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Accepted for Publication in ASCE Journal of Structural Engineering
August 2017
1
Pre-test Nonlinear Finite Element Modeling and Response Simulation of Full-Scale Five-
Story Reinforced Concrete Building Tested on NEES-UCSD Shake Table
Hamed Ebrahimian1(+), Rodrigo Astroza2(+), Joel P. Conte3(*) , Tara C. Hutchinson4
1 Postdoctoral Scholar, Department of Mechanical and Civil Engineering, California Institute of
Technology, 1200 E. California Boulevard, Pasadena, CA 91125
2 Assistant Professor, Faculty of Engineering and Applied Sciences, University of Los Andes, Alvaro del
Portillo 12,455, Las Condes, Santiago, Chile
3 Professor, Department of Structural Engineering, University of California San Diego, 9500 Gilman
Drive, La Jolla, CA 92093-0085
4 Professor, Department of Structural Engineering, University of California San Diego, 9500 Gilman
Drive, La Jolla, CA 92093-0085
+ Former Ph.D. Candidate, Department of Structural Engineering, University of California San Diego
* Corresponding author, email: jpconte@ucsd.edu
Abstract
A full-scale five-story reinforced concrete building specimen, outfitted with a variety of
nonstructural components and systems (NCSs), was built and tested on the NEES (Network for
Earthquake Engineering Simulation) - UCSD (University of California, San Diego) large outdoor
shake table in the period March 2011 - June 2012. The building specimen was subjected to a
sequence of dynamic tests including scaled and unscaled earthquake motions. A detailed three-
dimensional nonlinear finite element (FE) model of the structure was developed and used for
pre-test response simulations to predict the seismic response of the test specimen and for
decision support in defining the seismic test protocol and selecting the instrumentation layout for
both the structure and NCSs. This paper introduces the building specimen and the shake table
test protocol and describes the techniques used for the nonlinear FE modeling and response
simulation. Utilized as blind prediction, the pre-test simulation results at different scales (global
structural level, and local member/section/fiber levels) are compared with their experimental
counterparts for seismic input (base excitation) of increasing intensity from serviceability to
design levels. The predictive capabilities of the employed FE modeling techniques are evaluated
Accepted for Publication in ASCE Journal of Structural Engineering
August 2017
2
and possible sources of discrepancies between the FE predictions and experimental
measurements are investigated and discussed.
Keywords: Building structure, Reinforced concrete, Nonlinear response simulation, Nonlinear
time history analysis, Finite element method, Shake table test, Full-scale specimen, Blind
prediction.
1. Introduction
Nonlinear Finite Element (FE) modeling and response simulation is becoming an important part
of modern seismic design and assessment procedures. Nonlinear FE simulation techniques are
expected to predict not only the global response of the structure, but also the local response and
failure modes at the component level of a structure, at an affordable computational cost. Yet,
despite remarkable progress made in the field of computational structural mechanics, nonlinear
FE modeling and response simulation of reinforced concrete (RC) structures remains a
challenging task, especially when approaching the collapse damage state, in both research and
engineering practice. The challenges are due to the inherent nonlinearity of the RC behavior
caused by complex phenomena such as cracking, crushing, stiffening and strain softening, steel-
concrete interaction (bond-slip), local buckling and fracture of reinforcing steel, connection or
splice failures, etc. As a result of this complex behavior, a large body of research has been
published on the experimental, theoretical, and numerical aspects of RC behavior, including the
development of material (steel and concrete) constitutive models with varying degree of
complexity and of FE modeling techniques ideally able to capture accurately and efficiently the
complicated mechanics of RC structural components and systems. Compromising between
computational feasibility and prediction fidelity, a variety of computational techniques are
Accepted for Publication in ASCE Journal of Structural Engineering
August 2017
3
proposed in the literature for nonlinear FE modeling and response simulation of RC structures
(e.g., see (FIB Bulletin 45, 2008) and references therein for a state-of-the-art review).
Experimental studies, although expensive especially for large/full-scale laboratory specimens,
are essential to calibrate and validate nonlinear FE structural modeling and analysis methods,
especially for dynamic seismic response analysis. Different experimental methods are used to
test structural components, subassemblies, and systems at large/full-scale under seismic loads.
The simplest method is perhaps the quasi-static testing method, in which predefined time
histories of displacements or forces are directly applied slowly (i.e., without dynamic effects) on
the structural specimen (e.g., (Foutch et al., 1987)). Since the loading is applied quasi-statically,
a number of dynamic features of structural behavior, such as dynamic interaction of structural
and/or nonstructural components and systems and various rate-dependent and energy dissipation
phenomena, beyond material hysteretic energy dissipation, are not properly captured through
quasi-static testing. Other testing approaches, such as pseudo-dynamic testing methods, also
suffer shortfalls in simulating the dynamic response behavior of structural sub-systems and
systems at large/full-scale for seismic loading (Shing et al., 1996). In spite of the significant
progress made in real-time dynamic hybrid testing over the last decade (e.g., (Shing, 2008),
(Saouma & Sivaselvan, 2008)), large or full-scale shake table testing remains the most accurate
method to investigate the actual behavior of structural systems under seismic loads. Due to
various limitations in terms of cost of experiments, specimen size, and shake table size and
capacity, shake table tests are usually conducted at reduced scales, which is an issue since some
design details, construction materials, and damage and failure mechanisms cannot be accurately
reproduced in reduced scale models (e.g., spacing of reinforcement in concrete structures, size of
aggregates in concrete, quality and properties of welds, and degree of plastic strain and damage
Accepted for Publication in ASCE Journal of Structural Engineering
August 2017
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localization). Thus, structural behavior at the component and sub-component levels and local
failure modes can often not be investigated through reduced-scale shake table tests. For RC
structures, reducing the testing scale significantly affects important phenomena such as bond-
slip, shear failure mechanisms, reinforcing bar anchorage failure, rebar buckling and fracture,
and damage localization. To date, only a limited number of large or full-scale shake table tests
have been conducted on RC or steel building specimens (e.g., (Matsumori et al., 2006), (Kasai et
al., 2007), (Yamada et al., 2008), (Panagiotou et al., 2011), (Dao et al., 2011), (Sato et al.,
2011)).
In the period March 2011 - June 2012, a landmark research project, called BNCS (building with
nonstructural components and systems), was completed at the University of California, San
Diego (UCSD), which consisted of testing a full-scale five-story RC building specimen on the
NEES (Network for Earthquake Engineering Simulation) - UCSD large outdoor shake table (
(Chen et al., 2016), (Pantoli et al., 2016), (Pantoli et al., 2016)). The building was outfitted with a
variety of nonstructural components and systems (NCSs), including a functioning passenger
elevator, metal stairs, a complete facade system, interior partition walls, ceiling systems, piping
systems, and various roof mounted equipment (air handling unit and cooling tower). Different
architectural occupancies including a home office, laboratory environment, computer server
room, intensive care unit (ICU), and surgery unit were assigned to the various levels of the
building. The main objectives of the research project were to study the dynamic performance of
the full-scale RC building specimen including its NCSs under seismic excitations, investigate the
complex interaction between the main structure and the NCSs, and contribute to the development
of performance-based seismic design methodologies for NCSs. The building was first tested in a
base-isolated configuration with the foundation resting on four elastomeric bearings, one at each
Accepted for Publication in ASCE Journal of Structural Engineering
August 2017
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corner. After testing the base-isolated building, the elastomeric bearings were removed, the
building foundation was anchored to the shake table platen and the building was tested under
fixed base configuration.
Pre-test modeling and simulation in the form of advanced nonlinear FE analyses were performed
using the as-built characteristics and specifications of the building specimen. The main goals of
the pre-test FE simulations were to: (1) predict the experimental response of the building
specimen to the various seismic inputs to be applied, (2) estimate the seismic demands for the
NCSs, (3) inform the process of defining the seismic test protocol, and (4) provide decision
support in the selection of the instrumentation layout for both the structure and NCSs. To meet
its objectives, the selected FE simulation platform had to strike a balance between computational
efficiency and accuracy of the response simulation results. This paper describes the pre-test
modeling and simulation efforts for the building specimen under fixed base configuration. First,
the building specimen and the testing protocol are described. Then, the developed FE model of
the test specimen is presented in details. Finally, the prediction capability of the pre-test FE
model is evaluated by comparing FE prediction and measurement of some key response
parameters (both peak value and time history) at the global structure level and local member,
section, and fiber levels. Based on the results of the experimental-analytical correlation study,
shortcomings of the FE modeling techniques employed to develop the pre-test FE model of the
test specimen are investigated and the possible sources of discrepancy between numerical and
experimental results are discussed. Considering the near real-world conditions of the building
specimen and seismic test protocol, the experimental-analytical correlation study performed
herein provides a unique opportunity to evaluate realistically the accuracy of the employed
nonlinear FE modeling and simulation techniques for RC building structures subjected to seismic
Accepted for Publication in ASCE Journal of Structural Engineering
August 2017
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excitations of various intensities. Conclusions are drawn on improved modeling techniques and
future research required to improve the fidelity of nonlinear FE seismic response simulation for
RC building structures.
2. Overview of the shake table test program
2.1. Structural system of the building specimen
The building structural skeleton consisted of a two bays (in the longitudinal direction, which is
the shaking direction) by one bay (in the transverse direction) cast-in-place RC frame with a
footprint of
6.6 11.0 m
and a uniform floor-to-floor height of 4.27 m resulting in a total height
of 21.34 m from the top of the foundation to the top of the roof slab. Figure 1(a) shows the
structural skeleton while Figure 1(b) shows the completed building, including its facade.
(a)
(b)
Figure 1: Views of the building specimen: (a) bare structure and (b) completed building.
The building was designed assuming a high seismic zone in Southern California, and more
specifically for a site in downtown Los Angeles assuming stiff soil conditions (Site Class D). A
suite of seven, spectrally matched, maximum considered earthquake (MCE) ground motions
were used to design the fixed base structure. Target performance levels of 2.5% peak interstory
drift ratio and 0.7 - 0.8 g peak floor acceleration were selected during the conceptual design
Accepted for Publication in ASCE Journal of Structural Engineering
August 2017
7
phase. Moreover, three spectrally matched serviceability level earthquake ground motions were
selected and used to check the serviceability performance of the building. The building specimen
was designed and built based on the current design and construction practice in Southern
California.
The building specimen was supported on a grid of 1.5 m thick post-tensioned RC foundation
beams designed to remain uncracked and preserve linear elastic behavior during all the seismic
tests (Figure 2). For the first phase of seismic testing (under base-isolated configuration), the
building was lifted up and four high damping rubber (HDR) isolators were inserted inside
pockets in the north and south foundation beams below the corner columns (see Figure 2).
Subsequently, the isolators were removed and the foundation was anchored to the shake table
platen using post-tensioned rods installed along the foundation perimeter beams providing a
fixed base test configuration.
The building specimen had six identical 660 mm by 460 mm RC columns with a longitudinal
reinforcement ratio of
1 42
l.%
and a prefabricated welded grid consisting of #4 ties at 102
mm as transverse reinforcement. Two identical moment resisting frames, one on the north side
and the other on the south side of the building, defined the lateral load resisting system in the
shaking direction. The beam-column joints were designed with equivalent beam moment
capacities, but with different reinforcement details at the various floor levels of the building. The
beams at the second and third floors were reinforced with high strength steel with nominal yield
strength of 827 MPa. The fourth floor had post-tensioned hybrid upturned beams with special
moment-resisting frame (SMRF) detailing. The upturned beams were connected to the columns
at both ends using ductile rod connectors (Nakaki et al., 1994). The fifth floor beams consisted of
conventional moment frame beams with the addition of ductile rod connectors. The roof beams
Accepted for Publication in ASCE Journal of Structural Engineering
August 2017
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were detailed based on current requirements for SMRF as detailed in ACI 318-08 (ACI, 2008).
To provide adequate gravity support for the precast concrete cladding panels at the upper two
stories, lateral beams were added in the east bay of the building (see axis C in Figure 2) at the
fourth floor, fifth floor, and roof levels. The floor system consisted of a 0.2 m thick concrete flat
slab reinforced in both directions at top and bottom. In addition to a number of small perforations
to allow passage of building services (i.e., plumbing, electrical, and fire sprinklers) and
sensor/camera cables, each floor slab incorporated two large openings to accommodate a full
height elevator and a stair shaft. The perimeter of each slab was strengthened with band
(integral) beams (embedded in the slab) and thus, reinforcing the flat slab-column connections.
A pair of 0.15 m thick concrete walls, reinforced with a single grid of reinforcement in their mid-
plane, was placed in the north-south direction to encase the elevator shaft, to provide gravity
support for the elevator system, and also to provide additional transverse and torsional stiffness
for the building. To counterbalance the torsional stiffness provided by these shear walls located
in the west part of the building, the east bay of the building (axis C in Figure 2) was cross-braced
at all floor levels with
32 mm
steel rods anchored in the top and bottom concrete slabs. The
bare structure had a total weight of approximately 3010 kN excluding the foundation, which
weighed about 1870 kN. The completed building specimen, including all NCSs, weighed
approximately 4420 kN, excluding the foundation. Detailed information about the relative
contributions of the various NCSs to the total weight of the completed building is provided in
(Ebrahimian et al., 2014).
Accepted for Publication in ASCE Journal of Structural Engineering
August 2017
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Figure 2: Structural details of the building specimen (units are in meters).
2.2. Instrumentation layout
The building specimen, including NCSs, was instrumented with a large array of sensors
consisting of accelerometers, linear and string potentiometers, LVDTs, strain gauges, load cells,
GPS receivers, and high-speed digital cameras. Over 600 synchronized data channels were
logged at 240 Hz using a 16 bit A/D converter (the set of five GPS receivers was installed on a
standalone data acquisition system). The main accelerometer array measuring the response of the
structure consisted of four tri-axial force-balance EpiSensor accelerometers, one at each of the
four corners of each floor slab and of the foundation. These accelerometers had an amplitude
Accepted for Publication in ASCE Journal of Structural Engineering
August 2017
10
range of ±4 g, a frequency range DC-200 Hz, and a wide dynamic range of 155 dB. The data
acquisition system for the main accelerometer array consisted of Quanterra Q330 data loggers
from Kinemetrics, Inc. The procedure followed for data cleansing is described in details in
(Ebrahimian et al., 2014).
2.3. Seismic tests
The fixed base building specimen was subjected to a sequence of dynamic tests including six
earthquake base motions of increasing intensity (Table 1). More details about the scaling of the
intensity of the seismic test motions can be found in (Chen et al., 2013). After completion of the
seismic shake table tests, the FE model that was developed prior to these tests was rerun using
the base input motions achieved by the shake table, which differ from the target earthquake
motions due to the imperfect nature of the shake table controller. However, the FE modeling
assumptions and parameters, as described in the following sections, were not revised to preserve
a true comparison between blind predictions and experimental measurements. For each of the
fixed-base seismic test, the averaged east-west translational acceleration at the foundation level
was computed and used as the base input motion in the corresponding nonlinear time history
analysis. The time histories of these base input accelerations and their 5 percent damped linear
elastic relative displacement response spectra are shown in Figure 3.
Accepted for Publication in ASCE Journal of Structural Engineering
August 2017
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Table 1: Seismic tests performed in the fixed base configuration of the building specimen.
Test Name
Seed Earthquake Ground
Motion
Description
PGA
FB-1: CNP100
Canoga Park - 1994 Northridge
earthquake
Spectrally matched serviceability level
0.20g
FB-2: LAC100
LA City Terrace - 1994 Northridge
earthquake
Spectrally matched serviceability level
0.18g
FB-3: ICA50
ICA - 2007 Pisco (Peru)
earthquake
Original earthquake record, 50% scale
0.21g
FB-4: ICA100
ICA - 2007 Pisco (Peru)
earthquake
Original earthquake record, 100% scale
0.25g
FB-5: DEN67
TAPS Pump Station 9 - 2002
Denali earthquake
Spectrally matched earthquake, 67%
scale (Design level)
0.64g
FB-6: DEN100
TAPS Pump Station 9 - 2002
Denali earthquake
Spectrally matched earthquake, 100%
scale (MCE level)
0.79g
Note: (1) With the exception of FB-3 and FB-4, the earthquake ground motions listed are seed motions that were spectrally
matched and amplitude scaled as noted in the third column of the table. (2) The last column of the table specifies the measured
peak ground acceleration at the foundation level in the east-west direction.
Figure 3: Acceleration time histories of the first five seismic test motions achieved by the shake
table at the foundation level (east-west direction) and their 5% damped linear elastic relative
displacement response spectra.
3. Nonlinear Finite Element (FE) Modeling and Analysis
3.1. FE Simulation Platform
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The building specimen had a number of unique features that required special attention in the FE
modeling. The slabs were expected to influence significantly the earthquake resistance of the
structure due to the specific plan configuration of the building specimen. The stairwell opening
in the south-east corner of the floor plans was expected to affect the slab-frame interaction. The
elevator opening in the north-west portion of the floor plans was deemed to likely disturb the
load transfer mechanism through the floor diaphragms. Due to the special configuration of the
floor slabs, the “effective width” assumption, which is recommended by design codes to account
for slab-frame interaction, was considered not very appropriate in this situation. Furthermore, the
flat slab-column connections were expected to influence significantly the nonlinear seismic
response behavior of the building. Therefore, it was decided to explicitly include the slabs in the
nonlinear FE modeling of the building specimen. For this purpose, the DIANA finite element
analysis software (TNO DIANA BV, 2011) was selected as the FE simulation platform for this
pre-test simulation study. This software supports state-of-the-art nonlinear material constitutive
models for the analysis of RC structures. Moreover, these material models can be used in
conjunction with the structural type finite elements needed in this study such as 3D beam-column
elements and shell elements with embedded steel reinforcement.
3.2. Material constitutive models
The concrete constitutive model used is the rotating total strain smeared crack model with a
nonlinear inelastic concrete material law (Vecchio & Selby, 1991). As opposed to the discrete
crack approach, in which cracking in concrete is modeled as geometric discontinuities, in the
smeared crack approach (Rashid, 1968), the effects of cracking are implicitly taken into account
by modifying the stress-strain relation of the concrete material at the integration points of the FE
model. The direction of (potential) cracks at each integration point is determined based on the
Accepted for Publication in ASCE Journal of Structural Engineering
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direction of the principal tensile strains at each time step of the FE analysis, regardless of any
previous crack orientation (Cope et al., 1980). The rotating total strain crack model is based on a
co-axial strain-stress concept. In this model, the principal directions of the total strain tensor are
calculated and a uniaxial stress-strain relation is used to calculate the stress values in each of the
principal strain directions. Because there are no shear-strains in the principal strain coordinate
system, following the co-axial strain-stress concept, the shear-stresses in these axes are equal to
zero. The coupling effects of the stress-strain response of concrete across different principal
directions (due to cracking and confinement) are taken into account by modifying the stress and
stiffness in the various principal directions based on three rules: (1) the modified compression
field theory (Vecchio & Collins, 1986), based on which the compressive strength of concrete in
one principal direction is reduced as a function of the maximum tensile strains in the other
principal directions; (2) mechanics-based confinement, based on which the stress and strain at
the peak point of the compressive stress-strain curve are modified as a function of the
compressive stress in the other principal directions following the procedure suggested by Selby
and Vecchio (Selby & Vecchio, 1993); and (3) reduction of Poisson’s ratio due to lateral
cracking; the Poisson’s ratio is kept constant (
002.
in this study) before the concrete cracks
in tension; after cracking in a certain direction (e.g., principal direction i), all the related
components of the Poisson’s ratio (i.e.,
ij
and
ik
) are reduced as a function of the maximum
tensile strain observed in direction i, and eventually vanish as the ultimate tensile strain is
reached. Once the stress and stiffness in the principal strain directions are determined, the
principal stress tensor and stiffness matrix are transformed back to the element local coordinate
system. Next, they are integrated over the element domain through the principle of virtual
displacements to determine the element nodal resisting force vector and stiffness matrix, which
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are then transformed to the structural (or global) coordinate system and assembled to find the
structural (global) internal resisting force vector and stiffness matrix (refer to (Ebrahimian et al.,
2014) for a more detailed description of the concrete constitutive model used in this study).
The uniaxial tensile behavior of the concrete material model consists of an initial linear elastic
part followed by a nonlinear softening behavior according to the Reinhardt exponential softening
model (Reinhardt, 1984) as shown in Figure 4. In this figure,
c
E
denotes the concrete linear
elastic modulus defined as
5
3cc
ccc
f
E
where
cc
f
= confined compressive strength and
cc
=
strain corresponding to
cc
f
. The concrete tensile strength is taken as
0 33 (MPa)
tc
f . f
in
which
c
f
denotes the unconfined compressive strength of concrete determined based on uni-
axial compression tests performed on representative concrete samples obtained during
construction. The cracking strain is obtained as
t
tc c
f
E
and the ultimate tensile strain is denoted
as
tu
. The concrete material fails in tension upon reaching
tu
, i.e., when this strain is reached,
both the concrete tensile stress and stiffness vanish irreversibly. However, upon load reversal, the
concrete crack closes and the concrete material can regain its current level of compressive
resistance. The constant fracture energy concept is employed to avoid the spurious mesh
sensitivity caused by tensile softening (Bazant, 1976). Denoting the crack bandwidth (Bazant &
Oh, 1983) of a finite element by
h
, the ultimate tensile strain (
tu
) for this finite element is
derived such that the area under the post peak branch of the stress-strain curve in tension is equal
to
f
G
h
, where
f
G
denotes the tensile fracture energy and is considered a constant material
property equal to
125 Nm
(justified by experimental studies such as (Navalurkar et al., 1999)).
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For beam-column elements, the crack bandwidth is the length of the element, while for shell
elements, it is taken as the square root of the element area (TNO DIANA BV, 2011).
The uniaxial compressive behavior of the concrete material model consists of an initial linear
elastic part followed by two parabolic branches as shown in Figure 4. The values of
cc
f
,
cc
, and
cu
(the ultimate confined compressive strain) are computed based on the initial – undamaged –
properties of the concrete material and the confinement effect of the transverse reinforcement
(Mander et al., 1988). To account for the confinement effect,
cc
f
and
cc
are determined as the
average prediction of such effect from different models, namely the modified Kent and Park
model (Park et al., 1982), Mander’s model (Mander et al., 1988), Saatcioglu and Razvi’s model
(Saatcioglu & Razvi, 1992), and Attard and Setunge’s model (Attard & Setunge, 1996). The
ultimate compressive strain
cu
is determined following the suggestion of Scott et al. (Scott et
al., 1982) for beam-column components confined by hoop reinforcement. The shear walls and
slabs are modeled using material properties representing unconfined concrete, namely
cc c
ff
,
02
cc .%
(Mander et al., 1988), and
04
cu .%
(Scott et al., 1982).
In a well-detailed RC beam or column component subjected to combined axial and flexural
loading, damage is usually concentrated in a localized portion of the component, known as the
plastic hinge (PH) region. Similarly, when displacement-based beam-column FEs are used to
model and analyze the strain-softening behavior of the concrete material in the beams and
columns of a RC frame structure, the compressive softening behavior of concrete localizes
within specific elements. This localization results in non-objectivity and spurious sensitivity of
the simulation results to the finite element mesh discretization. To remove the mesh sensitivity
and regularize the localization in compressive failure, the softening (or post-peak) branch of the
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compressive stress-strain curve of the concrete material model is rescaled for each finite element
as a function of the compressive fracture energy,
c
G
, and the effective length or size (
h
) of the
element such that the post-peak dissipated energy (or the energy per unit area required to crush
the concrete) is independent of the element size (Willam et al., 1986). For each RC member
(beam, column, slab, or wall), the fracture energy in compression is determined from the
confined compressive strength and strain (
cc cc
f,
), the ultimate compressive strain (
cu
), and the
length of the PH region,
PH
L
, as
2
3
c cc cu cc PH
G f L
(1)
The compressive fracture energy,
c
G
, obtained from Eq. (1) is then applied as a constant material
parameter (or property) to all the finite elements defining the RC member and reflects the
confinement effects provided by the transverse reinforcement in the PH region of the member. In
this study, the length of the PH region (
PH
L
) for beams and columns is taken as one half the
depth of the structural member (Park & Paulay, 1975), while for walls and slabs, it is taken as
one half their thickness. A complete list of computed or derived material parameters for the
various RC components of the BNCS building is provided in (Ebrahimian et al., 2014).
The Modified Compression Field Theory (MCFT) (Vecchio & Collins, 1986) is used in DIANA
to continually update the uniaxial stress-strain material model for the concrete in compression
based on the maximum observed transverse tensile strains (TNO DIANA BV, 2010). “Model B”
as proposed by Vecchio and Collins (Vecchio & Collins, 1993) dictates the reduction in the
compressive strength of concrete in one principal direction due to tensile cracking in the other
principal direction(s).
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As illustrated in Figure 4, stress unloading and reloading in tension and compression follow
origin-centered linear secant paths. This is clearly a simplifying assumption (de Borst, 1993)
since, in reality, residual strains appear upon stress removal (unloading) both from a compressive
or tensile state.
0 31
2
(compression)
1: 0
2: 1
1
3: 0 5
5 1 1
4: 5 2
3 4 4 5
5: 1
c tc
.
tension
tc
t tc tu
tu tc
c cc
cc cc cc
cc cc
cc
E,
f,
E,
f,
f
2
cc cc cu
cu cc
,
Figure 4: Uniaxial stress-strain concrete material model
(Tensile stresses and strains are negative).
The modified Giuffré-Menegotto-Pinto (G-M-P) material model as proposed by Filippou et al.
(Filippou et al., 1983) is used to model the uniaxial hysteretic stress-strain behavior of the steel
reinforcing bars (rebars) embedded in the beam-column and shell elements of the FE model. It is
noted that the shear stiffness and dowel action of rebars are neglected in the FE model presented
here. The reinforcing steel material parameters (e.g., modulus of elasticity, initial yield
stress/strain, and kinematic/isotropic strain hardening parameters) are obtained through fitting of
the G-M-P model to experimental stress-strain data obtained from tensile tests performed on
representative rebar samples from the BNCS specimen. The reader is referred to (Ebrahimian et
al., 2014) for more details on the calibration of the G-M-P model and a comprehensive list of the
material parameters used in the FE model of the BNCS building presented herein. Preliminary
FE analyses performed using the BNCS FE model described here showed that the steel rod
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braces remain linear elastic during the shake table tests; therefore, they are modeled using a
linear-elastic material model.
3.3. Finite elements
The beam and column members are modeled using three-node Mindlin-Reissner displacement-
based 3D beam-column elements with 6 DOFs per node (i.e., 3 translations and 3 rotations per
node). The finite elements are based on an isoparametric formulation. The displacements of the
beam axis and the rotation of the cross-section of the beam are interpolated independently along
the element from the nodal displacements and rotations using quadratic shape functions (Hughes,
2000). The beam-column elements are not only integrated along their length, but also over their
cross sections. The primary strains at the integration points are the Green-Lagrange strains, from
which the Cauchy stresses are computed by satisfying the material constitutive models for the
concrete and reinforcing steel. For the sake of computational efficiency, different integration
schemes are adopted for the beam-column elements – along their length and over their cross-
section – based on their expected level of nonlinearity (see Table 2 and Figure 5). The columns
are assumed fixed at their base due to the very large stiffness of the foundation, which was
anchored to the shake table platen during the fixed base tests. The beam and column longitudinal
steel reinforcement is modeled as fully bonded embedded steel bars.
The slabs and shear walls are modeled using eight-node Mindlin-Reissner quadrilateral
serendipity shell elements with 6 DOFs per node including mechanics-based drilling degrees of
freedom. Numerical integration using two-by-two Gauss integration points over their plane and
three Simpson integration points across their thickness is applied to all shell elements. The steel
reinforcement mesh at the top and bottom of each slab is modeled as an orthotropic membrane
with an equivalent thickness, embedded in the shell element and fully bonded to the concrete.
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Providing strong bands along the free perimeter of the slabs, the integral beams are modeled
using regular beam-column elements as defined above. The cross section dimensions of these
elements are based on the actual dimensions of the confined concrete core of the corresponding
integral beam. These elements are reinforced with embedded steel bars, similar to the frame
beams. The steel rod braces are modeled using two-node directly integrated – one integration
point – 3D truss elements with three DOFs per node. Since the steel rod braces are resisting only
tensile loads (tension-only elements), their effective cross sectional area is reduced by half to
correctly account for their stiffness contribution to the BNCS FE model.
Some specific elements along each beam and column and across the slabs, which can potentially
develop localized nonlinearities, are referred to as PH elements. The length of these PH elements
is selected so as to represent the length of the physical plastic hinge region of the corresponding
member. The slab FE mesh discretization is designed manually considering five different
criteria: (1) assigning proper dimensions to the PH elements, (2) aligning the nodal points of
adjacent beam and shell elements, (3) maintaining regularity in the shape and uniformity in the
size of shell elements, (4) accommodating the modeling of the various beam-column-slab joint
details, and (5) accommodating different slab reinforcement details as specified in the design and
as-built drawings.
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Table 2: Numerical integration schemes for beam-column elements.
Component
Location
Integration scheme
Beams at
north and
south frames
PHs at floors 2, 3, and 4
ISB1: 3 (length), 3 (width), 7(depth)
PHs at floor 5 and roof
ISB2: 3 (length), 3 (width), 5(depth)
Others
ISB3: 3 (length), 3 (width), 3(depth)
Columns
PHs at story 1
ISC1: 3 (length), 3 (width), 7(depth)
PHs at stories 2 and 3
ISC2: 3 (length), 3 (width), 5(depth)
Others
ISC3: 3 (length), 3 (width), 3(depth)
ISB: Integration scheme for beam, ISC: Integration scheme for column.
(a)
(b)
(c)
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(d)
(e)
(g)
(f)
(h)
(i)
Figure 5: (a) Complete FE model of the BNCS test specimen; FE mesh discretization of (b) floor 2,
(c) floor 4, and (d) roof slabs; details of beam-column-slab joint located at (e) south-west corner of
floor 2, (f) south-middle point of floor 2, (g) south-east corner of floor 2, (h) south-middle point of
floor 4, and (i) south-west column (N: North, E: East, U: Up, and W: West; P/C: precast concrete;
units are in meters).
Figure 5(a) shows a 3D view of the FE model of the BNCS test specimen. Figures 5(b), (c), and
(d) show the FE mesh discretization of the floors 2, 4, and roof, respectively. The FE mesh
discretization of floors 3 and 5 is similar to that of floor 2. Figure 5 (e) shows the details of the
FE model of the column-slab joint located at the south-west corner of floor 2. Similarly, Figures
5(f), (g), and (h) show the details of the FE model of the beam-column-slab joints located at the
south-middle point of floor 2, south-east corner of floor 2, and south-middle point of floor 4,
respectively.
3.4. Modeling of inertia and damping properties
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The self-mass of the beams, columns, and shear walls is modeled by assigning the reinforced
concrete material mass density (
3
kg
2500 m
con
) to the corresponding finite elements. The
mass density of adjacent elements is corrected to avoid double-counting of the mass in the
overlapping regions of those elements. The mass density of the slab at each floor accounts for the
self-mass of the slab and the effective mass of the nonstructural components connected to that
slab. Thus, the equivalent mass density of the slab elements at each floor is calculated by adding
up the masses of all non-structural components located in the upper half story below and the
lower half story above the slab to the mass of the slab itself. Since the individual mass
contributions of the interior partition walls, ceilings, and balloon frame facade at stories 1 to 3 of
the building, and the furniture at each story are relatively small, their inertial effect is modeled as
a uniformly distributed mass over the floor slab. On the other hand, the mass contributions of the
precast concrete claddings at stories 4 and 5, the stairs and elevator (spanning the height of the
building) and the penthouse and cooling tower at the roof level are relatively significant;
therefore, they are each modeled as lumped masses.
Each precast cladding panel is connected to the floor slabs at four locations: two at the bottom by
means of in-situ welded connections, and two at the top by means of rod connections, restraining
only the out-of-plane movement of the panel. The translational mass of the panel in its out-of-
plane direction is distributed equally over all four support points. The translational mass of the
panel in its own plane is equally distributed over the two bottom connection points only, since
the top connections were designed to allow free translation of the panel in its plane. The cabin
and counterweight of the elevator system were held at the mid-height of the building (story 3)
during all fixed base seismic tests, while the elevator motor was installed at the roof level.
Consequently, the total mass of the elevator system is equally distributed over four points around
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the elevator slab opening at the roof and floors 3 and 4 as shown in Figures 5 (c) and (d). The
translational masses of the penthouse and cooling tower are distributed equally over their support
points, respectively, at the roof level as shown in Figure 5 (d). The consistent mass matrices,
including rotational inertia terms, for all finite elements are computed based on the assigned
mass densities and assembled together with the nodal lumped translational masses to obtain the
global structural mass matrix.
The damping characteristics of the structure (beyond the material hysteretic energy dissipation,
which is modeled explicitly) are modeled using the proportional Rayleigh damping (Chopra, 4th
edition, 2011) by defining a damping ratio of 2% at the first mode of the undamaged initial
linear-elastic model of the structure (with a period of
10 71sec
initial
T.
or frequency of
11 41 Hz
initial
f.
) and at 20 Hz. The corresponding initial damping ratios of the 2nd (coupled
longitudinal-torsional), 3rd (coupled lateral-torsional), 4th (2nd longitudinal), and 5th (2nd coupled
longitudinal-torsional) modes are 1.7, 1.4, 1, and 1%, respectively. The wide frequency range (
11 41 Hz
initial
f.
to 20 Hz) is selected to provide a nearly uniform damping ratio for modes
contributing to the response. The mass and stiffness coefficients of the Rayleigh damping matrix
are held constant during the time history analyses. However, the damping matrix is updated at
each time step of the nonlinear time history analysis by applying the stiffness coefficient to the
current (secant) stiffness matrix, since using the initial linear-elastic stiffness matrix to compute
the Rayleigh damping matrix is known to cause significant artificial damping effects ( (Charney,
2008), (Hall, 2006)). The secant stiffness matrix is available as part of the incremental-iterative
quasi-Newton method used to solve the nonlinear incremental equations of dynamic equilibrium
at each time step (see next section).
3.5. Nonlinear time history analyses
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Each nonlinear dynamic earthquake response analysis starts with the application of the gravity
loads quasi-statically and incrementally. The regular incremental-iterative Newton method is
used to solve the nonlinear static equilibrium equations for gravity loads. The nonlinear time
history analysis for earthquake base excitation is then performed using as initial condition the
state of the structure after application of the gravity loads. Newmark average acceleration
method (Chopra, 4th edition, 2011), with a constant integration time step size of 0.025 sec, is
used to integrate the equations of motion in time. This integration time step size was selected
based on a preliminary convergence study of the time history analysis results with respect to the
integration time step size. The quasi-Newton (secant) method based on the Broyden–Fletcher–
Goldfarb–Shanno (BFGS) stiffness update method (Matthies & Strang, 1979) is employed as the
iterative method to solve the nonlinear time-discretized equation of motion at each time step. At
the end of each time step, the last obtained secant stiffness matrix of the structure is stored and
used as the initial stiffness matrix at the first iteration of the next time step. The convergence
criterion is based on either the relative norm of the last incremental displacement vector or the
relative norm of the last unbalanced force vector, whichever occurs first, with a convergence
tolerance of
4
10
and the number of iterations per time step is limited to 30. If neither of the two
criteria is satisfied within 30 iterations, the iterative procedure at that time step is terminated.
Consequently, the current unbalanced force vector is transferred to the next time step and the
analysis continues. In the cases of unconverged time steps, the number of consecutive
unconverged time steps and the relative norms of the last displacement increment and
unbalanced force vectors are checked to ensure that they are within acceptable limits. The
employed convergence criterion is selected to balance computational demand and accuracy, and
is based on prior experience in modeling reinforced concrete components and subassemblies for
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correlating FE predictions with experimental measurements (Ebrahimian, 2015). More details on
the state of convergence of the model for various time history analyses are provided in
(Ebrahimian et al., 2014). The parallel direct sparse solver method (Schenk, 2000) is used to
solve the system of linearized incremental dynamic equilibrium equations at every iteration of
each time step.
To compare herein the FE predicted and measured building responses, a nonlinear time history
analysis is performed by applying the sequence of test earthquake ground motions after applying
the gravity loads. Thus, the input base motion consists of the sequence of the first five ground
motions (Table 1 and Figure 3), as reproduced by the shake table, with 5 seconds of zero padding
between any two consecutive motions. In this case, state of the structural model at the end of an
earthquake is used as initial state for the next earthquake and thus the analysis accounts for
cumulative damage effects. In a parallel effort, a nonlinear time history analysis is performed
separately for each test earthquake ground motion after application of the gravity loads. The
former analysis is referred to as “analysis with sequential effects”, while the latter one is defined
hereafter as “analysis without sequential effects”. Selected structural response parameters
obtained from the analyses with and without sequential effects are compared in Section 5 to
investigate the effects of cumulative damage on the response of the building structure to a
sequence of earthquakes.
4. Nonlinear time history analyses results
This section compares the FE predicted and measured (observed) building responses to the first
five seismic input motions, namely FB-1 through FB-5 (Table 1 and Figure 3). The sixth seismic
shake table test, FB-6: DEN100, is not included in this experimental-analytical correlation study,
since during that test, the building specimen experienced some failure modes (i.e., rupture of
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longitudinal reinforcement at the ends of several RC beams) that cannot be captured (simulated)
by the material model used for the steel reinforcement in the FE model presented above.
4.1. Structural response at the global level
Figures 6 and 7 compare the FE predicted and measured peak floor absolute accelerations
(PFAAs), peak interstory drift ratios (PIDRs), and peak total (inertial) story shears (PTSSs)
normalized by the total weight of the building (
4420 kN
t
W
) for each of the five floors or
stories of the building specimen. The total (inertial) story shear, referred to in short as story shear
hereafter, is defined as
6
115
i j j
ji
V m a , i , ,
(2)
where
i
V
is the story shear evaluated in the horizontal plane at mid-height between the ith and
(i+1)th floors (i.e., total shear force within the ith story) in the east-west direction,
j
a
is the
averaged absolute floor acceleration at the jth floor in the east-west direction and
j
m
denotes the
tributary mass of the jth floor.
In Figures 6(a)-(c), the coefficient of determination (
2
R
) measures the level of agreement
between FE predictions and experimental measurements for the peak values of the considered
structural response parameters at each floor level or story for the five different seismic tests. The
envelope plots in Figures 7(a)-(c) compare the FE predicted and experimentally measured
PFAA, PIDR, and PTSS, respectively, along the height of the building (the positive and negative
peak values are treated separately). To quantify the absolute relative difference between the FE
predicted and experimentally measured peak response parameters of the building more
comprehensively, the relative error measure (
i
E
) is defined. It expresses the relative closeness of
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the FE predicted and measured peak response value at the ith floor level (or story) of the building.
Denoting a peak response parameter obtained from the FE prediction and experimental
measurement at the ith floor level (or story) by
FE Pred.
i,
R
and
Meas.
i,
R
in the positive direction, and by
FE Pred.
i,
R
and
Meas.
i,
R
in the negative direction, respectively, the relative error measure,
i
E
, is
defined as
0
FE Pred. Meas. FE Pred . Meas.
i, i, i, i,
iMeas. Meas.
i, i,
ii
R R R R
E Max ,
max R min R
(3)
The value
0
i
E
indicates a perfect agreement between FE prediction and experimental
measurement for the peak response of interest at the ith floor level or story. The more
i
E
deviates
from zero, the larger the FE prediction error is. The distribution of this relative FE prediction
error is shown in the form of contour plots over the five seismic tests and the five floor levels or
stories in Figures 8(a)-(c) for the PFAA, PIDR, and PTSS, respectively.
By comparing parts (a) and (b) of Figures 6-8, it can be concluded that the PFAAs are predicted
more accurately than the PIDRs. The PFAAs are predicted more accurately at upper floors for
the low intensity seismic tests and at lower floors for the high intensity seismic tests as seen in
Figure 8(a). Figure 7(b) shows that in low intensity seismic tests, the PIDR is typically
overestimated at all stories, although more so at the middle stories of the building, while in high
intensity seismic tests, the PIDR is underestimated at the lower stories and overestimated at the
upper stories of the building. Figure 8(b) shows that the PIDR relative prediction error is more
significant in the low intensity (FB-1: CNP100 to FB-3: ICA50) than in the high intensity
seismic tests. Finally, the FE predictions underestimate the PTSS at all stories as can be seen in
Figures 6(c) and 7(c).
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It is hypothesized that the nonstructural components, especially the partition walls, contribute
significantly to the discrepancy between the FE predicted and measured PIDR response of the
building. The influence of partition walls on the earthquake response of buildings has been the
focus of other research studies (Wood, 2012). The influence of partition walls on the dynamic
response of building structures is more significant at low IDRs, since the walls are intact, well
connected to the structure, and contribute their full original stiffness. As the base motion
intensifies, the partition walls undergo damage and their connections to the building structure
deteriorate. For the BNCS test specimen, this occurred especially at the lower stories of the
building, where the IDR demand was the highest, while at the upper stories, partition walls
underwent little or no damage and therefore remained influential.
(a)
(b)
(c)
Figure 6: Correlation plot of FE predicted versus measured: (a) peak floor absolute acceleration, (b) peak
interstory drift ratio, and (c) peak total story shear (normalized by the total weight of the building) for each of
the 5 floors or stories.
(a)
(b)
(c)
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Figure 7: Comparison of FE predicted and measured: (a) floor absolute acceleration envelopes, (b) interstory
drift ratio envelopes, and (c) normalized total story shear envelopes over the height of the BNCS building (see
Figure 6 for definition of the symbols).
(a)
(b)
(c)
Figure 8: Contour plots of relative FE prediction error for: (a) peak floor absolute acceleration, (b) peak
interstory drift ratio, and (c) peak total story shear.
Figure 8(b) shows that the relative prediction error of the PIDR is largest at the 3rd story for the
low intensity seismic tests (FB-1: CNP100 to FB-3: ICA50). This can be explained by comparing
the total length of the installed partition walls at each story of the building, as reported in Table
3. The exterior balloon-framed walls are excluded from this table, since they have special
connection details that reduce their kinematic interaction with the structural system. Table 3
indicates that the 3rd story contains at least 50% more partition walls than the other stories. This
can explain why the PIDR relative prediction error is the largest at story 3 for the low intensity
seismic tests.
Table 3: Length of partition walls installed at each story.
Total length (m)
Story 1
Story 2
Story 3
Story 4
Story 5
Partition walls in
E-W direction
13.5
13.5
22.0
15.0
13.5
Partition walls in
N-S direction
3.5
11.0
15.5
7.5
6.0
The underestimation of the FE prediction of the PIDR at the lower stories of the building
specimen during the seismic tests of large intensity (see Figure 7(b) for FB-4: ICA100 and FB-5:
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DEN67) can be explained mostly by the difference between the actual and FE predicted
hysteretic response of the building structural components. The employed FE modeling technique
does not capture well the pinching hysteretic behavior typically observed in the cyclic response
of RC frames. Thus, the FE predicted hysteretic energy dissipation capacity of RC structural
components is larger than the observed one. Consequently, the FE predicted IDRs were lower
than the corresponding experimental results at the lower stories of the building, where the level
of response nonlinearity was the highest, see Figure 7(b) at the first two stories for FB-4: ICA100
and FB-5: DEN67. This explanation is in agreement with the discussion on the story level
responses (FE predicted vs. observed) provided in the next section.
To better investigate the effects of nonstructural components on the seismic response of the
building, the time histories of selected structural response parameters are compared in Figures 9
(a) and (b) between FB-1: CNP100 and FB-5: DEN67, respectively. These figures show the time
histories of (i) the roof drift ratio, defined as the horizontal roof displacement relative to the base
normalized by the height of the roof from the top of the foundation (
21 34 m
R
h.
), (ii) the
second story IDR, and (iii) the total base overturning moment normalized by the product of the
total weight of the building and the roof height. The total (inertial) base overturning moment (
B
M
) is computed as
6
2
B j j j
j
M m a h
(4)
where
j
h
is the height of floor j, measured from the top of the foundation. Figure 9(a) shows a
clear difference in the predominant period of the FE predicted and experimentally measured
response time histories, which is most likely due to the stiffness contribution of the nonstructural
components (mostly partition walls) to the building response. This stiffness contribution of the
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non-structural components, which is not accounted for in the FE model of the building, results in
a shortening of the natural periods of the building and of the predominant period of the response
time histories. By comparing Figures 9(a) and (b), it is observed that the discrepancy in the
predominant period of the FE predicted and measured response time histories reduces greatly in
the high intensity seismic test FB-5: DEN67. This can be explained by the extensive physical
damage suffered by the NCSs during the seismic tests prior to FB-5: DEN67. As a result, the
influence of the stiffness contributions of the NCSs to the building dynamic response is
significantly reduced for FB-5: DEN67. The contribution of the NCSs to the lateral stiffness of
the building specimen can also be shown by comparing the experimentally identified natural
periods of the bare building structure and the complete (total) building as presented in (Astroza
et al., 2016).
(a)
(b)
Figure 9: Comparison of FE predicted and measured time histories of selected structural response
parameters for the (a) FB-1: CNP100, and (b) FB-5: DEN67 seismic tests.
4.2. Structural response at the story level
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The plots of the TSSs versus the corresponding IDRs characterize the hysteretic response of the
building at the individual story levels. These plots are shown in Figures 10(a), (b), and (c) for
FB-1: CNP100, FB-4: ICA100, and FB-5: DEN67, respectively. Figure 10(a) shows that for FB-
1: CNP100, the FE prediction is in reasonable agreement with the measured response at the first
story especially compared to the third story, since less partition walls were installed at this story
(see Table 3). For all other stories, the measured response is significantly stiffer than the FE
predicted one, which can be explained by the influence of the nonstructural components
(especially the partition walls). As the base excitation intensifies from FB-1: CNP100 to FB-4:
ICA100 and to FB-5: DEN67, the nonstructural components suffer increasing levels of damage
and their influence on the dynamic response of the building structural system decreases, which
results in an increasing level of agreement between the effective stiffness of the FE predicted and
measured story level hysteretic responses at the upper stories. The FE predictions underestimate
the IDR demands in the lower stories during the FB-4: ICA100 and FB-5: DEN67 seismic tests
and the measured story responses have a higher level of material nonlinearity than the
corresponding FE predictions. The difference between the FE predicted and measured responses
at the lower stories during the high intensity seismic tests (FB-4 and FB-5) may originate from
improper modeling of the dissipative forces (defined in addition to the hysteretic energy
dissipated through inelastic action of the structural materials, steel and concrete) in the FE model
through linear viscous damping, which may result in high viscous damping energy dissipation
and low hysteretic energy dissipation.
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(a)
(b)
(c)
Figure 10: Comparison of FE predicted and measured TSS vs. IDR hysteretic response for
the (a) FB-1: CNP100, (b) FB-4: ICA100, and (c) FB-5: DEN67 seismic tests.
4.3. Structural response at the component level
To measure the beam end axial and flexural deformations, the north frame beams of the building
specimen were instrumented with a pair of linear potentiometers at each end of the beam. The
potentiometers were installed at the top and bottom of the south face of the beam as shown in
Figures 11(a) and (b). The beam end axial strain and curvature response histories can be obtained
using the data recorded from the linear potentiometers. Denoting the length of the potentiometer
by
l
, the separation distance between the two potentiometers at each beam end by
h
, and the
sensor measurement by , the average (over the sensor length) beam end axial strain,
Meas.
e
, and
beam end curvature,
Meas.
, are obtained as
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2
top
bot
bot top
Meas.
ll
e
,
top
bot
bot top
Meas.
ll
h
(5)
The FE predictions for the beam end axial strain and curvature are obtained by averaging the
axial strain and curvature at the three sections (integration points, see Table 2) of the first beam
element next to the column (PH element). Denoting the FE predicted axial strain at the top and
bottom integration points (located at the south face of the section to match the location of the
sensors) of the ith section of the PH element by
top
i
and
bot
i
, respectively, the FE predicted
average axial strain,
FE Pred .
e
, and average curvature,
FE Pr ed .
, at the beam end are computed as
3
1
1
32
bot top
ii
FE Pred . i
e
,
3
1
1
3
bot top
ii
FEPr ed . isec
h
(6)
where
sec
h
denotes the beam cross-section height (see Table 2). Figures 12(a) and (b) compare
the FE predicted and measured time histories of the beam end average axial strain at the west end
of the second floor beam of the north frame and average curvature at the east end of the second
floor beam of the north frame, respectively, for the FB-5: DEN67 seismic test. Moreover, Table
4 compares the peak values of the FE predicted and measured average axial strain and curvature
time histories of the second and third floor beams of the north frame. Although the FE predicted
beam end average axial strain and average curvature time histories are in good agreement with
the corresponding experimental measurements, the peak values of both the average axial strain
and average curvature time histories are overestimated by the FE prediction. This overestimation
can be due to various FE model errors or uncertainties such as those mentioned earlier. The
averaging effect contained in the experimental measurements can also be a source of discrepancy
between FE prediction and experimental measurement in this case. The length of the installed
linear potentiometers is approximately 0.5 m, which is clearly larger than the expected length of
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the physical plastic hinge region of the beam. Therefore, the measured axial deformation and
curvature are averaged over the first 0.5 m portion of the beam, while the FE predicted axial
strain and curvature are averaged over the length of the PH element, which is 0.36 m (see Figure
5). Therefore, the peak values of the FE predicted axial strain and curvature, averaged over the
expected plastic hinge length, are larger than those averaged over a length of 0.5 m.
(a)
(b)
Figure 11: Instrumentation of structural
components:
(a) schematic details of some of the north
frame instrumentation;
(b) linear potentiometers installed at the
east end of the second floor north beam;
(c) string potentiometers installed at the
base of the north east column.
(c)
The south middle, south-east, north middle, and north-east frame columns were instrumented at
their base with a pair of string potentiometers installed on their interior face to measure the
column base axial and flexural deformations as shown in Figures 11(a) and (c). The procedure to
obtain the column base average (over the sensor length and over the expected plastic hinge
length for the experimental and FE numerical results, respectively) axial strain and curvature,
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from both the experimental measurements and FE response predictions, is similar to that used for
the beams. Figures 13(a) and (b) compare the FE predicted and measured time histories for the
average axial strain at the base of the north middle column and the average curvature at the base
of the south middle column, respectively, in the case of the FB-5: DEN67 seismic test. Table 4
lists the peak values of the FE predicted and measured average axial strain and curvature time
histories of the instrumented column bases. As for the beam ends, the peak values of the average
axial strain and average curvature responses of column bases are overestimated by the
corresponding FE predictions. Again, this can be at least partially explained by the fact that the
length of the installed linear potentiometers (approximately 0.9 m) is larger than the expected
length (0.33 m) of the physical plastic hinge region at the column base (which is equal to the
length of the first beam-column element at the bottom of the column). It should be noted that
other sources of modeling error, such as bond slippage of longitudinal reinforcements in beams
and columns, also contribute to the discrepancies between the FE predicted and measured
component level responses. However, bond slip and averaging length have competing effects on
the presented results; therefore, the effects of bond slip are most likely obscured by the
difference in the numerical and experimental averaging lengths. A comprehensive comparative
analytical-experimental study of the building response at the component level is available in
(Ebrahimian et al., 2014).
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(a)
(b)
Figure 12: Comparison of FE predicted and measured (a) average axial strain time histories at
the west end of the second floor north beam and (b) average curvature time histories at the east
end of the second floor north beam for the FB-5: DEN67 seismic test.
(a)
(b)
Figure 13: Comparison of FE predicted and measured (a) average axial strain time histories at
the base of the north middle column and (b) average curvature time histories at the base of the
south middle column for the FB-5: DEN67 seismic test.
Table 4: Comparison of FE predicted and measured peak average axial strain and peak average
curvature at the instrumented beam ends at the second and third floors, and column bases at the
first floor.
Beam end / Column base
Axial Strain (%)
FE Pred. (Meas.)
Curvature (1/m)
FE Pred. (Meas.)
East end of the second floor north beam
1.90 (0.80)
-0.037 (-0.032)
West end of the second floor north beam
1.99 (1.60)
0.044 (0.033)
East end of the third floor north beam
2.50 (1.10)
0.020 (0.010)
West end of the third floor north beam
2.60 (1.66)
0.041 (0.040)
Base of the north middle column
0.65 (0.47)
-0.032 (0.019)
Base of the north East column
0.73 (0.44)
0.035 (0.023)
Base of the south middle column
0.71 (0.47)
0.024 (0.020)
Base of the south east column
0.72 (0.44)
0.035 (0.024)
4.4. Structural response at the steel rebar and concrete crack levels
Selected longitudinal steel rebars located in the north frame beams were instrumented at different
locations with strain gauges. Figure 11(a) shows the location of one of these strain gauges
installed on the outer top longitudinal rebar at the east corner of the third floor beam, which is
within the east plastic hinge region of that beam. This strain gauge is shown in Figure 14(a). The
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strain response time history measured through this strain gauge during the FB-5: DEN67 seismic
test is compared to the corresponding FE prediction in Figure 14(b). The FE predicted rebar
strain is obtained by averaging the rebar axial strain over the three monitored cross sections of
the east end beam PH element. At each cross section, the axial strain at the strain gauge location
is obtained from the axial strain diagram that varies linearly over the beam cross-section
(Reissner beam theory). Figure 14(b) shows that the FE model predicts pretty accurately both the
rebar strain time history and the residual strain at the end of the seismic test.
(a)
(b)
Figure 14: (a) Strain gauge installed on the outer top longitudinal rebar near the east end of the
3rd floor north frame beam; (b) comparison of FE predicted and measured strain time histories
for the FB-5: DEN67 seismic test.
During the inspection phases following each of the seismic tests, the initiation and propagation
of cracks on the top surface of each slab was carefully marked and documented. This information
was used to develop schematic crack maps such as the one shown in Figure 15(a) for the top
surface of the second floor slab after the FB-5: DEN67 seismic test. To obtain the FE predicted
crack maps, the computed maximum crack opening at the top surface of the slab is extracted
from each of the integration points located at the top surface of the slab shell elements and
plotted as a continuous contour map over the slab as shown in Figure 15(b). The FE predicted
maximum crack opening is obtained by multiplying the maximum simulated crack strain
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averaged over the four integration points on the top surface of each slab shell element with the
crack bandwidth of the element defined in Section 3.2. Figures 15(a) and (b) show that there is a
good correlation between the FE predicted and the observed crack maps at the end of the FB-5:
DEN67 seismic test.
(a)
(b)
Figure 15: Comparison of FE predicted and observed cracks on the top surface of the second
floor slab after the FB-5: DEN67 seismic test: (a) experimental observation; (b) FE
prediction of maximum crack opening (units: mm).
Before performing the FB-5: DEN67 seismic test, a sensitive linear potentiometer was installed
on the second floor slab across one of the major cracks near the north-middle column to measure
its opening time history during the FB-5: DEN67 seismic test. Figure 15(a) shows the crack and
sensor location on the observed crack map, while Figure 16(a) shows the sensor installed across
the crack. The crack opening time history measured through this sensor is compared with its FE
prediction in Figure 16(b). The FE predicted crack opening time history was obtained by first
averaging the crack strain over the integration points located on the top surface of the shell
element that contains the location of the sensor. The averaged crack strain is then multiplied by
the crack bandwidth of the element to yield the crack opening. Considering the various sources
of approximation and uncertainty involved in this experimental-analytical comparison performed
at the scale of a concrete crack, the correlation obtained is good.
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(a)
(b)
Figure 16: (a) Linear potentiometer (protected by a plastic cover) installed, prior to the FB-5:
DEN67 seismic test, across a crack on the top surface of the second floor concrete slab; (b)
comparison of FE predicted and experimentally measured crack opening time histories for the
FB-5: DEN67 seismic test.
5. Cumulative damage effects on the seismic response of the building specimen
As mentioned earlier, two types of analysis were performed for pre-test response simulation of
the BNCS test specimen, namely “analysis with sequential effects” and “analysis without
sequential effects.” The analysis with sequential effects accounts for the cumulative damage on
the response of the building structure to a sequence of earthquakes and is computationally more
demanding than the other analysis, which starts from an initial undamaged state for each
earthquake. To investigate the effects of cumulative damage, Figures 17(a) to (c) compare the
normalized PFAA predictions obtained from the two types of analysis for FB-3: ICA50, FB-4:
ICA100, and FB-5: DEN67. In these figures, the peak positive and negative values of the
predicted FAA at each floor level of the building are normalized by the corresponding peak
positive and negative values of the measured FAA. Similarly, Figures 17(d) to (f) show the
normalized PIDRs obtained from the two types of analysis for FB-3: ICA50, FB-4: ICA100, and
FB-5: DEN67. The predicted PIDRs are also normalized by the measured PIDRs in the positive
and negative directions. For the PFAA response prediction, some small to moderate differences
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are observed between the two types of analysis results for all three tests. In the case of the PIDR,
there are no differences for FB-5: DEN67; however, the analysis with sequential effects
improves the PIDR predictions for FB-3: ICA50.
(a)
(b)
(c)
(d)
(e)
(f)
Figure 17: Comparison of the building response prediction results obtained using the analysis
with and without sequential effects; PFAA normalized by the corresponding measured PFAA
for: (a) FB-3: ICA50, (b) FB-4: ICA100, and (c) FB-5: DEN67; PIDR normalized by the
corresponding measured PIDR for: (d) FB-3: ICA50, (e) FB-4: ICA100, and (f) FB-5:
DEN67.
6. Conclusions
This paper presented a detailed three-dimensional nonlinear finite element (FE) model used for
pre-test response simulation of a full-scale five-story RC building specimen, outfitted with a
variety of nonstructural components and systems, tested on the NEES-UCSD shake table. The
prediction capability of this pre-test FE model was investigated for serviceability to design level
earthquake tests – resulting in small to moderate levels of response nonlinearity excluding the
near-collapse limit state – by comparing the FE prediction and experimental measurement of
some key building response parameters at different scales from the global (structure) level to the
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story and structural component (i.e., beam and column) levels, and down to the level of a single
rebar and the local cracking on the top surface of a floor slab. It was found that the FE predicted
peak floor absolute acceleration (PFAA) responses are in better agreement with the
corresponding experimental measurements than the peak interstory drift ratios (PIDRs). For the
low intensity seismic tests, the FE prediction overestimated the PIDRs, especially at the middle
stories of the building. On the other hand, for the high intensity seismic tests, the FE prediction
underestimated the PIDRs at the lower stories and overestimated them at the upper stories. From
the low intensity seismic tests, the time histories of the measured structural response parameters
at the global (structure) level showed a shorter predominant period than the corresponding FE
predictions. The discrepancy between the FE predicted and measured predominant periods of the
structural response time histories decreased and vanished with increasing intensity of the seismic
tests. For the low intensity seismic tests, the measured total (inertial) story shear (TSS) force
versus interstory drift ratio (IDR) exhibited a significantly stiffer measured response than the FE
predictions at all stories except the first one. As the seismic tests intensified, the agreement
between the FE predictions and experimental measurements of the story-level hysteretic
responses improved. For the FB-5: DEN67 seismic test (highest intensity seismic test for which
the experimental-analytical correlation study was performed), the following findings were
obtained: (1) The measured TSS vs. IDR hysteretic responses at the first two stories showed a
higher level of response nonlinearity and displacement ductility demand than the FE
predications; (2) The FE predicted beam-end and column-base average axial and flexural
deformation time histories showed good correlation with the corresponding experimental
measurements; (3) The FE simulation predicted pretty accurately the strain time history
measured at a section of a longitudinal reinforcing bar within the plastic hinge region of a
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second-story frame beam; (4) The FE predicted crack map for a floor slab (top of second floor
slab) correlated well with the experimental observations; (5) FE prediction and experimental
measurement were also compared at the scale of a concrete crack. The FE prediction of the crack
opening time history of a dominant crack on the second floor slab correlated well with the
experimental measurement.
Some of the most probable sources of discrepancies between the FE predictions and
experimental measurements are given below. It should be noted that while quantifying the
contribution of each of these sources of modeling errors can be the subject of future studies, their
effects on the analytical-experimental discrepancies can be concluded from the results presented
in this study.
(1) The kinematic dynamic interaction between the structural system and the nonstructural
components and systems (NCSs), which are often neglected in structural FE modeling and
response simulation, can affect the seismic structural response significantly. These interactions
increase the effective stiffness (Astroza et al., 2016) and energy dissipation capacities of the
overall building. However, as the intensity of the seismic excitation increases, the NCSs suffer
progressive damage, undergo stiffness and strength degradation and, therefore, their
contributions to the lateral stiffness and energy dissipation capacity of the structural system
diminish.
(2) The material constitutive models used in FE analysis are imperfect. The finite elements used
to model the various structural components (e.g., columns, beams, slabs) are subject to restrictive
kinematic assumptions (e.g., cross-sections remain plane and perpendicular to the centroidal axis
of a beam-column element or to the mean surface of a shell element) which can result in
inaccurate hysteretic response simulation of structural components. More specifically, in this
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study, the pinching hysteretic behavior of RC flexural members could not be captured well using
the employed FE modeling techniques. The pinching hysteretic behavior of RC frame
components is a result of bond slip of the longitudinal and lateral reinforcements, shear
deformation, and cracking. Therefore, the FE predicted hysteretic energy dissipation capacity of
the structural components was larger than the actual energy dissipation capacity for the same
cyclic displacement loading history. Furthermore, it should be noted that accounting for bond
slip effects contributes to the flexibility of the FE model (e.g., (Sezen & Setzler, 2008)) and,
therefore, neglecting these effects in the FE analysis is yet another source of modeling error
contributing to the discrepancies between FE predicted and measured responses.
(3) For FE response simulation of the structural response to dynamic loads such as earthquakes,
the damping characteristics of a civil structure are usually modeled using the stiffness and mass
proportional Rayleigh damping model with constant mass and stiffness coefficients. The
adequacy of the Rayleigh damping model for nonlinear time history analysis of structures is
questionable. Moreover, there are several uncertainties in the process of defining Rayleigh
proportional damping, including: the damping ratios, the frequencies at which the damping ratios
are specified, the type of stiffness matrix used in defining the structural damping matrix (e.g.,
initial vs. secant vs. tangent stiffness matrix), whether or not and how the damping coefficients
should be updated during the time history analysis, etc. These open problems require further
investigations.
(4) Modeling and parameter uncertainties in the FE model are another source of experimental-
analytical discrepancies. Uncertainties in the material constitutive model parameters are an
important example.
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Considering the near real-world conditions of the building specimen and seismic loading
considered in this study, it is concluded from the observations and findings in this paper that
future research is still needed to improve the fidelity of nonlinear FE structural models of RC
building structures all the way to incipient collapse. Efforts are underway to update the pre-test
FE model presented in this paper by addressing the possible sources of experimental-analytical
discrepancies mentioned above as well as the model and parameter uncertainties.
Acknowledgements
This project resulted from the collaboration between four academic institutions: The University
of California at San Diego, San Diego State University, Howard University, and Worcester
Polytechnic Institute, the support from four major funding agencies/organizations: The National
Science Foundation, Englekirk Advisory Board, Charles Pankow Foundation, and the California
Seismic Safety Commission, and the contribution of over 40 industry partners. Additional details
may be found at bncs.ucsd.edu. Through the NSF-NEESR program, a portion of the funding was
provided by grant number CMMI-0936505 with Dr. Joy Pauschke as Program Manager. The
above financial support is gratefully acknowledged. Support of graduate students Consuelo
Aranda, Michelle Chen, Giovanni De Francesco, Elias Espino, Steve Mintz (deceased), Elide
Pantoli, and Xiang Wang, and the NEES@UCSD and NEES@UCLA staff as well as the
consulting contributions of Robert Bachman, chair of the project’s Engineering Regulatory
Committee, are greatly appreciated. Design of the test building was led by Englekirk Structural
Engineers, and the efforts of Dr. Robert Englekirk and Mahmoud Faghihi are gratefully
acknowledged. The authors also wish to thank Dr. Gerd-Jan Schreppers, Director of TNO
DIANA BV, for his technical support regarding the DIANA finite element modeling and
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simulation platform. Opinions and findings in this study are those of the authors and do not
necessarily reflect the views of the sponsors.
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