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A study of static torsional loading on drilled shafts

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A study of static torsional loading on drilled shafts
Creator:
Volmer, Brian Paul
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English
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xiii, 120 leaves : ; 28 cm

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Subjects / Keywords:
Dead loads (Mechanics) ( lcsh )
Torsion ( lcsh )
Shafts (Excavations) ( lcsh )
Soil mechanics ( lcsh )
Dead loads (Mechanics) ( fast )
Shafts (Excavations) ( fast )
Soil mechanics ( fast )
Torsion ( fast )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Bibliography:
Includes bibliographical references (leaves 115-120).
General Note:
Department of Civil Engineering
Statement of Responsibility:
by Brian Paul Volmer.

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|University of Colorado Denver
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|Auraria Library
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Resource Identifier:
747568676 ( OCLC )
ocn747568676
Classification:
LD1193.E53 2011m V64 ( lcc )

Full Text

A STUDY OF STATIC TORSIONAL LOADING ON DRILLED
SHAFTS
by
Brian Paul Volmer
B.S., University of Colorado Denver, 2008
A thesis submitted to the
University of Colorado Denver
in partial fulfillment
of the requirements for the degree of
Master of Science
Civil Engineering
2011


2011 by Brian Paul Volmer
All rights reserved.


This thesis for Master of Science
degree by
Brian Paul Volmer
has been approved
by
Hamid Z. Fardi
/

/
Date


Volmer, Brian Paul (M.S., Civil Engineering)
A Study of Static Torsional Loading on Drilled Shafts
Thesis directed by Professor Nien-Yin Chang
ABSTRACT
Torsional loading on deep foundations is a topic that has received less
attention than other load types, particularly the effects of combined-loading
and sequences of loading. This work has investigated some of the above
effects, but much more in-depth study is desired. A study of the torsional
response of drilled shafts is made using a new nonlinear finite element
analysis program, SSI3D, for both cohesive and cohesionless soils. This study
includes the influences of combined lateral-torsional and vertical-torsional
loading, which are found to be significant in some cases and highly dependent
upon the soil type. A comparison between the developed finite element
analysis and existing design methodology is made. It is found that some of
the design methods compare surprisingly well with the finite element analysis,
but some were a bit off. Also, because little full-scale testing has been done
for torsional loading and torsional loading testing is by nature more complex
than that of the more common vertical or lateral tests, a full-scale torsional
load test with accommodation for vertical and/or lateral loading is proposed in
the hopes of facilitating a better understanding of the behavior of deep
foundations under combined loading in different soils.
This abstract accurately represents the content of the candidate's thesis. I
recommend its publication.


ACKNOWLEDGEMENT
My thanks to God, my advisor, my family, and my friends for their support
and encouragement, without which this work would have never come to be.
I would like to give special thanks to Dr. Nien-Yin Chang (my advisor),
Kevin Lee (friend in geotechnical studies), Dr. Hien Nghiem (friend and
creator of SSI3D), Paul Volmer (my dad), and Cuong Vu (friend in
geotechnical studies) for their distinguished physical insight, criticism,
technical support, and patience.
I am very grateful for my great friend and fellow student in geotechnical
studies Shanna Malcolm, who prepared the greater portion of the drawings
shown in this work.
Also, I would like to thank the Achievement Rewards for College Scientists
Foundation (ARCS) for their financial support in my graduate studies. Their
aid is greatly appreciated.


TABLE OF CONTENTS
Figures........................................................................x
Tables......................................................................xiii
Chapter
1. Introduction................................................................1
1.1 Background.................................................................1
1.2 Objectives of Research.....................................................2
2. Literature Review..........................................................3
2.1 Introduction..............................................................3
2.2 Full-Scale Testing........................................................3
2.2.1 Stoll (1972).............................................................3
2.2.2 Tawfiq (2000)............................................................5
2.3 Response Theory...........................................................7
2.3.1 ONeill (1964)...........................................................7
2.3.2 Poulos (1975)............................................................8
2.3.3 O'Neill and Dutt (1976).................................................10
2.3.4 Randolph (1981).........................................................12
2.3.5 Chow (1985).............................................................13
2.3.6 Hache and Valsangkar (1988)............................................14
2.3.7 Georgiadis and Saflekou (1990).........................................14
2.3.8 Lin and Al-Khaleefi (1996).............................................18
2.3.9 Guo and Randolph (1996)................................................19
2.3.10 McVay, Herrera, and Hu (2003).........................................19
2.3.11 Zhang and Kong (2006).................................................20
vi


2.3.12 Hu, McVay, Bloomquist, Herrera, and Lai (2006).........................20
2.3.13 Guo, Chow, and Randolph (2007).........................................23
2.3.14 Kong and Zhang (2008)..................................................23
2.4 Design Methods............................................................23
2.4.1 McVay, Herrera, and Hu (2003)............................................24
2.4.2 Colorado Department of Transportation (2004)............................25
3. A Study Using the Finite Element Method (FEM)..............................27
3.1 Introduction..............................................................27
3.2 Choice of Program.........................................................27
3.3 Program Validation........................................................27
3.4 Choice of Material Models.................................................28
3.4.1 Material Model for Pile..................................................29
3.4.2 Material Model for Soil and Interface...................................29
3.5 Hypothetical Case in Clay.................................................29
3.5.1 Model Development........................................................29
3.5.1.1 Geometric Characteristics..............................................29
3.5.1.2 Material Parameters for Pile...........................................32
3.5.1.3 Material Parameters for Clay...........................................32
3.5.2 Load Cases for Clay......................................................35
3.5.2.1 Pure Torsional Load....................................................35
3.5.2.2 Pure Lateral Load......................................................36
3.5.2.3 Pure Vertical Load.....................................................36
3.5.2.4 Combined Lateral and Torsional Load....................................39
3.5.2.5 Combined Vertical and Torsional Load...................................42
3.6 Hypothetical Case in Sand..................................................44
3.6.1 Model Development........................................................44
3.6.1.1 Geometric Characteristics..............................................44
vii


3.6.1.2 Material Parameters for Pile.............................................46
3.6.1.3 Material Parameters for Sand.............................................46
3.6.2 Load Cases for Sand.......................................................49
3.6.2.1 Pure Torsional Load......................................................49
3.6.2.2 Pure Lateral Load........................................................49
3.6.2.3 Pure Vertical Load.......................................................50
3.6.2.4 Combined Lateral and Torsional Load.....................................54
3.6.2.5 Combined Vertical and Torsional Load.....................................57
4. Comparison of FEM Results with Existing Design Methodology...................59
4.1. Introduction................................................................59
4.2. Consistency in Comparison...................................................59
4.3. Presentation of Design Methods for Clay.....................................60
4.3.1. FDOT Structures Design Office Method......................................60
4.3.2. FDOT District 7 Method....................................................61
4.3.3. CDOT Method in Clay.......................................................62
4.4 Comparison of Methods in Clay...............................................62
4.5. Presentation of Design Methods for Sand.....................................66
4.5.1. FDOT Structures Design Office Method......................................66
4.5.2. FDOT District 5 Method O'Neill and Hanson...............................66
4.5.3. CDOT Method in Sand.......................................................67
4.5.4. FDOT District 7 Method....................................................68
4.6 Comparison of Methods in Sand................................................69
5. Proposal of Torsional Load Test..............................................74
5.1 Introduction................................................................74
5.2 Load Application Apparatuses................................................74
5.2.1 Torsional Load Apparatus...................................................75
viii


5.2.1.1 Wrench..........................................................75
5.2.1.2 Hydraulic System................................................78
5.2.1.3 Reactions.......................................................80
5.2.2 Accommodation for Lateral Load Application........................81
5.2.3 Accommodation for Vertical Load Application.......................83
5.3 Measurement Systems...............................................84
5.3.1 Video Recorded Displacement Measurements..........................84
5.3.2 Measurement of Load Application...................................85
5.3.2.1 Tolerance Analysis of Applied Load Measurements.................90
5.3.3 Measurement of Pile Displacement..................................97
5.3.3.1 Above Ground Surface............................................97
5.3.3.2 Below Ground Surface...........................................102
5.4 Summary of Equipment for Proposed Test.............................105
6. Summary.............................................................107
7. Conclusions.........................................................110
8. Recommendations for Future Research.................................112
References.............................................................115
IX


LIST OF FIGURES
Figure
2.1 Test Setup by Stoll (1972)...............................................4
2.2 Load-Rotation Curve by Stoll (1972).....................................4
2.3 Test Setup by Tawfiq (2000).............................................6
2.4 Basis of 1-Dimensional Numerical Model by O'Neill (1964)................8
2.5 Comparison of Calculated and Measured Model Torsional Responses by
Poulos (1975)..........................................................9
2.6 Comparison of Solution by Poulos and Model Test in Clay by O'Neill and
Dutt (1976)...........................................................10
2.7 Comparison of Solutions by Poulos and Model Tests in Sand by O'Neill and
Dutt (1976)...........................................................11
2.8 Discretization of Pile by Chow (1985)...................................13
2.9 Model for FEM by Georgiadis and Saflekou (1990).........................15
2.10 Axial Response Due to Axial Loading alone by Georgiadis and
Saflekou (1990).......................................................16
2.11 Axial Response Due to Combined Torsional-Axial Loading by Georgiadis
and Saflekou (1990)...................................................17
2.12 Torsional Load Response by Lin and Al-Khaleefi (1996)..................18
2.13 Reduction in Lateral Capacity Due to Torsion by Hu, McVay, Bloomquist,
Herrera, and Lai (2006)...............................................22
3.1 Geometric Arrangement of FEA Model in Clay...............................31
3.2 Pure Torsional Load Response in Clay....................................38
3.3 Pure Lateral Load Response in Clay......................................38
3.4 Pure Vertical Load Response in Clay ....................................39
3.5 Combined Lateral-Torsional Load Response in Clay........................41
x


3.6 Lateral Response Due to Torsion in Clay.................................41
3.7 Combined Vertical-Torsional Load Response in Clay.......................43
3.8 Vertical Response Due to Torsion in Clay................................43
3.9 Geometric Arrangement of FEA Model in Sand..............................45
3.10 Pure Torsional Load Response in Sand....................................52
3.11 Pure Lateral Load Response in Sand .....................................53
3.12 Pure Vertical Load Response in Sand....................................53
3.13 Combined Lateral-Torsional Load Response in Sand.......................56
3.14 Lateral Response Due to Torsion in Sand................................56
3.15 Combined Vertical-Torsional Load Response in Sand......................58
3.16 Vertical Response Due to Torsion in Sand...............................58
4.1 Comparison of FDOT District 7 and CDOT Method with FEA for Clay.........64
4.2 Comparison of FDOT District 7 and CDOT Method with FEA for Clay........65
4.3 Comparison of FDOT SDOF and District 7 Method with FEA for Sand........71
4.4 Comparison of All Design Methods with FEA for Sand.....................71
4.5 Comparison of FDOT SDOF and District 7 Method with FEA for Sand........72
4.6 Comparison of All Design Methods with FEA for Sand.....................72
5.1 Typical Wrench Design...................................................76
5.2 Typical Wrench Design..................................................76
5.3 Typical Wrench Design..................................................77
5.4 Isolated Lateral Load Application to Torsional Load Test...............82
5.5 Lateral Load Application in a Rotationally Displaced State..............82
5.6 Isolated Vertical Load Application for Lateral Pile Test (ASTM, 2009 a).83
5.7 Geometrical Description of Load Application.............................87
5.8 Profile of Relative Displacement Measurement of Arm Ends................89
5.9 Plan View of Relative Displacement Measurement of Arm Ends...............89
xi


5.10 Rotated Coordinate System.............................................93
5.11 Measurement Device Setup for Test Pile Displacements ..........98
5.12 Measurement Device Setup for Test Pile Displacements ..........99
5.13 Depiction of an Above Ground Pile Displacement in the General Sense..101
5.14 Mohr's Representation of Pure Torsional Load on a Cylinder ..........104
5.15 Test Pile Instrumented for Displacement Measurement..................105
xii


LIST OF TABLES
Table
4.1 Properties for Analysis of Hypothetical Cases.........................60
4.2 Design Capacities for Methods in Hypothetical Clay Case..............63
4.3 Design Capacities for Hypothetical Cases in Sand......................70
5.1 Perfect Measurement of Maximum Applied Load Magnitude.................95
5.2 Measurements of Maximum Applied Load Magnitude with Error.............95
5.3 Tabulation of Error Due to Various Load Application Components........96
5.4 Summary of Equipment for Proposed Load Test..........................106
xiii


1. Introduction
1.1 Background
Torsional loading on deep foundations is a topic that seems to have received less
attention than that of other load types. This lack of attention seems to be due to the
great value attached to understanding the commonly more critical vertical and lateral
load types. Nevertheless understanding pile response due to torsional loading is an
important concern and has been proven to be critical in some circumstances.
Additionally, understanding torsional loading seems to be gaining importance as
some structures are now requiring greater torsional loads of deep foundations. In
recent years the Florida Department of Transportation (FDOT) has enforced the
replacement of cable supported traffic signals and the like with mast and arm supports
in southern Florida to meet the large loads brought on by hurricanes (Hu, McVay,
Bloomquist, Herrera, and Lai, 2006). These mast and arm type signal supports cause
the associated foundational support tremendous torsional loading and are an excellent
example of the practical application for a better understanding of torsionally loaded
deep foundations. Other examples of practical applications are power line towers,
slender buildings, and especially offshore platforms (Kong and Zhang, 2008).
Upon a review of literature it was found that there exists a dearth of information
regarding the response of deep foundations under combined loading. This lack of
information is even more pronounced when the combined loading scenario involves
torsion. The attention that torsional loading has received has been primarily focused
upon pure torsional loading without consideration of the influences from axial and
lateral loads. However, numerical and physical models developed by (Hu, McVay,


Bloomquist, Herrera, and Lai, 2006) and (Georgiadis and Saflekou, 1990) suggest
that the interaction between lateral and torsional loading and axial and torsional
loading is significant. This suggestion is further substantiated by the full scale lateral-
torsional testing performed by (Tawfiq, 2000). Because it is almost inconceivable
that torsional loading be present without significant lateral and vertical loads for all
practical problems, it is felt that the influences of combined loading are important and
should be considered when analyzing torsionally loaded deep foundations.
Full scale testing gives the most reliable results for the determination of deep
foundation safety. Unfortunately full scale testing is currently only performed for
limited types of loading. Upon review of literature it was found that the full scale
testing methods used to study the performance of deep foundations under torsional
loading are somewhat behind that of other load types. In fact only two sets of full
scale torsional tests are known to have ever been performed. These torsional tests;
however, lacked the full scale testing standards currently available to that of lateral
and vertical testing.
1.2 Objectives of Research
This work is written to satisfy a number of objectives. The first is to review the
available literature regarding the full scale testing, behavior, and design of deep
foundations under torsional loading. The second is to perform a simple study of the
response of drilled shafts under torsional loading, including the effects of combined
lateral-torsional and vertical-torsional loading, using the Finite Element Method
(FEM). The third objective is to compare the results found by the FEM with existing
theory and design methods. And the fourth and last objective is to propose a
reasonable full scale torsional load testing method.
2


2. Literature Review
2.1 Introduction
This literature review is concerned with the determination of deep foundation
response to torsional loading. The results, methods, and instruments associated with
full-scale testing are of prime importance as this testing yields the most accurate
results for deep foundation behavior. Additionally, the methods by which the
torsional behavior of piles may be predicted are of important consideration as are the
methods that are used to design such foundations.
The following is broken up into three sections. The first section reviews past full-
scale torsional tests, the second reviews methods by which torsional response may be
determined, and the third reviews methods used in design to estimate the ultimate
torsional resistance of piles.
2.2 Full-Scale Torsional Load Testing
2.2.1 Stoll (1972)
Stoll performed the only known full-scale pure torsional load tests on piles. Two
tests were performed on steel cylindrical piles in sand in hopes of determining the
vertical frictional resistance of such. Each pile was 10.75 inches in diameter. One
pile was embedded in 55 ft of soil and the other in 70 ft. The testing apparatus is
considered elegant in nature. A simple beam was symmetrically affixed about each
pile center so that equal and opposite loads could be applied via hydraulic cylinders to
the beam ends creating a pure couple as shown in Figure 2.1. Pile displacements
were measured at the pile head by way of dial indicators. The load displacement
diagram obtained from the testing is also shown in Figure 2.2
3


side shear
Figure 2.1: Test Setup by Stoll (1972)
100
7 80
60
3
&
o 40
t
20
S' K V
/ / / r 7 l /
Tes \ pile v-e 1 i i
r / / f ^m. T Test pile A-3 f- -p /
4' r V 1 _ 2 xFxl 2 1 1 L i / / i / 1 1
t , / / M, i ' i 1 i -L
0.02 0.04 0.06 0.08 0.10 0.12
a -angle of twist at top of pile (radians)
0.14
Figure 2.2: Load-Rotation Curve by Stoll (1972)
4


2.2.2 Tawfiq (2000)
Tawfiq performed the only other known full-scale torsional load tests on piles. Three
combined simultaneous lateral and torsional load tests were performed on drilled
shafts 4 ft in diameter and 20 ft in embedment in profiles inclusive of both sand and
clay. A heavy beam end was affixed to each pile head and load was applied via
hydraulic ram to the opposing beam end such that a combined lateral and torsional
load resulted as shown in Figure 2.3. Pile displacement was measured by monitoring
the movement of laser beams from the lasers mounted on the pile head and strain
gages which were placed at various depths. Also, slope indicators were installed in
the test shafts for lateral rotational displacement measurements and ultimately lateral
defection calculation
From the testing of this work it was concluded by the author that combined lateral
loading may significantly increase the torsional capacity of a pile.
5


Figure 2.3 Test Setup by Tawfiq (2000)
I Beam Stiffener at Both Sides of the Beam
12" x 12" Steel Tube Beam
Filled with Concrete
V"' \
InstnmMed Shalt
Polymer Slurry
Mineral Slurry
Figure 2.22 Field Test Arrangement


2.3 Response Theory
The following presents the available literature on the theoretical response of piles
subjected to torsional loading.
2.3.1 O'Neill (1964)
O'Neill developed a 1-dimensional numerical model capable of handling nonlinear
behavior for piles under torsion. The basis of this numerical scheme is the
mechanical model shown in Figure 2.4 where the pile is broken up along the length
into a number of discrete elements. By this method, piles of various geometric and
both piles and soil profiles of various material properties may be handled.
The developed computational model was verified against model testing performed in
the laboratory. However, the computational inputs came from the results of the
model testing used for verification. Also, no attempt to develop solutions to the
response of torsionally loaded piles upon a basis of commonly available soil
parameters from practical site investigation is made. Thus, the practical benefits of
this work are extremely limited.
7


+ T
+ 8
+ M
RIGID
ELEMENT
N- I
RIGID
ELEMENT
N
RIGIO
ELEMENT
N+ I
Figure 2.4: Basis of 1-Dimensional Numerical Model by O'Neill (1964)
2.3.2 Poulos (1975)
Poulos developed parametric solutions to the response of piles under torsion.
Although the methods of solution may accommodate pile-soil slip at the interface, the
theory of elasticity seems to be relied upon for the solutions. From the solutions
developed it was found that, except for stiff piles, the amount of pile embedment does
not significantly affect the torsional response of the pile and that the load transfer
from pile to soil drops off rapidly with depth.
Poulos performed a number of both torsional and axial load tests on model piles in
clay. The model piles were constructed of aluminum rod with diameters ranging
from 0.5 inches to 1.5 inches and lengths ranging from 6 inches to 20 inches.
8


It was found that if the modulus of rigidity was back-calculated from the axial testing,
it could be used, with the developed solutions, to estimate the torsional response with
fairly good agreement as shown in Figure 2.5. Also, the adhesion at the pile-soil
interface was back-calculated from both the torsional and axial load model tests. A
strong agreement was found.
Figure 2.5: Comparison of Calculated and Measured Model Torsional Responses
by Poulos (1975)
9


2.3.3 O'Neill and Dutt (1976)
A discussion by O'Neill and Dutt (1976), shows that the solutions given by Poulos
(1975) are accurate for loadings up to 40 percent of the total resistance, however, for
loadings greater than this the solutions deviate greatly from the actual response of
model pile tests performed by the authors as shown in Figures 2.6 and 2.7. (Note: the
dashed line is that of Poulos and the solid is the measured response.) The authors felt
that this deviation was partly due to a variance in shear stress along the pile interface
with rotational failure. O'Neill and Dutt (1976) suggested that as the top of a pile
rotates, under torsional loading, the shear stresses along the interface near the top
reach a limiting value and are reduced (fail) while the shear stresses along the
interface at greater depths increase causing a sort of progressive failure and overall
variance in shear stresses at the interface which leads to a nonlinear response.
Figure 2.6: Comparison of Solution by Poulos and Model Test in Clay
by O'Neill and Dutt (1976)
10


pile head toachie. inch-pounds
Figure 2.7: Comparison of Solutions by Poulos and Model Tests in Sand
by O'Neill and Dutt (1976)
11


2.3.4 Randolph (1981)
Presented an expression for the torsional response of piles which may be written as;
d2(p 2utq
~dz2=XGf)]
t0
(2.1)
where

modulus, and (GJ)p is the torsional rigidity of the pile. By way of hyperbolic and
Airy functions, Equation 2.1 is solved for various cases of a torsionally loaded pile.
Also, an expression based upon pure elastic-plastic behavior for the angle at which
failure begins is presented.
An attempt at verifying the solutions and expression for failure is made. The load-
rotation curves and known pile properties given by the full-scale testing of Stoll
(1972) are used with the solutions developed by the author to back-calculate the shear
moduli of the soil profiles. These found shear moduli are determined to compare well
with the shear modulus as given by a combination of the Boussinesq solution and
settlement theory for raft foundations. Also, the expression for the rotation angle at
failure was found to give 0.027 radians for pile A-3 and 0.06 radians for pile V-4. In
comparing these values with Figure 2.2 it may be seen that reasonable results are
offered.
The author found through the solutions developed that the pile stiffness is insensitive
to the soil stiffness and that a large error in material properties, namely the shear
moduli, only results in a small error in estimating the torsional capacity. This being
the case, and as mentioned by the author, it is important to recognize that a small
error in a torsional load test may result in a large error in material properties if such
properties are estimated from said test.
12


2.3.5 Chow (1985)
Chow presented a 1-dimensional discrete element approach (FEM) for the analysis of
piles under torsional loading. The method breaks up the pile into a number of
discrete elements along the length of such as shown in Figure 2.8. The governing
equation used is given as;
d2xp
~GPJ^2+k'P^J = 0
(2.2)
where Gp is the modulus of rigidity for the pile, J is the polar moment of inertia of the
pile, xp is the angle of pile rotation, k^ is the subgrade reaction modulus, and z is the
depth. Verification was achieved by comparison with the testing of Stoll (1972) as
shown in Figure 2.2. As may be observed, good agreement is found. It is also
interesting to note the similarity of Equation 2.2 with Equation 2.1 from Randolph
(1981).
Through the work performed, the author found that piles under torsion can be dealt
with in an elegant manner using a 1-dimensional FEM.
nodel
L
C*^>node 2
%
Figure 2.8: Discretization of Pile by Chow (1985)
13


2.3.6 Hache and Valsangkar (1988)
Hache and Valsangkar developed analytical solutions to the governing equations
given by Randolph (1981) (see above) and Scott (1981). The authors presented
solutions for a pile under torsional loading in soil of two layers for both the cases of
homogeneous soil layers and that of linear increasing soil shear modulus. These
solutions expressed the rotation of the pile head as a function of a torsional response
factor for a given pile under known loading. The torsional response factor is a
function of pile geometry and stiffness as well as soil shear modulus and is presented
graphically by the authors for a variety of pile and soil properties. No attempt to
validate or verify these solutions was made.
2.3.7 Georgiadis and Saflekou (1990)
Performed both numerical (FEM) analysis and model testing for piles subjected to
combined axial and torsional loading. The FEM model was broken up into three
basic components. The pile itself was modeled with bar type elements as shown in
Figure 2.9. And the soil was modeled with two nonlinear springs at the appropriate
pile elements joint or nodes. One spring corresponds to the torsional resistance and
the other spring corresponds to the vertical. It is important to mention that these two
spring types (torsional and axial) are not independent of one another but the
interaction between the two are accounted for by considering a resultant total skin
friction at each node. The model tests for piles under axial as well as combined
torsional and axial loading were performed in soft clay. The model piles were
constructed of aluminum tubing of approximately 0.75 inches in diameter and 20
inches long.
Figures 2.10 and 2.11 show the results for axial response under axial loading alone
and combined torsional-axial loading as predicted by the FEM and given by the
14


model testing. As may be observed, the results given by numerical analysis closely
agree with that found by model testing. Also, by comparing the two figures it may be
seen that torsion reduces the axial capacity and increases the settlement of piles in the
soft clay model.
Figure 2.9: Model for FEM by Georgiadis and Saflekou (1990)
15


300
Figure 2.10: Axial Response Due to Axial Loading Alone by Georgiadis and
Saflekou (1990)
16


300
250
i
T55
Figure 2.11: Axial Response Due to Combined Torsional-Axial Loading
by Georgiadis and Saflekou (1990)
17


2.3.8 Lin and Al-Khaleefi (1996)
Lin and Al-Khaleefi analyzed a number of cases for a torsionally loaded concrete pile
using the FEM. First, the authors performed analysis using linear models for both the
pile and soil. Then the pile was modeled with a linear model and the soil with a
nonlinear model. Also, both the pile and soil were modeled using nonlinear models.
The numerical analysis was verified against the solutions given by Chow (1985) and
model tests performed by R. N. Dutt with excellent agreement. Through the analysis
performed the authors found that linear material models for pile and soil
underestimate the angle of rotation and load distribution for torsionally loaded
concrete piles as shown in Figure 2.12. Also, the authors found that a nonlinear soil
model and linear pile model underestimate the angle of rotation, as shown again in
Figure 2.12, but not the load distribution after concrete pile cracking.
Figure 2.12: Torsional Load Response by Lin and Al-Khaleefi (1996)
18


2.3.9 Guo and Randolph (1996)
Guo and Randolph (1996) presented analytical and numerical solutions for pile
behavior under torsional loading. These solutions were developed for application in
the cases of non-homogeneous soil. The authors chose to model non-homogeneous
soil by making the soil shear modulus a power function of depth. The three cases of
elastic, elastoplastic, and hyperbolic soil response were considered for the solutions
obtained. For both the elastic and elastoplastic solutions the governing was given by
Randolph (1981), again, by Equation 2.1. The solutions developed are verified
against the previous work of others including Stoll (1972), Poulos (1975), and Chow
(1985).
Through the presented solutions, the authors found that shear stress drops off
"rapidly" with radial distance from the pile. And authors conclude from this that soil
nonlinearity need only be considered close to the pile. Furthermore, it is found by
comparison with the work of others that perfect elastic-plastic modeling of the soil is
adequate for the determination of the torsional response of piles.
2.3.10 McVay, Herrera, and Hu (2003)
McVay, Herrera, and Hu performed eighty model tests on drilled shaft foundations in
sand under lateral loading and combined lateral-torsional loading in centrifuge. The
model piles were constructed of steel reinforced cement grout and were 1.33 inches in
diameter and ranged between 4 and 9.3 inches of embedment. Testing was performed
at loose, medium, and dense sand densities.
Through the testing performed a most interesting and unique finding was made. It
was found that lateral loading had virtually no influence on the torsional capacity of a
drilled shaft in sand. This is contrary to the conclusions of both Tawfiq (2000) (see
19


above) and Kong and Zhang (2008) (see below) who actually uses a term that
describes the increase in torsional capacity due to lateral loading.
2.3.11 Zhang and Kong (2006)
Zhang and Kong performed model pile tests subjected to torsional loading in
centrifuge. The testing was performed using both loose and dense sand. The piles
were constructed of aluminum cylinders that were approximately 0.62 inches in
diameter and 11.81 inches long with 10.63 inches of embedment.
The authors found that the torsional response in sand is approximately hyperbolic.
Also, an increase in soil density gives a significant increase in the torsional capacity.
And a twist angle of 4 degrees is approximately the point of the torsional capacity.
Additionally, by comparing the results of the torsional testing with that of axial load
testing performed by E.U. Klotz and M.R. Coop the authors found that the axial
capacity relative to the torsional capacity may vary upon the stress state of the soil.
For a lateral stress greater than the vertical, as in dense soil, the torsional capacity
may be greater than that of the vertical. While for a vertical stress greater than the
lateral, as in loose soil, the axial capacity may be greater than that of the torsional.
2.3.12 Hu, McVay, Bloomquist, Herrera, and Lai (2006)
Hu, McVay, Bloomquist, Herrera, and Lai bring the results of approximately ninety
model pile tests in centrifuge for lateral and combined lateral-torsional loading in
sand. The model piles were constructed of cement covered steel pipe to simulate
drilled shafts. These piles were approximately 0.84 inches in diameter and had pile
embedment to diameter ratios ranging from 3 to 7.
The authors found that torsional resistance in sand may be given fairly well by the
axial skin friction models. Also, it is found that the lateral capacities of piles are
20


reduced by the combined application of torsion. Furthermore, as may be of interest
later, the Broms' method was found to overestimate the lateral capacity of short piles.
Figure 2.13 shows the reduction in lateral capacity due to the combined application of
torsion. The keys in this figure may be confusing and warrant an explanation. This
study was developed upon the basis of studying the response of overhead (mast and
arm) cantilever traffic signal support. And the key in Figure 2.13 pertains to the point
of load application on the mast and arm. "No Torque" means the load is applied to
the mast, "Mid Mast" means the load is applied at the mid-point of the mast, and so
forth. Thus, "No Torque" implies pure lateral load, "Mid Mast" implies combined
lateral-torsional loading, and "Arm Tip" implies combined lateral-torsional loading
with a greater amount of torsion.
21


Lateral Load Capacity vs. Point of Load Application Along Mast Arm L/D>3
f 100 4 NoTorqut Mid Mast Arm Arm Tip
if on -
S n .
O Af\ -
** JO j-
o i
0 T l 3 orque/Li X itara i < 1 Lor id (n T 8 9
Lateral Load Capacity vs. Point of Loac Application Along Mast Arm L/D*5
>,100 < i 1 NoTorqut Mid Mast Arm A Arm Tip
& on _
S. 60 o 40 -
-
* 20 ft - I I
j
t ) ; T 2 3 < orqus/Lr l itera > 6 1 Load (n r D 3 9
Lateral Load Capacity vs. Point of Load
Application Along Mast Arm L/D*7
No Torque
Mid Mast
Arm
Arm Tip
Torque/Lateral Load (m)
Figure 2.13: Reduction in Lateral Capacity Due to Torsion
by Hu, McVay, Bloomquist, Herrera, and Lai (2006)
22


2.3.13 Guo, Chow, and Randolph (2007)
Guo, Chow, and Randolph developed solutions to the problem of a torsionally loaded
pile in a two layer non-homogeneous soil profile. Again the governing equation
developed by Randolph (1981), shown as Equation 2.1 above, is used. The solutions
are presented in terms of Bessel functions. Verification is carried out by numerical
analysis and comparison with the testing of Stoll (1972). The authors found that the
developed solution methods are adequate to model the torsional response of piles.
2.3.14 Kong and Zhang (2008)
Performed model group pile tests under torsional loading in centrifuge. The piles
were constructed of aluminum tubing 0.62 inches in diameter and 11.81 inches long
with 10.63 inches of embedment.
Of interest to this work, the authors observed that the torsional response of a single
pile is influenced by lateral loading. This is because torsional loading on a pile group
results in combined lateral-torsional loading for some of the individual piles. The
authors found that lateral load on an individual pile "tends" to increase the torsional
resistance in sand. This phenomenon was referred to as the "deflection-torsion
coupling effect" by the authors.
2.4 Design Methods
After completing a search of the available literature for design methods of torsionally
loaded piles, it was found that a great lack of information exists. In fact only two
organizations are known to the writer to provide such methods. One organization is
the Florida Department of Transportation (FDOT) and the other is the Colorado
Department of Transportation (CDOT). The methods of these organizations are
provided below.
23


2.4.1 McVay, Herrera, and Hu (2003)
McVay, Herrera, and Hu (2003) presented the three methods of design, for piles
under torsional loading, used by the Florida Department of Transportation (FDOT).
All three of the methods are capable of considering piles in layered soil. All FDOT
methods break the total torsional resistance of a pile into two components. And the
total torsional capacity is given by the sum of the resistance from the side of the pile
and the base.
The first method considered is the FDOT Structures Design Office Method. This
method is used to determine the torsional capacity of a pile in either sand or clay.
The side resistance of the pile is given by a simple equation involving "Coulombic
Friction" and assuming no lateral movement. In order to use the FDOT Structures
Design Office Method, only the most basic soil properties need be known. These
properties consist of the unit weight of the soil, interfacial friction angle, and the
lateral earth pressure coefficient.
The second method considered is the FDOT District 5 Method and its commonly
used variation the FDOT District 5 Method "O'Neill and Hanson". The FDOT
District 5 Method O'Neill and Hanson, which is of interest to this work, applies to
cohesionless soil. The District 5 Method uses the computer program SHAFTUF to
calculate the frictional resistance of the side of the pile, whereas, its variation uses the
overburden stress and a function of the Standard Penetration Test (SPT) blow count
to calculate the side friction. To use the District 5 Method, the computer program
SHAFTUF is required. Like the Structures Design Office Method, however, the
District 5 Method variation requires only a few basic soil parameters. These soil
parameters include the unit weight of the soil, the SPT blow count, and the interfacial
friction angle.
24


The last method is the FDOT District 7 Method. The District 7 Method was designed
to apply to clay soil, however, this method may be used to determine the total
torsional resistance of a pile in sand as will be shown in Chapter 4. This method
gives the side friction of the pile as a function of an interfacial adhesion factor,
cohesion, the interfacial friction angle, and the horizontal earth pressure with depth.
The District 7 Method requires more input information than the other FDOT methods.
These inputs include the unit weight of the soil, the soil cohesion, the soil-pile
adhesion, the interfacial friction angle, and the lateral earth pressure coefficient.
It is interesting to note that the calculations for the base resistances of the three FDOT
methods are so similar that the differences between them are seemingly insignificant.
2.4.2 Colorado Department of Transportation (2004)
The Colorado Department of Transportation (CDOT) (2004) (Appendices) presented
their current methods for design of piles under torsional loading. Two methods were
developed. One method is used for design in cohesive soil and the other for
cohesionless soil.
The method used for cohesive soil bears some similarity to that use by FDOT.
However, this method only requires one soil property, which is the cohesion.
The method used for design in cohesionless soils is more detailed than that for
cohesive. This method gives the frictional side resistance as a function of interfacial
friction angle and overburden stress using a lateral earth pressure coefficient. Special
interest lies in the way CDOT defines the lateral earth pressure coefficient. CDOT
feels that a sort of conical, rather than a cylindrical, failure plane involving a
discrepancy in failure wedge weight is involved in expressing the coefficient. This is
not fully understood since the lateral earth pressure coefficient is generally expressed
25


as a function of only the Overconsolidation Ratio and the internal friction angle of
soil. The expression used for base resistance is virtually equivalent to that used for
the FDOT Structures Design Office Method.
26


3 A Study Using the Finite Element Method (FEM)
3.1 Introduction
In order to study the response of deep foundations under torsional loading a finite
element analysis program is chosen and applied to a number of relatively simple load
cases. Two hypothetical models are developed for study. Each model involves the
analysis of the same single drilled shaft with material and geometric properties that
are considered to be typical. One model consists of a cohesive soil profile whereas
the other is cohesionless. Both models are subjected first to pure static torsional,
lateral, and vertical loads. Then each model is subjected to both combined static
lateral-torsional and vertical-torsional loads to study the effects of combined loading.
3.2 Choice of Program
The program chosen for this study is Soil Structure Interaction 3D (SSI3D). SSI3D is
a very new and remarkable 3-dimensional nonlinear finite element analysis program.
It was created by Dr. Hien Nghiem, a doctorial graduate of the University of
Colorado Denver (UCD).
3.3 Program Validation
SSI3D has been rigorously verified and validated by Dr. Nghiem. This verification
and validation includes the geotechnical scenarios of various loading conditions
imposed upon deep foundations. Verification of SSI3D, regarding the response of
deep foundations under loading, includes but is not limited to the well known Broms'
method (Broms, 1964) as well as the popular numerical programs PLAXIS,
ABAQUS, and ANSYS. Validation is achieved by comparison of SSI3D predictions
with full scale deep foundation test results obtained from a variety of soil and loading
conditions. The validation of SSI3D for the problems of consideration is not shown
27


in this work; however, the interested reader may consult (Nghiem, 2009) for the
presentation of some of this information and/or contact the geotechnical group with
the UCD department of civil engineering.
3.4 Choice of Material Models
In general, for the finite element analysis of deep foundations under loading, three
material models corresponding to three important physical aspects need be developed.
The three physical aspects mentioned refer to: the behavior of the pile itself, the
behavior of the soil surrounding the pile, and the behavior of the interface between
the pile and surrounding soil.
SSI3D is capable of utilizing quite a variety of well known material models. These
models include Lade, Modified Cam-Clay, Drucker-Prager, Tresca, Von-Mises, and
the Mohr Coulomb model.
The material models chosen for the study herein may be considered to be of a
simplistic nature. This so called simplicity is deliberate. In this particular case the
material models need be only as complex as observed behavior dictates. If a simple
material model is well validated, there should be no need to go to greater
complexities. It seems that applying complex material models in geotechnical finite
element analysis (FEA) has become an easy yet misunderstood task. In general, the
information provided by field investigation in practical deep foundation design seems
not to support the inputs that complex material models require. So, it may be said
that complex material models in geotechnical FEA are generally limited by the
inputs. This issue is avoided in this work by choosing relatively simple, well known,
reliable, and robust material models.
28


3.4.1 Material Model for Pile
In order to avoid unnecessary complexities in analysis, pure isotropic elastic theory is
chosen as the material model for the pile itself. This choice is felt to be justified by
validation performed by the creator of SSI3D. Dr. Hien Nghiem used the elastic
model to simulate the behavior of pile material in validation with full scale deep
foundation load tests with good result. Also, Gonzalez (2010) applied elasticity to the
simulation of pile materials in validating the well known FLAC program for deep
foundations under static loading.
3.4.2 Material Model for Soil and Interface
The Mohr Coulomb failure criterion is chosen as the material model for both the soil
media and interface of both the sand and clay models. It is well known that the Mohr
Coulomb model is somewhat simplistic when compared with some of the accepted
material models of this time i.e. the CAP models for cohesive soil and Lade's Model
for sand. The Mohr Coulomb criterion, however, is considered to be quite good and a
very valuable deep foundation research tool. The Mohr Coulomb model in SSI3D is
well validated for various load cases on deep foundations by Dr. Hien Nghiem. Also,
it is worth mentioning that the Mohr Coulomb model is well validated by Cesar
Gonzales (2010) in the FLAC program against full scale deep foundation testing.
3.5 Hypothetical Case in Clay
3.5.1 Model Development
3.5.1.1 Geometric Characteristics
A 3 ft diameter circular pile of 31 ft length is embedded 30 ft into a clay profile. The
model is of circular geometry to easily match the pile. In order to account for pile-
soil effects the soil model is 60 ft in diameter and 60 ft deep which corresponds to
approximately 10 pile diameters of distance between the surface of the pile and model
29


boundaries in every direction. The selected size of the drilled shaft is based upon the
somewhat typical sizes of such used in Colorado to support overhead cantilever
traffic signals, which of course are subjected to great torsional loading (CDOT,
2004). Please refer to Figure 3.1 as it shows the geometrical characteristics of the
FEA model in clay. The profile is broken up into 20 layers and consists of 7552 solid
"brick" elements and 8295 nodes. Little attempt was made to verify that the
developed model is acceptably fine. This due in part to the knowledge that the
developed model is considered to be exceptionally fine when compared with similar
and validated SSI3D models of the past. In addition, it is somewhat unreasonable to
expect one to run a similar model with greater fineness due to large amounts of
necessary computation time.
30


CLAY

60-0"---------------------^
Figure 3.1: Geometric Arrangement of FEA Model in Clay
31
^O'-O


3.5.1.2 Material Parameters for Pile
Elasticity theory requires that two material parameters be known. The two
parameters used in this work are the modulus of elasticity (Ec) and Poisson's ratio (v).
The American Concrete Institute (ACI) (2008) gives the modulus of elasticity of
normal weight concrete by Equation 3.1.
Ec = 57000^/; (psi)
(3-1)
where fc is the compressive strength of the concrete.
Using the seemingly typical concrete compressive strength of 5000 psi a
corresponding Ec value of approximately 4g6 psi is used.
Ec ~ 4e6 psi
(3.2)
The 6th edition of the Precast/Prestressed Concrete Institute (PCI) Design Handbook
(2004) states that a Poisson's ratio of 0.2 is typically used in design. Consistent with
this 0.2 is also used as Poisson's ratio here.
v = 0.2
(3.3)
3.5.1.3 Material Parameters for Clay
The Coulomb model for a purely cohesive soil requires significantly more input data
than that of elasticity theory. The unit weight y, cohesion cu, modulus of elasticity
Es, Poisson's ratio v, modulus of rigidity G, confined modulus (or oedometric
modulus) Eoeti, and the at rest lateral earth pressure coefficient K0 must all be
established for a purely cohesive soil model.
32


Now before going on it seems some more discussion need be given to the
assumptions governing the clay model. The clay is assumed to be of undrained
conditions, but it is not submerged in that the water table is assumed to be far below
that which would warrant consideration. Additionally, the profile is assumed to be
normally consolidated (NC). That is, the overconsolidation ratio (OCR) is equivalent
to 1.
To obtain a typical value for unit weight of clay Holtz and Kovacs (1981) is
consulted. It is found that a unit weight of 120 pcf is reasonable.
Y 120 pcf
(3.4)
This value for unit weight was applied to the entire soil mass of the model in a
uniform manner.
The development of cohesion is slightly more involved than that of unit weight. It is
well known that undrained cohesion is a function of effective stress. Acknowledging
this and further assuming that the clay profile is normally consolidated (NC) the
following equation derived from Ladd (1974) is used:
cu 0.2 ov
(3.5)
where av is the vertical effective overburden. So, the cohesion increases linearly with
depth. In order to find an acceptable starting point McCarthy (2007) is referenced.
McCarthy gives a range of between 500 and 1000 psf as values of cu for medium
clay. Taking the average, a value of 750 psf is applied to the top portion of the clay
profile. To find value at the bottom of the clay profile Equation 3.5 is used. As may
be seen in Equation 3.7 applying 60 ft of depth at a unit weight of 120 pcf the greatest
cohesion occurs at a value of 1440 psf.
33


Cu-top = 750 psf
(3-6)
Cu-bottom = 0-2(120 pcf 60 ft) = 1440 psf
(3.7)
In order to develop a model that incorporates increasing cohesion with depth the
cohesion was broken up into 20 components corresponding to the 20 layers of the soil
profile. This is done such that upper layer possesses a cohesive value of 750 psf and
every subsequent layer is increased by a constant amount ( 36 psf) until the bottom
layer is reached with a cohesion of 1440 psf.
McCarthy (2007) and Kulhawy (1990) are referenced for typical values of modulus of
elasticity in a medium clay. It is found that 150 ksf is a reasonable value and is
applied to the mass.
Es = 150 ksf
(3.8)
Fortunately, Poisson's ratio lies within a narrow range of numerical values and can be
estimated with some confidence for this reason. It is important to note, however, that
certain elastic parameters are very sensitive to the choice of Poisson's ratio. For the
purposes of this study this is a non issue in that representative values of soil are to be
selected in the general sense. That is, any value within the commonly accepted range
is considered satisfactory. According to McCarthy Poisson's ratio for saturated clay
lies between 0.4 and 0.5. Taking the average, a value of 0.45 is applied to the soil
mass.
v = 0.45
(3.9)
The shear modulus is given by elasticity theory. Since two material parameters,
Young's modulus and Poisson's ratio, have already been given, the other elastic
34


parameters may be found by some simple relations. The shear modulus may be
expressed in the following manner:
E.
G =
2(1 +u)
(3.10)
By plugging in the previously determined values of Young's modulus and Poisson's
ratio the following is obtained.
G =
150
2(1 + 0.45)
= 51.72 ksf
(3.11)
The constrained modulus may also be given by elasticity theory. Davis and
Selvadurai (1996) present the following expression:
Es( 1-u)
oed (1 + u)(l 2u)
(3.12)
A numerical value is obtained by plugging in the elastic parameters determine earlier.
Eoed = 568.97 ksf
(3.13)
Finally, the at rest lateral earth pressure coefficient is taken from McCarthy (2007) as
0.9 for a "representative" value in clay.
K0 = 0.9
(3.14)
3.5.2 Load Cases for Clay
3.5.2.1 Pure Torsional Load
The first case run in this analysis is of course that of pure torsional load since torsion
is the topic of interest. Here the pile is taken to an maximum loading at the pile head
of approximately 480 kip-ft. The program ended at a maximum rotational
35


displacement of 10.6 degrees at the pile head. It seems, upon viewing Figure 3.2, that
this response includes a rather abrupt "failure" at about 460 k-ft.
3.5.2.2 Pure Lateral Load
The second case run is that of pure lateral load at the pile head. A maximum load of
nearly 180 kips is reached with a maximum witnessed displacement of 2.52 inches.
Please refer to Figure 3.3 for a graphical depiction.
The developed response raises no concerns for the writer. CDOT (2004) contains
lateral load test data for two 2.5 ft diameter shaft with 22 ft of embedment in clay that
reached approximately 1 in. of displacement at 90 kips which is reasonably consistent
with the response developed herein. The Broms' method is chosen as a quick hand
computational method to check the lateral response results. Following the procedure
given in FHWA (2006) the ultimate lateral capacity given by the Broms' method is
found to be 248 kips. This value is much larger than the approximate 100 kips at 1
inch of displacement (which is often considered failure) as shown in Figure 3.3.
However, it is important to remember that the Broms' method is a "rough estimation"
method (CDOT, 2004). Because this is the case and SSI3D has been well validated
for lateral loading and CDOT (2004) gives a similar response for a similar case, the
lateral load response is considered to be reasonable.
3.5.2.3 Pure Vertical Load
A pure vertical load case is also performed. A maximum load of slightly more than
354 kips is reached with a maximum witnessed displacement of 2.48 inches. Please
refer to Figure 3.4 for illustration of the response curve.
Like that of the previously discussed lateral load case, the numerically developed
vertical load response does not raise any concerns. In order to check the vertical
36


response a quick hand computational method is consulted. The well known static
formula is used. In order to alleviate any possible confusion this formula is presented
here. The ultimate vertical capacity in clay is given by the total stress method as;
Qu Cu ave As T" Ctip Nc At
(3.15)
where a is the adhesion factor, cu ave is the average cohesion along the pile length,
As is the area of the pile skin, ctip is the cohesion at the pile tip, Nc is a bearing
capacity factor, and At is the area of the pile tip.
McCarthy (2007) and FHWA (2006) give the adhesion (a) as 0.9 and the bearing
capacity factor (Nc) as 9. This value of adhesion applies to cohesive soil with a pile
length to diameter ratio of 10 which is consistent with the hypothetical case in clay.
a = 0.9
(3.16)
Nc = 9
(3.17)
The average cohesion (cu ave) is given by the average of Equations 3.6 and 3.7 as 1.1
ksf and the cohesion at the tip is given by Equation 3.7 as 1.44 ksf. Plugging in these
values as well as the geometry discussed in Section 3.5.1.1, the ultimate lateral
capacity is determined to be 372 kips.
Qu = 370 kips
(3.18)
This value is not at all unreasonable when compared with the response of Figure 3.4.
37


Torsional Load (k-ft)
Torsional Load-Rotation at Pile Head
600
Figure 3.2: Pure Torsional Load Response in Clay
Lateral Load-Displacement at Pile Head
0 0.5 1 1.5 2 2.5 3
Lateral Displacement (inches)
Figure 3.3: Pure Lateral Load Response in Clay
38


400
Vertical Load-Displacement at Pile Head
Figure 3.4: Pure Vertical Load Response in Clay
3.5.2.4 Combined Lateral and Torsional Load
To observe the potential effects of combined loading on torsionally loaded piles a
number of cases are performed. Because the object of this study is to better
understand the torsional behavior of piles, the loading case are performed to see what
effect other parameters have on the torsional response. This being the case, the
possible permutations for various combined load cases are limited in that torsional
load is applied last. Also, because this is really the beginning of studies regarding
combined loading inclusive of torsion, it is felt that it is appropriate to perform
relatively simple cases. Only combined loads of two load types are considered. In
this section only lateral then torsional loading scenarios are considered.
In order to see the effects of various lateral loadings, lateral loads of various
magnitudes are applied to the pile head and then torsion is applied. Three cases are
39


run. First a small amount of lateral load is applied followed by torsion. Secondly a
moderate amount of lateral load is applied followed by torsion. Lastly, a large
amount of lateral load is applied followed by torsion. It seems, in general, that design
codes require piling to sustain less than 1 in. of deformation in the lateral direction
due to loading. This knowledge is used to govern the writer's consideration of small,
moderate, and large lateral loads. A small lateral load is considered to be that
corresponding to 0.25 inch of deformation, a moderate load is that corresponding to
0.5 inch of deformation, and a large load is that corresponding to 1 inch of
deformation. Figure 3.5 shows the torsional responses of the hypothetical pile after
the various amounts of lateral loading. Note that this figure also includes the case of
pure torsional loading, presented earlier, for comparison. The key in this figure and
all of the type follow the same convention. "0.25 L-T" corresponds to the torsional
response after 0.25 inches of lateral displacement is developed just as "1 V-T"
corresponds to a prior vertical displacement of 1 inch.
For this particular clay model it is easily seen that lateral loading seems to have little
effect on the torsional response of the pile. It is interesting to note that in this case
lateral loading actually reduces the torsional capacity which is counter to the writer's
expectations.
In addition to the effect a prior lateral load has on the torsional response of a pile it is
also of interest to understand how torsional loading influences the lateral response of
a pile for this same case of lateral and then torsional loading. Figure 3.6 shows the
lateral displacements of the hypothetical pile with torsion after the associated lateral
loading is complete. Interestingly, by inspection of Figures 3.5 & 3.6, the lateral
response is relatively stiff until torsional failure is initiated (the points of greatest
curvature on the torsional-rotation response curves). Then the lateral response softens
significantly.
40


Torsional Response with Prior Application
of Sustained Lateral Load at Pile Head
600
0.00 5.00
-A-----------
PureT
--0.25 L-T
-*-0.5 L-T
10.00 15.00
Rotation (Degrees)
Figure 3.5: Combined Lateral-Torsional Load Response in Clay
Lateral Displacement Due to Torsion
at Pile Head
600 -|
Lateral Displacement (inches)
0.25 L-T
0.5 L-T
1 L-T
Figure 3.6: Lateral Response Due to Torsion in Clay
41


3.5.2.5 Combined Vertical and Torsional Load
Here a number of vertical load then torsional load cases are performed. The
convention developed earlier in Section 3.5.5 corresponding to the amount of
deformation for large, moderate, and small lateral load applies here. A small vertical
load corresponds to 0.25 inch of deformation at the pile head, a moderate load
corresponds to 0.5 inches of deformation, and a large load corresponds to 1 inches of
deformation.
Figure 3.7 gives the torsional response for the vertical-torsional load cases including
that of pure torsion for comparison purposes. For this particular model it is
interesting to note that the prior application of vertical load results in a somewhat
drastic decrease in torsional capacity. It is speculated that this reduction in torsional
capacity is due to a pre-developed progression in stress, due to vertical loading, along
the pile soil interface. That is, it is believed that the previously applied vertical
loading initiates the progressive failure witnessed in both vertical and torsional loaded
piles such that the effective torsional capacity is reduced.
Like that for the lateral-torsional load cases above, it is of interest to see the vertical
responses due to torsion after the vertical loadings are applied. Figure 3.8 gives these
responses. As may be seen from Figures 3.7 & 3.8 the vertical response is very stiff
until the torsional response curve reaches the greatest curvature at which point the
vertical response become very soft.
42


Torsional Response with Prior Application
of Sustained Vertical Load at Pile Head
Rotation (degrees)
Figure 3.7: Combined Vertical-Torsional Load Response in Clay
Vertical Displacement Due to Torsion
at Pile Head
Vertical Displacement (inches)
Figure 3.8: Vertical Response Due to Torsion in Clay
43


3.6 Hypothetical Case in Sand
3.6.1 Model Development
3.6.1.1 Geometric Characteristics
Much like that for clay, here a 3 ft diameter circular pile of 31 ft length is embedded
30 ft into a sand profile. The model is of circular geometry to easily match the pile.
In order to account for pile soil effects the sand model is 60 ft in diameter and 60 ft
deep which corresponds to approximately 10 pile diameters of distance between the
pile surface and model boundaries in every direction. Again, the selected size of the
drilled shaft is based upon the somewhat typical sizes of such used in Colorado to
support overhead cantilever traffic signals. Please refer to Figure 3.9 as it shows the
geometrical characteristics of the FEA model in sand. The profile is broken up into
20 layers and consists of 7552 solid "brick" elements and 8295 nodes. As with the
clay model, the fineness of the model is trusted in comparing the number of elements
and nodes with similarly well validated SSI3D models.
44


o
Figure 3.9: Geometric Arrangement of FEA Model in Sand
45
60'-0


3.6.1.2 Material Parameters for Pile
The material properties used to model the pile for the hypothetical clay case are
considered to be representative of a typical drilled shaft. This being the case these
same parameters are used again here in the case of sand. For a more detailed review
of these elastic parameters please see Section 3.5.1.2.1.
The modulus of elasticity and Poisson's ratio are;
Ec~ 4f6 psi
and
(3.19)
v = 0.2
as consistent with Equations 3.2 3.3.
(3.20)
3.6.1.3 Material Parameters for Sand
The Coulomb model for a cohesionless soil requires significantly more input data
than that of elasticity theory. The unit weight y, friction angle (p, Young's modulus
Es, Poisson's ratio v, shear modulus G, confined modulus (or oedometric modulus)
Eoed, angle of dilation ip, and the at rest lateral earth pressure coefficient K0 must all
be established for a cohesionless soil model.
To obtain a typical value for unit weight of sand Holtz and Kovacs (1981) is
consulted. It is found that a unit weight of 118 pcf is reasonable.
y = 118 pcf
(3.21)
This value for unit weight was applied to the entire soil mass of the model in a
uniform manner.
46


To find a reasonable value for friction angle of a typical sand McCarthy (2007) is
consulted and it is found that a value of 35 degrees is reasonable.

(3.22)
McCarthy (2007) and Kulhawy (1990) are referenced for typical values of modulus of
elasticity in a "medium" sand. It is found that 700 ksf is a reasonable value and is
applied to the mass.
Es = 700 ksf
(3.23)
Poisson's ratio lies within a narrow range of numerical values and it seems that it is
often estimated in practice. Referencing McCarthy (2007), a value of 0.3 is
considered representative for Poisson's ratio in "medium" sand.
v = 0.3
(3.24)
Again, the modulus of rigidity is given by elasticity theory. Since two material
parameters, the modulus of elasticity and Poisson's ratio, have already been given, the
other elastic parameters may be found by some simple relations. The shear modulus
may be expressed in the following manner:
Es
r _____&
2(1 + u)
(3.25)
By plugging in the previously determined values of modulus of elasticity and
Poisson's ratio the following is obtained.
700
G = = 269.23 ksf
2(1+ 0.3) J
(3.26)
The constrained modulus may also be given by elasticity theory. Davis and
Selvadurai (1996) present the following expression:
47


E nt>ri
Es{ 1-v)
'ed (1+u)(1_2u)
(3.27)
A numerical value is obtained by plugging in the elastic parameters determine earlier.
Eoed = 942.31 ksf
(3.28)
Bolton (1986) presents the following expression for friction angle and angle of
dilation:
V = (Peril. + -8^
(3.29)
where be expressed as:
(p ~ (Peril.
iP =
0.8
(3.30)
Now Bolton (1986) also presents a table of numerical values for the critical friction
angle of various sands. Upon review of this table it is determined that a critical
friction angle of 33 degrees is representative.
(Peril. = 33
(3.31)
By plugging in this value for critical friction angle into Equation 3.26, it is found that
a dilation angle of 2.5 degrees results.
ip = 2.5
(3.31)
Finally, the at rest lateral earth pressure coefficient is taken from McCarthy (2007) as
0.5 for a "representative" value in clay.
48


(3.32)
Kq = 0.5
3.6.2 Load Cases for Sand
3.6.2.1 Pure Torsional Load
Like that of clay the first load case run is that of pure torsion. Here the pile is taken
to an maximum loading, at the pile head, of approximately 340 kip-ft with 10.94
degrees of rotation at the pile head as shown in Figure 3.10. This case, like that of
clay, also has a somewhat abrupt change at approximately 125 kips; however, unlike
the response in clay the torsional resistance continues to increase significantly after
this abrupt change.
3.6.2.2 Pure Lateral Load
The second case in sand is that of pure lateral load at the pile head. This case
warrants some discussion. As may be seen from Figure 3.11 two different lateral
response curves are plotted. One is labeled "Strict L" and the other is "Lax L".
"Strict L" corresponds to a numerical run where tight or strict tolerances of
convergence are maintained and "Lax L" corresponds to that of loose or relaxed
tolerances. At the present time SSI3D is incapable of achieving convergence for
every case with tight tolerances of convergence. Unfortunately SSI3D cannot give
the desired results for this pure lateral load scenario. For the purposes of this work
and the following analysis the run "Lax L" is used. This is due to the fact that this run
is capable of completion which makes possible the combined loading scenarios. The
run "Strict L" was simply a lucky run with tight convergence tolerances. Out of the
many runs performed for this particular case this run continued to just beyond 1 inch
of displacement. Unfortunately this run is incapable of completion and cannot be
used for analysis far beyond what is shown in Figure 3.11. It is important to show the
results for the run "Strict L", however, because this run is believed to be realistic or at
49


the very least more mathematically correct as compared to that of "Lax L". For the
"Lax L" run a maximum load of just over 46 kips is reached with a maximum
displacement of 0.33 inches.
Significantly more runs were performed for this case of lateral loading in sand than
all the other cases of this work. And the two response curves given below are the best
the writer has to offer. One reason for such difficulty in achieving convergence is
best thought to be due to the "stick and slip" behavior as demonstrated by the
irregular "Strict L" curve of Figure 3.11. It is believed that the soil against which the
pile reacts experiences a progressive series of passive failures as lateral load
increases. That is, as load is applied the load-displacement curve continues (sticks)
until a passive failure is reached and the load-displacement curve jumps (slips). This
jump behavior may obviously cause numerical difficulties when "hunting" for a
tolerable value for a point in the nonlinear solution.
As in the simple cases for clay, a quick hand computable method is employed as a
check for the solution developed. And again, the Broms' method is chosen here. The
Broms' method in accordance with the procedure of FHWA (2006) gives the ultimate
lateral capacity of this hypothetical scenario as 235 kips. This method is not too far,
considering that the Broms' method is only a rough estimation, from the 180 kips
given by "Strict L" of Figure 3.11. It is important; however, to remember that the
less correct run "Lax L" is used over "Strict L".
3.6.2.3 Pure Vertical Load
A pure vertical load case in sand is also performed. A maximum load of
approximately 560 kips is reached with a maximum displacement of 1.38 inches.
Please refer to Figure 3.12 for illustration of the response curve.
50


This shape of this curve is just what one with experience reviewing load test data in
sand should expect and it raises no cause for concern. In order to perform a quick
hand check a form of the static formula is used. Again, in order to alleviate any room
for misunderstanding, the method used is presented here. The ultimate capacity of a
vertically loaded pile is estimated by;
Quit = ov K tan(8) As + 0.6 N60(tsf) At
(3.33)
where a'v is the vertical overburden, K is the lateral earth pressure coefficient, 8 is
the interfacial friction angle, As is the skin area of the pile, iV60 is the SPT blow
count, and At is the area of the pile tip.
A value of 31.5 deg. is assigned to the interfacial friction angle 8 using McCarthy
(2007) as a reference once again. McCarthy (2007) gives the following ratio as the
range;
5
-7 = 0.8 1
(3.34)
for smooth to rough concrete. Taking the average of this range and multiplying by

8 = 31.5
(3.35)
After consulting McCarthy (2007) and Kulhawy (1990) for a typical SPT blow count
for the hypothetical case in sand it was found that a value between 15 and 20 blows
per ft is reasonable. So, using a SPT blow count value of 18 blows/ft and applying all
51


other necessary and values previously discussed for the hypothetical case in sand the
ultimate capacity is given as 328 kips.
Neo = 18 Blows/ft
(3.36)
and
Quit = 306 kips
(3.37)
This value certainly seems to compare well with the curve given by Figure 3.12.
52


250
Lateral Load-Displacement at Pile Head
T~
i
Strict L
Lax L
Figure 3.11: Pure Lateral Load Response in Sand
53


3.6.2.4 Combined Lateral and Torsional Load
As may be readily observed by Figure 3.13, only one combined lateral-torsional case
is run. This is due to the difficulty in developing the pure lateral load response curves
of Section 3.6.3. For this section a clean set of torsional response curves
corresponding to combined "large", "moderate", and "small" lateral loads is not
possible. Instead a single lateral-torsional load curve is presented where the lateral
loading applied prior to torsion is given by the "Lax L" run of Figure 3.11 in Section
3.6.2.2. The lateral load applied before torsion is the maximum value (46 kips) of
"Lax L" and the corresponding displacement is equivalent to 0.33 inches.
In addition to the difficulties in running the lateral load case there exists some
noteworthy difficulty in running the lateral-torsional case. Even though the
tolerances of convergence were relaxed for the case of lateral load, the torsional
portion of the combined lateral-torsional case also required relaxation of the
tolerances for convergence. So, while it is assumed that the lateral response used
(Lax L) is nonrealistic and because of this the combined lateral-torsional response in
nonrealistic, it may be reasonably further assumed that the combined lateral-torsional
response is nonrealistic due to its own relaxed tolerance of convergence. It may be of
interest to add, however, that in the cases where relaxed tolerances of convergence
were used relative to the work of this study softer responses resulted.
The effect of previously applied lateral load appears to have a significant effect upon
the torsional behavior in sand as demonstrated in Figure 3.13. It seems that the
additional soil strength given by the increase in lateral stress on the passive side of the
pile more than makes up for the loss of same on the opposite or "active" side of the
pile. Question as to the validity of this analysis may be easily brought to light given
the lack of mathematical correctness in that relaxed tolerances of convergence are
used. It is believed, however, that some important insight may still be obtained from
54


this data. Considerably more relaxed tolerances are use for the lateral-torsional case
than the pure torsional case and the relative magnitudes of these responses still differ
significantly. Now, if the response for relaxed tolerances of convergence tend to
yield softer results as discussed above, it seems logical that the increase in torsional
capacity due to combined lateral-torsional loading may be even more dramatic that
shown in Figure 3.13.
An attempt to observe the lateral response due to torsion is also made here, however,
the results lack promise. As may be seen from Figures 3.13 & 3.14 the lateral
response due to torsion is virtually linear and seems to lack the close dependency on
the torsional response like that witnessed in case of clay. Because of the consistency
of dependency on the torsional response of the previous and latter results, the results
here are unexpected and lead the writer to believe that this numerical analysis is
incapable of reaching any reasonable conclusions as to the lateral response due to
torsion for the lateral-torsional case in sand until SSI3D is improved to accommodate
such conditions.
55


Torsional Response with Prior Application
of Sustained Lateral Load at Pile Head
600
12.00
PureT
Lax L-T
Figure 3.13: Combined Lateral-Torsional Pile Response in Sand
56


3.6.2.5 Combined Vertical and Torsional Load
A number of vertical load then torsional load cases are also performed. Again the
convention developed earlier in Section 3.5.5 corresponding to the amount of
deformation for large, moderate, and small lateral load applies here. A small vertical
load corresponds to 0.25 inches of deformation, a moderate load corresponds to 0.5
inches of deformation, and a large load corresponds to 1 inches of deformation.
As may be seen in Figure 3.15, vertical loading prior to application of torsion has
little effect on the torsional capacity of the pile in this particular model in sand. It is
interesting, however, to see a small increase in torsional capacity. This behavior is
radically different from that demonstrated by the combined vertical-torsional loading
in clay. It is felt that this difference in response may be explained by the well known
and here employed Mohr-Coulomb model.
In purely cohesive soil an increase in confining pressure, under undrained conditions,
yields no greater shear strength, however, in cohesionless soil an increase in
confining pressure immediately produces much greater shear strength. As a pile is
loaded vertically that load is transferred to the soil. As this load is transferred to the
soil and a greater vertical stress is produced an associated lateral stress is produced
and the effective shear strength of the soil increases. Of course this increase in shear
strength leads to a larger torsional capacity for the pile.
Again, the response of the prior load type due to torsion is also investigated. As may
be seen from Figures 3.15 & 3.16 the vertical response due to torsion seems to be
closely related to the torsional response. Overall, the torsional-rotation response is
relatively soft and likewise the vertical response due to this torsional loading is soft
overall.
57


Torsional Response with Prior Application
of Sustained Vertical Load at Pile Head
0.00 2.00 4.00 6.00 8.00 10.00 12.00
Rotation (degrees)
PureT
0.25 V-T
0.5 V-T
1 V-T
Figure 3.15: Combined Vertical-Torsional Pile Response in Sand
Vertical Displacement Due to Torsion at
Pile Head
600
0.25 V-T
0.5 V-T
1 V-T
Vertical Displacement (inches)
Figure 3.16: Vertical Response Due to Torsion in Sand
58


4 Comparison of FEM Results with Existing Design Methodology
4.1 Introduction
This chapter compares some of the accepted existing analysis and design methods
with the numerical results of Chapter 3. Five design methods are considered for the
case of torsion. These methods make up all known accepted design methods in the
literature. All five methods are obtained from state departments of transportation.
Two of the methods supposedly apply to the case of a clay profile, two of the
methods supposedly apply to that of sand, and one of the methods apply to both clay
and sand profiles. This work show, however, that only two methods really apply to
the case of purely cohesive soil and four methods apply to that of purely cohesionless
soil.
4.2 Consistency in Comparison
In order to properly perform this task of comparisons, consistent numerical values for
the properties of the problems presented in Chapter 3 must be used here. That is,
proper comparison requires that the hypothetical cases of numerical analysis be the
same as that for the accepted analysis and design methods here. Table 4.1 presents
these values.
59


Table 4.1: Properties for Analysis of Hypothetical Cases
Properties for Comparative Study
Properties Clay Sand Pile Units
y 120 118 150 pcf
c 0.2 cr'v psf
a 0.9
35 deg.
6 31.5 deg.
* 2.5 deg.
E 150 700 576000 ksf
Eoed 568.97 942.31 ksf
V 0.45 0.3 0.2
G 51.72 269.23 ksf
Ko 0.9 0.5
Ns FT 15-20 Blows/ft
fc 5000 psi
D 3 ft
L 30 ft
4.3 Presentation of Design Methods for Clay
4.3.1 FDOT Structures Design Office Method
The FDOT Structures Design Office (SDOF) method applies to the case of either clay
or sand.
For the FDOT Structures Design Office Method the side resistance, using
"Coulombic Friction" with no lateral deformation, and the base resistance are given
respectively by;
1 1
Ts = K0Y-L2nDtan(S)-D
(4.2)
60


and
Tb = Wtan(8)(0.33)D
(4.3)
where K0 is the lateral earth pressure coefficient, y is the unit weight of the soil, L is
the embedment length, D is the pile diameter, S is the interfacial friction angle, and
W is the total weight of the pile. Combining the side and base resistances gives the
total torsional resistance;
1 1
Ttot = K0y-L2nDtan(S)-D + Wtan(8)(0.33)D
(4.4)
4.3.2 FDOT District 7 Method
The FDOT District 7 Method was developed upon the basis of the Alpha method or
Adhesive method for cohesive soil which gives the vertical capacity by way of an
adhesion factor a. For the FDOT District 7 Method the side and base resistances are
given respectively by;
D
Ts = nDL(ac + aKtan(8))
(4.5)
and
Tb=-(W + Ay)tan(8)(. 67)D
8
(4.6)
where D is the pile diameter, L is the embedment length, a is the interfacial adhesion
factor, a is the overburden pressure, K is the lateral earth pressure coefficient, 8 is the
interfacial friction angle, W is the weight of the pile, and Ay is the vertically applied
load. Combing the side and base resistances gives the total torsional resistance;
61


(4.7)
Ttot = nDL(ac + aKtan(S)) + -(W + Ay)tan(S)(. 67) D
2 o
4.3.3 CDOT Method in Clay
As stated in the literature review, little is known about the derivation of the CDOT
method for clay. The ultimate torsional resistance was simply given by CDOT (2003)
as;
D D2 D
T'clay = Ttot =nD(L- 1.5 D)c- +
(4.8)
where TCLAY is the ultimate torsional resistance, D is the pile diameter, L is the
embedment length, and c is the cohesion of the soil.
4.4 Comparison of Methods in Clay
Since the hypothetical cases considered are essentially homogeneous the following
expression for the overburden pressure a is developed.
a 2
(4.9)
By rearranging terms and substituting in Equation (4.9) where appropriate the total
torsional capacity of the FDOT Structures Design Office method, FDOT District 7
method, and CDOT method may be respectively written as Equations (4.10) (4.12).
62


nD2L
-aK0tan(8) + (0.33 )WDtan(8)
(4.10)
Ttot
nD2L
nD2L
Ttot 2aKtcm(6) --ac + (0.25)(VF + Ay)Dtan(8)
nD2{L 1.5D) nD3
Ttot =-----~-----c + ^^c
(4.11)
12
(4.12)
It is interesting to note some of the similarities between these three expressions.
Also, it is important to note that in the case of a purely cohesive soil where the
interfacial friction angle is assumed to be zero (8 = 0) the entire expression given by
the FDOT Structures Design Office method yields zero and is thus meaningless for
the hypothetical clay case of interest. This assumption also reduces the expression
given by the FDOT District 7 method.
By taking the average of the cohesion c, which is an appropriate action considering
the assumed linear variation, and inputting the values of the hypothetical clay case
given by Table 4.1, the following numerical values for FDOT Structures Design
Office, FDOT District 7, and CDOT methods are obtained.
Table 4.2: Design Capacities for Methods in Hypothetical Clay Case
Method for Clay Tlo, Units
FDOT Structures Design Office 0 k-ft
FDOT District 7 418 k-ft
CDOT 402 k-ft
63


In order to illustrate the comparison of these values with the numerical analysis
performed in the previous chapter corresponding horizontal lines are plotted in
Figures 4.1 4.2 along with the numerical results of Chapter 3 for torsional behavior
in clay.
Lateral-Torsional Load Response at Pile Head
600
PureT
0.25 L-T
0.5 L-T
1 L-T
Figure 4.1: Comparison of FDOT District 7 and CDOT Method with FEA for Clay
64


Vertical-Torsional Load Response at Pile Head
600
Pure T
0.25 V-T
0.5 V-T
1 V-T
Figure 4.2: Comparison of FDOT District 7 and CDOT Method with FEA for Clay
As may be seen the FDOT District 7 method and the CDOT method for clay seems to
perform quite well for the cases of combined lateral-torsional loading and for
combined vertical-torsional loading when the vertically applied load is small. For the
case of vertical-torsional loading when the vertical loading is large both design
methods overestimate the capacity such that an un-conservative estimation results. It
is of interest to note that District 7 method accounts for the case of combined vertical-
torsional loading with the vertical load Ay (see Equations (4.7) & (4.11)). The effect
of this load, however, is neglected when the interfacial friction angle (8) is zero and is
actually contrary to the numerical analysis of Chapter 3 when 8 is positive. That is,
when a non-zero interfacial friction is input the torsional capacity given by the
District 7 method increases with increasing vertical load while the numerical results
yield a smaller torsional capacity for increasing the applied vertical load. It seems
65


that a design method which accounts for the reduction in torsional capacity with
combined vertical loading may be appropriate.
4.5 Presentation of Design Methods for Sand
4.5.1 FDOT Structures Design Office Method
The FDOT Structures Design Office Method has already been presented, however, it
is here reiterated for purposes of clarity. The base and side resistances are given
respectively by;
Ts = K0y ^ L2nDtan(8) ^ D
(4.13)
and
Tb = Wtan(8)(033)D
(4.14)
where K0 is the lateral earth pressure coefficient, y is the unit weight of the soil, L is
the embedment length, D is the pile diameter, 6 is the interfacial friction angle, and
W is the total weight of the pile. Combining the side and base resistances gives the
total torsional resistance;
1 1
Ttot = K0y-L2nDtan(8)-D + Wtan(8)(0.33)D
(4.15)
4.5.2 FDOT District 5 Method O'Neill and Hanson
For the FDOT District 5 O'Neill and Hanson Method, the side resistance, using a
function of the Standard Penetration Test (SPT) blow count with overburden stress,
and the base resistance are given by;
66


and
D
Ts = nDLofi
L
p = 1.5 0.135 {for Nspt > 15)
N
(4.16)
Tb = {.67){W + Ay)tan{6)^
(4.17)
where D is the pile diameter, L is the embedment length, a is the overburden
pressure, $ is a function of blow count and embedment length, NSPT is the SPT blow
count, W is the pile weight, and 6 is the interfacial friction angle.
For an SPT blow count over 15 the factor /? must also fall between the limits given
by;
0.25 < p < 1.2
(4.18)
Combining the side and base resistances gives the total torsional resistance gives;
D , ^ D
Ttot = nDL(jp + (.67 )Wtan{8)
(4.19)
4.5.3 CDOT Method in Sand
For the CDOT method in sand soil the side resistance, using a function of overburden,
interfacial friction angle, a lateral earth pressure coefficient, and the base resistance
are given respectively by;
L D 2L
Ts KCdotY ^ ^CD0T ~ ~ s^n(P^
(4.20)
67


and
D
Tb=Wn-
(4.21)
where KCD0T is a lateral earth pressure coefficient, y is the unit weight of the soil, L is
the embedment length, D is the pile diameter, /r is equivalent to the tangent function
of the interfacial friction angle (tan(<5)), W and is the pile weight. Combining the
side and base resistances give the total torsional resistance;
2 L L D D
Ttot =jfiO--sin(p)y-LnDii-+ Wp-
(4.22)
4.5.4 FDOT District 7 Method
Although the FDOT District 7 method was developed for cohesive soil the inputs of
this method allow for the calculation in cohesionless soil. This being the case
curiosity implores its employment here. Again, the side and base resistances are
given respectively by;
D
Ts = nDL(ac + aKtan(S))
(4.23)
and
3
Tb = -(W + Ay)tan(S)(. 67)D
8
(4.24)
where D is the pile diameter, L is the embedment length, a is the interfacial adhesion
factor, a is the overburden pressure, K is the lateral earth pressure coefficient, S is the
interfacial friction angle, W is the weight of the pile, and Ay is the vertically applied
load. Combining the side and base resistances gives the total torsional resistance;
68


(4.25)
D 3
Ttot = nDL(ac + oKtan(8))- + -(W + Ay)tan(8)(. 67) D
4.6 Comparison of Methods in Sand
Craig (1997) gives the well known relationship between the at rest earth pressure
coefficient and friction angle as;
K0 1 sirup'
(4.26)
Applying this expression, Equation 4.9, and rearranging terms the total torsional
capacity of the FDOT Structures Design Office method, FDOT District 5 method,
CDOT method, and FDOT District 7 method may be respectively written as
Equations 4.27 4.30.
nD2L
Ttot = 2+ (0.33 )WDtan(8)
1 tot
nD2L
2
op + (0.335)WDtan(8)
(4.27)
[ tot
nDL2
3
1
oK0tan(8) + WDtan(8)
1 tot
7lD2L
-oKtan{8) +
nD2L
-ac + (0.25) (W + Ay)Dtan(8)
(4.28)
(4.29)
(4.30)
The similarity between the expressions for torsional resistance given above is
striking. A few differences do exist between these methods. All of the FDOT
methods square the pile diameter (D) and divide by two whereas the CDOT method
squares the pile length (L) and divides by three. The FDOT District 5 method unlike
69


all other methods replaces the product ( Ktan(8)) by a /^-factor. And the FDOT
District 7 method accounts for both cohesion and vertically loading. It is interesting
to note that although the FDOT District 7 method was supposedly designed upon
principles employed in cohesive soil, the method fits very well among the others for
the case of cohesionless soil. In fact, aside from the added consideration to vertical
loading in the resistance of the pile base, it is virtually indistinguishable from the
other FDOT methods in c = 0 soil.
By again applying Equation 4.9, inputting the values of Table 4.1, and substituting
the appropriate values for vertical load Ay, the following table is created. The values
shown for Ay used and shown in Table 4.3 are consistent with those used in Chapter
3 to obtain 0.25 inches, 0.5 inches, and 1 inch of displacement prior to application of
torsional load.
Table 4.3: Design Capacities for Hypothetical Case in Sand
Method for Sand T,ot Units
FDOT Structures Design Office 249 k-ft
FDOT District 5 Method 753 k-ft
CDOT 1,553 k-ft
FDOT District 7 Method
for Ay = 0 kips 245 k-ft
Ay = 264 kips 366 k-ft
Ay = 354 kips 408 k-ft
Ay = 482 kips 466 k-ft
These values have a very large spread. In order to compare these results with the
numerical analysis of Chapter 3 the capacities given by Table 4.3 are marked by dark
horizontal lines over the plots developed in the previous chapter.
70


Lateral-Torsional Load Rotation at Pile Head
600
Pure T
L-T
Figure 4.3: Comparison of FDOT SDOF and District 7 Method with FEA for Sand
1800
1600
1400
*- 1 1200
o
<0 o 1000
_)
15 c 800
o
*5? 600
o
400
200
0
Lateral-Torsional Load Response at Pile Head
_______________ CDOT Method
District 5 Method
Pure T
L-T
0.00
2.00
4.00 6.00 8.00
Rotation (degrees)
SDOF & District 7 Method (0 V)
10.00 12.00
Figure 4.4: Comparison of All Design Methods with FEA for Sand
71


500
450
Vertical-Torsional Load Rotation at Pile Head
District 7 Method 1V
District 7 Method 0.5 V
Figure 4.5: Comparison of FDOT SDOF and District 7 Method with FEA for Sand
1800
1600
1400
&
Jc 1200
*D
re o 1000
_i
"re 800
o
'Co 600
o
1- 400
200
0
Vertical-Torsional Load Response at Pile Head
CDOT Method
District 5 Method
District 7 Method (1 V)
Pure T
-0.25 V-T
0.5 V-T
1 V-T
0.00
2.00
4.00 6.00 8.00
Rotation (degrees)
SDOF & District 7 Method (0 V)
10.00 12.00
Figure 4.6: Comparison of All Design Methods with FEA for Sand
72


The spread of results given by the design methods is so dramatic that the plots above
were skewed significantly. From the figures above it seems that the FDOT Structures
Design Office method yields fairly reasonable results for the torsional capacity of a
drilled shaft in sand. Also, the District 7 method, which is again supposedly based
upon principles relative to cohesive soil, also yields fairly good results for torsional
capacities in sand. The increased capacity given by this method due to combined
vertical loading, however, overestimates that given by numerical analysis. In fact, the
increase in torsional capacity from combined vertical loading given by the numerical
analysis for this particular hypothetical case is so slight that accounting for it in a
design method seems to be unnecessary. If anything is to be done to account for the
effects of combined loading in sand, the numerical results of Chapter 3 suggest that
an increase in torsional capacity due to lateral loading be the more significant aspect.
Unfortunately the FDOT District 7 method is a drastic overestimation of the torsional
capacity as compared to the numerical results and the CDOT method is significantly
more so.
73


5 Proposal of Torsional Load Test
5.1 Introduction
As mentioned in the introduction, full-scale load testing offers the most reliable
results for the determination of deep foundation performance. Unfortunately, full
scale load testing has only rarely been performed for the case of applied torsion and
for the cases in which it was performed it lacked the standardization of other full
scale testing methods. In order to overcome these deficiencies this chapter proposes a
method for full-scale torsional load testing of drilled shafts.
In order to apply a pure torsional load it is suggested that a special symmetrical
"wrench" be constructed and affixed to the top of test shaft much like that of Stoll
(1972). Then, again like that used by Stoll (1972), it is suggested that equal and
opposite forces be applied to each end of the wrench to create pure torque (couple).
The equal and opposite forces are proposed to be applied with high capacity hydraulic
cylinders used in conjunction with either reaction piling or deadman blocking. To
measure the amount of loading with time a load cell with applicable data logger, pre-
calibrated pressure gages, and video recorders are to be used. To measure the
rotational displacement of the pile with time it is proposed that multiple video
recorders and properly orientated calibrated strain gages be used with a data logger.
5.2 Load Application Apparatuses
After review of full scale testing standards and related technical reports the writer
found that it is reasonable to break the design of full scale deep foundation testing
into two main categories. The first of these categories is the matter of load
application. And the second category is that of measurement. This particular section
74


is concerned only with the former of these categories, that is the means by which load
is applied.
5.2.1 Torsional Load Apparatus
5.2.1.1 Wrench
The wrench is the first of three load application components addressed in this section.
The wrench is responsible for directly inducing torque into the shaft by transmitting
applied force via hydraulic rams. Figures 5.1 and 5.2 presents a typical wrench
design for the testing of piles approximately 24 to 30 in. in diameter. And Figure 5.3
presents a typical wrench design for the testing of piles 36 to 48 in. in diameter. As
may be seen from these figures the wrench is made up of a number of various steel
members. The load from the hydraulic cylinders is first transmitted through a large
clevis which is attached to end plates by a stout pin lubricated for ease of motion.
There are four end plates with one on the top and bottom of the wrench arms at each
end. These end plates are secured to the arms by welding. Each of the four arms are
made of rectangular tubing as is the steel ring. The arms are attached to the steel ring
with four stout "arm to ring plates" one top and bottom on the two applicable sides of
the wrench. Each of these plates are attached by welding on the outermost side of the
arms and the innermost side of the ring section. The steel ring secures the heavy base
plate, which is also to be anchored to the test piles, by way of welding.
75


14 END l£
ASE l£W/ SIMPLE
OLT PATTERN
s16 RING TO BASE P
6x5x12 RECTANGULAR TUBE RING
PLAN VIEW
! 6x5x12 RECTANGULAR
' TUBE ARMS
t
PIN & CLEVIS
PRINCE 4 IN
HYDRAULIC CYLINDER
OMEGADYNE 30-K
LOAD CELL
Figure 5.1: Typical Wrench Design
END VIEW
Figure 5.2: Typical Wrench Design
76


t
s16 RING TO BASE ff.
14 END £
BASE Ft W/SIMPLE
BOLT PATTERN
9x7x12 RECTANGULAR TUBE RING
r
i
Figure 5.3: Typical Wrench Design
The wrench design has a number of requirements. It must not fail under the
considered range of loading. It must not yield excessive deflections under the
considered loading range. And it must maintain adequate connection with the test
shaft. That is, the connection made between the wrench and the test shaft must not
fail before the failure mode of consideration. The magnitudes of these requirements,
however, vary significantly with test shaft size. Because of the magnitude of this
variance, it is unfeasible to expect one wrench to be used for the testing of a wide
range of shaft sizes. Fortunately, the design and construction of a simple steel
structure like the proposed wrench is a small cost compared to the current total cost of
full scale load testing. The one value that seems reasonable to hold constant is the
length of the wrench arms. A wrench arm length of 10 ft. is considered acceptable.
This corresponds to a total wrench length of 20 ft. Going beyond this value would
seem to develop undesirable complications in test performance. That is, an overall
77


length of greater than 20 ft. would seem to make the manageability of the wrench
extremely difficult. Also, as may be deduced from later discussion, an arm length
greater than 10 ft. will lead to very large displacements of the wrench end during
testing which will make the use of readily available hydraulic cylinders practically
impossible.
Most of the wrench requirements mentioned above are stability based and therefore
concise. Some discussion, however, needs to be given to the one indicated
serviceability requirement. If the wrench is allowed to deflect too much, the resulting
complications in applied load and measurement thereof may destroy the value of the
associated testing. However, if one adheres to the general wrench design discussed
above and stability is achieved in accordance with the current American Institute of
Steel Construction Manual (AISC, 2006), it was found that deflections, for required
loadings, fell on the order of a fraction of an inch. This is considered to be
acceptable.
5.2.1.2 Hydraulic System
The hydraulic system is the second of the three load application components
addressed in this section. The hydraulic system is responsible for developing and
controlling the forces by which the wrench develops torsional load. It is made up of a
number of components. The system needs, of course, at least two double acting
hydraulic cylinders, hydraulic fluid pump(s), pump motor(s), hydraulic control
valves, hydraulic lines, and line fittings. As discussed earlier two sets of hydraulic
cylinders are to be used at each end of the wrench to input the load for the required
torque.
The hydraulic system has a number of requirements. It must be capable of applying
load to the test pile over the range of interest that the pile displaces. Based upon the
78


failure criterion given by FDOT the rotation of interest lies below 15 degrees of
rotation, however, based upon the available full scale test data and the numerical
analysis presented in this work the rotation angle of interest seems to be significantly
smaller at values less than 10 degrees. With wrench arms 10 ft. long this corresponds
to arm end displacement of approximately 1.7 ft. So, the hydraulic system needs to
be capable of applying load over 1.7 ft. of displacement. Uniformity in terms of
symmetry about the pile is also a requirement. That is, the load application at each
end of the wrench needs to be equal in magnitude at any given time so that pure
torsion may be achieved.
To ensure that the loads applied at each end of the wrench are uniform with respect to
one another only one set of hydraulic motor(s), pump(s), and control valves are to be
used to control both of the hydraulic cylinder sets. Furthermore each of the hydraulic
lines running to the two individual sets of cylinders need to be checked to be of
equivalent length for the same purpose of uniform load application. Again, symmetry
in load application is essential to the development of pure torsional loading.
In order to satisfy the above requirements, high capacity double acting hydraulic
cylinders are to be used in tension as shown in Figures 5.1 and 5.2. Although "push"
alone type hydraulic cylinders are commonly used in field testing of deep
foundations, it is felt that the "pull" action of the double acting type are considered to
be superior for a number of reasons. First of all buckling needs not be considered.
Also, because pull type cylinders are generally rigged with cable or slender rods,
unlike the large struts used with push cylinders, the direction of applied loading is
easily determined. This is due to the reality that flexible elements, like cable or
slender rods, are only capable of sustaining load along the longitudinal axis when in
tension. The one disadvantage to the pulling action given by double acting cylinders
is that the capability of force magnitude is less than that of the push type. Upon
review of available double acting hydraulic cylinders, however, the writer found that
79


rather high capacity cylinders (up to 50 kips in tension) are readily available for
reasonable cost. It may be interesting to note that a single 50 kip hydraulic cylinder
placed at each end of wrench with 10 ft. long arms corresponds to 1,000,000 ft-lbs of
torque. This is greater than the structural capacity of a 4 ft. diameter pile made with
concrete of 5,000 psi compressive strength. These hydraulic cylinders come in a
number of stroke lengths going on up to a couple of feet of stroke which is considered
adequate. The displacement due to the rotation of drilled shaft, deformation thereof,
deformation of reactions, and deformation of rigging associated with force
application should not be expected to go beyond 24 inches if a strict test is
maintained.
5.2.1.3 Reactions
Reactions are the third and last component of the force application system considered.
Reactions are necessary to induce the forces, developed by the hydraulic system, into
the wrench. There are a number of possible reactions. Piling, deadman blocking, and
anchors are all feasible types of reactions. The reactions for a given test need be
sized for each specific test considered. The most economical type of reaction is
dependent on the site condition as well as the test pile characteristics. The writer;
however, has developed an interest in using reusable anchors, more specifically
helical piles, as economical reactions for test loads. Now, determining the practical
feasibility of this idea is felt to be somewhat beyond the scope of this work, however,
the benefits associated with such a scheme seem to warrant further study.
In order to properly develop reactions for torsional testing, it is suggested that the
current "Standard Test Methods for Deep Foundations Under Lateral Load" provided
by the American Society for Testing and Materials be consulted as it is considered
adequate for the purposes discussed herein (ASTM, 2009 a).
80


5.2.2 Accommodation for Lateral Load Application
It will be desirable to determine the influence of combined loading on deep
foundations at some point. The wrench described above may be modified to
accommodate the isolated application of lateral load in addition to torsional load. It is
proposed that lateral load be applied through two large pin and clevis connections to
the base plate of the proposed wrench via high capacity pull type hydraulic cylinders
and a special rigging assembly as shown in Figure 5.4. Again, cable or slender steel
rods are to be used to transfer the load from the reactions through hydraulic cylinders
to the wrench and ultimately the test pile. It is important to notice the special
connection, in Figure 5.3, that splices the two cables/rods into one without sacrificing
the lateral mobility of such. The idea is that as the pile rotates due to torsional load
the application of lateral load will not be influenced and vice versa. As the pile
rotation progresses Cable 1 should move closer, but remain parallel, to Cable 2 as
shown in Figure 5.5. It is important that the pin and clevis attachments to the base
plate be located 180 degrees apart on the base plate so that no eccentric loading
results from the combination of applied lateral load and rotational deformation of the
test pile.
81


TO REACTION WITH HYDRAULIC PULL
Figure 5.4: Isolated Lateral Load Application to Torsional Load Test
TO REACTION WITH HYDRAULIC PULL
Figure 5.5: Lateral Load Application in a Rotationally Displaced State
82


5.2.3 Accommodation for Vertical Load Application
The torsional loading apparatus, above, may also accommodate the application of
isolated vertical load. In fact, the application of vertical loading is considered to be
somewhat simpler than that of lateral. The ASTM standard for full scale lateral load
testing has a section dedicated to the application of combined lateral and vertical
loading. This section is considered to be entirely adequate for the problem of
applying isolated vertical load through the base plate of the torsional load apparatus
and ultimately the pile. The interested reader should consult this section of the
current ASTM standard. The "ANTI FRICTION PLATE ASSEMBLY", shown
below in Figure 5.5 and, described in the standard are considered adequate.
$raunsniAU7GrtMK4aftMtt3 o m ouMmtva lono
wrmMMMuinojoiBCWOH3Atw*qssi
OT1:1 CMC UMT o TONS
(a) PLATE AND ROLLER ASSEMBLY
vertical
LOAD

TEST PLATE-/ LATERAL LOAD ^ TEST

a>
ft
AOTMAMAUnMMMUMl M THE*
Atm a m mja* n a cr ngjcd to ft
MM miMmiOWOCIWiagACtMOWWITHWEWMOWCMQ
AQOMCtMIttMCSI TNCWWOMaPTOUMwmoCATaMBO
rarr ro* cmamu fucmooold uoi nmti
astm a ms rm m imnt stssl kxtc 1 < m tmck pomoo as
MMN AMO wm< MMMUM SUWACC nOUQMCM OP 4 PCM AMSI
4S1
art; load lsmt tm p% i
(b) ANTI FRICTION PLATE ASSEMBLY
FKL I Typical AntWrtcUoo Davlcaa foe Comblnad Load Taat
Figure 5.6: Isolated Vertical Load Application for Lateral Pile Test (ASTM, 2009 a)
83


5.3 Measurement Systems
This section addresses the second of the two main categories associated with load
testing, which is measurement. Now, it is felt that it is appropriate to break the
measurement of load testing into two more categories. These two categories are: the
measurement of applied load and the measurement of pile displacement.
In general many of the measurements related to full scale load testing are made by
dial indicators or linear displacement transducers. This work, however, proposes a
different method for the measurement of displacements. It is proposed that video
recorders be used to monitor the movements associated with load testing. This
proposed method a number of significant benefits. And for the case of torsional
testing, there is a lack of feasible alternatives.
5.3.1 Video Recorded Displacement Measurements
It is now possible, with the current state of technology, to acquire fairly high
resolution and accurate displacement measurements by processing digital images
given by commercially available camcorders. In fact, Lee and Shinozuka (2006)
showed that the deformation of bridges due to dynamic loading may be determined,
in real time, relatively easily and accurately by this method.
There are quite a number of advantages to displacement measurements by digital
imaging over linear displacement transducers especially in the realm of field testing.
Digital imaging devices (camcorders) are robust overall. Linear displacement
transducers are not necessarily robust and require special care to prevent damage.
Camcorder performance is not dependent upon the rate of displacement. It has been
the writers experience, however, that the performance of linear displacement
transducers are susceptible to poor performance when subjected to high rates of
displacement. This is because linear displacement transducers are required to contact
84


what is to be measured, whereas camcorders are not. This point alone is a great
advantage to video recorded measurements. In full scale testing the displacement
measurement devices need be supported by soil away from the influences pile-soil
interaction due to movement of the test pile and reactions. This may be a relatively
large distance as ASTM requires that this distance be no less than 5 pile diameters.
For linear displacement transducers rigid supports are constructed to span these
distances. In the case of camcorders a portion of this battle is already won in that
camcorders require an inherent distance from whatever they are recording. Also, a
single camcorder is capable of measuring displacements in multiple dimensions, two
translations in the least, but linear displacement transducers are limited to one.
Camcorders are capable of measuring large displacements with a high degree of
resolution and accuracy. Linear displacement transducers are not considered to be a
feasible tool when measurements of large displacements are required. In addition, the
displacement measurements obtained through the processing of digital images, by
camcorders, give a visual and audio record which may be of great value to the
concerned test engineers. This is especially true when anomalies in test data are
encountered.
5.3.2 Measurement of Load Application
In every case of full scale load testing, including that of torsion, both magnitude and
direction of load application needs to be measured. Every load applied to a
foundation is a force vector and as such has both magnitude and direction. Now in
the case of vertical and lateral loading the measurement of load is considered to be
somewhat simpler than that of torsion. The magnitude is usually given as the
magnitude of force applied by hydraulic cylinders and the direction is given by the
orientation of the axes of the cylinders. So, it may be said that the force output by the
hydraulic cylinders give the magnitude of applied force and the geometrical
arrangement of the test pile, reaction piling, reaction beams, etc. gives the direction of
85


force. Furthermore, that direction is considered to be effectively constant throughout
testing. In general vertical and lateral testing the deformation of the test pile does not
result in a significant change in applied force magnitude as it deforms in line of the
direction of applied force. In the case of torsion, however, the rotational
displacement of the test pile will result in a change in applied moment magnitude as
the deformations involved are of a much more complex nature. Such that the applied
moment magnitude in torsional testing is dependent on not only the magnitude of
force developed by the hydraulic cylinders but the orientation load application
apparatus. Luckily the direction of the moment is considered to remain virtually
unchanged due to test pile deformation.
In order to more fully understand the suggested method of load measurement a more
detailed discussion needs to be given to the idea of moments. Moment (M) may be
defined by the following cross product;
M = r x F
(5.1)
where F is the applied force and r is the associated moment arm. Now in the case of
the proposed torsional load test the applied torque may be broken up into two separate
moments corresponding to the two distinct reactions, hydraulic cylinder sets, and
wrench arms. For these applied moments r is ideally given as the spatial vector from
the test pile center to the wrench arm ends (point of load application). This is the
distance from point A to point B in Figure 5.7. The determination of F is slightly
more involved. The direction of F is given by the spatial vector between the point of
load application and the point of reaction. This is the distance between point B and
point C in Figure 5.7. And the magnitude of F is given by the magnitude of force
applied by the associated hydraulic cylinder set.
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POINT C

HEAVY l£ AFFIXED
TO REACTION
PIN & CLEVIS
POINT B
Figure 5.7: Geometrical Description of Load Application
So, in order to obtain a full measurement of load application the spatial coordinates of
points A, B, and C need be known as well as the magnitude of load induced by the
hydraulic cylinders. It is proposed that the magnitude of hydraulic force produced by
the cylinders be measured with time by pressure transducers, installed in the
hydraulic lines, and perhaps tensile type load cells supported by an applicable data
logging system. The spatial coordinates of A, B, and C are to be made by some sort
of initial (prior to load application) simple global survey. As the test progresses, and
the test pile as well as the load application system changes, points A and B will
require additional "updated" measurements in order to remain within the tolerances of
acceptable measurement error for load application as currently given by the ASTM
87