Abstract
The possibility of acting impulsive loads such as blast and impact on gravity load-carrying structural members such as slabs during
their construction and service life cannot be ruled out. Studies on the response of RC slabs under impact loading are available in
the literature. However, the role of the shear reinforcements in the slab under impact is yet to be investigated. The slab subjected
to concentrated impact loading in the form of falling construction equipment, landslip hazards, and other similar events may cause
punching or perforation. Under quasi-static concentrated loading, the design parameters that contribute to the shear resistance
against punching are (1) concrete strength, (2) flexural steel, and (3) shear reinforcement with vertical legs. In this work, a threedimensional finite element model of a square concrete slab of normal strength concrete (30.10MPa), 1000mm x 1000mm x 75mm,
with tension reinforcement only (0.88%) subjected to low-velocity drop-weight impulsive impact is developed in
ABAQUS/Explicit computer code considering Concrete Damage Plasticity and Johnson-Cook models with strain rate effects and
validated with the experimental results in the open literature. The drop weight is a hard steel cone frustum-headed striker/impactor
with a flat impact face of a total mass of 105kg allowed to fall from 2500mm height, impacting the slab at its centroid. To study
the effect of the vertical shear reinforcement on the impact shear resistance of the slab, the shear reinforcement has been varied by
varying the stirrups’ width, spacing, and the number of compression reinforcement bars while keeping the impact load and other
design parameters such as concrete/steel strength, support conditions, slab thickness, and flexural tension steel constant. Numerical
simulations are executed and the outcomes are presented in terms of displacement-time plots, damage/stress profiles, damage
modes, and damage dissipation energy. The results so extracted are discussed and compared.
1. Introduction
In general, reinforced concrete (RC) slabs are not designed for extreme impulsive loadings but nevertheless, they are subjected to
the loadings such as projectile impact and blast. Researchers had investigated the response of RC slabs subjected to impulsive
loadings by hard impactors. To minimize the damage of the slabs, it seems necessary to understand their dynamic response and
corresponding load-carrying mechanism under low- and high-velocity impact loadings. The degree of local and global failure
modes of response depends upon the design parameters of the slab and impact. The local failure mode of response includes localized
damage in the form of scabbing/spalling of the concrete, perforation, and plugging while global failure mode may include
deformation of the impactor and/or deformation of the target structure through flexure, shear, or combination thereof.
A large-scale laboratory test setup to conduct experimental investigations on the response of RC members under impulsive loadings (blast and impact) is of prime importance. Nevertheless, conducting such experiments in this field demands a lot of
physical work in addition to the cost, time, and complexity involved with the instruments of the test is a herculean task. Numerical
techniques simplify and overcome the aforesaid difficulties and give reasonable acceptable solutions.
High-fidelity FEM-backed dynamic code, ABAQUS/Explicit, in vogue for solving complex problems of high strain rate
loadings for numerical modeling has been used in the present work to collaborate the experimental results in the open literature.
2. Objectives
Objectives of the research work presented herein are:
- To study the dynamic behavior of RC slab without shear reinforcement under low-velocity impact (<15m/sec).
- To investigate the influence of shear reinforcement on the punching shear resistance of the slab subjected to impact loading
by varying the stirrups’ width, spacing, flexural compression reinforcement within the stirrups, and compression steel with
shear stirrups under the impacted area.
3. Review of latest literature
In literature, a limited number of investigations have been carried out, experimentally and analytically/numerically, on the dynamic
response of RC slabs subjected to impulsive impact loading. Kojima [31] tested twelve square RC slabs of five different thicknesses
(60, 90, 120, 180, and 240mm) subjected to impact velocities of 100, 150, and 200m/sec. Localized damage in the form of
reinforcement rupturing, concrete scabbing, and perforation was observed. It was found that the damaged area increases with the
increase of the slab thickness under similar impact load. Chen and May [22] experimentally analyzed six square RC slabs of two
different dimensions: (1) 760mm x 760mm x 76mm, and (2) 2300mm x 2300mm x 150mm, under low velocity impact loads
(between 6.50 and 8.70m/sec). Few researchers [2, 19, 22, 25, 29, 30, 36-37, 39-40] had conducted parametric investigations to
study the influence of support conditions, steel ratio, and slab thickness on the behavior of the concrete slabs under impact loading.
In an experimental study, Zineddin and Krauthammer [46] evaluated the damage modes of RC slabs with different steel
reinforcement ratios subjected to concentric impact load of 2608kg from different heights of 152.40, 304.80, and 609.60mm. It was
found that more reinforcement in the slab resulted in localized punching failure while less reinforcement resulted in brittle concrete
failure. The slab behavior was found dominated by the local failure modes with increased drop height. Berthet-Rambaud et al. [21]
experimentally and numerically investigated the impact resistance of 12000mm x 4400mm x 280mm simply supported RC road
shed of concrete strength 32.50MPa subjected to impact load from two different heights of 15 and 30m. The deflection values were
compared and found similar to those obtained with the ABAQUS computer program. Researchers namely; Dancygier et al. [23]
and Sugano et al. [42], conducted experiments to investigate the damage modes of RC slabs subjected to high-velocity impact
loading. ร
gรฅrdh and Laine [3] numerically analyzed the effect of high-velocity impact on RC slabs using the ABAQUS software.
In these investigations, localized behaviors such as concrete spalling, scabbing, penetration, and shear plugging were found to
dominate the response of the slabs.
Mabrouk et al. [33] tested seven square RC slabs having different shear reinforcement layouts and flexural steel subjected to
quasi-static load. The punching shear resistance of the slab was greatly enhanced with close stirrups’ spacing (50mm) and higher
flexural tension reinforcement. Mohamed and Khattab [35] carried out dynamic analyses using the ABAQUS code to calculate the
punching shear resistance of RC slab provided with shear stirrups subjected to concentric static load. It was observed that the larger
diameter of the shear stirrups in the slab greatly improved its ultimate punching resistance. In addition, close stirrups’ spacing with
a higher diameter of the stirrups contributed further to excels the punching capacity of the slab.
Numerous strength-enhancing techniques were utilized by several researchers [28, 38] to ameliorate the punching shear
resistance of the slabs under concentrated quasi-static loading such as screw anchors, C-FRP laminates, shear heads/studs, and steel
fiber reinforced concrete.
RC slabs usually undergo punching failure mode under impulsive impact loadings. In general, the punching resistance of the
slab is influenced by (1) concrete strength, (2) thickness of slab, (3) flexural tension/compression reinforcement, and (4) shear
reinforcement. Literature reveals that no study to investigate the effects of the shear reinforcements on the punching shear resistance
of the RC slab subjected to low-velocity impact had been carried out. This intrigues the investigators to deepen the understanding
of the influence of shear reinforcement on the impact resistance of the slab.
4. Modeling of RC slab
3-D numerical model of the slab, impactor, and support system is shown in Fig. 1. The details of the flexural tension steel are given
in Fig. 2. In addition to the control model (i.e., slab S0 without shear stirrups), a total of eight finite element models of RC slab
with different shear reinforcement layouts as per Fig. 3 are generated in the ABAQUS computer code. It is worth noting that shear
reinforcements details shown in Fig. 3 are from Mabrouk et al. [33] experimental study on quasi-static punching response of RC
flat slabs. All the models are having identical tension steel with a total percentage of 0.88%, Fig. 2. The stirrups and the flexural
compression bars in each direction are identical. Also, the size and spacing of the stirrups in the two directions are the same. Models
S1-S6 are embedded with shear reinforcement in each direction along the middle of the slab while the last two models namely S7
and S8 are having stirrups only under/around the impacted area of the slab. In general, slabs S1 and S2 are used to investigate the
influence of changing the stirrups’ spacing from 100mm to 55mm with identical tension and compression steel. Slabs S3 and S4
are intended to examine the effect of increasing the number of compression reinforcement bars with identical stirrups’ spacing and
width, shown in Fig. 3. Slabs S5 and S6 are considered to analyze the influence of stirrups’ width and compression reinforcement
ratio while keeping the spacing of the stirrups constant. The clear span of the slab is 900mm [19, 40]. The used stirrups and
compression steel are of the same strength as the flexural tension steel but of 6mm diameter, Fig. 3.
It is noted that the repetitive impact of the drop weight has not been considered in the present analysis. The impactor is a hardsteel cylindroconical shape with a flat impacting face of 40mm diameter with 105kg mass allowed to drop (free-fall) from a height
of 2500mm at rest and is arranged to have a concentric impact on the slab. Self-weight of the slab is also taken into account along
with the impact load using the *LOAD_Y_GRAVITY keycard option in [1]. A little higher time step (1.0sec) than the time of freefall (0.71sec) is considered to take into account the self-weight of the impactor. All the degrees of freedom of the impactor are
restrained except the translation in Y-direction [40]. The slab is supported on a support system consisting of I-beams and columns,
reported in [40]. The columns have their base fixed. Default interactions in the ABAQUS code have been used to define the contact
between beams and columns and between the impactor and the slab. Hinges have been introduced between the common nodes of
the slab and supporting beams through connecting bolts used by Sadraie et al. [40] for stable boundary conditions of the slab (see
Fig. 1).
While generating FE models, the 8-node solid element is chosen to discretize the concrete, impactor (striker), supporting beams,
and columns; and steel reinforcing bars with 2-node beam elements. Default *GEN_CONTACT interaction keycard in [1] is used
to model the contacts between the impactor and the slab, and between the slab and the support system. ABAQUS consists of a
material library with ample plasticity-based material models to simulate the damage and non-linear behavior [4-20, 41, 43, 45]. As
per the literature, material models with supposed “simple-input” requirements are usually considered by a lot of scholars and
engineers owing to the available test data for material properties. The plastic behavior of the concrete is defined in ABAQUS by
Concrete Damage Plasticity (CDP) model [1, 24, 32, 34] considering strain rate effects, and the damage of the slab simulated using
an erosion parameter (*ERODE keycard) based on the maximum principal strain of the concrete (i.e., 0.00357). It is noted that the
original CDP model has been modified as per fib MODEL CODE 2010 (R2010) [27, 34] to incorporate the effects of strain rate on
the concrete subjected to impulsive impact loading. Detailed information on the CDP can be found in [1, 24, 34]. For clarity to
show the damage, the concrete elements are deleted from the FE simulation when ERODE has a value greater than 0.99 in
ABAQUS [1, 10, 19, 40]. In addition, the isotropic and kinematic hardening behaviors of the reinforcement steel are defined using
the Johnson-Cook approach considering a dynamic increase factor of 1.25 as suggested in UFC-3-340-02 [44]. The classical
elastoplastic idealization in [1] is considered for modeling the support system as well as the striker. For acceptable accuracy and
efficient mesh size, different element sizes viz. 20, 15, and 10mm were tried in ABAQUS. The static and dynamic properties of
the materials are given in Table 1.
The present study on the investigation of the influence of shear reinforcements on the punching resistance of RC slab is
concentric impact loading specific.
Referring to Fig. 4, the mode of damage with punching shear including failure of the bond between embedded steel and
surrounding concrete and formation of diagonal cracks along with maximum displacement, are closely matched and in excellent
agreement with experimental results of Sadraie et al. [40] with 10mm finite element size.
 |
| Table 1. Static and dynamic properties of the materials, reported in [19, 40]. |
5. Results and discussion
The following sub-sections discuss the numerical results obtained from the explicit finite element analyses conducted in the present
work:
5.1. Damage profile
In general, all the slabs fail due to the crushing of concrete exhibiting brittle failure mode. Fig. 5 and Fig. 6 show the damage
profiles of the slabs at their bottom and top faces. Table 2 presents the results computed for all the slabs. Referring to Fig. 5(a) and
Fig. 6(a), the damage caused to slab S0 at its top surface due to the impulsive load is localized at the contact area in the form of
punching shear and it propagates in flexure mode diagonally towards the corners but with reduced severity. The reduction in the
severity of damage in flexure mode is evident from the fact that the concrete does not crush along the diagonals. As can be seen
from Fig. 5(a) that the damage due to punching makes the reinforcing bars exposed. The slab S0 experiences total damage (DDE)
of 191.23J, Table 2. To control the punching failure of the slab, shear reinforcement in the two directions is considered.
The shear reinforcement provided in slab S1 not only decreases the punching but also flexural bond failure and formation of
diagonal cracks at the bottom surface in comparison to slab S0 without shear reinforcement, Fig. 5. Application of the shear
reinforcement in slab S1 decreases the total damage by 26% with respect to slab S0.
Reduction of the stirrups’ spacing from 100mm (S1) to 55mm (S2) with identical flexural compression reinforcement lessens
the severity of damage i.e., perforation and cracking both, and makes a significant decrease of the damage dissipation energy (DDE)
by 41% with respect to that of slab S1. Higher shear reinforcement changes the mode of failure from punching (S1) to scabbing
(S2) and controls the flexural bond failure emanated from the critical punching section in slab S1, thus minimizing the DDE of slab
S2 much less than all the other slabs (S3-S8), Table 2 and Fig. 5.
The effect of increasing the compression steel from two bars (S1) to three bars (S3) with identical spacing (100mm) of the
stirrups reduces the severity of diagonal cracking at the bottom surface of slab S3 but unaffected punching of the slab shows that
increase in the compression reinforcement contributes only to flexural resistance of the slab subjected to low-velocity impact, Fig.
5. Further increase of the compression bars from 3 (S3) to 5 (S4) is found to slightly excels the flexural resistance without affecting
the punching of the concrete supports the above inference.
350mm width of the stirrups in slab S5 with 100mm stirrups’ spacing and two bars in the compression zone, chosen in
accordance with the experimental study by Mabrouk et al. [33], slightly reduces the severity of diagonal cracking without improving
the concrete-steel bond failure as well as concrete perforation as compared to 240mm width of the stirrups in slab S1 with same
stirrups’ spacing and compression steel, Fig. 5. A marginal decrease in the DDE of 1.80% is recorded as can be observed from
Table 2. Similar observations on cracking and perforation have been found with regards to slab S6 consisting of five bars in the
compression zone with 350mm width of the stirrups at 100mm spacing, Fig. 5.
The damage behavior of slabs S7 and S8 with the shear reinforcements provided under/around the impacted area is found
comparable to that of slabs S1 and S2 with-through shear reinforcements, Table 2. It is worth mentioning that the above response
of the slabs with shear reinforcements considered in this study is for concentric impact on two-way slabs with isotropic flexure
reinforcements
 |
| Table 2. Computational results of the slabs (S0-S8). |
5.2. Slab displacement and stresses
The displacement profiles are shown in Fig. 7. The displacement time plot of the slabs subjected to impact load is presented in Fig.
8.
The profiles of normal stresses in the steel reinforcement and concrete are illustrated in Fig. 9 and Fig. 10, respectively.
Referring to Table 2, the nominal shear reinforcement provided in the form of stirrups does not contribute to minimizing the
slab displacement except in the case of slabs S2 and S8 with close stirrups’ spacing (55mm) having ๐ด๐ ๐ฃ ๐๐ฆ
๐ ๐๐ฃ
= 1.81 [26] under the
applied impact load; where Asv = Area of 2-legged stirrups (56.54mm2
), fy = 423MPa, b = stirrups’ width (240mm), Sv = stirrups’
spacing (55mm). The peak Y-displacement of slab S2 is found much less than that of the other considered slabs. The results reveal
that close stirrups’ spacing (55mm) with ๐ด๐ ๐ฃ ๐๐ฆ
๐ ๐๐ฃ
= 1.81 greatly improves the punching shear resistance of the slabs (S2 and S8)
subjected to concentric impact. The displacement response of slabs S7 and S8 is found comparable to that of slabs S1 and S2,
however, the normal stresses developed in the materials of slabs S1 and S2 are much less than in slabs S7 and S8, Fig. 8 and Fig.
9.
It is noted that the flexural tension reinforcement of slabs S1, S2, S4 and S8 does not yield i.e., maximum tensile stress is less
than the yield stress level (423MPa) of the steel. The presence of compression steel makes the slabs respond as under-reinforced
under concentric impact. The slabs provided with shear reinforcement with wide stirrups (350mm) make them respond in a similar
fashion. Yielded tension reinforcement for slabs S0, S3 and S5-S7 can be seen in Fig. 9
Comparing the stresses of concrete in slabs S2 and S8, the concrete at the impacted area on the bottom surface of slab S2 gets
crushed at higher compressive strength (34.03MPa > fc=30.10MPa) than the concrete of slab S8 (25.83MPa) shows that the slab
S2 with-through shear reinforcements responds excellent performance with regards to displacement and stresses developed in the
material(s), Fig. 10. Flexural reinforcements and shear stirrups in the two directions in the slab under the impact load seem to have
supported the concrete, and make to develop the compressive stresses before its crushing. Consequently, the flexural steel and
bottom horizontal part of the shear stirrups get develop tensile stresses while the concrete remains in compression.
6. Conclusions
Altogether nine two-way reinforced concrete slabs provided with identical flexural tension steel but having different compression
steel and shear stirrups layouts are analyzed under concentric impact using the ABAQUS/Explicit code in this research work.
Conclusions are as follows:
- (1) Ultimate failure of the slab under the impact load is essentially similar to the failure under quasi-static load [33] by crushing of
concrete.
- (2) Application of shear stirrups improves the punching resistance of the slabs thereby reducing the damage (DDE) by 26% in case
of 100mm stirrups’ spacing having ๐ด๐ ๐ฃ ๐๐ฆ
๐ ๐๐ฃ
= 0.99 and 41% in case of 55mm spacing of stirrups with ๐ด๐ ๐ฃ ๐๐ฆ
๐ ๐๐ฃ
= 1.81. The slabs provided
with-through shear reinforcements are found more effective than the slabs with the shear stirrups at the impacted area only with
regards to displacement, damage (perforation and cracking), and lower level of stresses in the flexural steel.
- (3) The effect of increasing the compression steel reduces the severity of the diagonal cracking at the bottom surface of the slabs
without influencing the punching resistance shows the increase in the compression steel contributes only to flexural resistance of
the slabs under impact loading.
- (4) The cracking resistance of the slabs improves by increasing the width of the stirrups from 240mm to 350mm with insignificant
influence on flexural bond failure and punching of the slabs.
This work recommends the investigations on the response of reinforced cement concrete slabs with shear stirrups subjected to
eccentric impact loading. To have deep insight into the dynamic response, a parametric study of varying materials, span, flexural
and shear reinforcements, seems to be of considerable interest subjected to concentric and eccentric impacts.
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