Numerical investigation on local damage of proposed RC panels under impact loading

Nuclear Engineering and Design 341 (2019) 377–389

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Numerical investigation on local damage of proposed RC panels under impact loading Duc-Kien Thaia, Duy-Liem Nguyenb, Seung-Eock Kima,

T

⁎

a

Department of Civil and Environmental Engineering, Sejong University, 98 Gunja-dong, Gwangjin-gu, Seoul 143-747, South Korea Department of Civil Engineering and Applied Mechanics, Ho Chi Minh City University of Technology and Education, 1 Vo Van Ngan St., Thu Duc District, Ho Chi Minh City, Viet Nam

b

A R T I C LE I N FO

A B S T R A C T

Keywords: Impact loading Reinforced concrete Panel LS-DYNA Dynamic analysis Local damage analysis

The effects of transverse reinforcing rebar on the penetration resistant capacity of the reinforced concrete (RC) panel still remains a challenging problem in the field of civil and structural engineering. In the present paper, we numerically analyze the penetration resistant capacity of three proposed panels with different transverse reinforcing rebar arrangements. The obtained results are then compared with reference solutions derived from the conventional RC panel using T-bars. The components of the RC panel, missile, and support system are fully developed. Material nonlinearity, which considers erosion damage, is employed in this simulation. The IRIS Punching tests are used for validating the numerical modeling of the RC panel subjected to impact loading. Parametric studies with varying transverse reinforcing rebar arrangements and ratios are performed to investigate the penetration response of RC panels. The present numerical result shows that the proposed panels offer a better penetration resistant capacity than that of conventional panels using T-bars. We thus recommend an efficient design of RC panels with a proposed transverse reinforcing rebar arrangement.

1. Introduction RC panels have been commonly employed to protect against impact loading, due to their economic advantage. Researchers have been interested in the penetration resistant capacity of RC panels and slabs. To investigate the local behavior and to study the effects of the deformable missile and the reinforcement on penetration resistance of RC panel, Kojima (1991) and Sugano et al. (1993, 1993) carried out several impact tests on models having various scale. Recently, the VTT Technical Research Center of Finland also performed a number of impact tests on the intermediate-scale panel with the dimensions of 2.1 m*2.1 m under soft and hard missile impact, interpreting its structural behaviors (e.g., see Saarenheimo et al. (2009) and Orbovic and Blahoianu (2011). Based on those test results, Oliveira et al. (2011), Borgerhoff et al. (2011), and Pires et al. (2011) presented several numerical study in order to study the RC panel’s structural behavior under missile impact loading. The aforesaid works provided some important information including the effect of reinforcement, pre-stress, and the deformable missile on penetration behavior of the panel. To improve the penetration resistant capacity of the RC panels under impact loading, Thai and Kim (2014, 2015) numerically investigated the effect of the reinforcement (longitudinal and shear bar)

⁎

ratio, concrete strengths, and reinforcement arrangement on the penetration response of the RC panels by proposing certain efficient designs of RC panels combining different parameters. Currently, the related design codes (e.g. ACI349 (American Concrete Institute, 2013) or ASME Section III Division 2 (The American Society of Mechanical Engineers, 2013) do not consider the use of the transverse reinforcing rebar for RC panels to withstand impact loading. Whereas, Orbovic et al. (Orbovic and Blahoianu, 2011; Orbovic et al., 2015) found that the transverse reinforcing rebar in form of T-headed bars induced a slight influence on improving the perforation resistance capacity of RC panels. While the influence of transverse reinforcing rebar in form of T-headed bars has been studied, the structural effect of the oblique shear bars has not been investigated. The oblique shear bars are expected to induce a better penetration resistance and its role needs to be adequately evaluated. To address the limitation as afore-mentioned, this work is devoted to a numerical simulation of RC panels having different reinforcement arrangements to study its effects on penetration resistant capacities. The numerical results are verified using the test data available in the works of Orbovic and Blahoianu (2011); (Orbovic et al., 2015) and Vepsa et al. (2011). A parametric analysis is performed to investigate the effect of the shear bar types and ratios on the penetration resistant

Corresponding author. E-mail addresses: [email protected] (D.-K. Thai), [email protected] (D.-L. Nguyen), [email protected] (S.-E. Kim).

https://doi.org/10.1016/j.nucengdes.2018.11.025 Received 2 July 2018; Received in revised form 30 September 2018; Accepted 26 November 2018 Available online 29 November 2018 0029-5493/ © 2018 Elsevier B.V. All rights reserved.

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model has a yield strength of 758 MPa, while the compressive strength of the lightweight concrete used for missile filler is 3 MPa. Table 1 list the material properties of the concrete, reinforcing rebar, and other steel components. 3. Finite element (FE) modeling Some achievements on numerical simulation of RC panel under impact loading presented in the previous papers by Thai and Kim (2014, 2015) are repeated in this study. For the sake of completeness and self-containment, some descriptions on FE modeling, constrained, contact, and material models are briefly presented in this section. 3.1. Modeling description The FE modeling of impact tests are developed using LS-Prepost 4.2 program. Fig. 4a shows the full model generated from a quarter model. Due to symmetricity, a quarter of the modeling is developed and analyzed as shown in Fig. 4b. The modeling of components such as panel, rebar, cover plate, roller, and missile are separately developed, and then the full model is subsequently assembled. The contacts between surfaces of components are taken into account. The dynamic structural solver of LS-DYNA (smp_d_R7.1.0 solver) (Software, 2007) is employed for numerical analysis. Fig. 5 shows the quarter FE modeling of the components. The panel as shown in Fig. 5a is modeled using solid elements. Fig. 5b illustrated the FE modeling of longitudinal rebar and the proposed shear bar type 2 (PSBT-2), using the Hughes-Liu beam (type 1) element. Connection between rebar elements is established by merging their duplicate nodes since those connections is assumed to be fixed together. Fig. 5c shows the cover plates and rollers, modeled by shell and solid elements, respectively. Solid element is also used for modeling the head and filled concrete of the missile, whereas, shell element is used for modeling the missile pipe and end plate (see Fig. 5d). Finite element mesh size has a significant effect on the FEA results. To determine the appropriate FE mesh size, numerical convergence are carried out with different number of FE through the thickness of the panel, ranging from 10 to 40 elements. The influence of the number of FE on the analysis results is shown in Fig. 6. It is shown that while residual velocity does not change very significantly as shown in Fig. 6a, scabbing area decreases very rapidly when the number of FE increase from 10 to 30 element, however it does not decrease very significantly when the number of FE increases from 30 to 40 elements, as shown in Fig. 6b. It can be concluded that the numerical convergence is reached when the number of FE is 30 elements or greater. This observation is found for both RC panels with and without T-bar. Therefore, in this study, the number of FE through the thickness of the panel of 30 elements, i.e. the mesh size of about 8.3 mm, is selected. This FE mesh size was also successful used by Orbovic et al. (2015) for the similar problems. The corresponding erosion criterion value calibrated to fit the experimental results is presented in Section 4. Table 2 reports the total element number of the components for a quarter model. To assemble the separated component models, the contact tools available in LS-DYNA program is employed. The contact algorithm is briefly presented in subsection 3.3. Lagrange-in-Solid option is used to model the bond between reinforcement and concrete. The inherent interactions between different parts or elements are treated using the Nodes-to-Surface and Surface-to-Surface options. The appropriate contacts between components are gained on the condition that the nodes set and segments set are used. In the case of the contact between missile and concrete panel, we define the missile segment set and concrete panel segment set as the slave and master part set, respectively. Whereas, in the case of missile and reinforcing bar contact, we define the reinforcing bar node set and the missile segment set as the slave and master part set, respectively. The boundary condition is applied to the nodes selected on the

Fig. 1. Description of RC panel and support.

capacity of RC panels using conventional RC panel using T-bars and proposed RC panels. Different shear bar ratios are considered. The ballistic limit of the missile and the reduction factors used in prediction of the panel thickness are then calculated, and important recommendations and conclusions are given. 2. Design of RC panels 2.1. Geometry description A series of RC panel models, adopted from experimental models used in the works of Orbovic and Blahoianu (2011); (Orbovic et al., 2015) and Vepsä et al. (Vepsa et al., 2011), are modeled and analyzed. The RC panel is clamped onto a steel frame system through the roller of 35 mm diameter as shown in Fig. 1. The dimensions of the panel is 2.1 m*2.1 m, the long span 2.0 m, and the thickness 0.25 m. Steel plates having thickness of 10 mm encases the RC panel’s edges to resist the undesired local damages. Fig. 2 shows four different designs of the RC panels with different transverse reinforcing rebars. RCP-TB panel, as shown in Fig. 2a, has transverse reinforcing rebar in form of T-bar, as used in the study of Orbovic et al. (Orbovic and Blahoianu, 2011; Orbovic et al., 2015). Fig. 2b, c, and d show the RC panel with the proposed shear bar type 1 (RCP-PSBT1 panel), type 2 (RCP- PSBT2 panel), and type 3 (RCPPSBT3 panel), respectively. All the four models of RC panel have two layers of 10 mm diameter longitudinal rebar with 90 mm spacing in each direction and a 25 mm concrete cover. Fig. 3 shows a schematic representation of the hard missile. The hard missile is made from a 10 mm thick steel pipe, having a diameter of 168 mm. For obtaining the sufficient mass and rigidity, the lightweight concrete is used to fill the missile. The missile with approximately mass of 47.0 kg and a total length of 640 mm is gained. 2.2. Properties of materials The concrete used for the panel has an unconfined compressive strength (cylinder test) of 60.0 MPa. The steel used for the reinforcing rebar and other components (cover plate, frame, and roller) has yield strength of 540 MPa and 550 MPa, respectively. The reinforcing rebar has a failure strain of 20.0%. In addition, the steel used for missile 378

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a) RCP-TB (Orbovic et al. [5, 13])

b) RCP-PSBT1

c) RCP-PSBT2

d) RCP-PSBT3 Fig. 2. Design of different RC panels.

(MAT#084), Johnson-Holmquist Concrete (MAT#111), and CSCM Concrete (MAT#159). Among them, MAT#084 and MAT#111 were found to be suitable used for simulation of RC structures under impact loading. Therefore, in this study, we model and compare the two models to find the most appropriate model for the given problem. Plastic-Kinematic Model (MAT#003) is employed for steel components and rebar. It is noted that MAT#084 and MAT#003 were successfully used in the previous works by Thai and Kim (2014, 2015), whereas MAT#111 was used in the same simulation by Mata (2017). Therefore, these models are presented in this subsection very briefly.

roller, whereas the symmetric boundary condition is applied to the nodes selected on the mid-span section of the model. A perfect bonding among missile pipe, filler, and head is modeled by merging their duplicate nodes. 3.2. Material model Materials utilized in this study include concrete and steel. In LSDYNA, there are several material models for concrete simulation such as Concrete Damage Rel3 (MAT#072R3), Winfrith Concrete 379

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expressed as a function of the pressure, strain rate, and damage. The normalized equivalent stress is defined as (Corporation, 2006)

σ ∗ = [a (1 − D) + bp∗n ][1 − c ln(ε ∗̇ )]

(5)

in which, a, b, c, and n are input parameters; D is the damage parameter; p∗ = p / fc′ is the normalized pressure; and ε ∗̇ = ε /̇ ε0̇ is the dimensionless strain rate. The model considers damage from both plastic strain and plastic volumetric strain, expressed as (Corporation, 2006) Fig. 3. Details of the missile (Orbovic and Blahoianu, 2011; Orbovic et al., 2015).

D=

J2 J2 I +λ +b 1 −1 (fc′ )2 fc′ fc′

1.016δ

ε̇ ET = ⎛ ⎞ ⎝ ε0̇ T ⎠ ⎜

⎟

(1)

⎜

1

3.3. Contact algorithm The contact algorithm is already described in detail in LS-DYNA Theory Manual (Corporation, 2006). It is briefly presented in this subsection for the sake of completeness and self-containment. The penalty method is generally employed for treating a contactimpact in LS-DYNA. To apply this approach, slave nodes are defined if it penetrates through the master surfaces. When the slave node ns penetrates through the master surface si, the interface forces are applied at the contact points. According to LS-DYNA Theory Manual (Corporation, 2006), interface forces vector fs are applied to the degrees of freedom of the master segment

⎟

(2) −1):

̇ and EC = γε1/3 ̇ ET = ηε1/3

(3)

The Young’s modulus strain-rate factor can be expressed as

⎛ ε̇ ⎞ EE = 0.5 ⎡ ⎢ ε0̇ T ⎣⎝ ⎠ ⎜

0.016

⎟

ε̇ +⎛ ⎞ ε 0 ⎝ ̇ C⎠ ⎜

⎟

0.026

⎤, ⎥ ⎦

(7)

where σd and σs are the dynamic and static strength, respectively; ε ̇ is the certain strain rate; and C and P are the Cowper-Symonds constants. According to Jones (Jones, 2011); the Cowper-Symonds constants C = 40.4 s−1 and P = 5 can be used for mild-steel.

−1):

• and for high strain-rate (ε ̇ > 30s

(6)

σd ε̇ P =1+⎛ ⎞ σs ⎝C ⎠

1.026α

ε̇ and EC = ⎛ ⎞ ⎝ ε0̇ C ⎠

D1 (p∗ + T ∗) D2

3.2.3. Steel material mode Steel material model used in this study is plastic-kinematic model (MAT#003 in LS-DYNA (Corporation, 2006). The kinematic-hardening model is employed in this simulation, i.e. β = 0. This analysis also considers the strain rate effects of steel model. The steel dynamic strength is taken into account by using the Cowper-Symonds equation as expressed as (Marais et al., 2004)

This model is controlled by four parameters: the two constants a and b control the meridional shape of the shear failure surface; the parameter λ = λ (cos3θ) controls the shape of the shear failure surface on the π-plane; and unconfined compressive strength of concrete, fc’. Damage and failure are not considered in Winfrith Concete. Therefore, the erosion criteria is used to consider the erosion damage of the panels. A sensitivity analysis is carried out to define the appropriate value for the erosion option, as shown in Section 4. The strain-rate effects are automatically taken into account in Winfrith model. The dynamic strength of concrete is equal to its static strength multiplying by the strain-rate enhancement factors. According to CEB-FIP (CEB-FIP Model Code, 1990) and Schwer (2010); the enhancement factors for tensile and compression are expressed as

• For low strain-rate (ε ̇ < 30s

Δεp + Δμp

in which, Δεp and Δμp are the equivalent plastic and plastic volumetric strain; D1 and D2 are damage constants; and T ∗ = T / fc′ is the normalized maximum tensile hydrostatic pressure.

3.2.1. Winfrith concrete (MAT#084) The Winfrith Concrete model, which includes strain rate effects and considers the crack width calculation, was developed based on the Ottosen shear failure surface model, expressed as

F = (I1, J2 , cos 3θ) = a

∑

fs = −lki ni

(4)

if l < 0,

(8)

i

and fm are applied to the four master segment’s nodes

To illustrate the strain-rate enhancement factors corresponding to various strain-rates, Table 3 shows the computed tensile, compressive, and modulus factors corresponding to concrete cubic strength fcu = 72.5 MPa.

f mi

= ϕi (ξi,ηi ) fs

if l < 0,

(9)

where, l = ni × [t − r (ξco,ηco)] < 0; ni = ni (ξco,ηco) is normal to the master surface, in which (ξco,ηco) is the contact point coordinates; and ki is the stiffness factor for master segment, which can be expressed as

3.2.2. Johnson-Holmquist concrete (MAT#111) This material model was developed based on the model proposed by Holmquist et al. (1993). Accordingly, the equivalent strength is Table 1 Material Properties.

* *

Material

Modulus of elastic E (GPa)

Poisson Ratio ν

Density ρ (Kg/m3)

UCS* (MPa)

UTS* (MPa)

Failure strain (%)

Aggregate size (m)

Concrete Lightweight concrete Rebar steel Missile steel Cover plate and roller steel

27.53 10.9 200 205 200

0.17 0.17 0.3 0.3 0.3

2,400 804 7,800 7,850 7,800

60 3 540 758 550

3.34 1 540 758 550

– – 20 20 20

0.008 – – – –

UCS: ultimate compressive strength. UTS: ultimate tensile strength. 380

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(a) Full model.

(b) A quarter model. Fig. 4. 3-D view of FE model.

ki =

fsi Ki Ai2 Vi

,

on the stiffness of contact. The stability stiffness of contact kcs is calculated by:

(10)

for brick elements, and

1 ⎞ kcs (t ) = 0.5 × SOFSCL. m∗ ⎛ ⎝ Δtc (t ) ⎠ ⎜

ki =

fsi Ki Ai max(shell diagonal)

,

⎟

(12)

(11) where, SOFSCL represents the soft constraint scale-factor; m* is a function of the slave mass and master nodes; and Δtc is set to the initial time step size. In case of meshing densities of the two contacting surfaces are similar, the segment based penalty formulation can be suitable used. The penalty stiffness is calculated by:

for shell element. In Eqs. (10) and (11), Ki represents the bulk modulus; Vi represents the volume; Ai represents the face area of the element; and fsi represents a scale-factor for the interface stiffness (defaulted to 0.10). To eliminate the excessive penetration caused by very soft materials, soft constraint penalty formulation is used to add the scale-factor

(a) Concrete panel model.

(b) Reinforcing rebar model (PSBT-2)

(c) Cover plate and roller models.

(d) Missile model.

Fig. 5. Finite element types and mesh. 381

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(a) Residual velocity

(b) Scabbing area Fig. 6. Effects of FE mesh size.

4. Validation of numerical model

Table 2 Total element numbers of a quarter modal for RCP-TB panel. Components

Beam elements

Shell elements

Solid elements

Panel Rebar T-head Missile cover Missile filler Cover-plate Roller Total

– 1,709 – –

– – 2904 381 – 12,150 – 15,435

330,750 – – 81 1,593 – 7,920 340,344

– – 1,709

Recent experimental data available in the works of Orbovic et al. (2015) and Vepsa et al. (2011) are employed for the purpose of validating of the numerical model. The reinforcement panel specimens are depicted in Fig. 7, while missile details are shown in Fig. 3. Table 4 shows the summary of selected impact tests and corresponding material properties. Table 5 presents the dimensions of the specimens and missile. To determine the appropriate material model for concrete in penetration simulation of RC panel, two different material models for concrete are employed and compared. Winfrith Concrete Model does not considers damage and failure. Therefore, damage and failure of the panel is investigated and captured by applying the tool *MAT_ADD_EROSION available in LS-DYNA. A sensitivity analysis is carried out to define an appropriate erosion value. Although there are 14 different criteria available in erosion option, Thai and Kim (2014) and Sagals et al. (2011) found that, the principal strain at failure is the most sensitive criterion. The erosion values in the range of ± 5.0% to ± 20.0% are allotted for the sensitivity analysis. The principal strain of ± 7.5% is then defined as the most appropriate erosion value. Whereas, Johnson-Holmquist Concrete Model requires a set of input parameters, which is derived from the test data. In this simulation, input parameters derived from the same punching tests in VTT and calibrated by Mata (2017) is selected. Fig. 8 compares the damage on the rear face of the panel between Winfrith Concrete (MAT#084), Johnson-Holmquist Concrete (MAT#111), and the test. It is shown that the material MAT#84 provides a better-predicted damage than that of MAT#111. Fig. 9 compares the residual velocity of the missile as the function of time between test conducted by Vepsa et al. (2011) and Calonius et al. (2011), FEA with MAT#084, and FEA with MAT#111. The comparison shows that although the usage of both material models for concrete predicts the residual velocity of missile accurately, however, MAT#084 predicts the degradation of the velocity-time curve more accurate than MAT#111. Therefore, MAT#084 is selected for the further simulation in this study. Two different panel models, without and with T-bars are analyzed and the FEA results are compared to the test data as shown in Fig. 10 and Table 6. Although the cracks are not shown in the tested panel, the total scabbing area obtained from the test includes the spalling area and which is not spalled but cracked under concrete surface. It is observed from the results that the developed finite element models can accurately predict the failure mode of the RC panel. In addition, the analysis results of residual velocities agree well with the test data. However,

Table 3 Calculated strain-rate factors corresponding to fcu = 72.5 MPa. Factor type

0

0.01/s

10/s

300/s

ET EC EE

1.00 1.00 1.00

1.20 1.11 1.15

1.39 1.25 1.33

3.05 2.74 1.43

2

kcs (t ) = 0.5 × SLSFAC .

⎧ SFS ⎫ ⎛ m1 m2 ⎞ ⎛ 1 ⎞ or ⎨ SFM ⎬ ⎝ m1 + m2 ⎠ ⎝ Δtc (t ) ⎠ ⎩ ⎭ ⎜

⎟⎜

⎟

(13)

where, SLSFAC is penalty scale factor; and SFS/SFM are slave/master penalty scale factors, which are defined by user. In this study, since the meshes of master and slave are refined and similar, the default value of the penalty scale factors (i.e. SLSFAC = 0.1, SFS = SFM = 1.0) are used as recommended by LS-DYNA Support. 3.4. Analysis setup In this study, the explicit dynamic analysis is adopted using LSDYNA solver (smp_d_R7.1.0 solver). Dynamic analysis of RC panels under different missile impact velocities of 70, 135, and 200 m/s are carried out. Based on the observation from the test data, we allot the analysis time of 0.02 seconds. To obtain the continuous behavior of structures, the output time interval of 1E-4 seconds is set. Using Winfrith model, the crack patterns of concrete component can be calculated and plot by using crack calculation algorithm. When strain rates are turned on (RATE = 0), the fracture energy (FE) is used to determine the crack width. Since there is no specific guideline on the FE for Winfrith concrete, the value of 95 N/m corresponding to aggregate size of 8 mm is used referred to CEB-FIP (CEB-FIP Model Code, 1990). 382

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Fig. 7. Details of the RC panel specimen (Orbovic et al., 2015; Vepsa et al., 2011).

comparison of scabbing areas between analysis and test results reveals some gaps. This is because the numerical model of the bond between the rebar and concrete and its reality is not identical, and the modeling of the horizontal and vertical bending rebar, which are arranged on the same plane, is also not identical to the reality. In conclusion, these analysis results show that the proposed FE modeling predicts the failure modes and damage of the RC panels subjected to hard missile impact accurately.

Table 5 Dimensions of the specimens and the missile.

5. Parametric study The focus of the present section is a parametric analysis investigating the structural dynamic behavior of the panels using different transverse reinforcing rebar designs. Different missile velocities such as 70 m/s, 135 m/s, and 200 m/s are taken into account in order to investigate the effect of different reinforcement arrangement and its ratio on the structural behavior of the panel with different failure degrees. Notice that only the perpendicular impact is examined in this study. This issue is essential as it was also analyzed in (Thai and Kim, 2014), revealing that the RC panel under perpendicular impact produces the most serious failure. The structural behavior of RCP-TB, RCP-PSBT1, RCP-PSBT2, and RCP-PSBT3 is investigated considering three transverse reinforcing rebar ratio (the area ratio of the transverse rebar to the transverse concrete section) of 0.13%, 0.5%, and 1.13%. Both input parameter and numerical result are then reported in Tables 7–9. The term “distance travelled” stated in the present study represents the distance that missile head travelled. Five different damage modes, classified in the work Thai and Kim (2014), are observed. It includes (1) Full Perforation Mode (FP); (2) Partial Perforation Mode (PP); (3) Full Scabbing Mode (FS); (4) Partial Scabbing Mode (PS); and (5) Penetration Mode (P).

Item

Unit

Amount

Total length of RC panel Length between supports Thickness of RC pane Cover-plate thickness Roller diameter Rebar diameter Shear bar diameter Missile diameter Missile length Total weight of the missile

m m m mm mm mm mm mm mm kg

2.1 2.0 0.25 10 35 10 12 168 64 47.4

5.1. Resistant capacity of panel The penetration resistant capacity of RC panels using different shear reinforcement arrangements is presented in this section. Different impact velocities and shear bar ratios (SBR) are considered as analysis parameters to investigate its effects on penetration resistant capacities of RC panels. Figs. 11–13 show the failure modes of panels having different SBRs under different impact velocities of 70, 135, and 200 m/ s, respectively. Whereas, the relationships between distances travelled of the missile and SBR are shown in Fig. 14a, 15a, and 16a. Analysis results show that, in the case in which the impact velocity of 70 m/s as presented in Figs. 11 and 14a, SBR has slight effect on improving the penetration capacity of RC panel. When SBR equals 0.13%, penetration resistance of conventional RC panel (RCP-TP) is higher than the proposed RC panels. However, an opposite conclusion is found when SBR is higher than 0.5%. Whereas, in the case where the impact velocities equals 135 m/s as shown in Figs. 12 and 15a, when SBR is equal to 0.13%, the resistant capacity of the proposed panels

Table 4 Summary of selected impact tests and corresponding material properties conducted by Saarenheimo et al. (2009) and Orbovic et al. (2015). No.

1 2

Test name

Test P2 Test No.2

Longitudinal rebar

D10 c/c90 D10 c/c90

Shear bar

None D12 c/c90

Missile

Reinforcement

Concrete

Missile weight (Kg)

Impact velocity (m/s)

Yielding strength (MPa)

Failure Strain (%)

Modulus of elastic (GPa)

Comp. strength (MPa)

47.46 47.40

135.0 102.2

540 550

18.67 17.90

27.535 26.224

64.70 56.55

383

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(a) MAT#111

(b) MAT#084

(c) Test (Vepsa et al.)

Fig. 8. Comparison of the damage on the rear face of the panel.

resistant capacities than that of the RC panel using conventional reinforcement having a ratio of 0.5% or higher. Among the four considered models, the RCP-SPBT2 and RCP-SPBT3 panels own the best penetration resistance. 5.2. Scabbing damage Scabbing damage of RC panels subjected to missile impact have been also of interest to many researchers. The relationships between scabbing area and SBR corresponding to different RC panel types under different missile velocities of 70, 135, and 200 m/s are shown in Figs. 14b, 15b, and 16b, respectively. From the analysis results, it is found that different arrangements of the shear bar also induce certain influences on the scabbing damage on the rear face of the RC panels. Nevertheless, these effects do not follow any proper role when changing the impact velocity. In case of a low missile velocity is taken, i.e., about 70 m/s, the scabbing damage does not occur on every panel types, except the RCP-TB panel with a SBR of 1.13%, as shown in Fig. 14b. In the case where the missile velocity is equal to 135 m/s as shown in Fig. 15b, when the SBRs are 0.13% and 1.13%, the scabbing area on the proposed panels is smaller than that on the conventional panel. However, when the SBR is 0.5%, the RCP-PSBT1 and RCP-PSBT2 panels have smallest and largest scabbing area, respectively, whereas the RCPPSBT3 and RCP-TP panels have the same scabbing. However, in case of the impact velocity is 200 m/s as presented in Fig. 16b, the RCP-PSBT2 and RCP-PSBT3 panels have the largest scabbing, whereas RCP-PSBT1 has smallest scabbing when the SBRs are 0.13% and 1.13% and the RCP-TP panel has smallest scabbing when SBR is 0.5%. In conclusion, when the impact velocity is about 70 m/s, the proposed panels show a better scabbing resistance than the conventional panel. However, when the impact velocity is equal or higher than 135 m/s, the proposed panels do not show any significant reduction of scabbing damage area on the rear face of the panels. The reason for these observed phenomena can be explained as bellow: Shear resistance and energy dissipation capacity of the proposed panels are better than that of conventional panel with T-bar. Thus, when subjected to the same impact velocity, penetration of the conventional panel is greater than that of the proposed panels. In other words, the conventional panel is more prone to be penetrated and the damage area on its rear face is smaller due to their less energy dissipation capacity. In contrast, the proposed panels are harder to be penetrated and the damage area on the rear face is greater because the ability of the impact energy dissipation, which is transferred to surrounding concrete cone in front of the missile nose, is better. As a result, when subjected to an impact velocity of about 70 m/s, the proposed panels exhibit a smaller penetration depth and the rear face of the panel is not broken, whereas the conventional panel with T-bar is penetrated deeper so that the rear face may be spalled. When the impact velocity is

Fig. 9. Comparison of missile velocity-time history.

RCP-PSBT2 and RCP-PSBT3 is the same as that of the conventional RC panel, while the RCP-PSBT1 shows a lowest penetration capacity. However, when the SBR is equal or higher than 0.5%, the resistance of proposed panels is much higher than the conventional one. Especially, RCP-PSBT2 and RCP-PSBT3 show a very good capacity in resisting the perforation of the missile. A similar conclusion is found in case in which the impact velocity is 200 m/s as shown in Figs. 13 and 16a, the RCPPSBT2 and RCP-PSBT3 show a better resistance than two other panels. Among the proposed panels, it can be observed that the RC panels RCP-PSBT2 and RCP-PSBT3 have better penetration resistant capacities than that of RCP-PSBT1 (see Figs. 14a, 15a, and 16a). That is because, in the case of RCP-PSBT1 panel type, the oblique shear bar is arranged in one diagonal direction (see Fig. 2b). Although the advantage of this type of arrangement is for convenience in installing the shear bar, its penetration resistance is not very good due to unbalance in absorbing the force induced by the missile. Meanwhile, in the RCP-SPBT2 and RCP-SPBT3 panels, the oblique shear bars are arranged in both diagonal directions (see Fig. 2c and d), which leads to a more symmetry in receiving the shear forces induced by impact force. The main difference between RCP-SPBT2 and RCP-SPBT3 panels are in the RCP-SPBT2 the oblique shear bars are arranged per two intersections of the longitudinal rebar, whereas in the RCP-SPBT3 the oblique shear bars are arranged per each intersections. More dense arrangement of the shear bars in RCP-SPBT3 leads to a higher penetration resistant capacity compared with that of RCP-SPBT2, although the difference is not very significant. In conclusion, the alternative RC panels offer better penetration 384

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(a) RC panel with bending rebar only

(b) RC panel with bending and shear bar

Fig. 10. Comparison of the local damage of RC panels.

Table 6 Comparison of the analysis results with that of the tests.

Table 8 Parametric analysis results of panel impact with V0 = 135 m/s.

Panel type

Method

Initial velocity (m/s)

Failure mode

Residual velocity (m/s)

Scabbing Area (m2)

Longitudinal rebar only Saarenheimo et al. (2009) Longitudinal rebar with Tbar Orbovic et al. (2015)

Test FEA Difference

135 135 0

Perforation Perforation –

45 45.7 1.6%

1.00 1.06 6.0%

Test FEA Difference

102.2 102.2 0

Perforation Perforation –

0.00 0.00 0.0%

0.348 0.312 10.34%

Table 7 Parametric analysis results of panel impact with V0 = 70 m/s. Specimen name

Ratio (%)

Distance travelled (m)

Scabbing area (m2)

Failure mode

RCP-TB-1 RCP-TB-2 RCP-TB-3 RCP-PSBT1-1 RCP-PSBT1-2 RCP-PSBT1-3 RCP-PSBT2-1 RCP-PSBT2-2 RCP-PSBT2-3 RCP-PSBT2-1 RCP-PSBT2-2 RCP-PSBT2-3

0.13 0.50 1.13 0.13 0.50 1.13 0.13 0.50 1.13 0.13 0.50 1.13

0.09 0.09 0.08 0.12 0.09 0.08 0.10 0.09 0.08 0.10 0.08 0.07

0.00 0.00 0.11 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

P P FS P P P P P P P P P

Specimen name

Ratio (%)

Distance travelled (m)

Scabbing area (m2)

Failure mode

RCP-TB-1 RCP-TB-2 RCP-TB-3 RCP-PSBT1-1 RCP-PSBT1-2 RCP-PSBT1-3 RCP-PSBT2-1 RCP-PSBT2-2 RCP-PSBT2-3 RCP-PSBT2-1 RCP-PSBT2-2 RCP-PSBT2-3

0.13 0.50 1.13 0.13 0.50 1.13 0.13 0.50 1.13 0.13 0.50 1.13

0.98 1.33 1.16 1.09 1.06 0.26 0.99 0.27 0.23 0.97 0.26 0.17

0.32 0.20 0.26 0.20 0.15 0.18 0.23 0.28 0.23 0.17 0.20 0.17

FP FP FP FP FP FS FP FS FS FP FS PS

Table 9 Parametric analysis results of panel impact with V0 = 200 m/s. Specimen name

Ratio (%)

Distance travelled (m)

Scabbing area (m2)

Failure mode

RCP-TB-1 RCP-TB-2 RCP-TB-3 RCP-PSBT1-1 RCP-PSBT1-2 RCP-PSBT1-3 RCP-PSBT2-1 RCP-PSBT2-2 RCP-PSBT2-3 RCP-PSBT2-1 RCP-PSBT2-2 RCP-PSBT2-3

0.13 0.50 1.13 0.13 0.50 1.13 0.13 0.50 1.13 0.13 0.50 1.13

2.47 2.52 2.57 2.78 2.46 2.20 2.33 1.85 0.40 2.29 1.83 0.38

0.21 0.20 0.18 0.15 0.23 0.17 0.26 0.30 0.28 0.23 0.26 0.36

FP FP FP FP FP FP FP FP FP* FP FP FP*

* The missile stopped onto the panels soon after perforation. 385

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Fig. 11. Failure modes of RC panels (V0 = 70 m/s).

are about 90 m/s, 120 m/s, 137 m/s, and 148 m/s, respectively. Whereas, the predicted ballistic limit using Degen formula is about 113.2 m/s. As compared to the conventional RCP-TB panel, it is interesting to see that the increments of ballistic limit for the proposed RCPPSBT1, RCP-PSBT2 and RCP-PSBT3 panels are determined by 33.3%, 52.2% and 64.4%, respectively. Whereas, in comparison with Degen prediction, the increments for the proposed RCP-PSBT1, RCP-PSBT2 and RCP-PSBT3 panels are determined by 6.0%, 21.0% and 30.7%, respectively. It is observed from the analysis results that in case of SBR of 0.5%, the proposed panels using the oblique shear bars have a better ballistic limit than the conventional panel using T-headed bars. Moreover, the proposed RCP-PSBT2 and RCP-PSBT3 panels induce a better ballistic limit in comparison with RCP-PSBT1 panel. This observation may lead to a conclusion that the oblique shear bars, using a symmetrical arrangement is the good solution for RC panel subjected to the impact loading. However, this conclusion is only based on a few analysis, which may need more investigation for further validation.

equal to 135 m/s or higher, both panel types are deeply penetrated or perforated, at this time, the proposed panels do not show any significant capacity in reducing the damage area on its rear face due to the complex combination between concrete and reinforcement.

6. Ballistic limit of the missile and panel thickness This section presents the analysis results of the ballistic limit of the hard missile impacting into different RC panel types and the required thickness of the panels. The ballistic limit, represented by V50, is the minimum initial velocity at which the missile has an even (50–50) chance of perforating the RC panel. Four different RC panels, having thickness of 0.25 m, longitudinal rebar ratio of 1.4%, and SBR of 0.5% are analyzed, in order to determine the corresponding ballistic limits. Fig. 17 represents a comparison of the ballistic limits between different panel types and that predicted using Degen formula (Degen, 1980). Analysis results show that the ballistic limits in the case of impacting the RCP-TB, RCP-PSBT1, RCP-PSBT2, and RCP-PSBT3 panels

Fig. 12. Failure modes of RC panels (V0 = 135 m/s). 386

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Fig. 13. Failure modes of RC panels (V0 = 200 m/s).

7. Conclusions

In practical designs, the RC panels should be designed in an appropriate manner so that the scabbing and perforation can be avoided as stated in ACI 349-01 (American Concrete Institute, 2001). NEI 07-13 (NEI 07-13, 2011) recommends using the empirical formulas of Chang and Degen to predict the scabbing and perforation thickness. Compared with the Chang formula (Chang, 1981) in the prediction of the scabbing thickness of the RCP-PSBT2 and RCP-PSBT3 panels with 0.5% shear bar ratio, the reduction factors of 0.80 and 0.78 are determined, respectively. Another comparison of panel thickness was required to prevent perforation damage mode predicted using Degen formula (Degen, 1980) to the analysis results. The present analysis results show that a reduction factor of 0.86 can be determined for the RCP-PSBT2 with 0.5% shear bar ratio. However, a smaller reduction factor of 0.84 is found for the RCP-PSBT3 instead. As presented in the previous discussion, the RCP-PSBT2 and RCPPSBT3 panels are found as efficient designs to withstand the hard missile impacts, and the RCP-PSBT2 is hence recommended for practical design. The main reason may be due to the fact that the arrangement of shear bar in RCP-PSBT3 is too complex, which often causes difficulty for worker to install, while the required thickness of this panel type is not reduced very significantly.

We have developed a reliable nonlinear FE model for fully modeling reinforced concrete panels under impact loading. Two different material models for concrete considering damage and strain rate effect are simulated and compared. The FE modeling is validated against the experimental data. We also present a parametric analysis to study the influence of the transverse reinforcing bar arrangement and its aspect ratio on the penetration response of RC panels. Based on the parametric analyses, efficient designs are thus recommended. Some major conclusions drawn from the study can be summarized as follows: (1). It is found that in the case in which the shear bar ratio is lower than 0.5% the proposed panels do not have the outstanding resistance in comparison with the conventional RC panel. However, when the shear bar ratio is set to be higher than 0.5%, the proposed panels have better resistance than the conventional panel, and the panels with proposed shear bar type 2 (RCP-PSBT2) and type 3 (RCPPSBT3) offer the best penetration resistant capacity among the four. (2). Different panel types have different effects on the scabbing damage occurring on the rear face of the panels. It is found that the proposed panels have an outstanding effect on reducing the scabbing

a) Distance travelled

b) Scabbing area

Fig. 14. Distance travelled and scabbing areas with respect to different transverse reinforcement ratio (V0 = 70 m/s). 387

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a) Distance travelled

b) Scabbing area

Fig. 15. Distance travelled and scabbing areas with respect to different transverse reinforcing rebar ratio (V0 = 135 m/s).

on the panels when the missile velocity is around 70 m/s. However, when the impact velocity is 135 m/s or higher, the scabbing propagation resistance of the proposed panel is not very outstanding in comparison with conventional panel. (3). In comparison with the conventional panel using T-bar having ratio of 0.5%, the increments of ballistic limit are found to be 52.2% and 64.4% for the panel with proposed shear bar type 2 and type 3, respectively. As a result, the panels with proposed shear bar type 2 and type 3 are recommended as efficient designs to withstand the hard missile impacts. (4). In comparison with Chang and Degen’s formulas recommended by NEI 07-13, which are commonly used to predict the panel thickness, some reduction factors are recommended. For scabbing thickness, reduction factors of 0.80 and 0.78 for the panel with proposed shear bar type 2 and type 3, respectively, are recommended. The same situation is found for the perforation thickness, but a reduction factor of 0.86 for panel with proposed shear bar type 2 and 0.84 for panel with proposed shear bar type 3 are also recommended. It is noted that those reduction factors are proposed based on the analysis of the panel having thickness of 0.25 m, therefore, further investigation is need for validating the proposed values. (5). For practical designs, we recommend using panel with proposed shear bar type 2 having SBR of 0.5%. To satisfy all required thickness, the scabbing thickness may be the design thickness of the panel. Therefore, by using the panel with proposed shear bar type 2, the design thickness of the panel can be reduced to about

Fig. 17. Residual velocity vs initial impact velocity.

20%. (6). It is also found from this study that the oblique shear bars using a symmetrical arrangement shows a significant influence on preventing the perforation of the panels. Different values of the oblique angle may differently alter the penetration resistant capacity of the panels. Nevertheless, the optimal oblique angle has not been determined yet, and that would be a very interesting research topic for our future work.

a) Distance travelled

b) Scabbing area

Fig. 16. Distance travelled and scabbing areas with respect to different transverse reinforcing rebar ratio (V0 = 200 m/s). 388

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8. Declaration of conflicting interests

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