST NO. C 3 TYPE OF SOIL : TRINITY CLAY MOISTURE CONTENT : 18%
SIZE OF FOOTING : r x 12" HEIGHT OF PULL ' 24
.... 0.5 0 I/"'"' ['\.
1.0 0 5 10 15 20
ANGLE OF DEFLECTJON,deor-
01/ cS 15 g .J
10 0
0
0 TEST NO. L 3 TYPE OF SOIL: TRINITY CLAY 33"!.
SAND 67% SIZE OF FOOTING : 4• 1 12.•
ANGLE OF DEFLECTION, deQrua
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