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INCREASING THE DUCTILITY OF REINFORCED CONCRETE PANELS TO
IMPROVE BLAST RESPONSE
Patrick Trasborg
Ph.D. Student, Lehigh University
117 IMBT Labs, ATLSS Dr, Bethlehem PA 18015
610-758-6254, [email protected]
Pierluigi Olmati
Ph.D. Student, Sapienza Università di Roma
Via Eudossiana 18 - 00184 Rome (ITALY)
+39-06-44585224, [email protected]
Clay Naito
Associate Professor, Associate Department Chair, Lehigh University
117 IMBT Labs, ATLSS Dr, Bethlehem PA 18015
610-758-3081, [email protected]
ABSTRACT
Government facilities and military installations have always been prime targets for terrorists. To
protect occupants within, these structures are required to meet minimum blast loads. With a
dramatic shift towards considering life cycle and environmental footprint of buildings, these
structures must also meet criteria for LEED certification. Sandwich wall panels are ideal
systems to satisfy both requirements; however, due to their slender geometry, wall panels do not
form the same resistance-functions as their more stout reinforced concrete counterparts. This
paper reviews blast design methodology and the U.S. Army’s damage level criteria for
reinforced concrete members controlled by flexural failure. To improve slender concrete
component’s behavior under blast loading, locally unbonding longitudinal reinforcement is
investigated both experimentally and numerically. Developed from numerical models, an
analytical model is devised to aid in the design of locally unbonded panels.
KEYWORDS
Blast Design, Precast Wall Panels, Local Unbonding, Improving Ductility
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PROJECT MOTIVATION
Government facilities, military installations, and civilian buildings alike have been and will
continue to be targets in terrorist attacks. The vehicle borne improvised explosive device
(VBIED) has become a prominent delivery method for attacking both domestic and foreign US
structures due to their high power and relative ease of deployment. The 1995 Oklahoma City
Bombing serves as a testament as to how devastating a VBIED can be. In addition to intentional
explosions, many industrial facilities are at risk of accidental detonations due to various
manufacturing processes that deal with sensitive materials. All of these buildings have blast
design requirements that must be met in order to ensure the safety of the occupants within.
In recent times, there has been a dramatic shift towards considering the life cycle and
environmental footprint of buildings constructed in the United States. Today, many state and
government agencies either encourage or mandate that newly constructed buildings attain a
minimum Leadership in Energy and Environmental Design (LEED) certification. An effective
and popular method to decrease operating costs and reduce the environmental impact of a
structure is to install a thermally efficient building envelope. Thus, in addition to meeting
thermal requirements, envelopes for government and military structures must also meet rigorous
blast criteria.
BACKGROUND
Concrete components can either be fabricated on-site (cast-in-place) or off-site in a factory
(precast). Cast-in-place requires that formwork (often lumber) be constructed in the
component’s final resting position and then stripped once the concrete has cured. Precast
components allow the piece to be built with reusable formwork (often steel) and after the
concrete has cured, the component is shipped to the construction site.
Precast concrete has many advantages over the cast-in-place concrete counterpart. The final
condition of a concrete product is highly sensitive to environmental conditions during the curing
process. The more finely controlled the environment is (such as humidity, temperature,
hydration effects, etc), the better control of the final condition of the concrete. For this reason,
precast components are often more aesthetically pleasing than cast-in-place components.
Additionally, precast concrete can often be more economical than cast-in-place concrete.
Formwork is generally the controlling factor in the cost of a concrete component, often making
up more than 60% of the total cost for construction of the concrete piece. As precast components
can be made with the same formwork repeatedly, the cost for constructing the component drops.
Finally, precast components will often allow for a more efficient construction process and
decrease the total construction time. Precast components are fabricated in the factory, shipped to
the work site, and then are placed into position while formwork would have to be built and time
for curing of concrete for cast-in-place components.
A precast component utilized prominently to create an energy efficient building envelope is the
sandwich wall panel. Sandwich wall panels are composed of two concrete layers (wythes)
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separated by a layer of insulation (1). Due to the separation of the concrete wythes by the layer
of insulation, the wythes may not act together (compositely) in resisting flexural demands when
an out of plane load is applied. In order to create a system that acts compositely, mechanical
connectors (shear ties) are placed throughout the length of the panel that connect the exterior
wythe to the interior wythe. The number and stiffness of the shear ties dictate the degree to
which the panel acts compositely.
BLAST DESIGN METHODOLOGY
This paper will focus on far-field detonations that tend to create a uniform pressure distribution
across the face of the component and cause a flexural failure mode as opposed to close-in
detonations that tend to cause localized effects such as spall and breach. Typical blast design
methodology utilizes time stepping methods to solve the differential equation of motion in order
to predict the response of the reinforced concrete component to the blast loading. In many cases,
structural components subjected to blast load can be modeled as an equivalent single degree of
freedom (SDOF) mass-spring system with a non-linear spring as shown in Figure 1 below (2).
Figure 1: Equivalent Spring-Mass SDOF System (2)
An equivalent SDOF system is created by developing appropriate transformation factors for the
system’s mass, damping, load and resistance. Furthermore, inherit with an SDOF analysis is the
assumption that the system behaves only in a single mode shape. As the system begins to deflect
under the blast load, it eventually yields and forms plastic hinges at various locations depending
on the applied boundary conditions. Thus in reality, the system’s mode shape changes with the
progression of plastic hinges. Therefore, the transformation factors are adjusted accordingly to
account for the change in mode shape. For a more detailed review on the development of
transformation factors, see the PCI Report on Blast-Resistant Design of Precast/Prestressed
Concrete Components.
For a simply supported, one way slab under uniform loading, it is assumed that a single plastic
hinge will form at center span of the panel. The resistance-deflection relationship for such a
panel is assumed to act in an elastic-perfectly plastic manner. Thus, at a certain deflection, the
component will continuously yield at near constant resistance until an ultimate deflection limit is
reached, at which point the component will fail (see Figure 2 below). This resistance-deflection
relationship (resistance function) serves as the property for the non-linear spring in the equation
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of motion. Thus, in order for an accurate prediction to be made of a component subjected to a
dynamic load, it is imperative that the resistance function be accurate.
Figure 2: Resistance-Deflection Relationship for Simply Supported Beam (3)
Once the time-history behavior of the component is known, it is desirable to determine the
amount of damage the component has taken. The US Army Corps has developed levels of
protection (LOP) which correlates a component’s ductility and/or maximum support rotation to a
given amount of damage (4). Ductility, μ, is measured as the maximum deflection of a
component divided by the deflection of the component at yield. Support rotation, θ, of a
component can be determined by Equation 1 below:
Equation 1: Calculation of Support Rotation
where Δmax is the maximum deflection at midspan and L is the span length before the blast
loading. Table 1 below provides the levels of damage for a reinforced concrete slab subjected to
a blast loading (4). A support rotation greater than 10 º is considered to be a blowout of the
component.
Table 1: US Army 2008 Response Limits for Flexural Controlled Non-Prestress Reinforced
Concrete (4)
Component Damage Level Superficial Moderate Heavy Hazards
Non-Prestress Panel μ≤1 2.0 º 5.0 º 10.0º
BEHAVIOR OF SLENDER REINFORCED CONCRETE COMPONENTS
A series of experiments were conducted at the Air Force Research Laboratory (AFRL) in
Tindall, Florida on prestress and non-prestress sandwich wall panels. Dynamic tests subjecting
panels to various charge detonations to examine panel behavior, shear tie tests to characterize
shear tie behavior and panel sensitivity, and static tests subjecting panels to uniform loading to
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determine resistance functions for sandwich wall panels were conducted. Only static tests
conducted on non-prestress panels will be discussed in this paper.
To determine resistance functions, simply supported sandwich panels were tested to failure under
a uniform static load (5). Uniform loading was simulated by subjecting the wall system to 16
individual but equal in magnitude point loads, applied by a single actuator through a loading tree
(see Figure 3). The midspan deflection of each sandwich panel was recorded in order to back
calculate the end rotation of each panel through Equation 1.
Figure 3: Loading Tree Configuration (5)
Non-prestress panels were broken up into groups that varied by shear tie configuration, foam
type and thickness, or wythe thickness. Three non-prestress panels were tested from each group
of panels and a resistance-rotation curve was computed for each panel. An average resistance-
rotation curve and standard deviation was determined for each group of panels. Finally, a
simplified multi-linear response curve was formed based on the average resistance-rotation
curve. Levels of damage for each panel group were determined by taking a given percentage of
the maximum pressure value (see Figure 4). Blowout was considered to have occurred when the
panel’s resistance reached 50% of the maximum pressure. More detailed information on
development of the sandwich panels resistance function can be found in reference (5).
Figure 4: Development of Sandwich Panel Resistance-Function (5)
Table 2 summarizes current US Army LOP and recommended response limits for non-prestress
wall panels based on the static, uniform loading tests (5). The response of the non-prestress
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sandwich panels creates two major differences when compared to blast design methodology.
First, blast design methodology assumes that a simply supported reinforced concrete component
will have an elastic-perfectly plastic response. In reality, the experiments revealed that the
panels behave in an elastic-hardening-softening behavior. The softening behavior is nearly
impossible to predict due to the highly non-linear behavior of concrete due to cracking and
heterogeneity of the material. Furthermore, modeling the softening behavior in current time-
stepping methods is extremely difficult and not practical for the practicing engineer whom will
be responsible for designing sandwich panels. Secondly, non-prestress panels did manage to
meet or outperform the criteria for superficial, moderate, and heavy levels of damage; however,
the panels failed to meet the criteria specified for hazardous or blowout levels of damage. This
implies that a panel design meeting current US Army standards may actually fail prematurely.
While US Army LOP criteria could be reduced for sandwich wall panels, this would also limit
wall panel’s application to certain government structures. An economical system would have to
be employed that meets both blast requirements and environmental requirements.
Table 2: US Army LOP versus Observed LOP (5)
Superficial Moderate Heavy Hazardous Blowout
Current Limits μ≤1 θ≤2.0º 2.0º<θ≤5.0º 5.0º<θ≤10.0º θ>10.0º
Observed Limits μ≤1 θ≤3.1º 3.1º<θ≤5.7º 5.7º<θ≤7.6º θ>7.6º
Tests were recently conducted by the authors on simply supported small scale, single wythe slabs
under a point loading. The panels were 3 in. thick, 12 in. wide, and had a clear span of 4ft. The
slabs were reinforced with 2 #3 bars at 2.5 in. deep in the longitudinal direction and #3 bars
spaced at 9 in. on center in the transverse direction. Conventionally reinforced slabs showed
excellent agreement with the results found in the tests conducted at the AFRL, with softening of
the slabs occurring at approximately 5º of support rotation (see Figure 5 below). From
observation during tests, it was noted that softening began to take place as the concrete
compression zone began to become unstable and crush (see Figure 6 below).
Figure 5: Conventionally Reinforced Small Scale Slab Response
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Res
ista
nce
[psi
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Support Rotation [deg]
Control Average
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Figure 6: Instability of Concrete in Compression Zone
LOCALLY UNBONDING PANELS TO IMPROVE DUCTILITY
Experiments were conducted to examine the effect on the behavior of a slab by locally
unbonding longitudinal reinforcement. Unbonding reinforcement refers to removing any
mechanical (bar deformities, friction, etc.) or chemical (adhesion between mortar paste and bar
surface) bond between the reinforcement and surrounding concrete, thus preventing any shear
transfer at the bar-concrete interface as is common in a conventionally reinforced component
with deformed bars (6). Slabs tested were of the same dimensions and reinforcement
configuration as the conventionally reinforced small scale slabs discussed in the previous
section; however, longitudinal reinforcement was unbonded from the surrounding concrete at the
center of the panel in the region of highest moment.
Three groups of panels were fabricated, one group of panels unbonded for a length of 7.5 in., one
group unbonded for a length of 15 in., and the final group unbonded for a length of 22.5 in.
Unbonded lengths were chosen based on the panel’s plastic hinge length, which was determined
by examining the panel’s curvature over the length as developed by a moment-curvature analysis
(see Analytical and Numerical Models on page 9). Unbonding of the bar-concrete interface was
achieved by sliding Teflon tubing over the reinforcing bars for the prescribed distance (see
Figure 7 below). Tubing with sufficiently thin wall section (1/32 in. thick) and an outer diameter
similar to the diameter of the reinforcement (7/16 in. diameter) was selected to minimize any
effect of enhancing the reinforcement. The ends of the Teflon tubing were taped shut in order to
prevent any grout from entering between the tubing and the reinforcement to ensure the rebar
remain unbonded.
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Figure 7: Unbonding of Longitudinal Reinforcement
Figure 8 below plots the resistance functions of the 7.5 in. unbonded length reinforced panels
versus the predicted resistance function formulated by conventional blast design methodology.
The panels behave in a near elastic-perfectly plastic manner, with the controlling failure
mechanism switching from instability of the compression zone to fracture of the longitudinal
reinforcement. Unlike the conventionally reinforced slabs, the unbonded panels did not exhibit a
softening behavior.
Figure 8: Performance of 7.5in Unbonded Length Reinforced Panels
Three panels from each unbonded group were tested to failure and average curves were formed
for each group. Figure 9 below plots the average curve for each unbonded group versus the
average curve for the conventionally reinforced panel. The response of the slab showed
sensitivity to unbonded length, with an increase in maximum measured support rotation and a
decrease in maximum achievable resistance. Moreover, the greater the unbonded length of the
panel, the greater the reduction in the panel’s post-cracking stiffness. Both 7.5 in. and 15 in.
unbonded groups failed in fracture of the reinforcement, while the 22.5 in. unbonded group could
not be failed due to lack of stroke on the testing apparatus.
0
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0 5 10 15 20
Res
ista
nce
[psi
]
Support Rotation [deg]
UFCUnbond Average
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Figure 9: Average Unbonded Length Curves versus the Control Panel
ANALYTICAL AND NUMERICAL MODELS
Conventional Panel Model
To predict the response of the conventionally reinforced panel, a fiber analysis was performed.
A fiber analysis approximates cross sectional geometry, reinforcement size and location, and
material properties by dividing the cross section up into discrete “fibers”. Each fiber is assigned
an area and a specific force-deformation relationship. Reinforcement layers are superimposed to
the cross section and are assumed to be located in a single fiber layer for simplicity despite the
reinforcement diameter. Figure 10 below provides the concrete and reinforcement material
properties incorporated into the fiber analysis. Stress-strain curves were obtained for concrete by
multiple cylinder tests. Popovics’ unconfined concrete model showed good correlation with the
experimental data (7).
0
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6
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12
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0 5 10 15 20 25
Res
ista
nce
[psi
]
Support Rotation [deg]
Control7.5" Unbond15" Unbond22.5" Unbond
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Figure 10: Concrete and Reinforcement Material Properties
In the fiber model, strains at the top of the concrete section were stepped until equilibrium could
no longer be satisfied. At this point, the section was considered failed and the fiber analysis was
terminated. From the fiber analysis, a moment-curvature relationship is developed for the
section. By knowing the boundary conditions and loading scenario, curvature over the length of
the section can be formulated. Finally, by integrating the curvature over the length with a virtual
moment, the load-deflection of the cross section can be formed. Figure 11 below shows the
results of the fiber analysis compared to bounded experimental results for the conventionally
reinforced control panel.
Figure 11: Fiber Analysis versus Bounded Experimental Results
Unbonded Panel Models
In order to investigate the unbonded panel behavior, finite element models (FEA) and simple
analytical models were developed. The goal of the FEA was twofold. The first goal was to
0 0.005 0.01 0.015 0.02 0.025 0.03
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Concrete Strain
Concr
ete
Str
ess
[psi
]
Ste
el S
tres
s [p
si]
Steel Strain
Popovic's
Model
Rebar
Rebar
Model
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determine the stress/strain distribution in the concrete and in the unbonded reinforcement. The
second goal was to understand the controlling failure mechanism in order to develop a simple
model to predict the resistance function of the unbonded panel. The FEAs are organized in two
categories: the ai plane stress models (models a1 and a2), and the bi beam element models
(models b1 and b2). Straus7®
was utilized to develop the FEA simulations (8).
The ai FEAs model the panel as plane structures with plate elements. The reinforcement was
modeled with truss elements and the unbonded zone is tied to the concrete only by discrete
contact elements in an attempt to simulate actual experimental conditions. The concrete was
modeled with four and three node constant stress plates. Model a1 (see Figure 12) contains a
discrete crack at mid-span and the concrete material properties were taken to be purely elastic.
Model a2 (see Figure 13) models the concrete using smeared cracking properties with Mohr-
Coulomb failure criteria and perfectly plastic behavior. The absence of softening in the concrete
constitutive law is the main limitation of model a2.
Figure 12: Plane Stress Model a1
Figure 13: Plane Stress Model a2
The bi FEAs model the panel with beam elements in the bonded region and with a compression
strut and tension strut in the unbonded region (see Figure 14 and Figure 15). The cross sectional
area of the compression strut was developed from the results of the ai FEA models while the
contact elements
contact elements
unbonded region
concrete
bonded region
discrete crack
contact elements
unbonded region
concrete
bonded rebar
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cross sectional area of the concrete tension strut was approximated to have a depth of twice the
reinforcement cover. The rebar tension strut cross sectional area was calculated from the amount
of reinforcement in the actual experimental panels. The compression strut is located at the top of
the beam and the tension strut is located at the center of the reinforcement. The distances from
the centerline are referred to as h and k, respectively. Model b1 (shown in Figure 14) only
accounts for axial deformation of the rebar strut while model b2 (Figure 15) connects the tension
strut to the beam element with pinned links in order to account for second order effects in the
reinforcements.
Figure 14: Beam Model b1
Figure 15: Beam Model b2
As expected, the stress in the rebar is constant over the unbonded region (Figure 16 from model
a2). This result indicates that second order effects contribution to the overall stress in the
reinforcement is minimal.
Figure 16: Model a2 Rebar Axial Force Distribution
Figure 17 provides the FEA predictions of the panels’ resistance function compared to the
experimental results. From the plot, it is clear that each FEA model correlates well with
compression truss
tension truss: rebar, concrete
rigid link
elastic beam
imposed displacements
unbonded region
k
h
compression truss
tension truss: rebar, concrete
rigid link
elastic beam
imposed displacements
unbonded region
k
h
pinned link
Lb
rebar axial force
distribution
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experimental results until yielding of the longitudinal reinforcement. Models a1 and b2 depict an
elastic-hardening response that deviates significantly from the experimental results as the panel
displacement progresses past yield. The hardening response of each model was attributed to the
fact that the concrete was treated elastically for model a1 and applying rigid links as opposed to
elastic links lead to a magnification of the panel curvature, and consequently higher steel strains
for model b2. Models a2 and b1 provided the best agreement with the experimental results,
suggesting that a simplified analytical model could be developed based on the kinematics from
each model.
Figure 17: Experimental and FEA Model Resistance Functions
Considering the results of the FEAs, the following simple analytical model was developed. The
kinematics shown in Figure 18 is assumed, which accounts for section rotation and large
displacements. The change in length of the unbonded reinforcement from section rotations is
given by Equation 2 where B is the internal moment arm and α is the support rotation of the
panel. The change in length of the unbonded reinforcement from large deflections is given by
Equation 3, where L1 is half the panel span length minus half the length of the unbonded region,
Lb.
Equation 2: Change in Rebar Length from Section rotations
Equation 3: Change in Rebar Length from Large Displacements
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Experimental - 1
Experimental - 2
Experimental - 3
a1
a2
b1
b2
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Figure 18: Kinematics of the Analytical Model
The force in the reinforcement was thus computed by Equation 4 where Kr is the stiffness of the
reinforcement. Consequently, the resisting moment can be calculated from Equation 5. Finally,
the load capacity of the entire system can be determined by considering statics as given by
Equation 6 and as shown in Figure 19.
Equation 4: Force in Rebar
Equation 5: Resisting Moment
Equation 6: System Load Capacity
Figure 19: Equilibrium of Analytical Model for Concentrated Load at Midspan
The results of the analytical model versus the 7.5 in. unbonded length are provided in Figure 20.
“Analytical without cut-off” refers to an analytical model that does not consider damage of the
Kconc
αKrebar
Δuu
L1
L
Ld
d
KINEMATICS
B
rigid beams
not to scale
MR
P/2
P/2 EQUILIBRIUM
L2
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compression zone, while “analytical with cut-off” limits the achievable compressive force
developed by concrete in the compression zone. The depth of the compression zone for the
analytical model is determined through conventional reinforced concrete methods (9). This
simplified analytical model adequately captures the yield point of the unbonded section and
conservatively estimates the ultimate obtainable displacement before rebar fracture. The model
could be refined by developing a more accurate method to determine the compression block
depth; however, for practical design purposes this simple analytical model may be suitable.
Figure 20: Results of Analytical Model versus Experimental Results
CONCLUSION
High risk facilities have minimum blast requirements in order to protect occupants within. With
recent emphasis on “green” buildings, many of these facilities are now mandated to meet LEED
certification requirements. Precast sandwich wall panels are ideal systems to meet both
protection and environmental criteria; however, due to the slender geometry of these panels, they
fail to meet hazardous and blowout LOP as set by the U.S. Army. Additionally, panels behave in
an elastic-hardening-softening behavior which deviates from the assumed elastic-perfectly
plastic response in current blast design methodology. To improve the ductility and behavior of
slender concrete components, experiments were conducted by locally unbonding the longitudinal
reinforcement in the region of highest moment for a distance corresponding to the predicted
plastic hinge length. Local unbonding showed to increase the panel ductility at a decrease
ultimate resistance. Additionally, panels showed sensitivity to the length of local unbonding,
increasing in ductility and decreasing in ultimate resistance with longer unbonded lengths.
Analytical and numerical models were developed in order to predict the behavior of unbonded
wall panels. The resistance function of such panels was seen to be strongly influenced by the
stress-strain behavior of the longitudinal reinforcement.
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Forc
e [l
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Analitical, without cut-off
Analitical, with cut-off
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ACKNOWLEDGMENTS
This project has received support from an NSF grant, PD 08-1637, and from PCI’s Daniel P.
Jenny fellowship.
REFERENCES
(1) PCI Committee on Precast Sandwich Wall Panels, “State-of-the-Art of Precast/Prestressed
Sandwich Wall Panels”, PCI Journal: Vol 2, No 2, March 1997
(2) PCI Blast Resistance and Structural Integrity Committee, “Blast-Resistant Design of
Precast/Prestressed Concrete Components”, PCI Report, July 2010
(3) Department of Defense, “Structures to Resist the Effects of Accidental Explosions”, UFC 3-
340-02, 2008, p. 1106
(4) U.S. Army Corps of Engineers, “Single Degree of Freedom Structural Response Limits for
Antiterrorism Design”, Protective Design Center Technical Report PDC-TR 06-08 – Rev 1, 2008
(5) Air Force Research Laboratory, “Analytical Assessment of the Blast Resistance of Precast,
Prestressed Concrete Components”, AFRL-ML-TY-TP-2007-4529 Interim Report, April 2007
(6) R. Park, T. Paulay, Reinforced Concrete Structures, John Wiley & Sons, 1975, p. 392
(7) S. Popovics, “A Numerical Approach to the Complete Stress Strain Curve for Concrete”,
Cement and Concrete Research, Vol 3 Iss 5, 1973, p. 583-599
(8) G+D Computing, HSH srl, “Theoretical manual, theoretical background to the Straus7® finite
element analysis system” Sydney, Australia, 2004
(9) EN 1992-1-1, “Eurocode 2. Design of Concrete Structures – Part 1-1: General Rules and
Rules for Buildings”, 2004
