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Characterization of environmental variability in identified dynamic properties of a soil-foundation-structure system

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Characterization of environmental variability in identified dynamic properties of a soil-foundation-structure system

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CHARACTERIZATION OF ENVIRONMENTALVARIABILITY IN IDENTIFIED
DYNAMIC PROPERTIES OF A SOIL-FOUNDATION-STRUCTURE SYSTEM

by
Ali Asghari
________________________________________________________________

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(CIVIL ENGINEERING)

December 2009

Copyright 2009 Ali Asghari

ii
Dedication
I dedicate this dissertation to all the parents who sacrifice their lives for their kids and
raise them responsibly so that they can constantly contribute to their societies; those who
educate their kids so wisely that they could be fully motivated in obtaining broader vision
in life and also provide them with peaceful environment so that they could pursue their
dreams enthusiastically.

iii
Acknowledgements
Had it not been for a collaborative teamwork, I would not have been able to accomplish
this research and dissertation. I would like to thank all those who helped in this effort. On
top of my list, I would like to appreciate my advisor, Professor Erik A. Johnson, for
providing inspiration and support to make this work possible.
I do not have enough words to say how grateful I am to have worked under the
supervision of my co-advisor, Professor Robert Nigbor; not only for his academic
guidance, but also for his fabulous personality that has always been a great source for
motivation and encouragement since I initiated my research career at USC.
I would also like to appreciate my Ph.D. committee members Prof. Sami Masri, Prof.
Roger Ghanem and Prof. Carter Wellford for their time and encouragement.
My valued friends Dr. A. Doostan, Dr. A. Sadjadpour, Dr. R.D. Nayeri, Dr. F. Banaei,
Dr. N. Nastar, Dr. M. Jahangiri, my dear cousin, Gita, my uncle and his wife, Shohreh,
have each also provided support in different aspects of my Ph.D. journey.
Most importantly, I would like to give my deepest gratitude to my very dear parents, my
loving wife, Setareh, and my in-laws whom without their constant encouragement and
understanding my degree might never have been accomplished. I would also like to thank
my dear grandma who has been a key supporter of my education from early on. I further
appreciate my brother, Iman, for his kind support to our parents which allowed me to
pursue my doctorate degree so conveniently whilst being far from my home and family.
Last but not least, I would like to appreciate the National Science Foundation and the
George E. Brown, Jr. Network for Earthquake Engineering Simulation (NEES) for
creating such unique facilities for advancement of earthquake engineering research, in
particular NEES@UCSB for operating and maintaining the SFSI Test Structure site.

iv
Table of Contents
Dedication....................................................................................................................ii
Acknowledgements.....................................................................................................iii
List of Tables ..............................................................................................................vi
List of Figures............................................................................................................vii
Abstract.....................................................................................................................xiv
Introduction..................................................................................................................1
Chapter 1: Background ................................................................................................5
Structural Health Monitoring and Damage Detection .................................................5
Environmental Effects .................................................................................................6
Soil-Foundation-Structure Modeling; Cone Models ...................................................9
Statistical Pattern Recognition...................................................................................13
Chapter 2: NEES SFSI Test Structure Facility..........................................................21
Site Geotechnical Characteristics ..............................................................................23
SFSI Test Structure Analysis and Design..................................................................25
Sensor Layouts and Descriptions...............................................................................35
Data Acquisition (DAQ) System ...............................................................................41
Chapter 3: Modal Properties Identification and Environmental Effects....................45
Introduction................................................................................................................45
Methodologies............................................................................................................46
Sources of Excitation .................................................................................................48
Impulse Response Measurement................................................................................50
Identified Parameters, Observations and Environmental Effects ..............................59
Temperature Dependency ..........................................................................................60
Ground Water-level and Soil Saturation Dependency...............................................66

v
Chapter 4: Modeling of SFSI Test Structure Behavior..............................................71
Introduction................................................................................................................71
Cone Modeling...........................................................................................................72
Coupled Dynamic Model for SFSI Systems..............................................................86
Parametric Study........................................................................................................91
Summary....................................................................................................................96
Chapter 5: Effect of Water Table Variation on the Rocking Frequency of a SFSI
system: Small-Scale Experiment ...............................................................................98
Testing Procedure ......................................................................................................98
Hypothesis................................................................................................................100
Test Specifications and Design................................................................................101
Experimental System Identification (Impulse Response)........................................107
Finite Element Modeling of the Prototype SFSI System.........................................109
Boundary Condition of the Prototype SFSI System ................................................113
Water-level Variation Effect on the Prototype SFSI System...................................115
Summary..................................................................................................................119
Chapter 6: Pattern Recognition and Regression Analysis Applied to the SFSI Test
Structure Data Set ....................................................................................................120
Introduction..............................................................................................................120
Data Cleansing for Robust Pattern Recognition Process.........................................121
Novelty Detection for Structural Damage Detection..............................................122
Methodology............................................................................................................124
Statistical Novelty Detection Model for SFSI Test Structure..................................128
Data Cleansing of the SFSI Data Set .......................................................................137
Three Dimensional Regression Analysis.................................................................145
Summary..................................................................................................................149
Conclusion ...............................................................................................................151
References................................................................................................................154

vi
List of Tables
Table 1: Result of the frequency analysis of the FEM with two different sections. 30
Table 2: SFSI test structure sensor locations, types and channel numbers. 40
Table 3: Identified model properties utilizing the curve fitting technique. 55
Table 4: Poisson’s ratio and elastic constants for soil mechanics. 82
Table 5: Properties of the SFSI test structure. 92
Table 6: Saturated vs. Dry characteristics of the soil at the site. 92
Table 7: Results of the rocking motion estimation of the SFSI test structure. 94

vii
List of Figures
Figure 1: The location of the NEES facility and the seismicity records at the site
(left) and photo of the Test Structure (right)......................................................22
Figure 2: Soil characteristic of the GVDA site at different depths; P-wave velocity,
S-wave velocity, 10Q factor (soil pressure resistance) and the density of the soil
are illustrated......................................................................................................24
Figure 3: 3D rendering of the initial SFSI Test Structure design showing the
positions of the pressure sensors underneath the foundation, and a shaker and a
camera under the ceiling. ...................................................................................26
Figure 4: Primary finite element model of the Test Structure. (Modeled by SAP)...29
Figure 5: Two dimensional diagram of the first rocking mode of the SFSI Test
Structure, which shows the original status (in black) compared with the
deformed status (in white). ................................................................................31
Figure 6: The Von-Mises stress analysis of the top and bottom slabs of the SFSI test
structure(left), and the foundation spring nodes(right). .....................................32
Figure 7: The FEM simulation of the top slab displacement due to a sinusoidal
harmonic input (at the resonance frequency of 10 Hz), applied at the center of
the top slab. ........................................................................................................33
Figure 8: 2D drawing of the final design and construction details of the SFSI Test
Structure.............................................................................................................34
Figure 9: The distribution of the sensors, horizontally and vertically, throughout the
GVDSA site for recording the ground motion...................................................36
Figure 10: Sensor descriptions and locations on/under the SFSI Test Structure.......39

viii
Figure 11: The data acquisition (DAQ) system used for the SFSI test structure
monitoring..........................................................................................................42
Figure 12: Snapshot of the user interface of the DAQ system. .................................43
Figure 13: Real-time features integrated with the DAQ system................................44
Figure 14: Different possible sources of excitation at the NEES facility site include:
F1: Permanent Shaker, F2: NEES@UCLA Linear Shaker, F3: NEES@UTexas
Mobile Shaker and natural earthquakes at the site.............................................48
Figure 15: The response of the top Slab (dashed line) versus the bottom slab’s
response (solid line) induced by the UTexas shaker..........................................50
Figure 16: Single Degree Of Freedom (SDOF) mass-spring-dashpot model............52
Figure 17: 3DOF transfer function curve fit to the SFSI frequency response...........55
Figure 18: The location of the accelerometer measuring acceleration on y-y axis....56
Figure 19: The accelerance function of the SFSI test structure; bracing response
(green line) and the top slab response (solid line). ............................................57
Figure 20: Time-domain curve fit to the measured displacement from a pressure cell
underneath the structure induced by a free vibration.........................................58
Figure 21: Typical daily variation in the identified rocking frequency of the SFSI
Test Structure from 11/20/05 to 11/23/05..........................................................61
Figure 22: First mode (rocking) frequency in East-West direction of the SFSI Test
Structure (pink squares) and ambient temperature recorded from 8/28/2005-
8/30/2005 (blue diamonds). ...............................................................................62
Figure 23: Identified rocking frequency versus the ambient temperature during the
18 months in 2005-2006. ...................................................................................62

ix
Figure 24: Picture of the SFSI Test Structure after the bracings were removed. ......63
Figure 25: Typical daily variation of the identified rocking frequency of the SFSI
Test Structure (recorded on 2 Jan. 2008) after the bracings were removed.......64
Figure 26: Histogram of 520 identified frequencies of the SFSI Test Structure
between 6/15/05 and 3/15/06 in the braced configuration.................................65
Figure 27: Probability density function (PDF) of identified frequencies; the blue
solid line and black dash line demonstrate the distributions for the braced and
un-braced configuration, respectively................................................................65
Figure 28: Observed trend of increases in the identified rocking frequencies of the
SFSI test structure over one month (6/17/2005−7/17/2005)..............................67
Figure 29: Measured ground water table under the SFSI test structure’s foundation
over one month (6/17/2005−7/17/2005). ...........................................................68
Figure 30: Fluctuation of the ground water table fluctuation under the SFS test
structure..............................................................................................................69
Figure 31: Variation in identified rocking frequencies of the SFSI test structure, and
a polynomial trend line (dashed line).................................................................69
Figure 32: Observation on the Water-level and the identified freq. at the site from
6/17/05 thru 9/4/05. Note: The water-level axis has been plotted reversely.....70
Figure 33: Truncated semi-infinite Cone Model (Wolf and Meek 2004)..................74
Figure 34: Frequency dependent spring and damping coefficients for rocking motion
of dry soil. ..........................................................................................................77
Figure 35: Equivalent Wolf’s Monkey-tail model (right) derived from the Spring-
dashpot model (left). ..........................................................................................78

x
Figure 36: Monkey-tail model of a soil-foundation system; inclusion of the mass for
the foundation. ...................................................................................................80
Figure 37: Effects of saturation on the wave velocities in different types of soils: (A)
P-waves, (B) S (shear) waves . (Yang and Sato, 2002) .....................................83
Figure 38: The conceptual notion of the trapped mass underneath the foundation of a
monkey-tail model. ............................................................................................84
Figure 39: Coupled dynamic model of soil-structure system for rocking motion;
representing SFSI test structure. ........................................................................87
Figure 40: The rocking frequency for a SFSI system ( =2, =1.25 (1.05) and
Poisson’s ratio=0.33 (0.5) for dry (saturated) soil. (Normalized structure
frequency = 2.68). ..............................................................................................93
Figure 41: The rocking frequency for a SFSI system (
€
h =1,
€
m = 0.16 (0.13) and
Poisson’s ratio=0.33 (0.5) for dry (saturated) soil. ............................................95
Figure 42: 3D rendering of the conceptual layout of the scaled prototype..............100
Figure 43: Schematic hypothesis in illustration: Water-level vs. Rocking Freq. ....101
Figure 44: Small-scale stick model (2DOF) of the SFSI test structure. ..................102
Figure 45: Schematic constraints for finding an optimal scale factor, illustrates the
trade- off between higher vs. lower value of N................................................103
Figure 46: Picture of the poured concrete and the steel pipe to represent a SDOF
system ..............................................................................................................106
Figure 47: Pictures of the test setup and water-table control system: (a1) PVC pipe
through which water can be directed inside the soil; (a2) A flexible transparent
tube for water-level measurement purposes; (a3)Drainage system to let the
water out. (b) small scale model sitting on a rigid foundation with a mass on
top. ...................................................................................................................107

xi
Figure 48: Illustration of the details of the hammer test configuration, including the
sensor which reads the acceleration normal to the YZ plane shown above.....108
Figure 49: Finite Element Analysis illustration : A) The meshed model, B) Von
Mises stress of the 1st bending/rocking mode , C) 1st bending/rocking mode
with adjusted color to show the rocking/bending phenomena.........................111
Figure 50: Stick model of a fixed-base SDOF model; representing the steel pipe
(outside diameter D = 2.67 cm and wall thickness t = 0.24 cm) used in the
experiment........................................................................................................112
Figure 51: Frequency analysis of the pipe for two cases: Threaded pipe has bending
frequency of 50 Hz (Left), compared to the pipe with no threads with 60 Hz.113
Figure 52:Stress distribution for the soil-foundation-structure model; result from the
Finite Element Analysis (color represents the stress levels, adjusted so that the
stress inside the soil stands out). ......................................................................114
Figure 53: The edge effect analysis of the rocking mode of the prototype model; the
estimated frequency by the FEM vs. the drum’s Radius. ................................115
Figure 54: Illustration of the details of the water-level measurement and the drainage
valve.................................................................................................................117
Figure 55: The trend of the identified rocking mode frequency variation in
correlation with the water-table fluctuation (fixed-base frequency = 50 Hz)..118
Figure 56: The Identified rocking frequency variation in correlation with the
normalized water level fluctuation; water level is raised and then drained as
shown by the arrow..........................................................................................119
Figure 57: Proposed conceptual schema for the pattern recognition process upon the
environmental effects on structural dynamic properties for SHM purposes. ..120
Figure 58: Conceptual representation of a structural parameter variation in one-
feature space versus the same data with an additional environmental feature
(e.g. Temperature)............................................................................................124

xii
Figure 59: Conceptual schema on the proposed Finite Eigen-space approximation
model on a 2-feature novelty detection problem. ............................................126
Figure 60: A potential outlier to be detected in a dataset with variable standard
deviation in a 2-feature novelty detection problem. ........................................127
Figure 61: Three dimensional representation of the SFSI data; identified rocking
frequency versus the ground water-level and the ambient temperature...........131
Figure 62: Identified rocking frequency versus the ground water-level under the
SFSI foundation. ..............................................................................................131
Figure 63: Plot of identified rocking mode frequency of the SFSI Test Structure
versus the ambient temperature. ......................................................................132
Figure 64: Conceptual representation of the

€
T
i
W
j
sub-space created by the
intersection of two finite environmental variables, and a new subsequent test
data (solid diamond). .......................................................................................133
Figure 65: The novelty detection of the SFSI Test Structure with no bracings (solid
diamond) against the same structure with bracings. ........................................136
Figure 66: Linear regression of identified frequencies dated 16 Oct. 2005 versus
measured temperatures on that day (top) and the residual results of the fit
(bottom)............................................................................................................139
Figure 67: Histogram of regression coefficients of daily temperature-frequency
analysis.............................................................................................................140
Figure 68: Linearly normalized frequencies with respect to the T= 55° F. .............140
Figure 69: The comparison between the identified frequencies versus the water level;
before (top figure) and after normalization (bottom figure). ...........................141
Figure 70: The normalized frequencies variation versus the water level fluctuation
for the winter (bottom left) and the summer (bottom right), respectively. ......142

xiii
Figure 71: Comparison between the water level variation and the identified freq. of
the SFSI test structure in the top and bottom figure, respectively. ..................143
Figure 72: Linear regression result of a fit to the Normalized frequencies versus the
water level variation (top figure) and the residuals (bottom figure)................144
Figure 73: Non-linear regression and 95% prediction bounds result of a fit to the
Normalized frequencies versus the water level................................................145
Figure 74: Three-dimensional demonstration of the temperature, water-level and
identified frequencies of the SFSI test structure, and the best-fit plane to the
collected data (estimated from multi-variat regression analysis). ...................147
Figure 75: Three-dimensional demonstration of the temperature, water-level and
identified frequencies of the SFSI test structure; the dispersion of the data
around the best-fit plane has been illustrated...................................................148
Figure 76: Three-dimensional demonstration of the temperature, water-level and
normalized identified frequencies of the SFSI test structure, and the best-fit
plane to the collected data (estimated from multi-variat regression analysis). 149

xiv
Abstract
For more than thirty years, researchers have attempted to establish effective local and
global methods for monitoring civil, aerospace and mechanical structures. The
unpredictable nature of soil and the nonlinear behavior of civil structures, however, make
monitoring rather complex. In fact, the combined soil-structure system can be influenced
by environmental factors on daily to annual time scales. Identification of structural
damage using vibration-based methodologies in the presence of such influences requires
some data normalization to reduce uncertainties and variations introduced by
environmental factors.
To better understand the correlation between environmental variations and the dynamics
of soil-structure interaction, semi-continuous monitoring of a large-scale field test
structure has been conducted. The analysis uses data from sensors placed at several
locations on the NEES Soil Foundation Structure Interaction (SFSI) Test Structure, which
is located on very well-characterized soil in southern California, as well as sensor arrays
monitoring the soil response under the foundation. A network of sensors was designed
and positioned to record temperature at various locations on the structure; some pertinent
soil properties are also monitored.
The observations of measured environmental data and the identified structural system
parameters demonstrated strong correlation between variations in the environmental

xv
features and in the dynamic properties of the structure; for example daily shifts in the
structure’s fundamental frequencies are as much as10% due to temperature change or
seasonal shifts due to ground water table variation under the foundation. An example is
given, based on novelty detection, of how “unusual” dynamic behavior can be indicated
for the SFSI test structure in the presence of environmental variations.
To explain the effect of the soil saturation on the rocking frequency of SFSI systems, a
predictive model based on Wolf's Cone Model approach was developed. The results from
parametric study validated the observations from both the SFSI test structure and the
scaled model of decreased natural frequency for dry soil. Further, the study shows that
the opposite effect — that is, higher natural frequency with soil saturation — occurs for
structures with different characteristics relative to the soil.
A 1/14 scale model of the SFSI test structure was constructed to validate the observed
effect of the water level under the foundation on the rocking frequency of SFSI systems
in a controlled laboratory environment. These experiments showed a similar correlation
between the identified rocking frequency of the scaled prototype and the rise and fall of
the water level under the foundation.
This work shows that understanding the environmental variability of an identified model
is critical to developing methodologies for cleansing data and reducing uncertainty to
allow more robust health monitoring in real civil structures.

1
Introduction
The dynamic behavior of civil structures is affected by environmental conditions, such as
temperature, humidity, soil moisture and precipitation. Temperature, with both ambient
and localized variations due to sunlight, rain or wind, causes thermal expansion that can
tighten or loosen bracing and joints or change the effective stiffness of some materials,
thereby changing the dynamic behavior. Rain may have mass and seepage pressure
effects, but also causes changes in the soil behavior, thus changing the dynamics of the
soil-foundation-structure system. Seasonal variation of soil moisture and water table will
also affect system dynamic behavior. Clearly, observed variations in structural behavior
of real structures outside the laboratory are due not only to changes in the structure alone,
but are also due to the induced changes in the soil and foundation.
Several different methodologies for the identification of structural damage have received
significant consideration in the civil engineering community over the past few decades.
In particular, vibration-based damage detection, as a nondestructive evaluation (NDE)
technique, has been widely studied in the research community and has begun to be put
into practice. In global vibration-based damage detection methodologies, the dynamic
behavior of a structural system is monitored continuously or at intervals tracking damage-
sensitive parameters. Chapter 1 provides background on this subject. In civil structures
(e.g., buildings and bridges) in particular, the combined soil-foundation-structure system

2
can be heavily influenced by environmental factors on daily to annual time scales. The
presence of such influences requires more meticulous considerations in both monitoring
and analysis, necessitating better understanding of the physics of the interaction between
the soil-foundation-structure system and the environment.
This dissertation describes an investigation of environmental effects on the dynamics of
the Soil-Foundation-Structure-Interaction (SFSI) Field Test Structure (Asghari et al.,
(2006) that is part of the George E. Brown Jr. Network for Earthquake Engineering
Research (NEES). The SFSI Test Structure, located in Garner Valley, CA, is a simple
(4m in length, width and height) open steel frame, with large reinforced concrete base
and top slabs, that is instrumented for both dynamic and static response experiments. It
has continuous and triggered monitoring and an internet-controlled shaker allowing
unattended forced vibration testing. Chapter 2 details the design, construction, and
operation of this test structure.
Monitoring data of the NEES SFSI Test Structure and its environment were collected
over a 2-year period. Chapter 3 describes this data collection and the processing and
analysis of the various types of data, including ambient, earthquake and forced vibration.
Observations show day-to-day shifts in the structure’s fundamental frequencies on the
order of 10% for the braced structure and 3% for the unbraced configuration. In addition
to longer seasonal trends that are related to temperature (e.g., summer vs. winter
temperatures), some variations are clearly related to precipitation. Specifically, the SFSI

3
structure data demonstrates a correlation between the fundamental frequency and the
level of the water table in the soil surrounding the test structure, with frequency
decreasing with higher water level (i.e., water-table closer to the surface of the ground).
Chapter 4 attempts to explain these observed behaviors through analytical modeling. For
better understanding of the physics of the effect of saturated versus dry soil under a soil-
structure system, and to explain the observed environmental effects, past research on the
dynamic behavior of rigid surface footings on poroelastic half-space is reviewed,
specifically the works of Halpern and Christiano (1986), Philippacopoulos (1989), Kassir
et al. (1989) and Todorovska and Al Rjoub (2006). Wolf (1985) provides a good basis for
an explanation of the observed phenomena. An equivalent linear model of the soil-
structure system is derived and used to explain the observed environmental dependencies
in the measured SFSI test structure’s dynamic response. It is shown that the apparent
rocking frequency of a SFSI system is a function of saturation level and might increase or
decrease, relative to the dry soil, depending on the relative characteristics of the structure
with respect to the soil under its foundation.
To understand these environmental dependencies at small strain linear levels of vibration,
small-scale controlled modeling of the SFSI test structure is described in Chapter 5. A
simple 1/14 scale physical model of the SFSI Test Structure was built and tested to
validate the observations from the SFSI Test Structure in more environmentally-
controlled conditions. The main focus of this experiment was to validate the observed

4
effect of water table variation upon the system’s modal properties. Indeed, the decreased
frequency of the SFSI structure with shallower (i.e., higher) water table is consistent with
the SFSI test structure but contrary to results reported by others (e.g., Bradford et al.,
2005) of frequency increases after heavy rain.
Pattern recognition tools can be applied to vibration-based structural health monitoring
for extraction of parameters of interest from noisy data. This approach is studied and
applied to the SFSI test structure data in an attempt to find a methodology for tracking the
structural response within the environmental “noise” found in this real field structure.
Chapter 6 gives background on pattern recognition and details these efforts in
conjunction with some regression analyses to cleanse the SFSI data set.
Based on the result of the current research and observations made on the SFSI test
structure, it is concluded that to establish more robust health monitoring in real civil
structures, it is crucial to study the environmental variability of identified modal
properties. Thus, it is necessary to develop methodologies for cleansing data and reducing
uncertainties caused by environmental variation on each site — further investigation on
this task is left to future research.

5
Chapter 1: Background
Structural Health Monitoring and Damage Detection
Structural Health Monitoring (SHM) and vibration-based damage detection have been
popular research topics for almost three decades. The oil industry expended considerable
effort in the 1970s and early 1980s for monitoring offshore platforms (Vandiver, 1977).
The civil engineering community has been investigating structural health monitoring for
bridges since the early 1980s (Doebling et al., 1996), though it has its roots in much
earlier studies to identify dynamic characteristics of structures.
Numerous industries and research communities have attempted to develop algorithms for
structural monitoring purposes. The essential premise of vibration-based damage
detection, as presented by Sohn et al. (2001), is that the dynamic response characteristics
of the structure would change due to the physical properties alteration of the structures
(e.g., reductions in stiffness resulting from the onset of cracks or the loosening of a
connection). Such variations (e.g., the resonance frequency) can be detected by utilizing
system identification methods and by monitoring the changes in the structure on a global
basis. Doebling et al. (1996), and a recent update by Sohn et al. (2004), present an
extensive survey of global vibration-based structural monitoring methods.
In addition to effects from damage, there are also measurable changes in resonance
frequencies of structures due to other factors (Cornwell et al., 1999). For instance,

6
weather conditions, rain/wind events, and soil nonlinear behavior are two important
factors which are a recent focus of attention in the research community.
Pioneers have conducted several long-term monitoring projects of buildings and bridges
to observe the environmental effects on natural frequencies and attempt to develop
different techniques (e.g., pattern recognition) to more accurately identify damaged
structures. It is commonly concluded that, in order to attain more accurate and reliable
vibration-based damage detection methodologies, the influence of environmental effects
should be recognized and eliminated. Several researchers (Farrar et al., 2000; Sohn et al.,
2002; Kullaa, 2002–2004) have emphasized the importance of removing environmental
or/and operational variations, and have proposed some data cleansing procedures for
SHM. Further, Kulla (2008) validated his proposed method (i.e., factor analysis) for
eliminating the influence of environmental effects by using both numerical models and
experimental data.
The effects of environmental variation on the SFSI test structure (identified frequencies)
and a mechanism for extracting them are discussed further in Chapter 3 and Chapter 6,
respectively.
Environmental Effects
The fact that environment can have an impact on structural dynamics has been known for
some time. As explained by Sohn and Law (2000), an experimental study in the UK

7
(Wood, 1992) showed that some concrete bridges absorbed moisture during periods of
damp weather, resulting in an increase in the bridge mass; clearly, this would tend to
decrease the natural frequencies of the structure (assuming, of course, that all other
properties remain fixed). Friswell and Penny (1997) discuss the difficulties of the damage
detection due to the environmental effects on dynamic properties, especially on highway
bridges. Sohn et al. (1999) showed that temperature changes caused 5% daily variations
in the natural frequencies of the Alamosa Canyon Bridge; these variations were several
times the expected damage-induced changes in natural frequencies, masking the effects
of damage. Sohn et al. (1999–2004) have also examined the changes of modal parameters
due to structural damage versus those caused by temperature changes.
Similarly, Porter et al. (2004) believe that, the variations in modal data due to changing
environmental conditions, creates uncertainty in deciding whether actual damage in the
structure have occurred. In the bridge health monitoring community, Peeters and De
Roeck (2001) focused on the impact of changes in environmental parameters on the
dynamics of structures. They contemplated that temperature may have an impact on the
material properties and the boundary conditions. Peeters et al. (2001) also discussed the
effect of temperature on measured eigenfrequencies as an inevitable issue for vibration-
based damage detection applications. Similarly, short-term and long-term monitoring and
study of the environmental effects on the Singapore–Malaysia Second Link bridge by
Omenzetter and Brownjohn (2006) revealed that it is possible that some of the observed

8
model changes may, in fact, have been caused by abnormal temperature variations and
were not associated with structural changes. In their research on monitoring of bridges,
Liu and DeWolf (2007) could also observe 4–5% changes in the natural frequencies
during the spring and winter. A recent study by Nayeri et al. (2008) presents the results of
time-domain modal identification of a full-scale 17-story building, based on ambient
vibration measurements. It is shown in their result that there is a strong correlation
between the modal frequency variations and the temperature variations in a 24-hour
period.
A structure that has, perhaps, received the most research attention over the years for its
dynamic properties is the Robert A. Millikan Library, located on the campus of the
California Institute of Technology (Caltech). Since its construction in the mid-1960s, the
dynamics of the Millikan Library have been studied through ambient and forced vibration
tests as well as through its response to small and moderate ground motions during various
earthquakes in southern California. Clinton et al. (2006) provides a good background of
some of the history of these studies. A test bed has been installed at Caltech for on-line
monitoring of the Millikan Library and one other Caltech building; implemented in the
Caltech Online Monitoring and Evaluations Testbed (COMET) website (Lam et al.,
2004), this computer-based system is designed to receive, analyze, and disseminate near-
real-time accelerometer data-streams from instruments in (currently) two facilities (Porter
et al., 2004).

9
Clinton et al. (2006) also reports the results of recent experiments showing the impact of
environment on vibration-based frequency analysis of the Millikan Library. The
observations showed that, in a particularly intense windstorm without rain, the natural
frequencies of the structure show consistent decreases of several percent for the duration
of the most intense winds, both for the rocking and the torsional modes of vibration. In
contrast, during a two-day, 4 in. rainfall, both translational and torsional natural
frequencies increased by about 3%, returning to the nominal values in 1–2 weeks.
Furthermore, a direct correlation between increasing temperatures and higher frequencies
were detected, probably from thermal expansion of the concrete (Bradford et al., 2005).
Clinton et al. (2006) conclude that the rain-induced increases in natural frequencies were
due to an increase in soil-structure stiffness caused by soil saturation and, perhaps, soil
swelling; they state that their hypothesis could be tested using pore-water pressure
measurements near the structure.
To investigate all of these environmental parameters, a fully instrumented test structure
would be of great value to be able to thoroughly study the various effects, incorporating
the soil-foundation-structure interaction phenomenon.
Soil-Foundation-Structure Modeling; Cone Models
In recent years, a number of studies have been conducted in the area of soil–structure
interaction modeling in various sophisticated ways. As a matter of fact, soil has very

10
complex characteristics and many researchers and engineers have attempted to develop
accurate, yet pragmatic approaches to model such systems. There are several reviews and
publications about this specific topic. For instance, Dutta and Roy (2002) have reviewed
quite a few idealization methodologies. They believe that, the use of a rigorous model
representing the real system will not necessarily lead to better results, because the
determination of the input parameters often involves quite significant uncertainties. They
also suggest two main avenues for modeling dynamic soil-structure interaction: a)
modeling the soil as an elastic half-space, b) modeling the soil with a lumped mass or
lumped parameter method. The advantages and limitations of these approaches have been
discussed by Seed and Lysmer (1975) and Hall et al. (1976).
One of the popular methods, known as Winkler’s idealization, represents the soil medium
as a system of identical but mutually independent and linearly elastic springs (Dutta and
Roy, 2002). Though this method introduces a good level of simplicity, the commonly
known problem with the use of this model is the intricacy of determining accurate input
parameters (e.g., the stiffness of springs). On the contrary, methods based on the elastic
continuum model have the advantage of less vagueness in the input parameters (e.g.,
modulus of elasticity) but they often lead to very complex mathematical formulations.
Also, the uncertainty in modeling boundary condition and contact surfaces still need to be
carefully quantified.

11
To address the disadvantages of the modeling approaches mentioned above, there are also
some suggested modified methods in the literature. For instance, Horvath (1993) presents
a modified formulation for the classical problem of beams on an elastic foundation. His
formulation shows how the continuity among the individual Winkler springs can be
achieved.
The scope of numerical methods is significantly wider than that of analytical methods;
thus, the use of the general-purpose finite element method has attracted a lot of attention
for studying the complex interactive behavior of soil-foundation systems. Furthermore,
some studies recommend that the infinite soil should be modeled by using the boundary
element method and the finite structure with the finite element method. Dobry and
Gazetas (1986) believe that these two different means of idealizations may be suitably
matched at the interface through equilibrium and compatibility conditions.
Some improvements also on the coupling of the finite element approaches have been
suggested. As a very good example, the analysis of a soil-structure interaction system
using a coupling model of finite elements, boundary elements, infinite elements and
infinite boundary elements has been presented in Zhang et al. (1999).
In the dynamic analysis of soil-structure systems, the presence of water in the soil, either
by causing soil saturation or by fluctuation of the water-table under the foundation, could
extensively add to the complexity of the soil modeling. The real deformation

12
characteristics of soil media, particularly in fine-grained-types of soil, are always time-
dependent, to some extent depending on the permeability of the soil media. An increase
in pressure in the pore water of soil and the contribution of the added mass both
significantly change the dynamic characteristics of the soil-structure interaction.
Several modeling approaches and studies of the dynamic stiffness and vibrations of rigid
surface footings on poroelastic half-space been presented. For instance, the two-phase
models which are based on the theory of wave propagation in fluid saturated poroelastic
soil, has been exploited by Todorovska and Al Rjoub (2006) to conduct a chain of studies
of a circular foundation embedded in a water-saturated poroelastic half-space. Their
theoretical model is mainly to explain the observed increase of the apparent frequencies
of the Millikan library in Pasadena, CA. The hypothesis in their work is that the observed
increases in frequency are due to the water saturation of the soil and increased soil-
foundation stiffness.
Another series of studies by Halpern and Christino (1986) investigated the compliance
matrices of a square rigid plate on a water saturated poroelastic half-space. Their
conclusion implies that the saturated soil shows more stiffness — for both rocking and
vertical motion. Philippacopoulos (1989) provided evidence that the effect due to
saturation on the impedance function is generally very significant for high dimensionless
frequency (i.e., between 3 and 6). In the discussion of his results, contrary to the others,
he states ‘‘the effect of the pore fluid is to generally reduce the stiffness and increase the

13
damping compared to the dry case.”. Kassir et al. (1996) also studied the impedances for
a drained surface circular footing for rocking and horizontal motions. They concluded
“for rocking motion, the presence of pore fluid significantly affects the impedance of the
dynamic system.”.
With a strength of material approach, Wolf (1994) has shown that a simple spring-
dashpot-mass model with frequency-dependent coefficients can represent soil-structure
systems. Wolf's approach is mainly by using conical bars and beams, called Cones. The
modeling technique used herein will be based on the Cone Modeling approach, which is
discussed further in Chapter 4.

Statistical Pattern Recognition
Various earthquake engineers and researchers have recognized that structural health
monitoring and damage detection are effectively applications of pattern recognition.
Structural health monitoring — as a systematic non-destructive procedure — is
performed to be able to classify a damaged structure. The main objective of classifying a
damaged structure is to ascertain, based on measured dynamic characteristics, if damage
is present or not. Often, after defining the sensitive features and training the system based
on a given existing data set, the equation of the classifier must be mathematically
determined.

14
It is important to note that the classifying process is usually prone to false identification
due to potential uncertainty in sensing/measurement/calculation of the selected feature(s).
Hence, defining the right features is a very crucial step for obtaining a precise, yet high
performance pattern recognition mechanism; therefore, it requires profound application
specific knowledge and experience.
When it comes to selecting damage sensitive features, it is imperative to understand that
structures are subject to changing environmental and operational conditions which affect
the measured signals; as a result, the process of classifying the structure (i.e., damaged
vs. undamaged) could be easily mislead. One solution would be that enough samples are
available and appropriate features (properties of interest) are included to train the
mathematical system. This process is described in Sohn et al. (2001) and Farrar et al.
(2000). It includes several systematic steps; data acquisition and cleansing followed by
data normalization are preprocesses before using the classification algorithm. Then,
feature extraction and information condensation is the delicate step to virtually build the
pattern recognition techniques for the SHM application.
Features essentially are types of data to be acquired for the pattern recognition problem
(e.g., frequency variation, environmental parameters, temperature, etc.). For damage
detection, the features are typically application specific. Each feature, in fact, would add
a new dimension to the pattern recognition problem, which may improve the accuracy of
the classification; however, an efficient low dimensional feature vector is practically

15
more affordable. To identify and quantify sources of feature variability for each
classification problem, intensive research with sufficient samples is required.
Pattern recognition problems are divided into two main categories: supervised versus
unsupervised. Most health monitoring problems though, will fit into the latter category as
data from the damaged structure is generally not available to mathematically train the
pattern recognition system. If supervised learning is required, there will be serious
demands associated with it: data from every conceivable damage situation should be
available. The two possible sources of such data would be either via computation or
modeling and experiment. Rather, in unsupervised learning, a threshold with a specific
margin is defined; the variation of certain features beyond that threshold would represent
a damaged status. Sohn et al. (2001) states that “the philosophy is simple: during the
normal operation of a system or structure, measurements are recorded and features are
extracted from data, which characterize the normal conditions. After training the
diagnostic procedure in question, subsequent data can be examined to see if the features
deviate significantly from the norm.”
That is said, herein a methodology for damage detection based on the concept of novelty
detection (Worden, 1997) is discussed, which is also founded in multivariate statistics. In
a typical novelty detection process, in contrast with a classification problem, classifier act
as a detector rather than as a classifier; that is, to detect whether the new test data
belongs to the cluster of the trained data or not. If not, it can be concluded that an

16
abnormality has occurred. This technique can be useful for damage detection purposes
where the data from the damaged case might not be available. Nevertheless, it is an
important qualifier that the novelty detectors should flag only certain deviations from
normal operating condition. It is important to remember that real systems are subject to
measurement noise and usually operate in a changing environment; therefore, the novelty
detector must be able to distinguish between a statistical fluctuation in the data and a real
deviation from normality (Worden et al., 2002). Fan et al. (2004) suggest a methodology
to create a margin around the trained data (by artificial novelties). Recent work by
Worden and Manson (2003) has also established a skeleton based on the novelty
detection. Yet another simple statistical technique was exploited by Ruotolo and Surace
(1997) in which, hypothesis testing for novelty detection is based on determining whether
the test sample(s) come from the same distribution as training data or not. Their test was
performed at 0.05 and 0.01 significance levels and showed promising results. In another
approach, Roberts (2000) discussed Extreme Value Theory (EVT) approach; that
concerns, low or high values in the tails of data distributions. Tax and Duin (2000)
suggest a method that is useful for quickly-decaying-probabilities distribution. Their
modeling is for normally distributed data and is based on the Mahalanobis distance. As a
statistical measure, the Mahalanobis distance was introduced by Mahalanobis (1936)
more than seventy years ago. In certain aspects, it is different from Euclidean distance;
the Euclidean distance is commonly used in mathematics and is dependent on the scale

17
measurement, and its main disadvantage is being blind to correlated variables. The
Mahalanobis distance by definition can take into account the covariance among the
variables in calculating distances by normalizing the distance with respect to the
covariance matrix. With this measure, the problems of scale and correlation inherent in
the Euclidean distance are addressed.
The Mahalanobis distance mainly relies on the covariance matrix computation, which is a
matrix of covariance between elements of a vector. In fact, it is a generalization of the
variance of a scalar-valued random variable to higher dimensions. Let x be an n×1 vector

(1)
of random variables
€
X
i
denote a point in n-dimensional space. Then the sample mean of
the whole population can be written as a vector consisting of the mean corresponding to
each variable
(2)
For each of these variables there is a finite variance. Since, in general, there are possible
correlations among the variables, the covariance matrix

can be defined as a matrix
whose (i, j) entry is the covariance of ith and jth variable;
€
∑
ij
=Ε[(X
i
− µ
i
)(X
j
− µ
j
)].

18
In the matrix form, the covariance matrix then can be written

€
∑ =
∑
11
∑
12
… ∑
1n
∑
21
∑
22
 ∑
2n
   
∑
n1
∑
n2
 ∑
nn












(3)
The diagonal terms in the covariance matrix are variances of the random variables
€
∑
ii
=σ
i
2
= var(X
i
) =Ε[(X
i
− µ
i
)
2
] (4)
Knowing all these terms, the Mahalanobis distance
€
D
M
(x) for the vector of random
variables is
€
D
M
(x) = (x−µ)
T
∑
−1
(x−µ)
€
(5)
Suppose there is a potential outlier

€
x
ζ
=[x
1
x
2
 x
n
]
T
, that needs to be tested against a
normal system, where

€
x
1
, x
2
, x
n

are selected variables (e.g., identified structure’s
natural frequency, mode shapes, operational temperature, etc.). Based on the
Mahalanobis definition, the distance between this point in n-dimensional space and the
training data (representing the normal condition) can be obtained by the following
formulation:
€
D
M
(x
ζ
) = (x
ζ
−µ)
T
∑
−1
(x
ζ
−µ) , where and are the mean vector and
covariance matrix of the data respectively.
There are several different methods that are utilized in the novelty detection approach.
For instance, methods based on simple distance measures, statistical approaches and
artificial neural networks are commonly used approaches. While previous work by

19
Worden (1997) has been focused on the neural network and statistical procedures, the
suggested statistical approaches for the novelty detection purposes are mostly to estimate,
based on statistical modeling, whether a test samples comes from the same distribution or
not (Odin and Addison, 2000). The distance of the sample from a class mean (considering
certain number of standard deviations away) could be another indicator for detection
novelties as suggested by Manson et al. (2001).
Again, novelty detection has become very popular, as stated by King et al. (2002), since
it can offer solutions for the cases that the data from the damaged condition is not
available. It also has the capability to be utilized for other applications that are more
complicated and quite often not with enough samples. It is clear that the success or failure
of a novelty detection approach is dependent upon the description of the normal condition
and the accuracy of corresponding data. Hence, the data needs to be collected from the
full range of structural/environmental conditions which may be encountered in any
testing situation. The disadvantage with this option is that much of the detector sensitivity
to damage may be lost within this broad definition of so-called “normal condition”.
To restore sensitivity, an alternative approach can be introduced, by dividing the normal
condition data into many sub-sets, each describing an environmental condition in which a
novelty detector is constructed, similar to what Cempel (1985) proposed. Thus, the
subsequent data would be tested against that sub-set alone. This approach is conceptually
similar to the statistical latent class analysis discussed by Clogg (1979, 1981),

20
McCutcheon (1987), Arminger et al. (1994) and Hagenaars and McCutcheon (2002).
This approach — similar to the finite mixture models — decompose a density function
into component density functions. The latent class analysis (LCA) for analyzing
categorical variables, widely applied in social and behavioral research, is a methodology
for finding subtypes in a set of multivariate categorical data. It is also well suited to many
health applications (Uebersax, 1990). Other common areas of LCA application include
psychology, education and marketing research. In another context, Wolfe (1970) and
Everitt (1996) consider finite mixture models whose underlying class probability
densities have been approximated by finite-length discrete signals and use finite mixture
densities to partition data from populations into subpopulations.

21
Chapter 2: NEES SFSI Test Structure Facility
The National Science Foundation (NSF) created the George E. Brown, Jr. Network for
Earthquake Engineering Simulation (NEES) to give researchers the tools to learn how
earthquakes impact the buildings, bridges, utility systems and other critical components
of today’s society. NEES is a network of 15 large-scale, experimental sites that feature
such advanced tools as shake tables and centrifuges, as well as a Soil-Foundation-
Structure-Interaction (SFSI) facility, that simulate and study earthquake effects. The
NEES SFSI facility provides a unique opportunity to study variations in structural
behavior due to changes in temperature, moisture and water table under the foundation
(Asghari et al. 2006). The SFSI facility, currently maintained by NEES@UCSB, is
located in southern California, close to two major active faults (see Figure 1, left), at the
Garner Valley Downhole Seismic Array (GVDSA).
The general objective of the SFSI test structure at GVDSA is to provide a well-
characterized, well-instrumented, simple structure for the study of soil-structure
interaction at large scale. The structure has a reconfigurable steel-frame founded on a
rigid, massive concrete slab on grade (see Figure 1, right). Dimensions are 4 × 4 × 4m,
approximately. The superstructure is of a size appropriate for testing on one of the NEES
shake tables or for the installation of one of the NEES eccentric mass shakers. Provisions
were made for mounting such shakers on the roof for active experiments to complement

22
passive earthquake monitoring (Nigbor and Asghari, 2003). Further a web-portal to
analyze the SFSI remotely was developed, the details of which can be found in Nigbor et
al. (2004a).
The sections below provide details of the SFSI test structure pertinent to the research
described in this dissertation. More details can be found at
http://nees.ucsb.edu/facilities/gvda.

Figure 1: The location of the NEES facility and the seismicity records at the site (left) and
photo of the Test Structure (right).

23
Site Geotechnical Characteristics
The Garner Valley site was constructed by researchers at UCSB in the 1990’s as a test
bed for site response studies. site is very close to the active San Jacinto fault, and there
are many small earthquakes under or near the site every year.
There are many previous investigations of the site, using various geophysical and
geotechnical techniques, that very thoroughly characterize the subsurface soil and rock
properties (Steidl et al., 2000).
For this research project, additional geotechnical and geophysical measurements were
done at the GVDSA site (Youd et al., 2004). Combined with the previous studies, these
show that the upper 18–25 meters consists of soil rich in organics and alluvium. Soil
types present are silty sand, sand, clayey sand and silty gravel. There is a gradual
transition from alluvium to decomposed granite from 18–25 meters. Decomposed granite,
mechanically similar to gravely sand, exists between 25 and 88 meters. At 88 meters, the
contact with hard competent granitic bedrock is reached. The water table fluctuates at the
GVDSA site depending on the season and rainfall totals. In the wetter years, the water
table is at, or just below, the surface in the winter and spring months. In the summer and
fall months, or the entire year when dry, the water table drops to 1–4 meters below the
surface.

24
To characterize the soil, extensive geotechnical experiments have been performed at the
site. Youd et al. (2004) and Steidl and Nigbor (2004) have carried out extensive research
for soil characterization at this site; as a result, most of the necessary static and dynamic
soil parameters of the soil for the soil-structure-interaction modeling have been
characterized. Figure 2 illustrates some of the properties of the soil at different depths.

Figure 2: Soil characteristic of the GVDA site at different depths; P-wave velocity, S-wave
velocity, 10Q factor (soil pressure resistance) and the density of the soil are illustrated.

25
SFSI Test Structure Analysis and Design
Since the 1960s, soil-structure interaction has been recognized as an important factor that
significantly affects dynamic building response, the motion of its base, and the motion of
the surrounding soil; this interaction often experienced during analysis and real
experiments. That is, lower of strains and forces in the building at resonant frequency due
to the inclusion of the soil. It may cause significant rotation of the base and changes the
natural frequencies of the structure as well. Furthermore, the foundation input motion
relative to the free-field motion is significantly impacted by the kinematic interaction
between the soil and foundation; at higher frequencies, the translation of the foundation is
reduced, but its rotation increases.
Various researchers (e.g., Bielak, 1971) observe that, by considering the soil-structure
system, the fundamental natural frequency always decreases, but the effective damping
can increase or decrease relative to the damping in fixed base models. When it comes to
SFSI research, an important and dynamically meaningful parameter is the relative
stiffness between the soil and the structure. The most fundamental challenge would be to
identify the stiffness of the soil, because it requires extensive laboratory and ad hoc
testing over each site. Since the NEES site’s soil parameters were determined by several
experiments in the course of a decade (Steidl et al., 2000), the soil of the site could be
considered as “well-characterized”; therefore, designing and building a test structure for
the soil-foundation-structure interaction research seemed very promising at this site.

26

Figure 3: 3D rendering of the initial SFSI Test Structure design showing the positions of
the pressure sensors underneath the foundation, and a shaker and a camera under the
ceiling.

The main intent for building this test structure is to facilitate studies of the physics of
soil-foundation-structure interaction in a controlled field setting. Thus, the SFSI test
structure is designed as an open frame with a large reinforced concrete (RC) base slab on
grade, four steel columns, a top steel frame, and a top RC slab to provide mass and in-
plane stiffness. Connections top and bottom are rigid, bolted moment connections.
Provisions were built-in for the addition of mass to the top or bottom slabs and for the
modification of stiffness through the removable braces.
The SFSI test structure, therefore, provides a medium-scale reconfigurable steel-frame
super structure, which would be of appropriate size for testing on one of the NEES shake

27
tables and for the field installation of large NEES eccentric mass shakers on the upper
slab. Certain provisions for mounting shakers on the roof for forced vibration
experiments to complement passive earthquake monitoring (Figure 3). General design
requirements for the GVDA SFSI Test Structure were as follows:
• Simple, spread footing at grade
• 700–1000 psf footing load to insure high soil stresses
• Superstructure size appropriate for NEES shake tables (4m in length and
width, 50 ton maximum)
• Steel moment frame to allow flexibility
• Configurable bracing system to allow stiffness/damping modification
• Strong RC rigid roof slab to allow mass addition and shaker mounting
• 7–10 Hz fixed-base natural frequency of superstructure (can be adjusted from
~5–15Hz with stiffness & mass)
• Cladding with flexible connections.
The procedures for designing the test structure was:
1. Idealization and modeling of the SFSI system
2. Analysis of response
3. Full-scale experimental verification of assumed model

28
First, a simple analytical model (stick model) was developed. Considering the design
criteria and first frequency to be ~10 Hz, and by performing some frequency analyses, the
preliminary size of the columns, and the mass and dimensions for the top and the bottom
slabs were obtained. In order to satisfy the dimension requirements, a square foundation
(4m in length) was proposed for the bottom slab, based on which the height of the
structure (4m) was decided. To perform frequency analysis on the structure and for
preliminary investigation on the effects of the soil-foundation interaction, a few finite
element models (three-dimensional model) were developed. Some time-history analyses
of these models assisted in assuring that the structure would meet the requirements for
possible future forced vibration experiments, shaker location and so forth.
The main 3D finite element model of the structure, which is shown in Figure 4, consisted
of four steel columns with rectangular hollow sections, two cross bracings on each side
and two shell elements to model the top and bottom concrete slabs. This model was
developed using SAP 2000 software. Various static and dynamic linear analyses were
performed on the following models for braced and un-braced configurations were
performed:
1. Fixed-based foundation model (soil-structure interaction excluded)
2. Soil-structure interaction model by introducing zero-mass spring elements under
the foundation.

29

Figure 4: Primary finite element model of the Test Structure. (Modeled by SAP)

In Figure 6 (right) the locations of the introduced massless spring elements are depicted.
Inspired by Wolf’s cone model (Wolf, 1985), the spring coefficients were defined to
represent the soil under the foundation.
As is common in many structural dynamic analyses, the first dominant modes of
vibration for the SFSI test structure were analyzed. To obtain the desired frequency
range, different columns’ size and shape (i.e., Tube/H section) were used for the
preliminary frequency analysis. The comparison between using Tube sections
(TS14×14×5/8) versus H sections (W12×106) is summarized in Table 1. Since the H
section column causes asymmetrical mode shapes, the square tube section seemed to be a

30
good candidate. Later, however, due to welding limitations, a thinner section, yet bigger
in size (i.e., TS16X16X1″) was used, which provides comparable bending resistance.
Table 1: Result of the frequency analysis of the FEM with two different sections.
3-D Model Frequency Analysis
Fixed base SFSI analysis
Tube
Section
H
section
Tube
Section
H
section
Mode
Shape
1
st
freq. [Hz] 10.17 6.54 7.16 5.55 (Rocking)
2
nd
freq. [Hz] 10.17 9.94 7.16 7.09 (Rocking)
3
rd
freq. [Hz] 17.24 12.47 13.86 11.49 (Rotation)
4
th
freq. [Hz] 49.02 45.87 16.42 16.42 (Vertical)

While the soil effect is taken into account, the first two modes for this symmetric
structure are combinations of rocking motion of the foundation along with the bending of
the structure. The higher modes of vibration, such as torsional motion about the z-axis in
Figure 5, vertical motion and so forth are of less interest in the current research.

31

Figure 5: Two dimensional diagram of the first rocking mode of the SFSI Test Structure,
which shows the original status (in black) compared with the deformed status (in white).

The RC foundation and the top slab were designed after a performing series of stress
analyses on the SFSI test structure. For instance, as is shown in Figure 6, the Von-Mises
stress, due to a static loading identifies the concentration of stress in the proximity of the
4 columns. After applying various combination of static and dynamic loading, the
thicknesses for the bottom and the top slabs, concerning the allowable stress criterion and
the desired mass on top and bottom, were designed at 50cm and 40cm, respectively.

32

Figure 6: The Von-Mises stress analysis of the top and bottom slabs of the SFSI test
structure(left), and the foundation spring nodes(right).

To ensure enough structural rigidity for the top and bottom slabs during the experiments
(e.g., forced vibration experiments), a few time-history response of the structure due to
sinusoidal harmonic loading  at various locations and with different frequencies 
were analyzed. To simulate a forced vibration experiment on the SFSI structure, a
harmonic force is applied at the center of the roof, which is the possible location of the
shaker. Since shakers are capable of generating forces with various frequency contents,
and knowing that the worst case scenario (i.e., highest displacement and stress) would
occur close to the natural frequency of the SFSI system, the response of the top slab due
to a sinusoidal input with frequency of 10 Hz was simulated. In Figure 7, the result of the
analysis is illustrated; clearly because of the resonance phenomenon, the response of the

33
top slab is amplified (relative to the input function) due to the fact that the applied force’s
frequency matches the structure’s first frequency.

Figure 7: The FEM simulation of the top slab displacement due to a sinusoidal harmonic
input (at the resonance frequency of 10 Hz), applied at the center of the top slab.

After performing several static and dynamic analyses on the SFSI test structure and
considering all the design requirements, the final design of the structure and the
foundation with all the construction detailing was proposed (Figure 8); for more details,
the interested reader is directed to the design report by Nigbor and Asghari (2003).

34

Figure 8: 2D drawing of the final design and construction details of the SFSI Test
Structure.

35
Sensor Layouts and Descriptions
To perform accurate and comprehensive experimental research, many sensors are
required to monitor a structural system. Questions for researchers monitoring a system
would be: What to measure? How to measure? How frequently to measure? Where are
the important locations to measure? Typical sensors for structural monitoring are
comprised of vibration sensors (accelerometers), strain gauges, pressure sensors and so
forth. There exist several different types of sensors pertinent to soil dynamics (e.g., pore
pressure sensors) as well.
The NEES facility at GVDA has a dense geotechnical array of accelerometers and pore
pressure sensors, with both horizontal and vertical arrays of sensors. The accelerometers
and pore pressure sensors throughout the site are installed for earthquake engineering and
seismology research. Thus, this facility is a unique opportunity for a soil-structure
interaction research because of the excellent site characterization and dense free-field
ground motion monitoring. Figure 9 shows a schematic of the geotechnical array. For
more details of the locations and types of available sensors at the site, see the report by
Steidl and Nigbor (2004).

36

Figure 9: The distribution of the sensors, horizontally and vertically, throughout the
GVDSA site for recording the ground motion.

Similarly, to measure and monitor the structure’s response, the SFSI Test Structure has
also been fully instrumented as shown in Figure 10. This sensor system was designed by
a team that included the author of this dissertation, and was installed by a small team
Consisting of Ali Asghari, Navid Nastar, and Robert Nigbor.
Sensors used on the SFSI structure include: accelerometers, soil pressure sensors, pore
pressure sensors, displacement sensors, and a rotational sensor. The accelerometers are
Applied MEMS SF1500S sensors, based on micro-electro-mechanical (MEMS)
technology. They have a full-scale range of +/-3g and a resolution of abut 1 micro g.
Their frequency response is flat from 0 to 1000 Hz. One tri-axial accelerometer package

37
is installed at the bottom of a 5 meter cased borehole directly underneath the middle of
the bottom slab. The others are bolter to different locations on the top and bottom slabs.
Four pressure cells were also installed, one at each corner of the foundation, after precise
dynamic calibration and careful installation during construction. Figure 10 includes a
photo of the sensor, which consists of an 18-inch diameter, 1 inch high closed stainless
steel bellows with rigid stainless steel pressure lines connected by welding. The actual
sensing mechanism is a strain gage-based pressure transducer at the free end of the
stainless steel tubing. These sensors were placed on graded and leveled native soil below
the bottom slab, and were tied to the reinforcing steel cage prior to pouring concrete.
Pressure lines were purged after slab curing to set a new baseline “zero” pressure at the
full weight of the structure. Note that these are dynamic pressure sensors capable of
measuring frequencies from about 0–20 Hz, covering the earthquake frequency range.
Four string pot displacement sensors were installed at the bottom corners of the bottom
slab to measure uplift. The potentiometer bodies are attached to the concrete slab, and the
tensioned cable is attached to a 2 m-long metal rod driven into the soil directly below the
slab corner.
All structural sensors were housed in weatherproof enclosures and their cables are routed
through watertight conduit back to the recording system.

38
In addition to the structural sensors, several sensors for measuring the environmental
parameters (e.g., ambient temperature) and ground water level were installed. A complete
list of structural sensors is tabulated in Table 2. The exact location of each sensor and the
channel number to which it is connected to the data acquisition system is also depicted in
Figure 10.
After the original construction of the SFSI site, to collect the preliminary data described
in the next section, the structure was equipped with two additional sets of sensors to log
the ambient temperature and water table level under the structure on an hourly basis.
Self-contained temperature loggers (Onset Instruments “Hobotemp”) were placed in the
soil under the bottom slab and underneath the top slab to measure soil and air
temperatures, respectively.

39

Figure 10: Sensor descriptions and locations on/under the SFSI Test Structure.

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40

Table 2: SFSI test structure sensor locations, types and channel numbers.
Channel No. Type of Instrument Location
1 Tri-axial Accel. (x) Bottom Slab
2 Tri-axial Accel. (y) Bottom Slab
3 Tri-axial Accel. (z) Bottom Slab
4 Tri-axial Accel. (x) Top Slab
5 Tri-axial Accel. (y) Top Slab
6 Tri-axial Accel. (z) Top Slab
7 Uni-axial Accel. (z) Bottom Slab
8 Uni-axial Accel. (z) Bottom Slab
9 Uni-axial Accel. (x) Bottom Slab
10 Uni-axial Accel. (z) Bottom Slab
11 Uni-axial Accel. (z) Bottom Slab
12 Uni-axial Accel. (x) Top Slab
13 Uni-axial Accel. (x) Shaker
14 Tri-axial Downhole Accel. (x) Under the Soil
15 Tri-axial Downhole Accel. (y) Under the Soil
16 Tri-axial Downhole Accel. (z) Under the Soil
17 Rotation Sensor (x-x) Bottom Slab
18 Rotation Sensor (y-y) Bottom Slab
19 Rotation Sensor (z-z) Bottom Slab
20 Pore Pressure Under the Soil
21 Spare n/a
22 Spare n/a
23 Spare n/a
24 Spare n/a
25 Soil Pressure Sensor Bottom Slab
26 Soil Pressure Sensor Bottom Slab
27 Soil Pressure Sensor Bottom Slab
28 Soil Pressure Sensor Bottom Slab
29 Displacement Transducer Bottom Slab
30 Displacement Transducer Bottom Slab
31 Displacement Transducer Bottom Slab
32 Displacement Transducer Bottom Slab

41
After the original construction of the SFSI site, to collect the preliminary data described
in the next section, the structure was equipped with two additional sets of sensors to log
the ambient temperature and water table level under the structure on an hourly basis.
A small electromagnetic shaker has been installed under the roof slab to allow active,
low-strain modal testing and experimentation. The shaker’s specifications provided by
the manufacture, APS Dynamic Electro-Seis, are as follows: Long Stroke Shaker Model
400, 100 lb (400 N) force, 30 inch/s velocity, 6.25 in peak-to-peak stroke. To monitor the
input force applied to the system by the shaker, a uni-axial accelerometer was also
attached on top of the shaker.

Data Acquisition (DAQ) System
The data acquisition (DAQ) system specification must be defined in accordance with
certain criteria including the number of sensors, the precision and bandwidth required for
transmitting data, etc. Since the location of the NEES site is fairly remote, a DAQ system
with real-time remote data transmission capability was one of the main requirements. The
high performance system that was customized for this project is a 32-channel real-time
data acquisition and analysis system, with manual and event driven triggering (on any 10
channels). The system has a sampling rate of up to 500 samples per second per channel
with 24-bit digital resolution. For most of the data collection described herein, a sampling

42
rate of 200 samples per second was utilized. The system also offers an extensive set of
remote tools for real-time monitoring, broadcasting streaming data (Internet, TCP, and
FTP), remote tele-control, and event driven notification. This DAQ system has been
customized by the Digitexx Company (http://www.digitexx.com) in desired ways to
provide remote sensing functionalities for the project (Figure 11). The real-time features
integrated with the DAQ system are: real-time response spectrum, real-time FFT, real-
time transfer function, a remote event-driven triggering mechanism and on-demand and
scheduled remote recording for statistical analysis studies.

Figure 11: The data acquisition (DAQ) system used for the SFSI test structure monitoring.

43
Digitexx’s DAQ system has several useful features such as high performance scalable
data acquisition software with multiple filtering and data recording and broadcasting
options. The interface of the program (Figure 12) provides a user-friendly control panel
to select, edit and mange the recording options (i.e., sampling rate, buffer size, averaging
option, multiple filtering, etc.).

Figure 12: Snapshot of the user interface of the DAQ system.

44
As illustrated in Figure 13, the end-user features of the system assist in performing some
preliminary real time analyses, such as real-time monitoring of all channels, real time
FFT, on-demand and scheduled recording, etc.

Figure 13: Real-time features integrated with the DAQ system.

45
Chapter 3: Modal Properties Identification and Environmental
Effects
Introduction
System identification for structural health monitoring purposes is often performed via
modal parameter estimation. It is commonly known that the Experimental Modal
Analysis (EMA) underwent a radical change with the implementation of the Fast Fourier
Transform (FFT) in early 1970s. A set of modal characteristics (e.g., modal frequency,
modal damping value and mode shape ) can be used to represent the modal behavior of a
linear structure.
Depending on the source of excitation, vibration-based EMA methods are categorized as
either forced vibration induced by an actuator, or ambient vibration relying on natural
excitation. Forced vibration is typically used when both the input(s) and the output(s) of a
system are easily producible and measurable. Nevertheless, the application of ambient
category (output-only EMA) methods is growing fast, not only in civil engineering, but
also in mechanical and aerospace engineering (e.g., to obtain the modal parameters of a
building or a car in road testing). There are numerous algorithms available that can be
used for each category to assist the system identification process. In this current work, the
combination of two widely-used methodologies (i.e., the Natural Excitation Technique

46
and the Eigensystem Realization Algorithm) along with impulse response analysis are
used.
The development of the Natural Excitation Technique (NExT) by James et al. (1992,
1993, and 1996), Farrar and James (1997) and Beck et al. (1994a, b, 1998) was a step
forward in identification of structures using response data only. Using NExT, assuming
stationarity of the input, one can convert the forced stochastic response to a deterministic
free vibration response. The cross-correlation function between the response vector and
the response of a selected reference degree-of-freedom (DOF) satisfies the homogeneous
equation of motion, provided the excitation is a stationary random noise. If the response
vector happens to coincide with a particular degree of freedom to be studied, the auto-
correlation function would be used accordingly. The Eigensystem Realization Algorithm
(ERA) (Juang and Pappa, 1985) can then be used to identify the modal parameters of the
system from the auto/cross correlation record.

Methodologies
To assure that the data collection/analysis or system identification is performed with
minimum uncertainty, there are many guidelines to be considered. To identify a particular
mode of a structure, the output data (location of the sensors) and the input (source of

47
excitation) should be carefully defined. They can be controlled to minimize distortion or
nonlinear response of the structure.
Furthermore, since there is always a well-known resolution trade-off between time-
domain and frequency-domain approaches, a systematic trial and error approach is
required to choose the right components for data processing that compromise on window
size, overlap of the windows, etc. For instance, in EMA it is commonly known that, for
averaging given time domain data, the window size must be large enough to include at
least 20 cycles of the first fundamental mode of the system. On the other hand, if the
window size is very large compared to the record length, it will result in less averaging
and more noisy correlation time histories.
That said, an accurate experimental modal analysis, in fact, requires a great deal of
experience when it comes to deciding the right testing approach and the data processing.
Despite the presence of uncertainties, utilizing different methodologies that converge to a
consistent set of results increases the level of confidence in the system identification
process; therefore, for the SFSI test structure, various methodologies with different
sources of excitations were utilized.

48
Sources of Excitation
The NEES site facility, as discussed in detail in the previous chapter, has been designed
and equipped to be capable of undergoing various forced vibration tests. As shown in
Figure 14, several possible real and artificial sources of excitation can be used at the
NEES facility.

Figure 14: Different possible sources of excitation at the NEES facility site include: F1:
Permanent Shaker, F2: NEES@UCLA Linear Shaker, F3: NEES@UTexas Mobile Shaker
and natural earthquakes at the site.

Note that some of the equipment are permanently installed at the site and have the
capability to be controlled remotely over the internet. There are also other mobile sources
: Natural Earthquake
Native Soil
Water Table 0-3 m
Pore Pressure
Accelerometer
F1
F2
F3
5m
5m
NEES@BYU SFSI Facility
F1 : Permanent Shaker
F2 : NEES@UCLA Shaker
F3 : NEES@UTexas Shaker

49
of the excitation that could be borrowed from other NEES facilities such as the
NEES@UTexas mobile shaker and NEES@UCLA’s linear shaker.
To identify the first (rocking) mode frequency of the SFSI test structure, as a first
estimate, a sinusoidal sweep signal with various frequency content (e.g., 5 to 25 Hz) is
introduced by the shaker on top slab. It is expected that the response of the top slab is
larger at certain frequencies of excitation than at others due to the resonance
phenomenon. However, modal parameter estimation relying on the excitation induced by
the shaker on top of the structure has limitations, because (1) the signals are subject to
shaker-structure interaction; (2) the shaker bandwidth may be restricted. Thus, to verify
the natural frequencies, the NEES@UTexas mobile shaker, which has the capability of
producing waves from shaking the ground both horizontally and vertically, was also used.
Figure 15 shows the responses of the top slab (dashed line) and bottom slab (solid line)
due to the sweep sine waves induced by NEES@UTexas shaker. Clearly, the input/output
signals are of high signal to noise ratio and the fundamental resonance frequency of the
system, at which the response amplitude is maximized, can be identified to be 9 Hz. It is
also important to remember when relying on both input (excitation) and output (response)
signals, the data from all channels should be very well synchronized.

50

Figure 15: The response of the top Slab (dashed line) versus the bottom slabʼs response
(solid line) induced by the UTexas shaker.

Impulse Response Measurement
The hammer test is another very common test to analyze the impulse response of the
structure for modal parameter estimation. Even though a hammer is a very simple source
of excitation, the result can be very informative and reproducible. However, as stated by
Brown et al. (1977), it is recognized that there are certain limitations associated with the
hammer test (e.g., relative less control over the frequency content of the excitation).
Not only is it used for the frequency identification of the SFSI test structure, but also for
the damping coefficient estimation of the few first modes of vibration (including the

51
torsional mode). For modal frequency estimation, the time-domain response can be
transformed (e.g., by FFT, PSD, etc.) to the frequency domain. In order to accumulate
sufficient energy in the output signal—which will result in better frequency-domain
analysis—several time-domain impulse responses of the top slab are joined together
(each response will be added to the end of the other) and then are utilized for frequency-
domain transformation. As far as the windowing for FFT analysis is concerned, the
interval of the impulse responses (in time-domain) are preferred to be evenly distributed
over time beforehand. For building structures, 10 impacts typically are required
(Reynolds and Pavic, 2000).
For estimating modal properties from measured data, numerous algorithms have been
developed and implemented in different formats. One of the common methodologies is
based on the least squares (i.e., curve fitting) tools. Excellent overviews of most of the
previously proposed algorithms and a mathematically consistent reformulation of those
have been presented by Allemang and Brown (1998).
In this current work, by utilizing MATLAB’s system identification toolbox, and by
exploiting the curve fitting approach, the modal parameters of the SFSI Test Structure
were analyzed and identified. The drawback of using the curve fitting tool in MATLAB
is that the initial guess should be in the vicinity of the answer otherwise some misleading
results might be obtained.

52
For a (single degree of freedom) mass-spring-dashpot model, shown in Figure 16, the
equation of motion can be written as:
€
˙ ˙ x + 2ζω
n
˙ x +ω
n
2
x =
F
K
ω
n
2
=
F
m
(6)
where ζ is the damping ratio (
€
c c
critical
), is the natural frequency, m is the mass, K is
the stiffness, F is the excitation force and
€
c
critical
= 2mω
n
.

Figure 16: Single Degree Of Freedom (SDOF) mass-spring-dashpot model.

Prior to the curve fitting process in the frequency domain, the frequency response
function (FRF) of the system is required. The FRF is simply a complex transfer function,
formed from either measured data or analytical functions, with real and imaginary
components. It represents the structural response (displacement, velocity, or acceleration)
to an applied force as a function of frequency.
The transfer function from force to displacement (representing the inverse of dynamic
stiffness), is called the receptance (or compliance) function and can be written as:
€
TF
d
(ω) =(1/K)
ω
n
2
(ω
n
2
−ω
2
+2iζω
n
ω)

(7)

53
where
€
i = −1. The accelerance function (acceleration response over the force), similarly
would be written
€
TF
a
(ω) =(1/K)
−ω
2
ω
n
2
(ω
n
2
−ω
2
+2iζω
n
ω)

(8)
The accelerance magnitude is:
€
TF
a
(ω) =(1/K)
−ω
2
ω
n
2
(ω
n
2
−ω
2
)
2
+(2ζω
n
ω)
2

(9)
or
€
TF
a
(ω) =(1/m)
−ω
2
(ω
n
2
−ω
2
)
2
+(2ζω
n
ω)
2

(10)
For preliminary modal parameter identification, the SFSI test structure is assumed to be a
linear SDOF system. The results of the experimental data (from forced vibration testing)
can be fit to the analytical FRF of the assumed SDOF system; two scenarios are
considered:
1. Sinusoidal sweep signals as excitation, which are induced by the shaker on the
top slab (mainly used for the rocking frequency identification).
2. By suddenly turning off the shaker at the resonance frequency, a free vibration is
created, which is used for estimating the damping coefficient.

54
Given the input signals and by measuring the output response, the frequency response
function of the structure is computed. Knowing the weight of the shaker and the
acceleration of the shaker (one accelerometer is attached on the shaker), the input force is
known. Thus, by measuring the output (acceleration) of the structure response on the top
slab, the accelerance function magnitude can be plotted as depicted in Figure 17 (dotted
line). Clearly, two additional modes are present. Therefore, a linear transfer function (TF)
from the superposition of three SDOF accelerance function is fit to the data. The
mathematical equation of the curve is obtained by summation of each function as
follows:
€
|TF
a
(ω) |=
ϕ=1
3
∑
(1/
m
ϕ
)
−ω
2
(ω
n
ϕ
2
−ω
2
)
2
+ (2ζ
ϕ
ω
n
ϕ
ω)
2
(11)
The best fit 3DOF transfer function (solid line) in Figure 17, computed by the curve
fitting tool of MATLAB, is used to estimate the modal properties. The two additional
peaks in the frequency domain are speculated to represent the bracings’ vibration modes.
The estimated frequencies and damping ratios corresponding to the SFSI test structure
rocking mode and two additional modes are tabulated in Table 3.

55

Figure 17: 3DOF transfer function curve fit to the SFSI frequency response.

Table 3: Identified model properties utilizing the curve fitting technique.
Mode
Frequency [Hz] Damping ratio
Rocking 8.65 0.0612
Bracing? 11.16 0.0029
Bracing? 11.50 0.0035

56

To better understand the cause for the two additional peaks in the experimental FRF of
the SFSI test structure, the effect of out-of-plane vibration of the bracings is studied. To
do so, the response of the bracings in a forced vibration experiment must be analyzed.
Therefore, an accelerometer is attached on the bracing intersection — sensing the y-y
direction in Figure 18 — while the response of the structure perpendicular to the bracings
plane (i.e., the y-y direction under the top slab) is measured.

Figure 18: The location of the accelerometer measuring acceleration on y-y axis.

The accelerance function of the bracings, along with that of the top slab of the SFSI test
structure, is plotted in Figure 19. The peaks of the FRF confirm the hypothesis that the

57
two extra peaks occurred due to the bracing modes in perpendicular direction of the
rocking vibration. In the figure, the dotted line shows the transfer function of the
bracings, whereas the blue solid line shows the accelerance of the top slab of the SFSI
test structure. In fact, Figure 19 clearly shows that the bracing has a mode (black circle)
that exactly coincides with one of the peaks observed in the top slab transfer function
(solid line). Thus, the hypothesis of the effect of the bracings on the top slab accelerance
is validated.

Figure 19: The accelerance function of the SFSI test structure; bracing response (green
line) and the top slab response (solid line).

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58

It is important to note that the identified frequency from this experiment (~9.37 Hz) is
slightly different from the result of the curve fitting approach reported in Table 3. Since
these two experiments were not performed at the same time, could environmental effects
justify this? In Section 4.7, which discusses the correlation of frequency variations with
temperature effects, it is seen that removing the bracings significantly reduces the
variations in the identified frequency.

Figure 20: Time-domain curve fit to the measured displacement from a pressure cell
underneath the structure induced by a free vibration.
!"#$%&'()(*+,-').,
/")(,-#('.,

59

The SFSI system parameter identification is also performed in the time domain. By
suddenly turning off the shaker after exciting at the resonance frequency, a free vibration
is created which can be used to estimate modal parameters. For instance, the signals from
the pressure cells underneath the structure (sensing the displacement of the corners of the
foundation) can be utilized for rocking mode parameter estimation. In Figure 20, the
displacement of the SDOF system — formulated in (12) — is plotted as solid red line
chose to fit the measured response (plotted as dotted blue line). The graph shows how the
rocking motion of the foundation is very similar to a damped SDOF system, the
displacement of which (for free vibration) can be formulated as:
€
x(t) = e
−ζω
n
t
x(0)cos(ω
d
t) +
˙ x (0) + (ζω
n
)x(0)
ω
d






sin(ω
d
t)






(12)
where
€
ω
d
=ω
n
1−ζ
2
is the damped natural frequency.

Identified Parameters, Observations and Environmental Effects
It is well-known that there are many sources other than damage that can cause variations
in identified dynamic properties of a structure. These sources of variation can be divided
into three main categories: (1) environmental conditions, such as temperature variation
and soil condition, (2) operational conditions, such as traffic conditions and excitation

60
sources, and (3) measurement and processing errors, including non-stationarity,
measurement noise and errors associated with digital signal processing. In this current
research, two major environmental effects on the identified modal properties are studied:
first the correlation of the identified rocking frequency with the ambient air temperature
and, secondly, its correlation with the water-level under the foundation.
In order to monitor the system over a long period, acceleration response data, from both
ambient and forced vibration tests, were taken periodically at the site over 18 months
during 2005 and 2006. Air and soil temperatures, soil pore pressure and water table level
were also monitored on an hourly basis to study short-term and long-term environmental
effects on the apparent frequency of the structure. Utilizing different system identification
techniques discussed previously, the modal properties of the SFSI Test Structure were
identified and their correlations with environmental effects were studied.

Temperature Dependency
To analyze the effect of the temperature and its correlation with the identified frequency,
a systematic procedure was implemented to collect the ambient vibration data while the
ambient temperature was measured under the top slab by a temperature sensor. As
illustrated in Figure 21, the typical variation of the identified fundamental natural
frequency (first mode) of the structure over a period of a couple days shows 10%

61
fluctuation of the identified frequency in a daily basis, with an increase in the rocking
frequency during the day time that starts to decrease in the afternoon. As illustrated in
Figure 22, the correlation between the collected temperatures and the identified frequency
over a two-day period is evident.

Figure 21: Typical daily variation in the identified rocking frequency of the SFSI Test
Structure from 11/20/05 to 11/23/05.

In Figure 23, the scatter plot of 520 identified frequencies during 18 months and their
corresponding ambient temperatures is shown; the positive correlation can again be
observed.

62

Figure 22: First mode (rocking) frequency in East-West direction of the SFSI Test
Structure (pink squares) and ambient temperature recorded from 8/28/2005-8/30/2005
(blue diamonds).

Figure 23: Identified rocking frequency versus the ambient temperature during the 18
months in 2005-2006.
Freq. [Hz]
Temp. [F]

63
Since the SFSI test structure is an open frame structure, it was speculated that the
bracings contributed significantly to the variation of the identified modal frequencies as
temperature changed. To verify this speculation, the bracings were removed from all
faces of the structure and data were again collected with a similar procedure.

Figure 24: Picture of the SFSI Test Structure after the bracings were removed.

Obviously, the rocking frequency decreased (from about 9Hz to about 6Hz) but,
interestingly, the daily variation of the identified frequency reduced significantly as well.
As illustrated in Figure 25, the rocking frequency of the system, as well as its variation
with respect to temperature, has been significantly reduced (from 10% daily variation
down to 3%) relative to the braced cases.

64

Figure 25: Typical daily variation of the identified rocking frequency of the SFSI Test
Structure (recorded on 2 Jan. 2008) after the bracings were removed.

To see the variation in identified frequencies, the histogram of 520 identified frequencies
for the braced configuration between 6/15/05 and 3/15/06 is plotted in Figure 26. The
mean and standard deviation of the rocking frequencies are computed for both braced ad
unbraced configurations. As shown in Figure 27, the estimated mean and standard
deviation for the braced configuration are
€
µ =9.35Hz

and
€
σ =0.47Hz. Fewer samples
were available from the unbraced configuration; the estimated mean and standard
deviations are
€
µ =6.02Hz and
€
σ =0.07Hz respectively. The estimated coefficient of
variation (CoV) for the braced and unbraced configurations are 5% and 1.1%,
respectively.

65

Figure 26: Histogram of 520 identified frequencies of the SFSI Test Structure between
6/15/05 and 3/15/06 in the braced configuration.

Figure 27: Probability density function (PDF) of identified frequencies; the blue solid line
and black dash line demonstrate the distributions for the braced and un-braced
configuration, respectively.

66
Because of the significant shifts in dynamic parameters from temperature effects, shifts
due to damage may be masked by these environmental effects. Hence, damage detection
would be more difficult in such cases. Consequently, understanding and detecting
(quantifying), subtracting or/and cleansing the effect of temperature conditions on the
estimated local and global structural parameters appears to be necessary. The regression
analysis and a methodology to normalize the data in Chapter 6 for achieving more robust
damage detection are developed to do this cleansing.

Ground Water-level and Soil Saturation Dependency
Rain may not only have mass and seepage pressure effects, but it also causes changes in
the soil behavior. A study of the correlation between the identified frequency and rainfall
was recently reported by Clinton et al. (2006). Their research focused on analyzing the
impact of environment on vibration-based frequency identification of the Millikan
Library, located on the campus of the California Institute of Technology (Caltech). In
particular, they observed that during a two-day, 4 in. rainfall, natural frequencies
increased by about 3%, returning to the nominal values in 1–2 weeks. They concluded
that the rain induced increases in natural frequencies through an increase in soil-structure
stiffness caused by soil saturation and, perhaps, soil swelling.

67
To investigate this phenomenon on the fully instrumented SFSI test structure at the NEES
facility, the water level under the foundation (as opposed to rainfall) is measured and
used herein. Even so the measurement of the ground water-level under foundations is
practically more difficult than rainfall quantity but, the NEES facility provided fully
instrumented structures including the water table sensors.
During the preliminary monitoring of the SFSI test structure between 6/17/2005 to
7/17/2005, an increasing trend in the identified rocking frequencies of the structure was
noticed (Figure 28). Thus, besides the daily temperature effect, the question arose as to
whether any other environmental variation (e.g., ground water table) could have impact
on the natural frequency of the structure.

Figure 28: Observed trend of increases in the identified rocking frequencies of the SFSI
test structure over one month (6/17/2005−7/17/2005).

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68
As part of the sensor network at the site, the water-level sensors allowed the ground water
table under the foundation to be monitored. Thus, changes in the dynamics of the soil-
foundation-structure system in conjunction with the water-level fluctuations could be
investigated. The water table level for the same monitoring period, 6/17/2005−7/17/2005,
was logged. As shown in Figure 29, the water table under the foundation dropped during
that time, albeit not very significantly. Thus, a longer monitoring period, particularly to
investigate the effect of more significant variation of water table on the identified
frequency, was planned.

Figure 29: Measured ground water table under the SFSI test structureʼs foundation over
one month (6/17/2005−7/17/2005).

The ground water table fluctuation under the SFSI test structure was monitored for a
longer period, from jun. 2005 to Sep. 2005 as illustrated in Figure 30. The data collected
!"#$%&'()&
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69
from the site showed some correlation between the ground water-level and the identified
rocking frequency of the structure. As illustrated in Figure 32, the identified frequency
and water table as functions of time at the site between 6/17/05 through 9/4/05 for the
braced configuration is graphed.

Figure 30: Fluctuation of the ground water table fluctuation under the SFS test structure

Figure 31: Variation in identified rocking frequencies of the SFSI test structure, and a
polynomial trend line (dashed line)
!"#$%&'()&
*"$+,&&'-)&
3.20
3.40
3.60
3.80
4.00
4.20
4.40
Depth [ft] .
3.20
3.40
3.60
3.80
4.00
4.20
4.40
Jun-09 Jun-09 Jul-09 Jul-09 Jul-09 Aug-09 Aug-09 Aug-09 Sep-09
Depth [ft] .
&&&&&&&&./0123 & &&&&&&&./4123 & &&&&5/6123 &&&&& &7"$123&&&
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!"#$%
Freq. [Hz]
$$$$$$$$*+,-)# $ $$$$$$$*+.-)# $ $$$$/+0-)# $$$$$ $123-)#$$$

70

Figure 32: Observation on the Water-level and the identified freq. at the site from 6/17/05
thru 9/4/05. Note: The water-level axis has been plotted reversely.

Admittedly, the daily fluctuations due to temperature make it difficult to see the long-
term effects of the more slowly changing water table level. However, using a moving
average to smooth out the shorter-term trends, and looking at the data over a long period,
as is in Figure 32, the water table level shows some correlation with variation in
identified natural frequency. Higher water table level has, likely, a dual effect on the soil-
structure interaction: decreasing the stiffness of the soil (at least at the small motion
levels used here), and increasing the mass of the moving structure-foundation-soil-water
system. It is also likely that the water table affects the damping of the system as well.
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71
Chapter 4: Modeling of SFSI Test Structure Behavior
Introduction
For decades, numerous studies have been conducted in the area of soil-structure
interaction modeling. Since soil-structure systems have very complex characteristics,
many researchers and engineers have attempted to develop accurate, yet pragmatic
approaches to model such systems. More detailed background can be found in section 0.
To explain the observations made on the variation of the rocking frequencies of the two
SFSI systems (i.e., the SFSI test structure in Chapter 3 and the small-scale prototype
introduced in Chapter 5), a model is developed in this chapter based on the cone
modeling approach. The main intent of the modeling is to characterize the effect of soil
saturation on a single-degree-of-freedom structure on a foundation sitting on a sandy soil.
For both SFSI systems, pragmatic idealizations of the soil-media, which could assist
studying the physics of the soil-structure interaction were investigated; eventually a
strength-of-material modeling technique inspired by the Cone Modeling (Wolf, 1997)
approach is proposed.
By introducing the empirical concept of the trapped mass under the foundation that
moves in-phase with the foundation, the rocking frequency of SFSI systems as a function
of soil saturation is parametrically studied. It is shown that the shift (increase or decrease)

72
of the rocking frequency of the SFSI system is strongly dependent on the characteristics
of structure relative to the soil under its foundation.

Cone Modeling
Since the intent of this study is for low-strain vibration-based structural monitoring, it is
important to remember that the modeling implicitly assumes that the soil remains linearly
elastic with linear-hysteretic material damping. Linearity is justified since the
displacement of the foundation is just fractions of millimeter in the test described in the
previous chapters. In addition, it is assumed that the structure is on rigid foundation
resting on the surface of a homogeneous soil half-space.
Even though several rigorous mathematical approaches for soil modeling based on three-
dimensional elasto-dynamics are available, Wolf (1997) suggests that these methods —
due to their considerable mathematical complexity — obscure the physical insight of the
problem; as a result, they are more applicable for the applied computational mechanics,
rather for practical civil engineering design. Thus, the Cone Modeling approach, which is
based on a simple physical model with a small number of degrees of freedom, appears to
be a favorable candidate to be utilized for better understanding of the aforementioned
SFSI systems. Exploiting this approach, vibrations of a foundation on the surface of, or
embedded in, a layered half-space using conical bars and beams (i.e., cones), can be

73
analyzed (Wolf and Deeks 2004). In this method, as they stated, “the complicated exact
formulation of three-dimensional elastodynamics is replaced by the simple one-
dimensional truncated semi-infinite description of the theory of strength of materials.”
In order to avoid the complicated analysis associated with wave propagation techniques
that involve rigorous mathematical formulations, cone models were originally proposed
several decades ago. Indeed, the spring-dashpot-mass model is a derivative of the cone
modeling approach (Figure 33). Meek and Wolf (1992) state that it can be regarded as a
first step towards developing a strength of-materials approach to foundation dynamics;
analogous to beam theory in structural analysis with a restricted deformation behavior
(i.e., plane sections remain plane). In the spring-dashpot-mass (lumped-parameter)
model, there are certain important assumptions; for example, the dynamic loads are
assumed to be applied directly on the structure. Nevertheless, for earthquakes and other
excitations introduced into the dynamic system via the soil, this approach can still be
used with a few modifications.
Using the cone model, Wolf (1994) proposed that the half-space below the foundation to
be modeled as a truncated semi-infinite rod with its area varying as in a cone with the
same material properties. To model the soil with linear elastic behavior and hysteretic
material damping, horizontal layers are usually characterized by elastic modulus E (or
constrained modulus, ), shear modulus G, Poisson’s ratio ν, mass density ρ, damping

74
coefficient ζ either overlying a half-space or fixed at its base, shear-wave velocity ,
dilatational or P-wave velocity and the rigid disk foundation equivalent radius (or
half of the width of a square foundation), and apex height as a function of ν. The
angle of the cone depends on Poisson’s ratio and on the wave velocities of the soil under
the foundation. The aspect ratio represents the opening angle and can be computed for
each degree of freedom such that the behavior of the foundation on the half-space and the
cone on the low-frequency limit coincide.

Figure 33: Truncated semi-infinite Cone Model (Wolf and Meek 2004)

By utilizing such a simplified physical model, the complicated three-dimensional wave
propagation plus the body and surface waves could be represented by a one-dimensional
model. Now, by looking at a harmonic excitation, this model can explain the physics of
the problem and the rigorous mathematical solution.

75
For harmonic excitation with frequency of ω, the complex response u(ω) of a given
dynamic system can be written as :

€
u(ω) =Re[u(ω)]+ iIm[u(ω)] (13)
The corresponding force amplitude P(ω) is formulated as

€
P(ω) =S(ω)u(ω)

(14)
where the stiffness matrix S(ω) can be formulated as:

€
S(a) =K[k(a) +iac(a)] (15)
k(a) and c(a) represent frequency dependent stiffness and damping, respectively, while
parameter a is introduced as the dimensionless frequency and formulated as follows:

€
a =
ωr
eq
c
S
(16)
where ω,

and are angular frequency, equivalent radius of the foundation and the
shear wave velocity in the soil, respectively. If the foundation is square, use
€
r
eq
=B 2
where B is the width of the foundation. The dimensionless spring coefficient k(a) governs
the force that is in phase (or 180 degree out of phase) with the displacement (real part),
and the dimensionless damping coefficient c(a) describes the forces that are 90 degrees
out of phase (imaginary part).
The rocking static stiffness coefficient is introduced as , relating the rocking motion of
a square foundation to the moment applied to the foundation as follows:

76

€
K
r
=
GB
3
2(1−ν)
(17)
where G, ν and B specify shear modulus, Poisson’s ratio of the soil and the width of the
square foundation.
Further, Wolf (1994) introduces a discrete-element models (Figure 35) representing
foundations on surface of halfspace. The rotational cone’s dynamic coefficients are
obtained by a general strength-of-material approach using the approximate Green′s
functions of the double-one models (Wolf, 1994). A bending moment with amplitude
€
M
o

is applied, resulting in a rocking equilibrium element, while horizontal motion is
constrained as shown in Figure 33. The cone representing a beam with its moment of
inertia increasing with depth z as
€
I(z) =
z
z
o






4
I
o
(18)
where
€
I
o

is the area moment of inertial of the foundation, about an axis perpendicular to
the page. The amplitude of the bending is
€
M(z) =ρc
p
2
I(z)θ(z)
,z
(19)
where
€
θ(z) is the amplitude of the rocking motion and
€
()
,
is the derivative notion.
By solving the he equilibrium equation for a massless foundation, and by writing
dynamic stiffness coefficient as

77
€
S
r
(a) =K
r
k
r
(a) +iac
r
(a)
[ ]
(20)
the dimensionless spring and damping coefficients are
€
k
r
(a) =1−
1
3
a
2
Bc
p
2






2
z
o
c
s
( )
2
+ a
2
(21)
€
c
r
(a) =
2
3
z
o
B
c
s
c
p
a
2
Bc
p
2






2
z
o
c
s
( )
2
+a
2
(22)
To understand the effect of these frequency dependent terms as a function of
dimensionless frequency, the spring and damping coefficient for a foundation on a dry
sand is plotted in Figure 34. According to these plots, it is expected that the spring
coefficient decreases drastically as the dimensionless frequency increases and remains
constant for higher values of a (i.e., for a > 3). In contrast, the damping coefficient tends
to increase for dimensionless frequency up to a < 3, but then remains almost constant.

Figure 34: Frequency dependent spring and damping coefficients for rocking motion of
dry soil.
!"#$%&'#(&)%''!*+%,-.!!! !!"#$%&'#(&)%''!*+%,-.!!!
!!!"/$0#&1!2(%34#%&5.!"6!#!
!70+#&1!2(%34#%&5.!$6!#!
!
c
r
(a)
!
k
r
(a)
!
k
r
(a)
!
c
r
(a)

78
In a practical sence, to convert a typical cone model to a spring-dashpot-mass model,
Wolf (1994) introduced models for rocking motions as shown in Figure 35. His so-called
Monkey-tail model (right) shows an equivalent spring-dashpot model (equivalent to
Figure 35, left).

Figure 35: Equivalent Wolfʼs Monkey-tail model (right) derived from the Spring-dashpot
model (left).

Considering the cone modeling approach, the corresponding rocking motion properties of
this so-called Monkey-tail model are defined as follows:

€
K
r
=
3ρc
p
2
I
o
z
o

€
M
r
=ρI
o
z
o

€
C
r
=ρc
p
I
o
(23)
where
€
K
r
,
€
M
r
,
€
C
r
are rocking stiffness, mass moment of inertia and damping coefficient
of the soil, and , known as the apex height. It can be shown that the models in Figure
35 are equivalent by writing the equilibrium equations for the monkey-tail model as
follows:
€
M
o
(t) =C
r
˙
θ
1
(t)−
˙
θ
2
(t)
( )
+K
r
θ
1
(t) (24)

79
€
M
r
˙ ˙
θ
2
(t) +C
r
˙
θ
2
(t)−
˙
θ
1
(t)
( )
= 0 (25)
Considering the cone model properties, it can be concluded that
€
M
r
C
r
=
z
o
c
p
(26)
Substituting (26) in (25),
€
z
o
c
p
˙ ˙
θ
2
(t) +
˙
θ
2
(t) =
˙
θ
1
(t) (27)
By solving this second-order differential equation, the following convolution integral, by
using the impulse response function h(t), can be written:
€
˙
θ
2
(t) = h(t−τ)
˙
θ
1
(τ)dτ
0
t
∫
(28)
By substituting (28) in (24), the equilibrium equation can be written as:
€
M
o
(t) =K
r
θ
1
(t) +C
r
˙
θ
1
(t)− h(t−τ)C
r
0
t
∫
˙
θ
1
(τ)dτ (29)
It can be verified that the result of the time domain formulation of the monkey-tail’s
model coincides with the spring-dashpot model in Figure 35 (left). Further in this current
study, the equivalent monkey-tail model is used.

80

Figure 36: Monkey-tail model of a soil-foundation system; inclusion of the mass for the
foundation.
Next, by including the mass of the foundation (Figure 36), a mass moment of inertia term
is added to the equilibrium equations. Therefore, equations (30-31) can be re-written as
follows:
€
M
o
(t) =C
r
˙
θ
1
(t)−
˙
θ
2
(t)
( )
+K
r
θ
1
(t) +J
o
˙ ˙
θ
1
(t) (30)
€
0 =M
r
˙ ˙
θ
2
(t) +C
r
˙
θ
1
(t)−
˙
θ
2
(t)
( )
(31)
where
€
J
o
=m
f
B
2
12
+
D
2
3






,
€
m
f
and D are moment of inertia about the rocking axis, mass
and depth of foundation, respectively.
For harmonic excitation, these equations are transformed to:
€
M
o
(ω) =iωC
r
θ
1
(ω)−θ
2
(ω)
( )
+K
r
θ
1
(ω)−ω
2
J
o
θ
1
(ω) (32)
€
0 =−ω
2
M
r
θ
2
(ω) +iωC
r
θ
1
(ω)−θ
2
(ω)
( )
(33)
By eliminating
€
θ
2
(ω) ,

81

€
M
o
(ω) =K
r
1−
ω
2
(M
r
/K
r
)
1+ω
2
(M
r
2
/C
r
2
)
−ω
2
J
o
K
r
k
r
          
+iω
M
r
C
r
ω
2
(M
r
/K
r
)
1+ω
2
(M
r
2
/C
r
2
)






c
r
        












S
r
                      
θ
1
(ω) (34)
It is noticed that the dynamic stiffness can be written as:
€
S
r
(a) =K
r
[k
r
(a) +iac
r
(a)] (35)
where a is a dimensionless frequency:
€
a =
Bω
2c
S
(36)
By substituting the cone modeling parameters, the frequency-dependent terms of the
dynamic stiffness,
€
k
r
(a)

and
€
c
r
(a)

can be formulated as follows:
€
k
r
(a) =1−
1
3
a
2
Bc
p
2z
o
c
S






2
+ a
2
−
4
3
z
o
J
o
ρI
o
B
2
c
p
c
S






2
a
2
(37)
€
c
r
(a) =
z
o
3
B
2
c
S
c
p
a
2
Bc
p
2z
o
c
S






2
+a
2

(38)
Further, for a square foundation, the aspect ratio can be obtained by matching the static
stiffness coefficient of the foundation to that of the corresponding cone.

€
3ρc
p
2
I
0
z
0
=
GB
3
2(1−ν)

(39)
Therefore the aspect ratio can be written as:

82
€
z
o
B
=
1
2
(1−ν)
c
p
c
S






2

(40)
where as shown in Figure 33, is a function of the foundation’s width and two
important input parameters of a cone model, the pressure and shear wave velocity in the
soil under the foundations. The relationship between Poisson’s ratio and the elastic
constants for soil with mass density ρ, wave propagation velocities (shear waves) and
(dilatational waves) can be obtained from the formulas given in Table 4. Please note
that the constrained modulus can be formulated in terms of Young’s Modulus E, and
shear Modulus G as
€
E
c
=
1−ν
(1+ν)(1−2ν)
E =
1−ν
1−2ν
G (41)

Table 4: Poissonʼs ratio and elastic constants for soil mechanics.
Poisson’s Ratio Constrained Modulus Shear Modulus
€
ν =
c
p
c
S






2
−2
2
c
p
c
S






2
−2

€
E
c
=ρc
p
2

€
G =ρc
S
2

83
As shown in Figure 37, the shear wave velocity is not impacted by the saturation level;
however, the P-wave velocity increases as the air proportion decreases (saturation
increases). In fact, an increase in saturation level, causes >> ; as a result, according
to the Poisson’s Ratio formula in Table 4, as tends to infinity, the Poisson’s ratio
approaches 0.5.

Figure 37: Effects of saturation on the wave velocities in different types of soils: (A) P-
waves, (B) S (shear) waves . (Yang and Sato, 2002)

In the cone modeling approach, a saturated and un-drained soil (i.e., when Poisson’s ratio
ν approaches 0.5) is considered to be nearly incompressible soil, requiring certain
modeling considerations. Meek and Wolf (1993b) believe that as the P-wave velocity
tends to infinity, it causes anomalous behavior, not only for cones, but for rigorous
solutions as well. In such cases, a special technique for the Cone models has been offered
by Meek and Wolf (1993a). Based on their calculations, they suggest that the axial-wave

84
velocity relationship
€
c
p
=2c
S
should be enforced for the cone models. Thus, the aspect
ratio formulation can be simplified as shown below:

€
z
o
B
=2(1−ν)

(42)
Further, Meek and Wolf(1993b), particularly for nearly incompressible soils, suggest that
the idea of a trapped mass under the foundation should be taken into account. To model
the contribution of the mass of the soil under the foundation, they introduce a trapped
mass of soil beneath the foundation, which moves as a rigid body in phase with the
foundation (i.e.,

€
ΔJ
r
) with no additional degree of freedom (Figure 38).

Figure 38: The conceptual notion of the trapped mass underneath the foundation of a
monkey-tail model.

Thus, the corresponding equilibrium equations can be re-formulated as follows:
€
M
o
(t) =C
r
˙
θ
1
(t)−
˙
θ
2
(t)
( )
+K
r
θ
1
(t) + (ΔJ
r
+J
o
)
˙ ˙
θ
1
(t) (43)
€
M
r
˙ ˙
θ
2
(t) +C
r
˙
θ
1
(t)−
˙
θ
2
(t)
( )
= 0 (44)
For harmonic excitation, they can be written as

85
€
M
o
(ω) =iωC
r
θ
1
(ω)−θ
2
(ω) ( ) +K
r
θ
1
(ω)−ω
2
(ΔJ
r
+J
o
)θ
1
(ω) (45)
€
−ω
2
M
r
θ
2
(ω) +iωC
r
θ
1
(ω)−θ
2
(ω)
( )
=0 (46)
By eliminating
€
θ
2
(ω) ,

€
M
o
(ω) =K
r
1−
ω
2
(M
r
/K
r
)
1+ω
2
(M
r
2
/C
r
2
)
−ω
2
ΔJ
r
+J
o
K
r
+iω
M
r
C
r
ω
2
(M
r
/K
r
)
1+ω
2
(M
r
2
/C
r
2
)












S
r
                        
θ
1
(ω) (47)
Consequently, it is expected that, for perfectly incompressible soil with Poisson’s ratio
exactly equal to 0.5, the real-valued mass term of the dynamic stiffness,
€
−ω
2
(ΔJ
r
+ J
o
),
would dominate the response which would result in reduction of the dynamic stiffness of
the discussed spring-mass-damper model.
For the rocking motion, the trapped mass moment of inertia is formulated as follows:

€
ΔJ
r
=
1.2
24
H ν −
1
3





 ν −
1
3





 ρB
5
(48)
where
€
H(x) =
0, x < 0
1 , x≥ 0



.
It is clear that according to the dynamic-stiffness formulation the stiffness is decreased,
proportional to the square of frequency, by a mass trapped under the foundation and
moving in phase with it because the soil is nearly or perfectly incompressible. Practically
speaking, this formulation implies the rocking frequency of saturated soil-foundation-
structure system, at some point, is becoming less than the dry case frequency.

86
Including the trapped mass effect, the dynamic stiffness coefficient for the rocking
motion can be written as follows:
€
k
r
(a) =1−
1
3
a
2
Bc
p
2z
o
c
S






2
+ a
2
−
4
3
z
o
J
o
ρI
o
B
2
c
p
c
S






2
a
2
−
1.2
3
H ν −
1
3





 ν −
1
3





 1−ν
( )
a
2

(49)
It is obvious that the last term in (49) is the contribution of the trapped mass which would
vanish for (dry sand). Again, according to this empirical formulation, the trapped
mass contributes for ν > 1/3 and increases linearly with ν.

Coupled Dynamic Model for SFSI Systems
To better understand the physics behind a coupled soil-structure system for rocking
motions, a dynamic model is introduced as shown in Figure 39. In this model, the
structure is represented with a mass m and a static spring with coefficient k (the lateral
stiffness of the structure), which is connected to a rigid mass less bar of height H.
Considering the foundation of width B, the soil dynamic stiffness has been modeled with
the frequency dependent coefficient utilizing the cone model for the soil with the
following properties: mass density , shear wave velocity , frequency dependent

87
stiffness coefficient
€
k
r
(a), static stiffness

and dimensionless frequency parameter
€
a =
1
2
ωBc
s
−1
.

Figure 39: Coupled dynamic model of soil-structure system for rocking
motion; representing SFSI test structure.

The equilibrium equation for the whole soil-foundation-structure system, can be written
€
m mH
0 J
o






˙ ˙ u
˙ ˙
θ






+
k 0
−kH K
r
k
r
(a)






u
θ






=
0
0






(50)

To find the system eigenvalues

€
λ =ω
2
, the characteristic equation can be obtained by
solving an eigenvalue problem, which leads to the following equation
€
det
k−mλ −mλH
−kH K
r
k
r
(a)−J
o
λ






= 0 (51)

88
Since the term
€
K
r
k
r
(a)−J
o
λ is a function of a, above equation will yield to a frequency
dependent equation as below:
€
(k−mλ)(K
r
k
r
(a)−J
o
λ)−mλkH
2
=0 (52)
Rearranging (52) by collecting terms of like powers of
€
λ gives
€
mJ
o
λ
2
−(mK
r
k
r
(a) +J
o
k +mkH
2
)λ− +kK
r
k
r
(a) =0 (53)
Solving (58) for gives
€
λ =
mK
r
k
r
(a) +J
o
k +mkH
2
± mK
r
k
r
(a) +J
o
k +mkH
2
( )
2
−4mJ
o
kK
r
k
r
(a)
2mJ
o

(54)
The fixed-base natural frequency
€
ω
s
of the structure can be simply computed as

€
ω
s
=
k
m
(55)
The rocking natural frequency can be expressed, using the stiffness derived from the cone
model in section 5.3 and ignoring any base mass, as

€
ω
r
=
K
r
k
r
(a)
mH
2
(56)
Using the fixed base frequency and the massless foundation rocking frequency, (61) can
be simplified and re-written as follows:

89
€
λ =
T ± T
2
−4J
o
m
2
ω
s
2
(J
o
+mH
2
)ω
r
2
2mJ
o
(57)
where
€
T =m(J
o
+mH
2
)ω
r
2
+J
o
mω
s
2
+m
2
ω
s
2
H
2
. Let
€
J
o
=εmH
2

€
λ =
T ± T
2
−4m
4
H
4
ε(ε +1)ω
s
2
ω
r
2
2εm
2
H
2
(58)
where
€
m
2
H
2
(ε +1)ω
r
2
+εm
2
H
2
ω
s
2
+m
2
ω
s
2
H
2
and the
€
m
2
H
2
terms cancel out, giving
€
λ =
(ε +1)(ω
r
2
+ω
s
2
) ± (ε +1)
2
(ω
r
2
+ω
s
2
)
2
−4ε(ε +1)ω
s
2
ω
r
2
2ε

(59)
In some analyses, the rotational inertia of the foundation is ignored. For example,
Todorovska and Al Rjoub (2006) assume the fundamental frequency of the coupled
system is related to the rocking and fixed base frequencies, by
€
ω
−2
=ω
s
−2
+ω
r
−2
. To verify
this, the limit of
€
(ε +1) as ε tends to zero can be considered. As
€
ε→0(i.e., massless
foundation), the right-side tends to infinity for the “+” solution and to for “−“ solution.
Since the first mode is of interest here, only the “−” solution needs to be considered.
Using L’Hôpital’s rule, the limit, as approaches zero is
€
λ =lim
ε→0
1
2
(ω
r
2
+ω
s
2
)−
2(ε +1)(ω
r
2
+ω
s
2
)
2
−4(2ε +1)ω
s
2
ω
r
2
2 (ε +1)
2
(ω
r
2
+ω
s
2
)
2
−4ε(ε +1)ω
s
2
ω
r
2








(60)

€
λ =
1
2
(ω
r
2
+ω
s
2
)− (ω
r
2
+ω
s
2
)−
2ω
s
2
ω
r
2
(ω
r
2
+ω
s
2
)











 =
ω
s
2
ω
r
2
ω
r
2
+ω
s
2
(61)

90
Or, more simplified, can be written as:

€
λ
−1
=ω
−2
=ω
s
−2
+ω
r
−2
(62)
Thus, the fundamental frequency ω of the coupled soil-structure system with a massless
foundation, which is a combined rocking and structural bending mode, can be obtained in
terms of the fixed-base bending frequency of the structure

and the rocking frequency

of a rigid structure and foundation on the soil. This equation also implies that the
equivalent fundamental frequency of the soil-structure system is always smaller than
that of the fixed-base frequency of the structure . Nevertheless, for the modeling of the
SFSI test structure, the mass moment of inertia of the foundation is considered (i.e., ).
For the SFSI test structure , and
€
m = 0.8m
f
; thus
€
ε≅0.11.
Since the dynamic stiffness of the foundation for the rocking motion includes frequency-
dependent term, cannot be solved by a straight hand calculation; instead, it requires a
numerical iterative solution. By utilizing a program in MATLAB, a symbolic formulation
is created. Then, by substituting the parameters of the SFSI test structure problem, the
characteristic equation can be solved for .
Further, to perform a parametric study, it is convenient to introduce a set of
dimensionless parameters as follows that relate the properties of the structure to itself and
to the soil:
!
B =H
!
B =8D

91
€
s = normalized structure frequency =
€
ω
s
H c
S

(63)
€
h = slenderness ratio =
€
H b (64)
€
m = mass ratio =
€
m ρb
3

(65)
The ratio of the natural frequency of the fundamental vibration mode of the coupled
system to that of the fixed-base structure (i.e., ) is called the SFSI stiffness factor,
which, depending on the extent of the SFSI effect, would vary between zero and one.
Note that, due to complexity of the (59) and its dependence on several soil-structure
parameters, the SFSI stiffness factor is very crucial for SFSI analysis, yet is not easily
obtained.

Parametric Study
This modeling approach is capable of estimating the SFSI effect on the rocking motion of
any soil-structure system that can be modeled as described in the previous section (e.g.,
water towers, telecommunication towers, etc.). In particular, it is employed for
characterizing the effect of the soil saturation on the identified rocking mode frequency
of the SFSI test structure and of the small-scale prototype. To better understand and
explain the SFSI rocking frequency variation of both SFSI systems, a parametric study is

92
performed. Based on the properties of the SFSI test structure given in Table 5 and the soil
characteristics at the site, given in Table 6 (discussed in Chapter 2), the dimensionless
parameters are evaluated; (normalized structure frequency) = 2.68,

=2 and

=1.25
for dry soil or
€
m =1.05 for saturated soil.

Table 5: Properties of the SFSI test structure.
SFSI test structure Properties
H [m] m [kg] b [m] m
f
[kg]
4 16000 2 20000

Table 6: Saturated vs. Dry characteristics of the soil at the site.
Soil Properties

ρ
€
[kg/m
3
]

€
[m/s]
€
[m/s]

Dry 1600 300 150 0.33
SFSI Site
Saturated 1900 1600 150 0.50

The fundamental frequency of a soil-foundation-structure system, relative to the fixed
base frequency, is illustrated in Figure 40 as function of normalized structure frequency

93
for both dry and saturated soil. The specific normalized structure frequency
€
s = 2.68 of
the NEES SFSI test structure is indicated with an arrow on Figure 40.

Figure 40: The rocking frequency for a SFSI system ( =2, =1.25 (1.05) and Poissonʼs
ratio=0.33 (0.5) for dry (saturated) soil. (Normalized structure frequency = 2.68).

The SFSI test structure has parameters and solution as shown in Table 7, which causes
different SFSI effects for the dry and saturated cases. The first bending mode frequency
of the fixed-base SFSI test structure is about 16 Hz — computed with the finite element
!"#$%&'()*+,-#./-.#)+0#)1.)2/3+
4546+,782),,+0%/-"#+

94
analysis described in Chapter 2. Thus, the model here predicts that the first mode of
vibration for the SFSI system (rocking + bending) should be 8.9 Hz, which should
increase to about 10 Hz upon the full saturation of the soil. The SFSI stiffness factor for
the dry case is predicted to be about 0.56, as opposed to 0.63 for the saturated case. The
results of the numerical solution for the dry and saturated cases of the SFSI test structure
are tabulated in Table 7. According to the results of the modeling, it can be concluded
that the rocking mode frequency of the SFSI test structure, from a dry soil to fully
saturated soil, is predicted to increase by about 10%, which is in contradiction with the
trend of identified rocking frequencies variation of the SFSI test structure as described in
Chapter 3.

Table 7: Results of the rocking motion estimation of the SFSI test structure.

€
f
fixed−base
[Hz]
€
ω
s
[s
−1
]
€
ω [s
−1
]

€
f
SFSI
[Hz]
Dry 16 2.68 2 1.25 100.5 56.10 0.56 8.93
Saturated 16 2.68 2 1.05 100.5 63.31 0.63 10.08

As illustrated in Figure 40, it is obvious that relative soil-structure stiffness has a very
important role in the effect of soil-structure interaction. With increase of , the effect of
the soil (in lowering the rocking stiffness of the system) also increases. Also, it is
important to remember that those predicted modeling results are highly dependent upon

95
the other presumed characteristics of the soil relative to those of structure. For instance,
as illustrated in Figure 41, for a SFSI system with wider foundation, say twice as much as
that of the SFSI test structure (i.e., B = 8m), the predicted SFSI stiffness factor — as a
function of normalized structure frequency — would be of different trend. That is, the
SFSI stiffness factor for a saturated soil case starts to be lower than that of the dry case
for normalized structure frequency greater than 3.

Figure 41: The rocking frequency for a SFSI system (
€
h =1,
€
m = 0.16 (0.13) and Poissonʼs
ratio=0.33 (0.5) for dry (saturated) soil.

!"#$%&'()*+,-#./-.#)+0#)1.)2/3+
4546+,782),,+0%/-"#+

96
It is also believed that the observation and modeling reported on the Millikan Library
published by Todorovska and Al Rjoub (2006) could be similarly justified. The
hypothesis postulated in their work is that the observed increases in frequency are due to
the water saturation of the soil. The Millikan library is a 9-story reinforced concrete
structure on an embedded foundation; however, the dynamic coupled SFSI system is the
simplest representation of a structure modeled as a SDOF structure with a surface
foundation that can be exploited for the modeling of the similar structural systems and
structures with shallow foundation. The speculation is that there might be other
environmental variables (e.g., soil moisture) that could affect on the soil stiffness and
consequently on the rocking mode of the SFSI systems, which are out of the scope of this
research.

Summary
The prediction of dynamic behavior of SFSI systems is very complicated; the presence of
the soil and its interaction with the structure are the main contributors to this complexity.
In order to properly model the soil’s behavior, various material and environmental
parameters need to be taken into account.
In this current study, Wolf's Cone Model was utilized to explain the effect of soil
structure interaction and saturation of the soil on the observed variability in the rocking

97
frequency of the SFSI test structure. Further, a model representing the coupled SFSI
system was developed. The saturated soil has been modeled with higher P-wave velocity
and, consequently, higher Poisson’s ratio in the soil model. Further, by introducing the
empirical concept of the trapped mass under the foundation (moves in-phase with the
foundation), the rocking frequency of SFSI systems as a function of soil saturation was
parametrically studied. It was shown that the shift (increase or decrease) of the rocking
frequencies of SFSI systems were strongly dependent on the characteristics of structure
relative to the soil under its foundation. In addition, the sensitivity analyses (by changing
the input parameters value) were carried out to study the sensitivity of some of input
parameters. The width of the foundation, for instance, was shown to have significant
effect on the rocking frequency of a SFSI system on the saturated soil.
Unfortunately, this model does not predict the observed decrease in the SFSI test
structure’s fundamental rocking frequency as the water table increases. The effects of
other environmental parameters (e.g., moisture in the soil, etc.) or soil behavior — such
as cohesion or expansion — are speculated to be significant enough that they should be
investigated further for this particular case. Suggested investigations might include soil
sampling and laboratory testing for cohesion and expansion, better soil moisture
measurements, and localized in-situ soil property measurements underneath the structure.
Future research attempting to model the observed behavior should perhaps look at a more
complete physics-based approach to this particular soil.

98
Chapter 5: Effect of Water Table Variation on the Rocking
Frequency of a SFSI system: Small-Scale Experiment
In order to characterize and reproduce the observed variation in structure’s identified
rocking frequency and its correlation with the ground water-table under the foundation, a
small-scale laboratory-size experiment was designed. Since the SFSI test structure might
not experience a full range of different water-table levels during a reasonable monitoring
period, the key advantage of a scaled model in the laboratory is that the system
identification of the prototype could be performed under certain artificially created and
controlled water table conditions. The main challenge, however, is to ensure that the
prototype has dynamic properties similar to the original SFSI test structure for the
intended testing purposes while still easy to set up for various configurations for studying
different aspects of interest. The most important step in designing the experiment was to
determine an appropriate scale factor for the specific scope of experiment (e.g., rocking
mode frequency and relative stiffness with respect to the soil).

Testing Procedure
The main intention here is to identify the modal properties of a scaled model while the
water level is changing in a controlled fashion. The scaled prototype must provide a soil-

99
foundation-structure system with appropriate laboratory-size layout. The layout of the
experiment includes a simple single-degree-of-freedom (SDOF) fixed-base structure with
concrete foundation sitting on top of a sandy/silty soil as illustrated in Figure 42. The
water table and saturation of the soil are controlled by adding water through the funnel.
The water level in the soil is measured by simply reading the water level in the
transparent tube installed at the bottom of the drum.
The response of the system can be recorded for identifying the rocking mode frequency.
The impulse response of the stick model, created by the hammer test excitation, is
recorded by an accelerometer on top of the structure while the water-level under the
foundation is gradually changed. Indeed, as the water is added gradually through the
funnel, it was possible to control the water-level to any desired level for performing a
system identification. In contrast with a real-world experiment, water can be easily added
all the way up to the ground level.

100

Figure 42: 3D rendering of the conceptual layout of the scaled prototype.

To make sure that the soil, after full saturation, is readily reusable for more testing, a
small drainage pipe was put in place at the bottom of the drum to provide water drainage.
Note that full drainage of the water might not return the soil back to its normal dry
condition; in fact, damp soil has different dynamic characteristics compared to the dry
soil, the effect of which will be discussed later in this chapter.

Hypothesis
The hypothesis of this experiment is that the identified first frequency (rocking mode) of
the small scale model would be changed due to the variation of the water table under the

101
foundation, with the same trend as observed for the SFSI test structure. Based on the
observations discussed in Chapter 3, it is speculated that the identified rocking frequency
of the simplified experimental structure, will change as the water level varies under the
foundation. The change trend is expected to be in negative correlation with the identified
frequency, meaning that when the water table goes down the identified frequency would
increase (Figure 43).

Figure 43: Schematic hypothesis in illustration: Water-level vs. Rocking Freq.

Test Specifications and Design
Due to the presence of the soil-foundation-structure interaction, it is expected that the
small scale prototype model will respond with a combination of the rocking of the
foundation as well as the bending of the structure (Figure 44).

102

Figure 44: Small-scale stick model (2DOF) of the SFSI test structure.

In addition to the shape and type of the foundation, the stiffness of the soil relative to the
structure is the dominating factor that governs the soil-structure interaction effect. Hence,
to design the foundation of the prototype model, the properties of the soil relative to the
SFSI test structure should be replicated in the small scale experiment. That is, about half
of the rocking flexibility of the soil-structure system is to be provided by the soil and the
other half by the structure through bending.
Since the small-scale prototype is considerably smaller than the SFSI test structure, some
modifications on the test configuration as well as on the instrumentations is inevitable.
Finding a proper scale factor for the prototype model is of great importance; it will affect
the natural frequency of the model and needs to be addressed carefully. For instance, as
stated by Powrie (2004), if the model is scaled with linear dimensions N (i.e., full size

103
model length is N times larger than the small-scale length), the frequency of the small
scale prototype would be larger by a factor of N. For measuring the dynamic response of
such systems properly, the sensitivity of the instruments and potential sampling rate
limitations of data acquisition (DAQ) systems must be known prior to the design of the
experiment.
The optimal value of the scale factor, depending on the available instruments and DAQ
system as well as experiment setup, is obtained after some heuristic iteration. For
instance, the data acquisition system might not be capable of recording data with a very
high sampling rate; if the sampling rate is not more than twice the natural frequency,
aliasing will distort the data. Aliasing is a phenomenon that occurs whenever a signal has
frequency content above Nyquist frequency of the sampling.

Figure 45: Schematic constraints for finding an optimal scale factor, illustrates the trade-
off between higher vs. lower value of N.

104
As illustrated in Figure 45, practical laboratory limitations must be considered in the
dimensions of the experiment. For example, to ensure that the possible disturbance
induced by the boundary conditions on the rocking mode frequency is negligible, the
scaling factor needs to be big enough to ensure that enough clearance from the edge of
the space that contains the soil.
Another concern for the context of current study is to ensure that, compared to the
original model, the same level of soil-structure-interaction exists. Thus, the relative soil-
structure properties (e.g., mass and slenderness ratio) for the small scale prototype model
should be similar to the NEES SFSI structure. It is convenient to introduce a set of
dimensionless parameters as follows that relate the properties of the structure to those of
the soil: Let the slenderness ratio =
€
H /b

and mass ratio
€
m =
€
m ρb
3
, where H, m, ρ and
b are the height of the structure, the top mass, the density of the soil and half of the width
of the foundation, respectively. Based on the dimension of the original SFSI test
structure, regardless of the scale factor, the slenderness ratio and the mass ratio of the
prototype should be 2 and 1.25, respectively. = 2 implies that the height of the
structure should be about equal to the width of the foundation. Given that the diameter of
the 55 gallon drum that will contain the soil specimen is around 60 cm, to have enough
clearance, the width of the foundation should not exceed 30 cm.

105
With all these practical and technical constraints, particularly the foundation dimension
and the DAQ sampling rate, the scale factor N = 14 was chosen and used to compute the
foundation dimension, the height of the structure and the top mass. A square concrete
foundation (28 cm × 28 cm × 3.5 cm) reinforced by a layer of a steel mesh at the bottom,
was poured (Figure 46). The mesh was a stainless steel wire mesh (25 cm × 25 cm) with
10 mesh/inch and wires 0.5 mm in diameter. As illustrated in Figure 46, a steel pipe,
representing the columns of the test structure, was screwed into a steel flange and fully
embedded within the concrete to create a fixed-base connection at the bottom. Knowing
the equivalent area moment of inertia of the four columns of the SFSI test structure (i.e.,
€
I
eq
≅ 3.8e5
€
cm
4
) and scaling factor N = 14, the area moment of inertia of the prototype
model needs to be around 10
€
cm
4
. Off-the-shelf steel pipes are usually found with
threads on both ends with various length and various standard diameters. The closest size
matching the design (to provide equivalent bending stiffness), was the 12 in (30.45 cm)
long pipe with 1 inch internal diameter. Some shorter pipes (same diameter) were also
procured to allow for testing with other columns length.

106

Figure 46: Picture of the poured concrete and the steel pipe to represent a SDOF system

To contain the soil, a 55-gal drum was filled two-thirds with sand so that it would provide
sufficient height (h ≈ 60 cm) of soil which is almost twice the width of the foundation of
the scaled stick model to make sure enough clearance from the bottom of the drum has
been provided. The water-table level in the soil will be manually controlled and measured
via a PVC pipe and a flexible transparent tube, respectively. Figure 47 illustrates the
experiment layout. The top mass, analogous to the top slab of the SFSI test structure,
must be firmly fixed to the pipe so that there would be no noise due to the vibration of the
mass itself. Further, the top mass must provide a flat surface allowing a firm attachment
of the accelerometer for reading in any desired direction. Thus, an 8 lb (3.6 kg) piece of
metal (trailer hitch) was attached on top of the steel flange as depicted in Figure 47.

107

Figure 47: Pictures of the test setup and water-table control system: (a1) PVC pipe
through which water can be directed inside the soil; (a2) A flexible transparent tube for
water-level measurement purposes; (a3)Drainage system to let the water out. (b) small
scale model sitting on a rigid foundation with a mass on top.

Experimental System Identification (Impulse Response)
In order to identify the rocking/bending frequency, the impulse response of the small
scale prototype model can be measured and the frequency of the system can be estimated
in either frequency or time domain. Since it is not possible in practice to create a perfect
unit-impulse excitation, it can be approximated with a pulse of sufficiently short duration
relative to the impulse response that excites the desired mode(s) of interest. The impulse
excitation of small and medium size structures usually can be performed by a hammer
test (swift hammer blow).

108
For experimental impulse excitation, depending on the size and configuration of the
structure, a proper hammer (weight, type, etc.) must be selected. Often, by looking at the
(time domain) impulse response induced by a given hammer, a suitable hammer, that
could produce reasonably neat and clean signals for a given mode of vibration, would be
selected.

Figure 48: Illustration of the details of the hammer test configuration, including the sensor
which reads the acceleration normal to the YZ plane shown above

The experimental system identification of the small-scale prototype was carried out by
measuring its impulse response (time domain) for two configurations: fixed base and
sitting on the soil (presence of the soil-structure-interaction). For measuring the impulse
response, an accelerometer was attached on the top of the trailer hitch (sensing normal to
the YZ plane) as shown in Figure 48. The sensor was made by the Vellman Oscillator
Company, model # APS 230, with a sensitivity of 0.1 Volt/g.

109
After a number of impulse excitations tests and measurements, the apparent rocking
frequency of the scaled model for the fixed-based and on the dry-sand are identified as 50
Hz and 30 Hz respectively. Thus, the presence of soil-foundation-structure-interaction
has reduced the fundamental frequency as much as 40%; that is, the SFSI stiffness factor
is = 0.6 for the dry soil case.

Finite Element Modeling of the Prototype SFSI System
To better understand and study the small-scale model (Figure 47, right), a solid finite
element model of the soil-foundation-structure system was developed (Figure 49A). For
performing a series of frequency analyses, a linear (small-strain) FEM was modeled and
analyzed with he CATIA and ELFINI programs, respectively. Both programs are
products of Dassault Systemes Company (http://www.3ds.com).
The analysis of soil-foundation interaction, especially in the case of embedded
foundation, is very complicated and requires careful modeling of the interface between
the foundation and the soil. Thus, a complete real-world soil-foundation-structure system
usually would be partitioned into two substructures (i.e., the soil-foundation and the
structure) to account for the excavated site vs. free field. The introduced scaled model
however, is a fixed-based structure on a surface foundation; therefore, the interface
between the foundation and the soil was simply modeled as a rigid connection between

110
the two media which are meshed by linear 4-node tetrahedral finite elements. To model
the boundary condition of the soil, since the soil was contained inside the drum, the
degrees of freedom on the outer periphery of the cylindrical-shape meshed solid
(representing the soil) were constrained to have no outward radial motion while free for
all other degrees of freedom.
The properties of the steel pipe with the 8 lb mass on top and the concrete (foundation)
were assigned (Compressive strength of the concrete: 30 MPa, Density : 2300
€
kg/m
3
,
Poisson's ratio : 0.2) through the standard library of existing materials offered by the
software. As for the soil, the physical properties of sand, such as shear modulus, are
obtained for the density ρ = 1600
€
kg/m
3
, shear wave velocity at the site, = 150 m/s,
and Poisson’s ratio ν = 0.33.
Utilizing the Lanczos eigensolution technique, a frequency analysis was carried out on
the model; the first 1
st
and 2
nd
modes of the vibration (bending plus rocking motion in two
perpendicular directions), for the fixed-base and the SFSI case, were computed to be 50
Hz and 30 Hz, respectively, which were in agreement with the experimental
identification. The result of the frequency analysis and the Von Mises stresses associated
with the 1
st
mode of vibration (Figure 49 B,C) demonstrate that the bending of the pipe
along with the rocking of the soil-foundation system contributes to the 1
st
natural
frequency of the SFSI system.

111

Figure 49: Finite Element Analysis illustration : A) The meshed model, B) Von Mises
stress of the 1st bending/rocking mode , C) 1st bending/rocking mode with adjusted color
to show the rocking/bending phenomena

The fixed-base bending frequency of the steel pipe was identified, both experimentally
and by FEM frequency analysis, to be around 50 Hz. From beam theory, however, the
lateral stiffness of a (fixed-based) steel pipe, with area moment of inertia about 10
€
cm
4
with known Young’s modulus (E=210 GPa), and length l = 28 cm, is computed from
. and with an 8lb mass on top, the bending frequency would be expected to be
about 60 Hz, which is around 20% higher then the FEM fixed-base result. Since the pipe
that was used in the experiment had threads at both ends, which can be seen on the top of

112
the pipe in Figure 46, it was speculated that the difference between the identified first
mode frequency of the fixed-based and the theoretical expected frequency might be due
to reduction of the wall thickness of the pipe where the threads are located. To validate
this speculation, two finite element models of the pipe were created. The two models are:
a) steel pipe with threads at both ends (i.e., an effective thickness of 0.12 cm over the two
top and bottom 2 cm at each end) shown in Figure 51-left, and b) steel pipe with no
threads (0.24 cm effective thickness) and fixed at the bottom (Figure 51-right). Similar
frequency analyses of these two cases show that thinner cross-section at the bottom of the
pipe can cause different rocking frequency of the fixed-base cases.

Figure 50: Stick model of a fixed-base SDOF model; representing the steel pipe (outside
diameter D = 2.67 cm and wall thickness t = 0.24 cm) used in the experiment.

113

Figure 51: Frequency analysis of the pipe for two cases: Threaded pipe has bending
frequency of 50 Hz (Left), compared to the pipe with no threads with 60 Hz.

Boundary Condition of the Prototype SFSI System
For a real-world structure, the soil horizon is continuous; a physical model must endeavor
to provide a lateral boundary as far away as possible that the free field condition is
simulated with reasonable accuracy. In the present experiment, the wall of the drum is a
physical boundary, and must provide enough clearance to minimize the distortion
induced by the boundary on the soil stress field, the soil strain field and, most
importantly, the rocking frequency of the SFSI model. The Von Mises stress distribution

114
inside the soil corresponding to the rocking motion of the SFSI system is shown in Figure
52.

Figure 52:Stress distribution for the soil-foundation-structure model; result from the Finite
Element Analysis (color represents the stress levels, adjusted so that the stress inside
the soil stands out).

To make sure that enough clearance from the edge of the drum has been provided (i.e., no
impact on the rocking mode frequency of the prototype), a frequency analysis of the
finite element model was performed with varying drum radius. The resulting rocking
frequency is shown in Figure 53 as a function of drum radius. The effect of the edge of
the drum on the rocking mode starts to fade away for a drum radius larger than 250 mm.
Thus, the boundary condition in this experiment (260 mm radius) causes negligible error
in the estimation of the roc.

115

Figure 53: The edge effect analysis of the rocking mode of the prototype model; the
estimated frequency by the FEM vs. the drumʼs Radius.

Water-level Variation Effect on the Prototype SFSI System
The main objective of this experiment is to verify that the observation made on the
variability in identified rocking frequency of the SFSI test structure due to change in the
ground water-level could be reproduced in a small-scale prototype in a controlled
laboratory condition (i.e., by raising the water-level under the foundation). The
experiment was expected to confirm that the identified rocking frequency for the
saturated soil would slightly drop compared to the dry case.

116
The water-level under the foundation is manually increased by adding water via a funnel
inserted deep into the soil as illustrated in Figure 42. The water-table level is measured by
the transparent tube as illustrated in Figure 54, and is adjusted to a certain depth either by
adjusting the input water or by controlling the output via the drainage valve. Water-level
distance from the foundation is marked on the drum’s wall (Figure 54). A series of
experimental impulse response (hammer) tests were carried out to identify the rocking
frequency of the soil-structure system at certain desired water levels.
To facilitate comparison of dynamic characteristics for various structure scales, it is
convenient to introduce a dimensionless water table depth (i.e., η=h/B) where h is water-
level distance under the foundation and B is the width of the foundation. The water-table
depth under the original SFSI test structure, during the monitoring period fluctuated from
3 to 4 feet under the foundation. Since the foundation is a square shape of 4 meters (13 ft)
in width; therefore, the normalized water-level depth was around η = 0.3. The small-scale
prototype sits on a foundation of 0.28 meter width. The experimental system
identification was performed for various water table depths, much deeper all the way up
to grade level (i.e., fully saturated soil).

117

Figure 54: Illustration of the details of the water-level measurement and the drainage
valve.

Starting from a totally dry soil three impulse response experiments (hammer test) are
performed at each desired level of water in the soil. In Figure 55 and Figure 56, the result
of the averaged identified rocking frequency and the normalized water depth for the
scaled model tests for η< 0.45 are graphed. The results are comparable to the observed
behavior of the SFSI test structure, with shallower water table resulting in lower
identified rocking frequency. To determine the effects of deepening water table level,

118
several experimental system identifications were performed at several water-levels after
draining some water from the drainage valve. The identified frequencies were observed
to be of similar trend, (deeper water level increased rocking frequency), but when water
depth η grew larger than about 0.20, the rocking frequency were larger while draining
than while filling. As Tayabji et al. (2000) suggest the change in moisture can cause
changes in soil stiffness properties, here it is likely that the significant moisture caused
this frequency increase (higher damping was also observed).

Figure 55: The trend of the identified rocking mode frequency variation in correlation with
the water-table fluctuation (fixed-base frequency = 50 Hz).

30.0
29.9
29.7
29.1
28.8
28.4
27.5
28.3
30.0
31.0
27.0
27.5
28.0
28.5
29.0
29.5
30.0
30.5
31.0
31.5
32.0 0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
1 2 3 4 5 6 7 8 9 10
Identified Frequency [Hz]
Normalized water-table level (h/B)
Water-table level
Identified Freq.

119

Figure 56: The Identified rocking frequency variation in correlation with the normalized
water level fluctuation; water level is raised and then drained as shown by the arrow.

Summary
In order to characterize the water table effects on the dynamic properties of the SFSI test
structure and to reproduce the observed variation in structure’s identified rocking
frequency and its correlation with the ground water table under the foundation, a
laboratory-size model was designed and constructed. The results from tests on this small
scale model confirm the trends seen in the large-scale SFSI test structure. The major
technical challenge that was encountered during the experiment — which needs to be
investigated in future related work — was the behavior of the soil-structure interaction
due to presence of moisture in the soil.
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120
Chapter 6: Pattern Recognition and Regression Analysis
Applied to the SFSI Test Structure Data Set
Introduction
It is commonly known that the Structural Health Monitoring (SHM) process requires the
extraction of a number of damage-sensitive feature(s) from measurement of dynamic
response of a system over time. Therefore, it is recognized that SHM and damage
detection are, in fact, applications of pattern recognition that are focused primarily on the
identification of damage sensitive features.

Figure 57: Proposed conceptual schema for the pattern recognition process upon the
environmental effects on structural dynamic properties for SHM purposes.

121
As conceptually illustrated in Figure 57, the main objective of classifying a damaged
structure is to ascertain, based on measured dynamic characteristics, if damage is present
or not. After defining the sensitive features and training the system based on a given
existing data set, the equation of the classifier — often with certain margin — must be
mathematically determined. Then the trained system can classify that a new data set
would belong to a damaged or undamaged class. Even though the implementation of
statistical pattern recognition procedures on damage-sensitive features is not widely
practiced (Farrar et al., 1999), the development of an automated health monitoring
system often engages some statistical approaches. To statistically identify and quantify
sources of feature variability for each classification problem, intensive research with
sufficient samples is required. The type and location of the sensors and other hardwares
(e.g., data acquisition/transmittal/storage) need to be determined as well.

Data Cleansing for Robust Pattern Recognition Process
In general, all sources of variability cannot be extracted out of the pattern recognition
problem. Usually to be able to quantify such uncertainties, proper measurements and
grounding are necessary. Obviously the data cleansing process, depending on the nature
of each application, requires adequate experience and pertinent knowledge.

122
For structural monitoring purposes an important question would be as to how frequently
the data is to be collected in order to train a robust pattern recognition system? Since the
environmental/operational effects are widely-known as sources of noise/distortion in
monitored data, it is necessary to collect data almost continuously for relatively long time
intervals to be able to cleanse the data accordingly. One of the most common procedures
for cleansing data is to normalize the measured responses by the
operational/environmental inputs. Farrar et al. (1999) believe that damage produces
changes in the feature distribution with a correlated trend produced by environmental
variability. Worden et al. (2002) recommend that the normalization process should also
include some measure of the environmental parameters. Thus, several features need to be
identified and assembled into feature vectors; however, usually a low dimensional feature
vector is more desirable, and sometimes a combination of two or more features would be
assembled into one feature vector.

Novelty Detection for Structural Damage Detection
It is important to be reminded that the main well-known disadvantage of the pattern
recognition approach for structural damage detection purposes is that, data from both
damaged and undamaged systems might not be available. To address this issue, one of
the unsupervised learning techniques (i.e., the novelty detection) has been discussed and

123
employed in this work. The novelty detection which is a specific (2-class) unsupervised
learning is well recognized as the fundamental requirement of a good classification when
the test data contains information about objects that were not known at the time of
training.
In the realm of the Novelty Detection, there exist several approaches among which the
statistical models have shown very promising results in practice. These models
implement the algorithms that operate on the damage-sensitive features to detect
damage(s). During training the system, if enough samples for each feature are not
collected, the possibility of false indications of damage increases. The False indications
of damage may fall into two categories: 1) False negative: the damage exists but cannot
be detected. 2) False positive: the damage doesn’t exist, though the classifier would
indicate the existence of damage. Obviously, each false declaration would lead to
different applicative ramifications. While the false negative case implies that a damaged
structure has been missed to be detected, the latter case can be considered as a
conservative option; with potentially several socio-economical impacts.
The novelty detection approach provides an indication only about the presence of damage
in a system of interest; that is, the novelty detection is only a level 1 approach which
implies that just the existence of abnormality is supposed to be detected but still there are
many situations where this suffices, i.e. safety critical systems where any fault on the
system would require it to be taken out of service.

124
Methodology
In the technique that is presented in current work, the values of particular monitored
parameter(s) (e.g., temperature, etc.) during normal behavior of the system are used to
establish statistics for the variation of a given structural characteristic (e.g., identified
frequency). And subsequently, the variation of a given structural parameter can be
virtually reduced by inverse projection of the 1 dimension scattered data onto a 2 (or
higher) dimension space as illustrated in Figure 58.

Figure 58: Conceptual representation of a structural parameter variation in one-feature
space versus the same data with an additional environmental feature (e.g. Temperature).

Then, by discretization of the newly introduced monitoring feature (e.g., temperature)
into finite intervals (horizontal axis in 2D space of Figure 58), new subspaces are created.

125
As a result, a new subsequent test data would require to be compared merely with the
data of “normal condition” within its corresponding subspace (e.g., subspace in Figure
58), that has been monitored along with the structural feature(s).
This process which assist reducing the effect of environmental variation in the observed
data is considered as part of the larger spectrum of normalization as explained by
Worden et al. (2002). The idea is to create a novelty indicator which has been normalized
with respect to changes in the structure. In the other words, the statistical properties of the
structural variation can actually be expressed as a function of defined environmental
feature(s).
For the purpose of the structural damage detection, especially when the
soil/environmental effects are also taken into account, the problem would often involve
more than just one feature and thus lead to the multivariate analysis which is essential to
precisely define the so-called “normal condition”. The multivariate data set consisting of
s observations in n variables can be represented as s samples in n-dimensional space
which is more complex compared to a univariate statistics.
The Mahalanobis distance, for instance, can be utilized as an appropriate statistical
measure to facilitate a multivariate outlier analysis. Given the mean value and the
standard deviation , mathematically the threshold can be expressed as
€
µ ±ασ ; in which
would be an applicative factor that represent statistical confidence level upon which

126
the alarm level would be determined. Assuming a normal distribution for the data, and by
allowing for being 1 or 2 and etc., different confidence level, i.e., 68.2%, 95.4%, etc.
can be reflected respectively. The threshold level therefore, is a quantity its value at a
given time being dependent on the estimated mean and definite deviation away from the
mean point. This being said, the Mahalanobis distance notion can be used to detect and
declare a possible novelty situation. Since the computation associated with the eigenvalue
decomposition (Basis transformation) might be very complicated, a methodology has
been suggested in this work.
The gist of the proposed approach is to eliminate the eigenvalue decomposition step by
discretizing the dataset over finite interval with respect to a given random variable(s)
(e.g., ) which could create discretized subspace as illustrated in Figure 59.

Figure 59: Conceptual schema on the proposed Finite Eigen-space approximation model
on a 2-feature novelty detection problem.

127

Then, each subspace approximately can be represented by a finite eigen-space; as a
result, the Mahalanobis distance (and corresponding threshold) would be simply defined
just upon each sub-space and independent from the rest of the training data. This
approach would clearly have certain advantages when it comes to dealing with a
structural feature with variable standard deviation on each sub-space; for example due to
a non-linearity phenomenon in different mode-shapes. Consequently the standard
deviation would not require to be estimated over the whole range of the data and instead,
it would be counted for in the Mahalanobis distance definition of each approximated
eigen sub-space accordingly as shown in Figure 60.

Figure 60: A potential outlier to be detected in a dataset with variable standard deviation in
a 2-feature novelty detection problem.

128

For instance, if and are two random variables representing two predefined
features, then any data point (a potential outlier as shown in Figure 60) which falls into a
given subspace (e.g.
€
(X
1
)
k +3
), would be exclusively analyzed and its (Mahalanobis)
distance would be compared with the data representing the system’s “normal condition”
within that subspace, only.
With similar approach, when the environmental variability is present, the statistics of the
normal conditions, in a changing environment, simply can be expressed as functions of
the environmental parameters. In case of civil structures, however, the “normal
condition” due to environmental variability might be represented with constant standard
deviation; that could be also verified by observing the collected data from the SFSI Test
Structure.
Statistical Novelty Detection Model for SFSI Test Structure
In a sense, the novelty detection approach can be considered as a statistical outlier
problem. It implies that similar to a typical outlier analysis, after defining the “normal
condition”, the subsequent data is analyzed to see how significantly it departs from the
rest of population; the postulation is that the outliers are generated from an abnormal
(damaged) condition. Often by assuming a Gaussian distribution for the samples, a

129
decision boundary (threshold) value needs to be established as well. And the idea is that
only training data from the normal operating condition of the structure or system is used
to establish this diagnostics. Often the potential outlier can be tested based on deviation
statistics which is the distance from the estimated mean of the data set while normalized
with respect to the estimated standard deviation. Thus by determining a threshold, the
level of disagreement of a candidate outlier is essentially compared against certain
predefined criteria. That would allow the outlier to be judged as statistically likely or
unlikely to identify abnormal condition. Consequently, depending on the importance and
sensitivity of each structural system, an applicative statistical distance from the norm
requires to be characterized. Depending on each application, the potential outlier itself
may or may not be included (inclusive vs. exclusive) in the training data set. For damage
detection processes, however, it is not usually included. The threshold value depends
upon whether an inclusive or exclusive strategy has been utilized. For the SFSI test
structure, an exclusive approach has been proposed.
To develop a statistical pattern recognition model for the data collected from the SFSI
test structure, the statistical novelty detection approach is deployed. It is observed that the
identified modal properties of SFSI test structure have been subject to variation that is
usually due to changing environment. Therefore, the novelty detector must be able to
distinguish between a statistical fluctuation in the data and a real deviation from
normality, which would lead to including more features. Even though relatively large

130
feature vector is not desirable, yet the inclusion of environmental features along with the
structural features seems to be inevitable.
To compare new data only with reference data from the same environmental conditions,
two possible situations can be perceived: (a) the environment is uniquely characterized by
a group of measurable parameters (temperature, ground water-level, etc.); (b) due to
some limitations the environmental variations cannot be characterized. The current work
is an attempt to mainly address the former situation. The idea is that (during structural
monitoring of SFSI test structure) to build a set of reference models parameterized by the
environmental variables. The algorithm proposed in this work, is an outlier analysis and
outlines how it can be adapted to deal with soil and environmental variations. A case
study is carried out which implemented the introduced procedure on the monitored data
collected from the fully instrumented SFSI Test Structure over 18 months (for more
details see Chapter 2). The data included the output of the accelerometer under the top-
slab of the structure subject to ambient vibration (from which the rocking mode
frequency can be identified), measured ambient temperature and the ground water-level
under the foundation. The data is illustrated in three dimensions in Figure 61. The plots in
Figure 62 and Figure 63 are showing the identified rocking mode frequency versus
measured water-table and versus the ambient temperature, respectively.

131

Figure 61: Three dimensional representation of the SFSI data; identified rocking frequency
versus the ground water-level and the ambient temperature.

Figure 62: Identified rocking frequency versus the ground water-level under the SFSI
foundation.
40
50
60
70
80
2
2.5
3
3.5
4
4.5
5
6
6.5
7
7.5
8
8.5
9
9.5
10
10.5
Temp.[F]
Water!level [ft]
Freq. [Hz]
2 2.5 3 3.5 4 4.5 5
8
8.5
9
9.5
10
10.5
Water!level [ft]
Freq. [Hz]

132

Figure 63: Plot of identified rocking mode frequency of the SFSI Test Structure versus the
ambient temperature.

The collected environmental data from the SFSI Test Structure is parameterized by two
measurable variables (i.e., ambient temperature t and water-level under the foundation
w), in addition to the structural variable (identified rocking frequency) f.
For each sub-space confined within the intersection of the two environmental variables
and
€
w
j
(see Figure 64), while the environmental effects have been taken into account, the
statistical parameters for such a sub-space would be function of environmental variables
(i.e., t, w) and can be written as follows:

€
µ
T
i
W
j
= µ T
i
,W
j
( )

and

€
σ
T
i
W
j
=σ T
i
,W
j
( )
.
40 45 50 55 60 65 70 75 80
8
8.5
9
9.5
10
10.5
Temp.[F]
Freq. [Hz]

133

Figure 64: Conceptual representation of the

€
T
i
W
j
sub-space created by the
intersection of two finite environmental variables, and a new subsequent test data (solid
diamond).

Consequently, the test data,
€
x
ζ
= t
i
w
i
f
i
[ ]
T
, with measured temperature
€
t
i
, water-level
€
w
i
, and identified frequency
€
f
i
, can be analyzed upon the corresponding

€
T
i
W
j
eigen-
space with univariate mean and standard deviation (e.g.,

€
µ = µ
T
i
W
j
{ }
). That implies that

134
with a single structural variable, the Mahalanobis distance could be reduced to a
univariate case:

€
D
M(T
i
W
j
)
(x) =
f
i
− µ
T
i
W
j
σ
T
i
W
j
(66)
Thus, a new subsequent data, say the solid diamond in Figure 64 (identified frequency,
water-level and temperature are 8.6 Hz, 4.13 ft and 67° F, respectively), is tested merely
against the so-called “normal condition” within that specific region depicted in the plot.
As discussed above, depending on the distance (Mahalanobis) and the defined confidence
level (
€
ασ ), the novelty in the system can be detected.
In this example, the width of each sub-space has been uniformly, yet arbitrarily chosen.
The narrower the sub-spaces are, the more discretized spaces, but of course with less data
point would be created. Therefore, depending on the number of existing samples and
desired precision, different widths are selected. Herein, and for the

€
T
65~70
W
4~4.25

subspace can be estimated as follows:

€
µ
T
65~70
W
4~4.25
=9.52 Hz and

€
σ
T
65~70
W
4~4.25
=0.35 Hz.
Suppose that the alarm level (threshold) has been defined such that for the Mahalanobis
distance greater than, say 2, the abnormality warning or alarm will be set off.
Statistically, that means that for the test point more than 2

€
σ
T
65~70
W
4~4.25
away from the
mean (corresponding to approximately a 95% confidence level), a novelty in system

135
would be detected. The Mahalanobis distance of the test data (i.e., f = 8.6 Hz) can be
calculated as following:

€
D
M(T
65~70
W
4~4.25
)
(x) =
8.6−9.52
0.35
=2.63 (67)
In other words, the test data resides a distance 2.6σ from the sample mean within that
subspace. Thus, depending on the designated alarm or warning level, it can be declared as
a novelty in the structure.
The proposed procedure was also used to see if the second configuration in which all the
bracings were removed would represent a damaged case compared to the first
configuration. As a matter of fact, the SFSI Test Structure with no bracings is of
significantly lower rocking frequency and should be confidently detected as a novel
condition compared to the braced configuration.
A data point from the unbraced configuration was randomly selected which carries
information on the identified frequency, temperature and ground water-level at the site
collected in January 2007. As illustrated in Figure 65, the selected potential outlier
(shown as a solid diamond) has an identified frequency of 6 Hz, while the ambient
temperature and the water-level are logged as 48° F and 4.2 ft under the foundation,
respectively. Again, the environmental features (i.e., t and w) are divided into certain sub-
spaces within which the structural feature would be compared with the normal condition.

136
The and
€
w
j
sub-spaces corresponding to the testing data points are illustrated in Figure
65.

Figure 65: The novelty detection of the SFSI Test Structure with no bracings (solid
diamond) against the same structure with bracings.

Similarly the mean, the standard deviation and the Mahalanobis distance can be estimated
for the intersection of these sub-spaces as follows:

€
µ
T
45~50
W
4.0~4.5
=9.02

Hz
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137

€
σ
T
45~50
W
4.0~4.5
=0.2 Hz.

€
D
M(T
45~50
W
4.0~4.5
)
(x) =
6−9.02
0.2
=15.1
As expected, the testing data is significantly (15

€
σ
T
45~50
W
4.0~4.5
) away from the mean of the
normal condition in that sub-spaces; therefore, it would be declared as a novelty case for
the original SFSI Test Structure.

Data Cleansing of the SFSI Data Set
The primary statistical analysis on the collected data set in Chapter 3, showed significant
variability (i.e., 10%) in the identified rocking frequencies of the SFSI test structure. In
addition to the identified frequency of the test structure, the temperature and water table
level at the site from 6/17/05 through 9/4/05 were also collected. Then, it was shown
(Figure 22, Figure 29) that the variation of the identified frequencies and those
environmental parameters were correlated.
The data analysis by utilizing statistical approaches — compared to deterministic
methods — requires several validation and cleansing processes before being able to
provide any strong assertions. Therefore, to achieve a higher level of certainty upon the
quantitative correlation between the identified frequencies of the SFSI test structure and
the measured environmental parameters, more investigation is needed. First, to separate

138
the effects of the temperature and the water level on the frequency variation of the SFSI
test structure, herein some data cleansings in conjunction with the correlation analyses
are applied to the SFSI data set. Subsequently, to study the combined effects of
temperature and water table variation on the identified frequencies, a three dimensional
regression analysis is performed.
By examining the variability trend of the two environmental parameters in the data set,
one can easily notice that while temperature has a daily and seasonal fluctuation, the
water level changes only in a seasonal basis. That is said, the temperature effect on the
identified frequencies can be normalized and isolated from the water-level-variation
effect. To cleans the data from the temperature effect — assuming that the effect is linear
— the normalized identified frequencies with respect to an arbitrary temperature, say T =
55° F, is computed. As a result, a temperature-effect-free measure of correlation between
the identified rocking frequencies of the SFSI test structure and the depth of the water
level under the foundation is obtained.
To have a quantitative measure of the daily effect of the temperature, a linear curve is fit
to the data for those days that enough identified frequencies and measured temperatures
are available. For example, in Figure 66 a linear fit (and the residuals) to the scattered
plot of identified frequencies for a given day (i.e., 16 Oct. 2005) versus the measured
temperature is shown. The regression coefficient (0.19 Hz/ºF) indicates the slope of the
line resulted from the linear least square fitting to the data for that day.

139

Figure 66: Linear regression of identified frequencies dated 16 Oct. 2005 versus measured
temperatures on that day (top) and the residual results of the fit (bottom).

To obtain more precision, this process is repeated for several days and the histogram of
the estimated regression coefficients has been plotted in Figure 67. The estimated mean
and standard deviation for all these coefficients are 0.16 Hz/ºF and 0.02 Hz/ºF,
respectively. Consequently, the data can be normalized with respect to daily temperature
variation, by 95% (2σ) confidence interval as is shown in Figure 68. The equation of the
normalized data set can be written as

€
f
55°
= 0.16
Hz

F
[ ]
(±0.04). (t− 55

[F]) + 8[Hz] (68)
54 54.5 55
!0.4
!0.2
0
0.2
0.4
Residual
54 54.5 55
9
9.2
9.4
9.6
9.8
10
Freq. [Hz]
Temp. [F]

Freq = 0.19*Temp ! 0.61
16 Oct. 2005
linear

140

Figure 67: Histogram of regression coefficients of daily temperature-frequency analysis.

Figure 68: Linearly normalized frequencies with respect to the T= 55° F.
0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 0.21
0
5
10
15
20
25
Regression Coef. [Hz/°F]
Counts

Temperature!Frequency Regression Coefficient
35 40 45 50 55 60 65 70 75 80
5
6
7
8
9
10
11
12
Temp. [F]
Normalized Freq. [Hz]
!!""

141
Further, the normalized (temperature-effect-free) identified frequencies are plotted versus
the water level depth in Figure 69 (bottom) and is compared with the original data (top).
It is noticeable that the normalized frequencies have significantly decreased, while the
ground water level has raised (i.e., lower water level).

Figure 69: The comparison between the identified frequencies versus the water level;
before (top figure) and after normalization (bottom figure).

To better understand the correlation between these environmental parameters and the
identified rocking frequencies of the SFSI test structure, the data is divided into two sub-
1.5 2 2.5 3 3.5 4 4.5
8
8.5
9
9.5
10
10.5
11
Water!level [ft]
Freq. [Hz]
1.5 2 2.5 3 3.5 4 4.5
4
6
8
10
12
Water!level [ft]
Normalized Freq. [Hz]

142
categories; summer (i.e., May, June, July, August, September and October) vs. winter
(i.e., November, December, January, February, March and April). First, the correlation
coefficients between the temperature and the water level for the winter and the summer
data are computed as 0.8 and 0.04, respectively. That implies that the decoupling of the
temperature and the water level effects on the identified frequencies would be more
intricate for the summer data set. The high correlation between these two parameters can
be explained based on the fact that there was almost no precipitation at this site during
summer 2005. The normalized frequencies vs. the water level data for both summer and
winter are shown in Figure 70.

Figure 70: The normalized frequencies variation versus the water level fluctuation for the
winter (bottom left) and the summer (bottom right), respectively.
1.5 2 2.5 3 3.5 4 4.5
5
6
7
8
9
10
11
12
Water!level depth [ft]
Normalized Freq. [Hz]

1.5 ft < water!level depth < 4.5 ft
1.5 2 2.5 3 3.5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
10
Water!level depth [ft]
Normalized Freq. [Hz]

Summer Data Points
3.5 4 4.5
9
9.5
10
10.5
11
11.5
Water!level depth [ft]
Normalized Freq. [Hz]

Winter Data Points

143
It is also important to note that while the identified frequencies and the temperature are
pretty correlated (Correlation Coef. ≅ 0.3), overall the normalized frequencies and the
water level data are highly correlated (Correlation Coef. ≅ 0.8). The normalized
frequencies and the water level variation are plotted in Figure 71. It can be seen that as
the depth of the water level increases the normalized frequencies increase as well. In
Figure 72, the result of a linear regression and the residuals of the fit are plotted.

Figure 71: Comparison between the water level variation and the identified freq. of the
SFSI test structure in the top and bottom figure, respectively.

50 100 150 200 250 300
2.5
3
3.5
4
4.5
5
Selected Data Point
Water!level [ft]

50 100 150 200 250 300
7
8
9
10
11
Selected Data Point
Normalized Freq. [Hz]

Water level Variation
Frequency Variation

144

Figure 72: Linear regression result of a fit to the Normalized frequencies versus the water
level variation (top figure) and the residuals (bottom figure).

Further, to improve the regression result, a non-linear curve is fit to the normalized
frequencies data set. By utilizing MATLAB’s curve fitting toolbox, a power function
(e.g.,
€
f (x) = ax
b
+ε) for the prediction of the normalized frequencies is tried, where x
would represent the water level depth, a and b are the parameters to be estimated and ε is
the associated error. The result of the fit along with the 95% prediction bounds are plotted
in Figure 73. The a, b parameters of the fit are estimated as 5.23 and 0.42, respectively.
1.5 2 2.5 3 3.5 4 4.5
!2
!1.5
!1
!0.5
0
0.5
1
1.5
2
Residuals
1.5 2 2.5 3 3.5 4 4.5
4
5
6
7
8
9
10
11
12
Water!level depth [ft]
Normalized Freq. [Hz]

Freq. (normalized) = 2.4* Water!level + 0.61
Data set
linear

145
The goodness of the fit is computed as
€
r
2
≅0.7, which is very close to the result of the
linear fit.

Figure 73: Non-linear regression and 95% prediction bounds result of a fit to the
Normalized frequencies versus the water level.

Three Dimensional Regression Analysis
By fitting a linear plane to the available data of three variables (i.e., temperature, ground
water table and the rocking frequencies of the braced structure), the effect of
environmental variability in identified frequencies can be characterized.
1.5 2 2.5 3 3.5 4 4.5
3
4
5
6
7
8
9
10
11
12
13
Fit with 95% prediction bounds,Freq. [Hz]
Water!level [ft]

fit (power function)
95% prediction bounds
Normalized_freq vs. water_level

146
Utilizing the least-squares fit, which is the most common type of linear regression, the
best-fit plane’s coefficients are estimated; i.e., the constant
€
f
o

(frequency) and the
coefficients a and b (corresponding to temperature and water-level) for the following
equation are estimated:
€
f = f
o
+ at +bw (69)

where f, t and w are random variables corresponding to identified frequency, temperature
and water level, respectively. The formulation for computing the coefficients are as
follows:

€
a =
w
i
2
∑ ( )
t
i
f
i
∑ ( )
− t
i
w
i
∑ ( )
w
i
f
i
∑ ( )
t
i
2
∑ ( )
w
i
2
∑ ( )
− t
i
w
i
∑ ( )
2
(70)

€
b =
t
i
2
∑ ( )
w
i
f
i
∑ ( )
− t
i
w
i
∑ ( )
t
i
f
i
∑ ( )
t
i
2
∑ ( )
w
i
2
∑ ( )
− t
i
w
i
∑ ( )
2
(71)

€
f
o
= f − at − bw (72)
where
€
f , and are based on the 520 data points from the braced configuration, the
plane parameters
€
f
o
, a and b are 8.3979 Hz, 0.0079 Hz/°F and 0.1433 Hz/ft, respectively.
As a result, the plane that best fits to the collected data, for the braced SFSI test structure,
can be written as:
f = 8.3979 [Hz] + 0.0079

€
Hz

F
[ ]
t + 0.1433
€
Hz
ft
[ ]
w (73)
!
!
!
t
!
w

147
The best-fit plane (as a result of a linear regression), and the data are plotted on a three
dimensional axis in Figure 74. This simplified solution could assist in finding outliers
representing abnormal (damaged) condition for the SFSI test structure.

Figure 74: Three-dimensional demonstration of the temperature, water-level and identified
frequencies of the SFSI test structure, and the best-fit plane to the collected data
(estimated from multi-variat regression analysis).

In Figure 75, the dispersion of the collected data around the fit-plane is also shown. It is
noticed the data is heavily dispersed around the linear plane.

148

Figure 75: Three-dimensional demonstration of the temperature, water-level and identified
frequencies of the SFSI test structure; the dispersion of the data around the best-fit plane
has been illustrated.

Similarly, a three dimensional regression analysis is performed on the normalized
(temperature-effect-free) data versus the water level and the measured temperature data
points. The normalized data points — as expected — show less dispersion around the
best-fit plane (Figure 76).

149

Figure 76: Three-dimensional demonstration of the temperature, water-level and
normalized identified frequencies of the SFSI test structure, and the best-fit plane to the
collected data (estimated from multi-variat regression analysis).

Summary
As elaborated, the novelty detection approach could be shown as a good classification
technique when the training data does not contain information about the damaged
condition. The notion of the developing statistical models as a promising approach to
enhance the damage detection of the structural health monitor was also discussed.
0 10 20 30
40 50 60 70
80
0
1
2
3
4
5
6
7
8
9
10
11
12
Temp. [F]
Water!level [ft]
Temp. Normalized Freq. [Hz]

150
In addition, the environmental variations suggested to be extracted out by introducing
finite sub-spaces created over the environmental features and by discretization of each
feature (e.g., temperature) into finite intervals. Therefore, a new subsequent test data
would require to be compared merely with the data of “normal condition” within its
corresponding subspace with reduced variation.
Further, to cleans the data with respect to the environmental parameter(s), some
regression analyses were carried out. In fact, the data was normalized with respect to the
temperature effect, which has a daily variation. As a result, the normalized data set could
assist in better understating of the effect of the other environmental parameter (i.e., water
level under the foundation) on the variability of the identified frequencies.

151
Conclusion
The environment — temperature, rainfall, humidity, etc. — affects dynamic properties of
structures, which, in turn, impact the robustness of structural health monitoring
techniques that use global dynamic response measurements. In this study, the controlled
conditions of the NEES SFSI test structure at GVDSA were used and modeled to
quantify these environmental effects on the soil-foundation-structure system. Repeated
experimental modal analyses, coupled with monitoring of temperatures and ground water
level, has resulted in the following conclusions:
• Significant correlation between the identified structural properties and measured
environmental parameters (i.e., temperature and ground water-level under the
foundation) is present in this soil-foundation-structure system.
• Temperature effects on the measured modal frequencies of the structure are quite
significant. Depending on the configuration of the structure, daily temperature-
correlated variations are 3–10%.
• Saturation of the soil appears to have very complex effects on the dynamic
properties of the SFSI system. While the saturation effects are partially masked by
daily temperature-induced variability, the soil saturation is found to be on the
order of a few percent. It depends on several factors, including:
1. soil properties: type, stiffness, drained versus un-drained condition, etc.

152
2. foundation shape and type (i.e., surface versus embedded).
3. relative dynamic properties of the fixed-base structure and the soil-
structure system.
Further, a small-scale prototype model of the SFSI test structure was used to validate the
observed variation in the full-scale SFSI Test Structure’s identified fundamental
frequencies. The increase of the water-level in the dry soil showed a trend similar to that
observed in the SFSI test structure. The moisture in the soil seems to be affecting both
the fundamental rocking frequency and damping of the SFSI system.
Different methodologies for modeling of soil-structure interaction systems were
discussed, emphasizing that the intended use of each model needs to be specifically
defined so that a proper predictive model can be developed. To model the soil saturation
effect on the rocking frequency of a simple SDOF system representing the SFSI test
structure, it was shown that the apparent fundamental rocking frequency of a SFSI system
is a function of saturation level and soil properties and might increase or decrease
depending on the characteristics of the structure relative to the soil. The simplified cone
model applied in great detail in this research does not predict the observed decrease in the
SFSI test structure’s fundamental rocking frequency as the water table increases. The
effects of other environmental parameters (e.g., moisture in the soil, etc.) or soil behavior
— such as cohesion or expansion — are speculated to be significant enough that they
should be investigated further for this particular case. Suggested investigations might

153
include soil sampling and laboratory testing for cohesion and expansion, better soil
moisture measurements, and localized in-situ soil property measurements underneath the
structure. Future research attempting to model the observed behavior should perhaps look
at a more complete physics-based approach to this particular soil.
Most vibration-based damage detection approaches can be described by a pattern
recognition paradigm. A methodology for generalized detection of damage with
environmentally-controlled variability has been proposed based on idea of novelty
detection. Environmental variations can be extracted by introducing features (such as
temperature) and then, by discretization of the newly introduced monitoring feature into
finite intervals, new subspaces are created within which subsequent test data are
compared with data of “normal condition”. The notion of using novelty detection to
develop robust statistical models for damage detection was discussed. This discussion is
just a start; further research will be needed to apply this generalized technique to the SFSI
Test Structure and to other full-scale structures.
Based on this research, it can be concluded that studying the environmental variability of
identified vibration-based parameters and developing methodologies for cleansing data
are critical to establishing more robust health monitoring in real civil structures.

154
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Abstract (if available)

Abstract For more than thirty years, researchers have attempted to establish effective local and global methods for monitoring civil, aerospace and mechanical structures. The unpredictable nature of soil and the nonlinear behavior of civil structures, however, make monitoring rather complex. In fact, the combined soil-structure system can be influenced by environmental factors on daily to annual time scales. Identification of structural damage using vibration-based methodologies in the presence of such influences requires some data normalization to reduce uncertainties and variations introduced by environmental factors.

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Asset Metadata

Creator Asghari, Ali (author)

Core Title Characterization of environmental variability in identified dynamic properties of a soil-foundation-structure system

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Civil Engineering

Publication Date 11/03/2009

Defense Date 10/13/2009

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag Damage Detection,modal analysis,OAI-PMH Harvest,soil-structure interaction,Structural health monitoring,system identification

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Johnson, Erik A. (committee chair), Ghanem, Roger Georges (committee member), Masri Sami F. (committee member), Nigbor, Robert L. (committee member), Wellford, L. Carter (committee member)

Creator Email asghari@usc.edu,asghari007@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m2712

Unique identifier UC1342637

Identifier etd-Asghari-3361 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-272251 (legacy record id),usctheses-m2712 (legacy record id)

Legacy Identifier etd-Asghari-3361.pdf

Dmrecord 272251

Document Type Dissertation

Rights Asghari, Ali

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email cisadmin@lib.usc.edu