614 christopher chud lundgreen 2010 kr

Damping Ratios for Laterally Loaded Pile Groups in

Fine Grained Soils and Improved Soils

by

Christopher “Chud” Lundgreen

A project submitted to the faculty of

Brigham Young University

in partial fulfillment of the requirements for the degree

Master of Science

Department of Civil and Environmental Engineering

Brigham Young University

August 2010

BRIGHAM YOUNG UNIVERSITY

GRADUATE COMMITTEE APPROVAL

of a project submitted by


This project has been read by each member of the following graduate committee and by majority

vote has been found to be satisfactory.

Date

Kyle M. Rollins, Chair

Date

Travis M. Gerber, Member

Date Fernando S. Fonseca, Member

Accepted for the Department

E. James Nelson, Graduate

Coordinator

ABSTRACT

Damping Ratios for Laterally Loaded Pile Groups in

Fine Grained Soils and Improved Soils


Department of Civil and Environmental Engineering

Master of Science

A set of pile groups were loaded laterally both statically and cyclically to determine static

load-displacement curves and damping ratios as a function of displacement. Tests were

performed on piles in native undisturbed clay as well as soils treated with a variety of soil

improvement techniques such as jet grouting, soil mixing and flowable fill. Damping ratios were

determined based on the hysteresis loops for each pile group at a number of displacement levels.

The measured damping ratio was relatively unaffected by the number of cycles and only

moderately affected by the soil improvement technique. Measured damping ratios were typically

between 15 and 25% which is consistent with limited data in the literature for small displacement

vibration tests. Charts are presented to show the range of damping ratio found through this

study.

Keywords: damping, cohesive soils, soil improvement, cyclic loading, pile groups

ACKNOWLEDGMENTS

I would first and foremost like to thank my advisor, Dr. Kyle M. Rollins, for his help and

guidance on this endeavor. He was willing to take me on as his student and pursue a masters

degree. I would also like to thank my committee for their guidance and support and everyone

else in the Civil and Environmental Engineering Department at Brigham Young University. In

addition, I thank the secretaries, especially Janice, who work tirelessly for the students. I also

want to thank my wife Emily for her support even when it wasn't the easiest of times for both of

us. My parents were also a great inspiration in helping me pursue an advanced degree and I want

to thank them for that. I would like to thank the US Forest Service for helping me pursue and

finance my education. Three individuals I want to thank are Bill Vischer, Marcia Hughey, and

Jerry McGaughran. Bill has provided invaluable and seasoned geotechnical experience. Marcia

has provided me with resources and direction within the agency. Jerry McGaughran was the

individual who is responsible for introducing me to Forest Service Engineering. Last of all I want

to thank Ryan Stone, my first engineering supervisor who instilled the importance of going

beyond a bachelors degree.

v

TABLE OF CONTENTS

1 INTRODUCTION...................................................................................................................... 1

1.1 Damping for Soil-Structure Systems ........................................................................... 2

2 PREVIOUS STUDIES ............................................................................................................... 7

3 SITE CONDITIONS ................................................................................................................ 21

4 MATERIALS AND TEST SETUP......................................................................................... 31

5 ANALYSIS AND RESULTS .................................................................................................. 39

5.1 Analysis Methodology ............................................................................................... 39

5.2 Results ........................................................................................................................ 43

5.2.1 Results for Pile Group in Virgin Clay ...................................................... 45

5.2.2 Results for Pile Group with Flowable Fill ............................................... 49

5.2.3 Results for Pile Group with Soil Mix Wall .............................................. 53

5.2.4 Results for Pile Group Surrounded by Jet-Grout Columns .................. 57

5.2.5 Results for Pile Group with Adjacent Jet-grout Columns ..................... 60

5.2.6 Results for Pile Group with Compacted Fill ........................................... 64

5.2.7 Results for Pile Group New Flowable Fill ............................................... 67

5.3 Summary .................................................................................................................... 69

5.4 Reconciliation of Differences ................................................................................... 71

6 CONCLUSIONS ...................................................................................................................... 73

REFERENCES ............................................................................................................................ 75

APPENDIX .................................................................................................................................. 77

Appendix A – Raw Data ................................................................................................... 77

vii

LIST OF TABLES

Table 2- 1: Halling et. al. 2000 data.............................................................................................. 10

Table 3- 1: Soil strength parameters for the Legacy Parkway test site ......................................... 26

Table 4- 1: Breakdown of each test, pilecap, and material. .......................................................... 34

Table 5- 1: Symbolic area calculation by coordinates .................................................................. 40

Table 5- 2: Area calculations of the first hysteresis loop ............................................................. 42

Table 5- 3: Area, stiffness, displacement, and damping for Loop 1 ............................................. 43

Table 5- 4: Denominator factor for calculating shear strain ......................................................... 44

Table 5- 5: Denominator factors from Skempton (1951) ............................................................. 44

Table 5- 6: Summary of findings from this study ......................................................................... 70

Table A- 1: Test 1 pilecap 1 results .............................................................................................. 78









Table A- 10: Test 5 pilecap 4 results ............................................................................................ 87




viii

Table A- 14: Test 9 pilecap 2 raw data ......................................................................................... 91

Table A- 15: Test 10 pilecap 2 results .......................................................................................... 92








Table A- 23: Test 14 pilecap 1 results ........................................................................................ 100






ix

LIST OF FIGURES

Figure 1- 1: Radiation damping as shown from Gazetas (1975) .................................................... 4

Figure 1- 2: Generalized hysteresis loop ........................................................................................ 5

Figure 2- 1: Damping ratio vs. intertia ratio from Gazetas (1975) ................................................. 8

Figure 2- 2: Rollins et. al. 2009 damping ratio data for gravel backfill ......................................... 9

Figure 2- 3: Hardin & Drnevich 1972 data for damping ratio of Lick Creek silt ......................... 11

Figure 2- 4: Hardin & Drnevich 1972 relationship for damping ratio and shear strain amplitude12

Figure 2- 5: Seed et. al. 1986 data showing damping ratio decrease with confining stress ......... 13

Figure 2- 6: Damping ratio as a funciton of PI from Vucetic & Dobry 1991for shear strains of

1.0% and 0.01% ............................................................................................................................ 14

Figure 2- 7: Damping ratio as a function of PI from Vucetic & Dobry 1991 with shear strain of

0.1% .............................................................................................................................................. 15

Figure 2- 8: Damping ratio as a function of cyclic shear strain for gravels based on cyclic triaxial

shear tests conducted by eight researchers after Rollins et. al. 1998 ............................................ 16

Figure 2- 9: Zhang et. al. 2005 data showing damping ratio vs. shear strain with geologic age of

soil ................................................................................................................................................. 18

Figure 2- 10: Zhang et. al. 2005 data showing damping ratio as a function of PI and shear strain

....................................................................................................................................................... 18

Figure 2- 11: Zhang et. al. 2005 data showing varying confining stress, shear strain, and geologic

age effects on damping ratio ......................................................................................................... 19

Figure 3- 1: Location of the Legacy Test site ............................................................................... 21

Figure 3- 2: (a) Borehole log, (b) a plot of Atterberg limits and natural water content versus

depth, along with, (c) a plot of undrained shear strength versus depth ........................................ 23

x

Figure 3- 3: Plots of cone penetration test (CPT) sounding 2 data ............................................... 27

Figure 3- 4: Plots of cone penetration test (CPT) soundings ........................................................ 28

Figure 3- 5: Plots of cone tip resistance and shear wave velocity versus depth from seismic cone

testing ............................................................................................................................................ 29

Figure 4- 1: Pile plan view ............................................................................................................ 32

Figure 4- 2: Plan view of pilecap setup ........................................................................................ 33

Figure 4- 3: Profile view of pilecap setup ..................................................................................... 33

Figure 4- 4: Virgin clay test setup................................................................................................. 35

Figure 4- 5: Setup for compacted fill and flowable fill tests ........................................................ 36

Figure 4- 6: Setup for surrounding jet-grout columns, adjacent jet-grout columns, and soil mix

wall ................................................................................................................................................ 36

Figure 4- 7: Test setup for centered jet-grout columns and new flowable fill .............................. 38

Figure 5- 1: Load-Displacement data for Test 1 Pilecap 1 ........................................................... 40

Figure 5- 2: Loop 1 of the first set of hystersis loops on Test 1 Pilecap 1 ................................... 42

Figure 5- 3: Virgin clay damping ratio histogram ........................................................................ 46

Figure 5- 4: Virgin clay damping ratio for each load cycle .......................................................... 47

Figure 5- 5: Virgin clay damping ratio ranges .............................................................................. 48

Figure 5- 6: Flowable fill damping ratio histogram ...................................................................... 50

Figure 5- 7: Flowable fill damping ratio for each loading cycle .................................................. 51

Figure 5- 8: Flowable fill damping ratio ranges ........................................................................... 52

Figure 5- 9: Soil mix wall damping ratio histogram ..................................................................... 54

Figure 5- 10: Soil mix wall damping ratio for each load cycle .................................................... 55

Figure 5- 11: Soil mix wall damping ratio ranges ........................................................................ 56

xi

Figure 5- 12: Surrounding jet-grout columns damping ratio histogram ....................................... 58

Figure 5- 13: Surrounding jet-grout columns damping ratio for each load cycle ......................... 59

Figure 5- 14: Surrounding jet-grout columns damping ratio regions ........................................... 60

Figure 5- 15: Adjacent jet-grout columns damping ratio histogram............................................. 61

Figure 5- 16: Adjacent jet-grout columns damping ratio for each load cycle .............................. 62

Figure 5- 17: Adjacent jet-grout columns damping ratio regions ................................................. 63

Figure 5- 18: Compacted fill damping ratio histogram ................................................................ 64

Figure 5- 19: Compacted fill damping ratio for each load cycle .................................................. 65

Figure 5- 20: Compacted fill damping ratio regions ..................................................................... 66

Figure 5- 21: New flowable fill damping ratio histogram ............................................................ 67

Figure 5- 22: New flowable fill damping ratio for each load cycle .............................................. 68

Figure 5- 23: New flowable fill damping ratio regions ................................................................ 69

Figure A- 1: Test 1 pilecap 1 raw data .......................................................................................... 78









Figure A- 10: Test 5 pilecap 4 raw data ........................................................................................ 87


xii




Figure A- 15: Test 10 pilecap 2 raw data ...................................................................................... 92








Figure A- 23: Test 14 pilecap 1 raw data .................................................................................... 100






1

1 Introduction

Pile foundations for buildings, bridges and other structures are often subjected to

dynamic loadings produced by ship impact, wave action, wind, and earthquake shaking. Under

dynamic loading, damping may offer significant resistance to lateral movement in addition to the

static spring stiffness of the soil-structure system. However, most simplified design methods

neglect damping resistance and rely on an equivalent static loading approach. This may be a

result of the fact that very few full-scale lateral load tests have been performed to determine an

appropriate damping ratio for pile groups. The paucity of test data is explained by the fact that

full-scale testing is relatively expensive and logistically difficult to perform.

To improve our understanding of the lateral resistance of pile groups under dynamic

loadings, a number of lateral load tests were performed on full-scale pile groups as part of this

study. These tests involved pile groups in native cohesive soil as well as pile groups where the

surrounding soil was improved using a variety of soil improvement techniques such as: soil

mixing, jet grouting, placement of flowable fill, and excavation and replacement with compacted

fill. Load tests were performed statically in an incremental fashion to displacements of 0.125,

0.25, 0.5, 0.75, 1.0, and 1.5 inches. However, at each increment three cycles of loading were

applied at a frequency of about 1 Hz. Results from these tests were used to compute the

damping ratio. The results from the static load tests are reported by Adsero (2008), Herbst

(2008), Miner (2009) and Lemme (2010).

2

1.1 Damping for Soil-Structure Systems

The lateral resistance of a pile group due to an applied load P is given by the equation

(1-1)

where Fi is the inertia force, Fd is the damping force and Fk is the spring force. The resistance

can also be expressed by the equation

(1-2)

where m is the mass, a is the horizontal acceleration, C is the damping coefficient, v is the

horizontal velocity, k is the static spring stiffness and x is the horizontal displacement.

To facilitate comparisons between systems with different masses and stiffnesses, the

damping coefficient is often normalized by the critical damping coefficient Cc to obtain the

damping ratio, ξ, as given by the equation,

(1-3)

The critical damping coefficient is the damping coefficient for which the displacement

goes to zero after one cycle of motion. An alternative definition for the damping ratio is given

by the equation

3

(1-4)

where ωo = natural frequency of the system, hereafter referred to as (Kramer 1996).

The damping measured in a load test is a result of two kinds of damping, namely

radiation damping and hysteretic damping. As explained by Gazetas (1975), radiation damping

occurs as energy is absorbed into the soil as waves radiate out from the point of loading and

propagate through the soil medium. This geometrical effect is illustrated in Figure 1-1. As the

wave moves further from the source the volume available for dissipating the energy increases.

Hysteretic damping accounts for the energy loss in the soil due to viscosity and plastic

deformations as the soil is loaded and unloaded. As discussed subsequently, the hysteretic

damping typically increases as the displacement and resulting shear strain increase.

The total energy loss from radiation and hysteretic damping results in a hysteresis loop in

the load-displacement curve rather than a straight elastic line. The damping ratio for the soil-

structure system can be defined by the equation

(1-5)

where Aloop is the area inside the hysteresis loop; k is the stiffness in units of force/length and is

calculated by the change in force/length (F/u); and u is the single amplitude displacement

Rollins et al. (2009). A hysteresis loop is shown in Figure 1-2, which is a graphical

representation of cyclic loading and unloading plotted against displacement or shear strain. For

the lateral pile group load tests in this study a combination of both hysteretic and radiation

4

damping, namely swaying radiation damping, developed. Equation 1-5 was used to compute the

composite damping ratio based on the load test measurements for each soil improvement

technique. These results are then compared to determine if there is any consistent pattern to the

measured damping ratio relative to the various soil improvement techniques.

Figure 1- 1: Radiation damping as shown from Gazetas (1975)

5

Figure 1- 2: Generalized hysteresis loop

As stated before the total damping can be obtained from a hysteresis loop. When the

hysteretic damping, , the stiffness, K, and the natural frequency, , are known. The hysteretic

dashpot coefficient, cm, may be calculated as

6

(1-6)

and then total damping coefficient, C, may be calculated as shown.

(1-7)

where cr is the radiation damping coefficient. If the total damping coefficient is known, the

radiation damping coefficient can be calculated. Once C is known, the damping ratio x, can be

calculated as shown

(1-8)

where k is stiffness and m is mass. This is similar to equation 1-4 and C can be applied to both

the y and z directions.

7

2 Previous Studies

As noted previously, the measured damping ratio for soil-structure interaction problems

is a result of both radiation damping and hystertic damping. Hypothetically, radiation damping

is expected to provide the major contribution to the overall damping of the soil-structure system

because of the large-scale test setup outside of a laboratory. The rationale for this is due to the

geographically large setting; ample room is provided for the cyclic loading to dissipate in the

soil. Verifying or denying this hypothesis is a major reason for conducting this study. Relatively

few full-scale lateral pile group load tests have been performed to evaluate the damping ratio for

pile group-soil interaction because of the cost and logistic difficulties of performing these tests.

In contrast, there is a vast body of information on the hysteretic damping of soil based on small-

scale laboratory testing which addresses soil type, shear strain, confining pressure and plasticity

index.

Radiation Damping

Gazetas (1975) present a summary chart showing the relationship between damping ratio and

inertia ratio in four radiation damping categories which is presented in Figure 2- 1. Inertia ratio is

the ratio of the soil moment of inertia to the moment of inertia of the foundation. The categories

are as follows; vertical, swaying (which is a horizontal movement), torsion, and rocking. As

stated before, the lateral pile group tests involve radiation damping due to a swaying and rocking

motion. The damping ratio for swaying is less than that for vertical motions but much higher

8

than that due to rocking or torsion. Over a wide range of inertia ratios the damping ratios range

between 10 and 50%. With the typical range of interest for foundations under cyclic horizontal

loading, the range is between 20 and 35%.

Figure 2- 1: Damping ratio vs. intertia ratio from Gazetas (1975)

9

Figure 2- 2: Rollins et. al. 2009 damping ratio data for gravel backfill

Rollins et al. (2009) performed cyclic lateral load tests on a large pile cap with and

without backfill adjacent to the cap. The pile cap was 11 ft by 16 ft in plan view with a thickness

of 5.5 ft and was supported by six 12.75 inch diameter steel pipe piles. The backfill consisted of

sand and gravel. Their results are presented in Figure 2- 2. Their study showed damping ratios

between 25% and 35% and each test showed very little variation with the number of load cycles

or with the level of displacement at which the test was performed.

Halling et. al. (2000) used an eccentric mass shaker and a 12-pound sledge hammer to

evaluate the damping ratio of a pile cap in relatively soft clay without any backfill around the

10

pilecap. The pile cap was 9 ft by 9 ft in plan view with a thickness of 3 ft and was supported by

nine 12.75 inch diameter steel pipe piles in a 3x3 arrangement. The mass shaker was used to

induce sinusoidal vibrations, whereas the sledge hammer was used for the impact vibrations,

which was hit in the center of the pilecap. The mass shaker caused a maximum displacement of

0.02 mm/kN (3.5x10-6

in/lb) with steady state excitation frequencies of 5 to 8 Hz in increments

of 0.2 Hz, 8 to 10 Hz in increments of 0.1 Hz, and 10 to 20 Hz in increments of 0.5 Hz. The

damping ratio was found to be approximately 14-19% with the half-power band width method.

Their results are presented in Table 2- 1.

Table 2- 1: Halling et. al. 2000 data

11

Hysteretic (Material) Damping

A very large number of laboratory studies have been done on the hysteretic or material

damping ratio of soils. Hardin & Drnevich (1972) in a Terzaghi lecture tried to further advance a

general stress-strain model for soils. A small part of their discussion included damping ratio.

They presented a couple case studies and damping ratio was one of the parameters discussed.

The discussion here will be brief in interest of conciseness. Figure 2- 3 shows a decreasing trend

of damping ratio with number of load cycles in Lick Creek silt. Figure 2- 4 shows the same silt

with an increasing damping ratio at a very low strain rate.

Figure 2- 3: Hardin & Drnevich 1972 data for damping ratio of Lick Creek silt

12

Figure 2- 4: Hardin & Drnevich 1972 relationship for damping ratio and shear strain amplitude

Seed et. al. (1986) performed widely-cited work in which damping ratio was defined as a

function of cyclic shear strain. They found that the damping ratio tended to decrease as

confining pressure increased. Seed et al. (1986) provided curves based on additional data for

sand and for gravels in Figure 2- 5.

13

Figure 2- 5: Seed et. al. 1986 data showing damping ratio decrease with confining stress

Based on data from tests on a wide variety of soils, Vucetic and Dobry (1991) developed

curves defining the material damping as a function of plasticity index. These curves are shown

in Figures Figure 2- 6 and Figure 2- 7. For a given cyclic shear strain, the damping ratio was

found to decrease as the plasticity index increased. These curves have been widely used in

geotechnical earthquake engineering practice.

14

Figure 2- 6: Damping ratio as a funciton of PI from Vucetic & Dobry 1991for shear strains of 1.0% and

0.01%

15

Figure 2- 7: Damping ratio as a function of PI from Vucetic & Dobry 1991 with shear strain of 0.1%

In 1998, Rollins et al. developed curves defining material damping for gravels. For the

same cyclic shear strain, they found the damping ratio to be somewhat lower than that for sand

and gravels defined by Seed et. al. (1986) as shown in Figure 2- 5. Rollins et al also found that

the increases in confining pressure led to a decrease in damping ratio for a given shear strain as

was the case for sand.

16

Figure 2- 8: Damping ratio as a function of cyclic shear strain for gravels based on cyclic triaxial shear tests

conducted by eight researchers after Rollins et. al. 1998

Recently another study was done from more of a geological perspective with data from

three sites in South Carolina corresponding with three different geologic ages (Zhang et al.

2005). The specimens in their experiments were subjected to resonant column and torsional shear

testing. According to Zhang the damping ratio is a function of geologic age and other soil

properties. Zhang presented several charts, the first of which is Figure 2- 9; which shows that the

damping ratio tends to increase as the geologic age increase. This chart shows damping as high

as 25% for cyclic shear strains of 1%. Following in Figure 2- 10 is Zhang's chart with damping

ratio as a function of shear strain and plasticity index with data taken from Vucetic & Dobry

17

(1991). Again, this is the same range as the previous chart. Vucetic & Dobry's study was

primarily on the influence of Plasticity Index (PI) on damping ratio. They assert that with

increasing shear strain, PI and decreasing void ratio; the damping ratio decreases relative to low

PI soils. They also point out that there are many factors that affect damping ratio including

geologic age, void ratio, soil type, overconsolidation ratio (OCR) and initial stress states.

One last set of charts done by Zhang in the same study shows damping ratio as a function

of shear strain with differing confining pressures with geologic age and are shown in Figure 2-

11. An important point is that all of Zhang's charts except Figure 2- 10 are for non-plastic soils.

Zhang’s study, among others are laboratory tests which will exhibit more hysteretic damping

than radiation damping. This is due to the confined nature of a laboratory test in general with

little possibility of the loading dissipating with distance from the loading source. The

significance of Figure 2-10 for this study is to verify the material damping ratio and confirm

whether or not this experiment is governed by the expected radiation damping or not.

18

Figure 2- 9: Zhang et. al. 2005 data showing damping ratio vs. shear strain with geologic age of soil

Figure 2- 10: Zhang et. al. 2005 data showing damping ratio as a function of PI and shear strain

19

Figure 2- 11: Zhang et. al. 2005 data showing varying confining stress, shear strain, and geologic age effects

on damping ratio

21

3 Site Conditions

The test site is near Legacy Parkway in North Salt Lake City, Utah as shown in Figure 3-

1. Legacy Parkway is a new stretch of Interstate Highway 15 which is exclusively in Davis

County. Geotechnical site conditions where the pile cap load tests were performed were

evaluated using field and laboratory testing. Field testing included one drilled hole with

undisturbed sampling, four cone penetration test (CPT) soundings, and shear wave velocity

testing. Laboratory testing included unit weight and moisture content determination, Atterberg

limits testing, and undrained shear testing.

Figure 3- 1: Location of the Legacy Test site

22

A generalized soil boring log at the test site is provided in Figure 3- 2. The depth is

referenced to the top of the excavation which was 2.5 ft above the base of the pile cap as shown

in the figure. The soil profile consists predominantly of cohesive soils; however, some thin sand

layers are located throughout the profile. The cohesive soils typically classify as CL or CH

materials with plasticity indices of about 20 as shown in Figure 3-1(a). In contrast, the soil layer

from a depth of 15 to 25 ft consists of interbedded silt (ML) and sand (SM) layers as will be

highlighted by the subsequent plots of cone penetration test (CPT) cone tip resistance.

The liquid limit, plastic limit and natural moisture content are plotted in Figure 3-1(b) at

each depth where Atterberg limit testing was performed. The water table is at a depth of 1.5 ft.

The natural water content is less than the liquid limit near the ground surface suggesting that the

soil is overconsolidated, but the water content is greater than the liquid limit for soil specimens

from a depth of 5 to 27 feet suggesting that these materials may be sensitive. Below a depth of 30

feet the water content is approximately equal to the liquid limit suggesting that the soils are close

to normally consolidated.

23

Figure 3- 2: (a) Borehole log, (b) a plot of Atterberg limits and natural water content versus depth, along

with, (c) a plot of undrained shear strength versus depth

The undrained shear strength is plotted as a function of depth in Figure 3-1(c). Undrained

shear strength was measured using a miniature vane shear test or Torvane test on undisturbed

24

samples immediately after they were obtained in the field. In addition, unconfined compression

tests were performed on most of the undisturbed samples. Both the Torvane and unconfined

compression tests indicate that the undrained shear strength decreases rapidly from the ground

surface to a depth of about 6 ft but then tends to increase with depth. This profile is typical of a

soil profile with a surface crust that has been overconsolidated by desiccation. However, the

undrained shear strength from the unconfined compression tests is typically about 30% lower

than that from the Torvane tests. The unconfined compression tests at a depth of 27 and 48 ft

appear to have been conducted on soil with sand lenses because the measured strength is

substantially lower than that from the Torvane test and are not likely to be representative of the

soil in-situ. The undrained shear strength was also computed from the cone tip resistance using

the correlation equation

(3-1)

where qc is the cone tip resistance, is the total vertical stress, and Nk is a variable which was

taken to be 15 for this study. The undrained shear strength obtained from Eq. (3-1) is also plotted

versus depth in Figure 3-1(c) and the agreement with the strengths obtained from the Torvane

and unconfined compression tests is reasonably good. Nevertheless, there is much greater

variability and the drained strength in the interbedded sand layers is ignored. A summary of

laboratory test results is provided Table 3-1.

Four cone penetration tests (CPT) were performed across the test site and plots of cone

tip resistance, friction ratio, and pore pressure are provided as a function of depth for the second

25

CPT sounding in Figure 3-2. In addition, the interpreted soil profile is also shown. From the

ground surface to a depth of about 15 feet the soil profile appears to be relatively consistent with

a cone tip resistance of about 6 tsf and a friction ratio of about 1%. However, one thin sand layer

is clearly evident between 6 and 8 ft. The cone tip resistance, friction ratio, and pore pressure

plots clearly show the interbedded silt and sand layering in the soil profile between 15 and 27 ft.

below the ground surface.

Figure 3-3 provides plots of the cone tip resistance, friction ratio and pore pressure versus

depth as a function of depth for all four of the CPT soundings. The measured parameters and

layering are generally very consistent for all four sounding which indicates that the lateral pile

load tests can be fairly compared from one site to the next.

Figure 3-4 provides a plot of the shear wave velocity as a function of depth obtained from

the downhole seismic cone testing. The interpreted soil profile and cone tip resistance are also

provided in Figure 3-4 for reference. The shear wave velocity in the upper 10 ft of the profile is

between 300 and 400 ft/sec which is relatively low and suggests a low shear strength. Between a

depth of 10 to 20 ft the velocity increases to about 550 ft/sec. This increase in velocity is likely

associated with the interbedded layer which contains significant sand layers. Below 20 ft, the

velocity drops to a value of around 500 ft/sec and remains relatively constant to a depth of 45 ft.

26

Table 3- 1: Soil strength parameters for the Legacy Parkway test site

27

Figure 3- 3: Plots of cone penetration test (CPT) sounding 2 data

28

Figure 3- 4: Plots of cone penetration test (CPT) soundings

29

Figure 3- 5: Plots of cone tip resistance and shear wave velocity versus depth from seismic cone testing

31

4 Materials and Test Setup

Tests were performed on four pile groups. Each pile group was composed of nine test

piles driven in a 3 x 3 arrangement. Each of the pile groups were driven to a depth of 40 feet

below the ground surface. The test piles were 12.75 inch outside diameter steel pipe piles with a

0.375 inch thickness. The plan view of the pile cross section is shown in Figure 4-1. A 5000 psi

compressive strength concrete in-fill was used in the pile with six #8 longitudinal bars with an 8

inch diameter #4 spiral bar. The moment of inertia of the pile itself was 279 in4. Angle irons

were attached to some piles to protect strain gauges which increased the moment of inertia to 342

in4. The steel was in accordance with American Society of Testing and Materials (ASTM) A252

Grade 3 with a yield strength of 58,700 psi. The pile caps were placed on top of the excavation at

2.5 feet below the ground surface. The piles were embedded into a reinforced concrete pile cap.

Nominally, each cap was 8.75 ft x 9.3 ft in plan and 2.5 ft thick.

A typical setup of the test piles and pile caps are shown in plan view in Figure 4-2. Figure

4-3 has the respective profile view. Many tests were performed on the site but not all will be

presented in this study. To increase the lateral resistance of the pile groups a variety of soil

improvement techniques were employed and included, excavation and replacement with

flowable fill, excavation and replacement with compacted granular fill, soil-mixing, and jet-grout

columns. Tests were also performed on untreated virgin clay as a comparison. Table 4-1 shows

the breakdown of each test, pilecap, and improvement technique which was a part of that

particular test section.

32

Figure 4- 1: Pile plan view

33

Figure 4- 2: Plan view of pilecap setup

Figure 4- 3: Profile view of pilecap setup

34

Table 4- 1: Breakdown of each test, pilecap, and material.

A plan view of each of the different test setups will be shown to clarify the descriptions.

Figure 4-4 shows the setup for the virgin clay and Figure 4-5 shows the flowable fill and

35

compacted fill setup. In Figure 4-6 the setup for the soil mix treatment, pile group surrounded by

jet-grout columns, and the adjacent jet-grout columns are presented. The virgin clay is no soil

treatment with the soil stratum as presented previously.

Figure 4- 4: Virgin clay test setup

The flowable fill test was excavated to 5.5 ft below the bottom of the cap. It was designed

to have an unconfined compressive strength of 100 psi but ended up being between 20 and 30

psi. The compacted fill was excavated to a depth 3.5 ft below the bottom of the pilecap and

compacted to about 93% of the modified proctor density.

36

Figure 4- 5: Setup for compacted fill and flowable fill tests

Figure 4- 6: Setup for surrounding jet-grout columns, adjacent jet-grout columns, and soil mix wall

Jet-grout was utilized in the form of mixing soil and cementitious material. The jet-grout

columns were of two types, pile group surrounded by jet-grout columns and adjacent jet-grout

37

columns. The grout columns extended 10 feet below the pilecap. The slurry mixing rate was

about 26 pounds per cubic foot of soil (about 20% by weight). The jet-grout compressive

strength was 680 psi on average with a range between 350 to 850 psi, based on both cored and

cast samples.

Soil-mixing or mass mixing treatment was performed by mixing the virgin clay with the

grout spoils with an excavator bucket until uniformity seemed to be achieved based on visual

inspection. The treatment had a 1 to 1 ratio of soil and grout spoils with about 13 pounds of

cement per cubic foot of soil (about 10% by weight).

The new flowable fill treatment was a redo of the flowable fill treatment with an

increased compressive strength of about 90 psi which was much closer to the desired value. The

higher strength flowable fill was placed behind the pilecap at 6 feet deep. It should be noted that

flowable fill is a cementitious material with fly ash, slag, fine aggregates, and water.

38

Figure 4- 7: Test setup for centered jet-grout columns and new flowable fill

The load was applied statically to six target deflections which were 0.125, 0.25, 0.5, 0.75,

1.0, and 1.5 inches. The actuators contracted or extended at a rate of approximately 1.5

inches/min. At each deflection increment, three load cycles were applied at a frequency of 1 Hz

with a single amplitude deflection of about 0.1 inch. The results and analyses described in this

study are focused exclusively on the cyclic loading portions of the testing program. Results of

the jet grouting load tets are provided by Adsero (2008), results of the soil mixing tests are

presented by Herbst (2008). Miner (2009) presents the results tests involving excavation and

replacement with flowable fill and Lemme (2010) provides the results of the tests involving

excavation and replacement with compacted granular fill.

39

5 Analysis and Results

5.1 Analysis Methodology

After the testing was performed the relevant data was extracted and analyzed for each

test. In Figure 5-1, the raw data for Test 1 Pilecap 1 is shown with load in kips on the y-axis

plotted versus displacement in inches on the x-axis. The three sets of hysteresis loops for this

particular displacement increment can also be seen, these were obviously the objects of interest

in this analysis. Equation 1-5 was used to calculate the damping ratio and used the area

calculation by coordinates method (Crawford 2002) to calculate the area of each hysteresis loop

shown in Table 5-1 in conjunction with equation 5-1.

(5-1)

where total 1 and total 2 are the summation of column 1 and column 2, respectively, as shown in

Table 5-1. Each column row is the product of coordinate x(i+1) and y(i) or x(i) and y(i+1).

It should be noted that all damping ratios presented from this study are a result of both

soil and pile-group interaction and not just soil.

40

Table 5- 1: Symbolic area calculation by coordinates

Figure 5- 1: Load-Displacement data for Test 1 Pilecap 1

41

Figure 5-2 shows a plot of the first set of hysteresis loops for Test 1 Pilecap 1 with

graphical markers to help show one of the loops; the thick solid line defined by the peak

displacement points from one end of the loop to the other is the stiffness. Thereafter, calculations

are shown for the area, stiffness, total displacement, and the damping ratio for that particular

loop. The peaks on the hysteresis loops were a combination of peak displacement and peak load

unless one was obviously more pronounced than the other.

Table 5-2 summarizes the calculations for hysteresis Loop 1 on Test 1 Pilecap 1, and

Table 5-3 presents the area, stiffness, displacement, and damping ratio calculated for each loop.

These calculations and results are presented to show the methodology of obtaining the final

results. Calculations for the other pile caps and tests are presented in the Appendix.

42

Figure 5- 2: Loop 1 of the first set of hystersis loops on Test 1 Pilecap 1

Table 5- 2: Area calculations of the first hysteresis loop

43

Table 5- 3: Area, stiffness, displacement, and damping for Loop 1

5.2 Results

This section summarizes the results obtained from this study. The results are divided

between the various soil improvement types. Table 5-4 provides the mean, standard deviation,

the maximum minimum damping ratios along with shear strain values for each material. It is

easy to see that the ranges for all of the tests fall within the ranges of the previous studies

presented earlier, with exception of the pile group surrounded by jet-grout columns. Shear strain

was calculated using the following equation 5-2 from Gazetas (1984). Several points must be

made in conjunction with equation 5-2. The equation is inherently for single piles and in that

particular case the factor of 2.5 in the denominator is correct. The factor will vary depending on

the material type and configuration according to a personal communication from Gazetas &

Rollins (2010). The original equation is given as

(5-2)

where e(z) effective shear strain at depth z, is Poisson’s ratio, b is the pile diameter, and yd(z)

is the lateral deflections at depth z. The average strain values were calculated based on an

44

assumed Poisson’s ratio of 0.4. The pile diameter was the single pile diameter of 12.75 inches

for the virgin clay and compacted fill. Though the equation is for single piles, this study will

assume the strains will be comparable for a pile group. This unfortunately presents an unknown

amount of uncertainty. The other treatments act as a composite pile and the widths were changed

accordingly.

Table 5- 4: Denominator factor for calculating shear strain

Virgin Clay

Compacted Fill

Sur. Jet-Grout

Adj. Jet-Grout

Flowable Fill

New Flowable Fill

Soil Mix

B (in) 12.75 12.75 126 144 105 120 105

B (ft) 1.06 1.06 10.5 12 8.75 10 8.75

L --- --- 10 12 5.5 6 10

L/B --- --- 0.95 1 0.63 0.6 1.14

Factor 2.5 2.5 1.9 1.9 1.7 1.7 1.95

The factors come from Skempton (1952) and each factor is based upon the L/B ratio. In

this case, L is depth from the surface of the soil treatment and B is width of the soil treatment

normal to the direction of loading. The applicable factor is in the far right column.

Table 5- 5: Denominator factors from Skempton (1951)

45

5.2.1 Results for Pile Group in Virgin Clay

The median PI is 19 for the profile of virgin clay. Using the Vucetic & Dobry data in

Figure 2- 10 for the average shear strain of virgin clay, the material damping ratio is about 13%.

The results from Vucetic and Dobry all involve laboratory tests of varying sorts including

resonant columns, simple shear, and triaxial tests and the number of loading cycles varies from 1

to 1,000. These other tests are obviously setup differently from the full scale tests in this study

and may yield some differences.

These results and those presented here after are organized in three distinct parts. The first

chart is the data distribution or histogram of the damping ratio. The second chart shows the

computed damping ratio for each displacement increment plotted versus the number of cycles.

Finally, the third chart shows the mean, the mean plus-and-minus one standard deviation bounds

and the lower and upper boundaries.

The histogram for the pile group in virgin clay is presented in Figure 5-3 and 29 of the 55

data points have damping ratios which fall within the range of 14 to 25%. The histogram shows

a roughly normal trend, however, there is significant scatter and a strong right skew. The raw

data points are shown as damping ratios plotted against load cycle in Figure 5-4 for the pile

group in virgin clay. Figure 5-5 shows the mean, standard deviations, and upper and lower bound

ranges for damping ratio versus the number of loading cycles for virgin clay. It should be noted

that the upper and lower boundaries are limited to three standard deviations to filter out any

unreliable data. The upper and lower boundaries are plus and minus three standard deviations,

respectively. There are few items to point out. One of them is that at the minimum boundary the

46

magnitude of the damping ratio is very close to the minus one standard deviation. The damping

ratio at the second cycle is about 6% greater than the first and third cycles. This is most likely a

coincidence since the mean plus one standard deviation is relatively constant. Another anomaly

is there is a greater difference in magnitude between the upper boundary and the mean than the

lower boundary and the mean, this shows the distribution is not symmetric and validates the

skew seen in the histogram. A close examination of the raw data points show that the point

density is substantially lower in the upper regions which mean these points are possibly outliers,

the data distribution is not normal, or the data points follow the right skew.

Figure 5- 3: Virgin clay damping ratio histogram

47

Figure 5- 4: Virgin clay damping ratio for each load cycle

48

Figure 5- 5: Virgin clay damping ratio ranges

49

5.2.2 Results for Pile Group with Flowable Fill

The results for flowable fill are presented in a similar manner as for the virgin clay. The

histogram for this load test is provided in Fig. 5-6 and 42 of the 75 data points have damping

ratios which fall within the range from 14% to 25%. The histogram in Figure 5-6 shows a

normal distribution. Figure 5-7 shows the raw data for each loading cycle show some outlier

points in the upper regions. Figure 5-8 shows a consistent trend with the mean, standard

deviations, and the lower boundary, only the upper boundary is irregular. The upper boundary of

the damping ratio for the pile group in flowable for the first and third cycles are about 8 to 9%

greater than the second cycle. This is probably coincidental and these two points may be outliers

given the consistency with the mean, standard deviations, and the lower boundary.

50

Figure 5- 6: Flowable fill damping ratio histogram

51

Figure 5- 7: Flowable fill damping ratio for each loading cycle

52

Figure 5- 8: Flowable fill damping ratio ranges

53

5.2.3 Results for Pile Group with Soil Mix Wall

The results for the soil mix wall presented in a similar manner as for the previous two.

The histogram in Figure 5-9 shows almost no visible skew. The data show 23 of the 29 points

fall within the 14 to 25% damping ratio value. For a small number of points, the histogram

shows a close to normal distribution but this is uncertain.

The point density is less for the smaller damping ratio values on the first loading cycle

compared to the lower point density at higher damping ratio values for the second and third

loading cycles as seen in Figure 5-10. Figure 5-11 shows the mean, standard deviations, and

boundaries and validates the described trend. Only a couple points for each loading cycle change

the trend from being more consistent. It is difficult to say if these points are outliers or not

because of such a small of data points available for the soil mix wall.

54

Figure 5- 9: Soil mix wall damping ratio histogram

55

Figure 5- 10: Soil mix wall damping ratio for each load cycle

56

Figure 5- 11: Soil mix wall damping ratio ranges

57

5.2.4 Results for Pile Group Surrounded by Jet-Grout Columns

The results for the pile group surrounded by jet-grout columns are presented in a similar

manner as for the previous results in Figure 5-12. The histogram shows 18 of the 62 points fall

between the 14 to 33% damping ratio. The first important observation is the pile group

surrounded by jet-grout columns is substantially higher in damping ratio than any other material

and the spread has a lot of variation. This could be because cementitious materials are generally

heterogeneous materials and this may be a manifestation of that behavior. Soil in nature is

generally also a heterogeneous material but the borings from this particular site show this

particular soil stratum is relatively homogenous. Looking at the raw data in Figure 5-13 shows a

good portion of this is in the first loading. This could be because of a “crushing” effect after the

first load cycle decreasing the particle sizes. As stated before the damping ratio is the highest of

any other material. A possible reason might be the setup is creating an “equivalent pier” effect.

Cementitious materials also have a much higher modulus of elasticity than soil. The mean and

standard deviations in Figure 5-14 show a relatively constant relationship between load cycles

and damping ratio except for the variation seen in the first loading cycle. Up until this point in

stating the results, the damping ratio has only marginally improved at best with the previous

three soil treatments. The pile group surrounded by jet-grout columns increases the mean

damping ratio but still not very much. Also, the number of loading cycles seems to be of little or

no importance as to the change of damping ratio but it is difficult to say given only three cycles.

This will be revisited in the conclusion section.

58

Figure 5- 12: Surrounding jet-grout columns damping ratio histogram

59

Figure 5- 13: Surrounding jet-grout columns damping ratio for each load cycle

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Figure 5- 14: Surrounding jet-grout columns damping ratio regions

5.2.5 Results for Pile Group with Adjacent Jet-grout Columns

The results for the adjacent jet-grout columns are presented in a similar manner as for the

previous results. The data spread is very consistent, shown in the histogram in Figure 5-15 which

is likely not a normal distribution. The histogram shows 18 of the 41 points fall within the 14 to

25% damping ratio value. These results are closer to the first three tests, lending to a difference

between the cemented material surrounding the pilecap rather than being adjacent to it. The raw

data is presented in Figure 5-16 and confirms the consistency of the data points. The mean and

standard deviations range, in Figure 5-17, show a steady trend for damping ratio regardless.

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Figure 5- 15: Adjacent jet-grout columns damping ratio histogram

62

Figure 5- 16: Adjacent jet-grout columns damping ratio for each load cycle

63

Figure 5- 17: Adjacent jet-grout columns damping ratio regions

64

5.2.6 Results for Pile Group with Compacted Fill

The results for the compacted fill are presented in a similar manner. The histogram is

presented in Figure 5-18 with 20 of the 42 points being in the 14 to 25% damping ratio range.

The data spread shows again a roughly normal distribution. The raw data is presented in Figure

5-19 which shows a relatively consistent point density for all of the load cycles. The mean,

standard deviations, and the boundaries are seen in Figure 5-20 and the trend seems to be

relatively constant. With this in mind, this trend matches Rollins et al. (2009) which deals with

granular soils.

Figure 5- 18: Compacted fill damping ratio histogram

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Figure 5- 19: Compacted fill damping ratio for each load cycle

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Figure 5- 20: Compacted fill damping ratio regions

67

5.2.7 Results for Pile Group New Flowable Fill

The results for the new flowable fill are presented in a similar manner as for the previous

results. The data distribution, in Figure 5-21, is right skewed with only a couple of outliers. Also

shown is 30 of the 39 points are within the 14 to 25% damping ratio range. The raw data, in

Figure 5-22, show a very large outlier of about 41% at the first load cycle. The mean and the

minus one standard deviation trend lines, in Figure 5-23, increase by about 5% and 10%,

respectively, from the first loading cycle to the third. It is difficult to ascertain a certain

mechanism since there are so few data points.

Figure 5- 21: New flowable fill damping ratio histogram

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Figure 5- 22: New flowable fill damping ratio for each load cycle

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Figure 5- 23: New flowable fill damping ratio regions

5.3 Summary

Through the course of reporting these results there have been unexplainable jumps of the

damping ratio, usually at the second cycle, or unexplainable outliers. The reader must remember

that the damping ratios calculated in this study aren’t just for the soil or soil treatment but for the

soil or soil treatment and pile group interaction. With that in mind, the damping ratio still appears

to be minimally affected by the soil treatment, the best being the surrounding jet-grout columns

with a median damping ratio of about 50% and a mean damping ratio of about 64%. The fact that

70

only three loading cycles were applied gives a limited view of damping. However, with the data

available from Vucetic & Dobry (1991), material damping can be calculated, given a PI and

shear strain. In Table 5-6 is the findings of damping ratio for this study, including median, mean,

standard deviation, maximum, and minimum damping ratio values. Shear strain is also included

and differences can be seen between the materials treated as single piles (virgin clay and

compacted fill) and those treated as equivalent piers. As stated in chapter 2, according to Vucetic

& Dobry (1991) the material damping is about 13% (for virgin clay) which is over half of the

damping contribution of the total damping ratio which goes against the earlier hypothesis. In

regards to the shear strain, since the compacted fill and virgin clay were treated as individual

piles, shear strain was simply assumed to be comparable to that of the whole pile group.

Unfortunately, this presents a bit of uncertainty in the analysis.

Table 5- 6: Summary of findings from this study

Damping Ratio Shear Strain

Median Mean Std Deviation Max Min Block or Pile Group

Virgin Clay 19.6% 23.7% 12.0% 57.6% 5.2% 0.21%

Flowable Fill 22.4% 22.2% 7.9% 44.5% 7.7% 0.06%

Soil Mix 17.7% 18.7% 6.3% 33.1% 6.2% 0.05%

Surrounding Jet-Grout Columns 52.8% 64.9% 52.8% 256.1% 12.3% 0.01%

Adjacent Jet-Grout Columns 25.6% 25.0% 8.2% 40.0% 9.5% 0.02%

Compacted Fill 26.1% 27.3% 9.9% 61.6% 9.9% 0.27%

New Flowable Fill 19.1% 19.0% 10.8% 72.6% 2.1% 0.07%

71

5.4 Reconciliation of Differences

There are some similarities and differences in damping ratio between our study and those

conducted by others. All of the damping ratio values for the virgin clay in this study match fairly

well with the other studies presented. All of differences are relatively small and within our own

standard deviation.

When dealing with damping ratio, it is important to know the contribution of both

material and radiation damping. Hysteretic damping can be calculated by using the various

charts presented in Chapter 2 if strain and PI are known. The total damping can calculated with

a hysteresis loop. The difference between the two is the radiation damping.

There are minor differences between this study and Halling et. al. 2000; their average

values are between 5 and 10% lower than this study. This may or may not be the result of

different vibration inducing machines. From the study on coarse gravels in Rollins et. al. 2009

there was little change in damping ratio with number of loading cycles. Their average is between

25% and 35%, this matches up reasonably well with these results. The results from this study

have much more scatter than Rollins et. al. 2009 but the mean and standard deviation are within

the range. The damping ratio given by Gazetas (1975) for radiation damping also matches up

very well.

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6 Conclusions

1. The measured damping ratio for the pile group in virgin clay was about 20% with a

standard deviation of about 12%.

2. For most of the soil improvement treatments involved (flowable fill, soil mixing, and

compacted fill, jet grouting adjacent to cap), the damping ratio was relatively unaffected

by the treatment process. Mean damping ratios for these cases were typically 18% to

28% with a standard deviation of 6% to 10%.

3. Jet grouting around the pile group itself led to an increase in the mean damping ratio of

about 100% relative to the pile group in virgin clay. The damping ratio increased to a

value of 50% to 60% with a standard deviation of about 50%. This may be due to the

formation of a large “equivalent pier” which acts like a large single pile.

4. For the displacement levels involved in these tests, the damping ratio was relatively

unaffected by the number of cycles or the static displacement level at which the cyclic

test was performed.

5. For the shear strain levels of the virgin clay and compacted fill involved in this testing

program (0.2%), the material (hysteretic) damping would be expected to be about 13%.

This suggests that the majority of the damping measured in this testing program would be

a result of material damping rather than the expected radiation damping stated in chapter

2.

75

References

Crawford, W. G. 2002. Construction Surveying and Layout. 3rd ed. Creative Construction Publishing.

Gazetas, G. 1975. Foundation Engineering Handbook. Ed. H. F. Winterkorn and H. Y. Fang.

Van Nostrand Reinhold New York.

Gazetas, G., and R. Dobry. 1984. Horizontal response of piles in layered soils. Journal of

Geotechnical Engineering 110, no. 1: 20-40.

Gazetas, G., and K. M. RollinsLetter to C. A. Lundgreen. 2010. [Fwd: Re: Shushi Eater]. July

28. https://mail.google.com/mail/?shva=1#label/Project/12a1ab182c83fb45.

Halling, M. W., K. C. Womack, I. Muhamad, and K. M. Rollins. 2000. Vibrational testing of a

full-scale pile group in soft clay. In Proc. 12th World Conference on Earthquake

Engineering, Auckland. Vol. 1745.

Hardin, B. O., and V. P. Drnevich. 1972. Shear modulus and damping in soils: design equations

and curves. Journal of the Soil Mechanics and Foundations Division, ASCE 98, no. 7:

667-692.

Kramer, S. L. 1996. Geotechnical Earthquake Engineering. Prentice Hall.

Rollins, K. M. 2007. Quarterly Progress Report to the National Cooperative Highway Research

Program (NCHRP) on Project 24-30. Quarterly Progress Report. Project 24-30. National

Highway Cooperative Research Program (NHCRP), December.

Rollins, K. M., M. D. Evans, and N. B. Diehl. 1998. Shear modulus and damping relationships

for gravels. Journal of Geotechnical and Geoenvironmental Engineering, ASCE 124, no.

5: 396-405.

Rollins, K. M., T. M. Gerber, and K. H. Kwon. 2009. Increased Lateral Abutment Resistance

from Gravel Backfills of Limited Width. Journal of Geotechnical and Geoenvironmental

Engineering, ASCE 136, no. 1: 230-238.

Seed, H. B., R. T. Wong, I. M. Idriss, and K. Tokimatsu. 1986. Moduli and Damping Factors for

Dynamic Analyses of Cohesionless Soils. Journal of Geotechnical Engineering, ASCE

112, no. 11: 1016-1032.

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Skempton, A. W. 1952. The Bearing Capacity of Clays. In Soil Mechanics Papers Presented at

the Building Research Congress 1951, 180. National Research Council, Canada.

Vucetic, M., and R. Dobry. 1991. Effect of soil plasticity on cyclic response. Journal of

Geotechnical Engineering, ASCE 117, no. 1: 89-107.

Zhang, J., R. D. Andrus, and C. H. Juang. 2005. Normalized shear modulus and material

damping ratio relationships. Journal of Geotechnical and Geoenvironmental

Engineering, ASCE 131, no. 4: 453-464.

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Appendix

Appendix A – Raw Data

Following are the raw data of load-displacement curves for each test and pilecap with their

respective load, damping ratio, area of hysteresis loop, displacement, and stiffness.

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Figure A- 1: Test 1 pilecap 1 raw data

Table A- 1: Test 1 pilecap 1 results

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Table A- 14: Test 9 pilecap 2 raw data

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