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Experimental and Numerical Study on Unequal Lateral Impact Behaviorof RC Square Members

34 Khalil AL-Bukhaiti1, Hussein Abas2, Liu Yanhui3, Zhao ShiChun4 and Dong Aoran5

5 1PhD Candidate of Civil Engineering, Southwest Jiaotong University6 2Msc student of Civil Engineering, Southwest Jiaotong University7 3Assistant Professor of Civil Engineering, Southwest Jiaotong University8 4Associate Professor of Civil Engineering, Southwest Jiaotong University9 5Msc student of Civil Engineering, Southwest Jiaotong University

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Abstract: This paper aims to investigate RC square members' response under the effect of an unequal lateral impact force. Impact performances of RC members were first examined by using the drop-hammer impact test system. The importance of unequal lateral impact load was highlighted and addressed by obtaining the RC members' failure mode and dynamic response characteristics. Four different types were experimentally investigated in detail. A finite element (FE) modeling method was proposed and demonstrated to reasonably predict RC members' impact responses. Moreover, evaluating the effect of impact position, height, and hammer mass on the dynamic response characteristics under an impact force was performed. Superior predictions of the numerical model were confirmed with experimental results regarding impact force history, deflection time history, and failure modes, indicating the model's and parametric studies' validity. The findings drawn from the experimental and numerical studies can facilitate improving the impact-resistant performance of structural members.

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Keywords: height and mass combination; failure Mechanism; damage parameter; unequal lateral impact; stress wave; Contact stress; deflection time history; impact energy.

1.25 Introduction

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Reinforced Building structure may need to be reinforced during its life cycle for the following reasons: (1) the building function changes, and the applied load increases. (2) The structural design specification changes, resulting in the original design not meeting the design requirements. (3) Environmental impact, resulting in material degradation, leading to a reduced structural capacity [1] [2]. Reinforced concrete structures are one of the commonly used types of building structures. There are many ways to strengthen the reinforced concrete structures. Building structures are often subject to accidental loads, such as impacts, explosions, and extreme earthquakes [3]. For example, near high-speed rail stations, there may be impacted from derailed trains. Bridges may hit by ships, and skyscrapers may hit by aircraft [4]. Nevertheless, these accidental loads' effects cannot be considered [5], such as the current specification to reinforce existing structures due to the limited development specifications. Many researchers and designers have studied the analysis and design of reinforced concrete (RC) structures for resistance against extreme loads (such as earthquake, blast, and impact). Furthermore, with the increasing number of terrorist attacks and accidental collisions globally,the request for the impact-resistant design of buildings has increased. The impact of structures has attracted much attention in protection engineering, structural engineering, and even national defense engineering. Accordingly, numerous experimental, analytical, and numerical studies have been behaved toward understanding and developing methodologies predicting RC structures' behavior under impact loads. Due to the wide application of concrete materials and the complexity of impact loads, the research on the impact resistance of reinforced concrete structures has always been an important topic in engineering disaster prevention and mitigation. Many scholars have conducted experiments and numerical studies on reinforced concrete members' dynamic impact resistance. Loedolf [6] used a horizontal pendulum with a buffer at the front to study the dynamic response and failure mode of reinforced concrete columns under hard collisions. Fujikake et al. (Fujikake, Li, and Soeun, 2009) conducted drop-weight impact tests on reinforced concrete beams with different reinforcement ratios. They established a two degree of freedom spring-mass model to predict the impact response of members. Saatci et al. [8] studied the influence of the shear mechanism of reinforced concrete beams on crashworthiness through a drop weight test. Zhao Debo et al. [9] discussed the impact resistance and research methods of reinforced concrete beams using the drop-weight impact test. Xu Bin et al. (Dou, Du, and Li, 2014) carried out an experimental study on the impact resistance of reinforced concrete beams. They analyzed the crack development and failure modes of the beam during the impact. Liu Fei et al. (Liu, Luo, and Jiang, 2015) discussed the impact

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response process and failure mechanism of reinforced concrete beams in dynamic damage propagation and impact energy conversion using numerical simulation methods. Zhao Wuchao et al. [12] the damage cap model is used to discuss the influence of material parameters and modeling methods on the simulation results of reinforced concrete beams under impact loads. However, most current research on the impact resistance of reinforced concrete components focuses on the impact force, component deformation, and failure mode. The control parameters studies generally focus on the impact object's quality and speed, component reinforcement ratio, and stirrup ratio. In terms of concrete strength and other aspects, these studies on the impact resistance and failure mechanism ofactual structural members under impact load are not comprehensive and in-depth. Secondly, the research on the damage mechanism of reinforced concrete members under impact load is also not widespread. Based on the above problems, the finite element software ABAQUS was used to simulate the impact test of existing reinforced concrete elements numerically. First, the numerical model's reliability was verified by comparing it with the experimental results. Secondly, impact position, height, and weight of RC members' performance are discussed. The members are mainly the common cross-section, reinforcement, and height of typical concrete members were usually used in the high-speed railway of buildings station. The scale is 1:10, and the impact point's position had been calculated according to the train head and the slide way height.

2.18 Materials and Methods Analysis

19 2.1 Test devise, loading, and measurement scheme2021222324

The test was carried out on the DHR-9401 drop hammer impact tester of the Taiyuan University of Technology. This study investigates the failure mode, impact force, and the RC members' deformationunder the lateral impact scenario. The section's dimensions and reinforcement details are as shown inFig.1. The numbers in Tab.1 defined by the initials of Chinese Pinyin, "F," stands for square members,the first "H" for concrete, "2" for member numbering, as shown in Tab.1.

25 Table1. RC Test specimen's information

No. Longitudinalreinforcement ratio Volume stirrup ratio Impact

heightnumber of test

specimens factorFH1 2.01%(4ϕ8) 0.62%(ϕ4@50) 1 2

heightFH2 2.01%(4ϕ8) 0.62%(ϕ4@50) 2 2

FH3 6.16%(4ϕ14) 0.64%(ϕ4@50) 2 2 Longitudinal reinforcementratio

FH4 2.01% (4ϕ8) 0.31%(ϕ4@100) 2 2 stirrup ratio

(a) (b)

Figure.1 The schematic diagram for a) Specimens dimension b) Cross Section

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The maximum height of the drop hammer guide is 13.47m, and the maximum impact speed can reach15.7m/s. The cross-section of the drop hammer is rectangular, 80mm long, and 30mm wide. Made of chromium (Cr) with high hardness and little deformation under the impact, the weight of a single massis 65 kg. In this test, the total impact head and mass are 270 kg. To clarify the structural member's dynamic response characteristics under the lateral impact, the members are placed in the impact test machine, as mentioned in Liu et al. [13].

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1 2.2 Material properties2 2.2.1 Steel Bar345

According to the "Metal Material Tensile Test Method" (GB/T228-2010) [14][13] and the average ultimate tensile strength (fu) of the steel bar is measured. Parameters such as modulus (E) and elongation (δ) are detailed in Tab.2.

6 Table.2 Rebar performance indicators

Material fuu/MPa E/MPa δ

Longitudinal reinforcement 320 2.1x105 0.21

Stirrup 520 2.0x105 0.22

7 2.2.2 Concrete89

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The concrete strength grade is C30. Concrete test blocks were fabricated by a number of cubics (150 × 150 × 150mm) simultaneously with members' casting. After 28 days of curing in water, the compressive strength test was carried out according to Liu et al. [13], the measured average compressive strength of concrete for 28 days f'c= 43.5 MPa.

3.12 Crack Development

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Due to the imaging distance limitation, the imaging range is only concentrated in the right half of the specimen (i.e., the short-span region). The crack is difficult to observe in the early stage of the impact marked with arrows. The direction of the arrow is perpendicular to the direction of the crack. Fig.2 shows the destruction process of each component captured by the high-speed camera. From Fig.2, when the drop hammer is in contact with the members (0.4ms), two vertical cracks can be observed at the impact point section in specimen FH2 compared to one vertical crack in specimen FH1. Then, at 1.6ms, an oblique cracks were observed between the impact point and the bottom right part of the support in specimen FH2. At the same time, diagonal cracks appeared in specimen FH1 at 4ms.

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Regarding specimen FH3, although the appearance of oblique cracks at 1.6ms, local cracks appeared near the point of impact, indicating concrete’s crushing at the contact zone. Besides, the specimen FH4 suffered from two prominent diagonal cracks at 1.6ms due to the reduction in longitudinal and transverse steel ratio. At (4ms), the cracks then widened quickly and extended downwards the right support, eventually leading to all members' destruction.

Figure.2 Crack development

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1 TEST RESULTS AND DISCUSSION

2 4.1 Interaction Analysis and Impact Time History34567

The degree of freedom defines as the number of independent coordinates required to specify the masses' displaced positions relative to their original location. If the hammer mass can consider as a rigid body in comparison to the impacted members. The hammer can thus model as a single degree of freedom (SDOF) system. The equation of motion of the hammer according to Newton's second law can be expressed as:

mhṻh + f(t)= 0 (1)89

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In equation 1, mh, ṻh are the mass and acceleration of the hammer, respectively. f(t) is the recorded impact force by the load cell mounted in the hammer. When the hammer is dropped freely from a specific height, then the change in hammer speed with time can be described as follow: -ṻh(t)= v0 - ∫t

0f(t)mhdt

(2)

11 Where v0 is the initial impact velocity of the hammer.1213

As presented, the peak impact force for all specimens is concentrated between 294kN to 493kN during (<4ms); the impact time history curves are as shown in (Fig.3).

Figure.3 Impact time history curve

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According to the impact force trend, the impact force curve can divide into three stages: the peak stage, the plateau phase, and the unloading stage. Among them, the peak point occurs at the moment when the drop hammer is in contact with the member, which is due to the massive differencein speed between the hammer and the concrete members. At this stage, the member's deformation is minimal, the support not entirely provides. Fig.3 shows that the peak impact force in specimen FH1 (294kN) is lower than that of specimen FH2 (493kN). Thus, it can conclude that the peak impact forceincreases with the increase of drop hammer height, which is similar to other impact test trends in previous works [8][15].

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1 4.2 Deflection time history analysis234567

Fig.4 shows the deflection time history curve of each member, two different stages identified in the vertical displacement curve: (1) Loading stage, in which the displacement increases from zero to the maximum value; (2) the Unloading stage, in which the displacement decreases from the maximum to the residual value. The deflection shows a slight rebound after reaching the maximum value, indicating that although all specimens have undergone different severe damage types, they still have a residual lateral Carrying capacity.

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The tendencies showed in vertical displacement data generally consistent with specimen damage findings extensions indicated above. From Fig.5, it can note that both the peak displacement and residual displacement at 200mm away from the right support increases with the increase of the drop hammer height for the RC specimens, which have the same reinforcement configuration and different impact height, specimens FH1 and FH2 with a maximum deflection of 52mm and 117mm, respectively. On the other hand, the increase in reinforcement ratio with the same impact energies tends to decrease the maximum deflection, where the results revealed a reduction in maximum deflection (75mm) for the specimen FH3, compared to (117mm) and (125mm) in specimens FH2 and FH4, respectively. The increase of the reinforcement ratio contributes to increasing the members' lateral stiffness, which was prominent in the loading stage, as mentioned above.

Figure.4 Deflection time history curve

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Finally, in specimens FH4, deflections' time history after unloading indicated a constant value without vibration. That indicates the member was severely damaged and exhibited perfect plastic deformation.

20 4.3 Impact force-deflection curve212223242526

As shown in Fig.5, the impact-deflection curves were obtained by combining the impact force and deflection time-history curves. The area under the curve is the energy consumption of the entire member during the impact process. As mentioned above, using the high-speed camera picture after processing, the deflection in this test has been collected. It is noteworthy that the deflection time-history points and the impact time-history curves were not in the same time interval. Therefore, the deflection was not synchronized with the impact force time-history.

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To synthesize the impact-deflection curve, this section utilizes the interpolate module in Origin 19 pro software to supplement the missing points in the deflection time-history curve by linear interpolation

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such that the coordinates points of the deflection and impact force curves lie at the same time interval.From Fig.5, it revealed that when the impact force peaks, the deflection of all members occurred in a small duration (<3 mm), where (20-25) % of the whole kinetic energy is transferred from the impactor to the RC specimens. After the end of the impact force, the impact force enters the plateau stage, in which the deformation of the member begins to develop significantly, and the remaining energy is transferred during this stage. Finally, the specimen starts to unload. Only a small rebound (<5 mm) releases the stored elastic energy due to the severe damage.

Figure.5 impact force-deflection curve.

5.8 Finite Element Modeling

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To save time and money on further investigations on the dynamic response of RC members. ABAQUS Explicit finite element software was utilized to model RC test specimens. The simulation's outcomes were verified with the results of experimental works. ABAQUS Explicit software can provide various contact definitions and material models commonly used to solve non-linear problems with incremental dynamic analysis characteristics.

14 5.1 Material Idealization

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The drop hammer was modeled in finite element software by using linear elastic material models. While an idealized linear-elastic perfectly-plastic behavior for the steel bars is defined to software [16](Hu, Lin, and Jan 2004).

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Regarding concrete behavior, this paper introduced concrete damage plasticity (CDP). This model represents one of the main constitutive models offered by ABAQUS software. It was defined theoretically by Lubliner et al. [18]and then further developed by Lee and Fenves[19].

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In addition to compressive and tensile behavior, other CDP parameters are defined in the software based on recommendations of SIMULIA [20]. Where: Dilation angle (31), Eccentricity (0.1), Fb0/fc0 (1.16), k ratio (0.667) and Viscosity (0).

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(a) (b)Figure.6 The uniaxial response of concrete a) in compression, b) in tension.

1 5.2 Mesh Refinement, Contact Definition, and Strain Rate 23456

The RC specimen's numerical model subjected to transverse impact loading consists of three-dimensional solid elements with a linear reduction integration unit (C3D8R), simulating the concrete block. In addition, 4-node 3-D bilinear rigid quadrilateral (R3D4) elements have been utilized for the impact hammer, as illustrated in Fig.7. In contrast, the longitudinal and transverse reinforcements were modeled as a linear truss element (T3D2), which only stresses the axial direction.

(a)

(b)Figure.7 (a) Modeling assembly; (b) Finite element meshing.

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Next, the experimental specimens' support conditions were modeled. The practical setup demonstrates that the edges of the test specimens act as totally restricted supports. As a result, fixed support was given for both sides of the member to make consistent with the experimental test and simulate such behavior. A further obstacle in the numerical simulation is the modeling of the surfaces of contact. Abaqus/Explicit gives two algorithms for modeling contact interactions. In this article, the SURFACE_TO_SURFACE_CONTACT option has been selected to simulate the contact between a rigid body (impactor) and a deformable body (RC-member); this option offers sophisticated detection algorithms to maintain proper and efficient contact conditions.

15 Simultaneously the software considers the first surface as a master surface and the second surface

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as a slave surface. Although using this algorithm is computational time effective, it is still possible for the master surface (nodes) to penetrate the slave surface and creates a problem in the analysis. Therefore, using a sufficiently refined mesh on the slave surface (RC-members) compared to the master surface (rigid hammer) helped minimize this problem. Finally, the ultimate dynamic bond at failure is 70-100 percent higher than that under quasi-static loading conditions in the reinforcement bars, as reported by Weathersby [21]. Also, the steel deformation under the impact load is restricted to a region just a few centimeters below the impact point (Bentur, Mindess, and Banthia, 1986), whichimplies that, under impact conditions, there is not enough time to establish a substantial bond-slip along the length of the steel bar. Therefore, perfect constraints between the concrete and the reinforcing bars were assumed and defined via EMBEDDED_EELMENTS. Finally, concrete and steel represent strain rate sensitivity materials. Therefore, The effect of strain rate was introduced to the software with the help of equations demonstrated in Liu et al. [13].

6.13 Validation of Finite Element Analysis Results

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To assess the FE model's integrity and accuracy, it is valuable to validate the FE results with the experimental outcomes. Therefore, this section has first introduced the comparison between experimental outcomes and the acquired FE results using ABAQUS software 2019 for specimen FH1. Second, a parametric analysis was then conducted to demonstrate different RC members' behavior under the transverse impact loads. However, in this paper, the most precise strategy was employed by enabling the compression damage parameter (d c ) in the CDP method. Fig.9 shows the crack pattern and damage mode of the experimental observations and the numerical simulation at various time stages. It can be seen that the damage of the concrete obtained by the analysis at 0.4 ms shows the development of diagonal cracks emerging from the impact zone and then propagate downwards with an angle of approximately 45 degrees. Vertical crack starting from the bottom surface of the specimen at the impact zone and the concrete crushing underneath the impact point was also picked up in the analysis at a time of 4 ms, which was similar to the experimental test case.

0.4 ms 1.6 ms

4 ms 10 msFigure.9 Crack development compression between the experimental and numerical results at

different time stages for specimen FH1.

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Moreover, to further verify the numerical model, the evaluation of time histories of impact load and deflection curves for the test results and FE predictions is illustrated in Fig.10. As mentioned above, different instruments were implied for data acquisition. It can be seen from Fig. 10a that the peak impact force in the numerical simulation is (282KN) at 0.07 ms against (294KN) at 0.19 ms in the test for specimen FH1. It is noteworthy that the discrepancy in the first peak may be attributed to several factors such as the load cell arrangement and the occurrence of massive concrete crushing at the

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impact point. In addition, the models generated by the software were able to accurately predict the key point within the impact force curve, which is the mean impact force (Pm) and impact duration (Td). The mean impact force can be taken as pure pules, as evident in previous literature [1] described in equation (10) below. The total contact duration between the hammer and the RC members is as defined in previous research [2].

FE =Iatd= ∫td

0F(t)dttd

(10)

(a) (b)Figure.10 The comparison between the experimental and the FE histories of a) impact force;

b) deflection

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The deflection-time histories curves at 200 mm away from right support for the modeled specimens are plotted in Fig.10b. The correlation between the FE and experimental deflection history indicated models' ability to capture these curves very well for both specimens. Tab.3 presents more details concerning the validation of the experimental tests.

10 Table 3 Comparison of main results collected from FE models and experimental outcomes.

No. Peak impactforce Pmax. (kN.)

Diff. a %

Duration Td (ms)

Diff. a %

Mean impactforce Pm(kN.)

Diff. a %

Maximumdeflection δmax.

(mm)

Diff. a %

Exp. FEA Exp. FEA Exp. FEA Exp. FEAFH1 294 282 4.1 49.99 39.35 21.3 30.23 31.63 4.6 51.18 50.44 1.4

11 Diff.a = (FEA - Exp.Exp. ) × 1007.12 Parametric Study

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Given limited literature on RC members subjected to unequal impact loads conditions. This study's analysis results offer a good prospect to investigate these RC members' behavior via applying a parametric analysis on many variables, which intend to influence the RC member's capacity. Therefore, in this section, further models were simulated and discussed on the effect of hammer position, height and weight.

18 7.1 Effect of hammer position192021222324

The effect of impact position on RC square members' behavior prone to impact loads has not been well documented in the previous studies; thus, it is executed in this section as a part of the parametricanalysis. The simulation analysis was investigated herein by changing the hammer position as a ratio (α) from the right support (x) to the mid-span point by considering RC members' clear span as 900 mm. Three values, 0.44, 0.72, and 1, were selected for α; the value 1 represents the original one taken from the verification analysis of specimen FH1.

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Fig.11 depicted the history of displacement (δ - t) for α= 0.72, and 1. The displacement history exhibited drift and vibrate with a small amplitude after the maximum value indicating the members were slightly damaged compared to the (δ - t) curve for α =0.44, which was already displayed in Fig.10b.

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a) α=0.72 b) α=1Figure.11 Deflection time history for the members at a different position, a) α=0.72, b) α=1

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In Fig.12, the relationship between the maximum deflection δmax and the ratio α is plotted. The results revealed that δmax. decreases by 98.5% with the increment of α from 0.44 to 0.72. On the other hand, the maximum deflection also decreases by 8% when α increases from 0.72 to 1. The decrease of δmax. as the hammer moves from support to the mid-span might be attributed to the presence of fixed support, which generates resistance to the impact energy. Strictly speaking, when the RC member hits by a striker with α=0.44, the stress wave propagation cannot activate the left support's reaction forces. These may be due to crushing damage near the impact zone and diagonal cracks forming from the impact point downwards the right support. Thus, a considerable reduction in the concrete’s Young modulus and the stress wave velocity propagation occurs, which is previously confirmed by Isaac [25]; in his study, the author reported that the dominating propagating wave is not a shear wave but a lower velocity wave. When α=0.44, although a diagonal crack was observed between the impactpoint and bottom surface of the right support, activation of left support has been designated.

Figure.12 Relationship between the maximum deflection δmax. and impact location α.

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To further interpret the decrease in maximum deflection of the square RC members when α=1, the leftreaction force's activation with various α values is drawing in Fig.13. It is noteworthy that the peak impact force for various α ratios has changed marginally. However, comparing the reaction force for different impact positions shows an obvious rise when the α value increases. That Indicates the wave velocity does not disperse due to the slight damage that exists in the members. In comparison to the members with a small α value, which experience an interaction between the coming and reflected waves resulting in lower propagation velocity. Besides, it can conclude that even though the square RC members are adequately reinforced with a transverse bar. However, the opportunity of the shear failure occurrence near the fully restricted supports under impact loading conditions increases. This is similar to the previous studies' trends [13](Demartino, Wu, and Xiao, 2017).

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Assessing the feasibility of changing α value for the RC members under impact load by comparing themodels' final failure mode for various impactor locations in Fig.14. One may notice that as the impactor moves away from the support, vertical cracks under the impact point (concrete's bottom tension fibers) and the top extreme concrete fibers at the supports are dominant.

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Figure.13 Left reaction force record for different α ratio

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It can conclude that the increase of α value for square RC members subjected to impact events contributes to failure mode transition from brittle shear to a more ductile one and, consequently, reducing the maximum deflection.

Time αratio Failure Mode Comparison

0.3 ms

0.44

0.72

1

1.2 ms

0.44

0.72

1

Figure.14 Stress wave and activation of left support for different α ratio

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1 7.2 Effect of different combinations of impactor weight and height234567

At the time of impact, the impulse forces are proportional to the hammer's momentum and impact force duration (Tachibana, Masuya, and Nakamura, 2010). Therefore, to understand the RC members' dynamic response under unequal impact force, this section examines and discusses an extensive study on the effect of different impactor mass. Tab.4 shows the variation of impactor mass, which was considered for each impact velocity. Model FH1, discussed in the previous sections, was selected as a control specimen in this study.

8 Table 4 Variations of impactor mass

No. Velocity (m/sec.) Impactor mass mi (kg)FH1_1.5_ mi 5.43 100,150,200,250,270FH1_2_ mi 6.26 100,150,200,250

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With the further increase in the impact height to 1.5 m and the introduction of the various hammer mass (270, 250, 200, 150, 100) kg, the peak impact force and total duration become (310, 309.856, 309.418, 309.048, 308.243) kN and (56.31999, 36.08, 29.66019, 22.35009, 12.37029) ms, respectively. Finally, at 2 m, the impact force and duration are (279.2, 279.996, 280.408, 280.928) kN and (34.47014, 25.09024, 16.01994, 8.22024) ms, respectively.

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In the initial contact moment, the peak impact force attracts a great deal of attention because it could play an important role in the case of a brittle failure [28]. The results indicate that the reduction of hammer mass applied to the RC members has comparatively a very small influence on the peak impact force under the same impact height. In contrast, the decrease of impactor mass reduces the total duration (Td) of the impacted members. That is confirmed with many studies and exists in the literature (Tachibana, Masuya, and Nakamura, 2010)[29]. However, the increase in the impact height leads to rising in the loading rate. Thus, an improvement in the elastic modulus and strength of the concrete occurs, as confirmed by the research of Xiao et al.[30]. Thereby, the peak impact force and the total impact duration increase with the increase of impact height.

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It is noteworthy that the relative movement between the impactor and the RC members influences theimpact force's formation. The decrease in impact force from the first peak to the second peak was attributed to two main reasons: one is the dramatic reduction in the velocity between the drop mass and the RC member. Another is that the contact zone between the impactor and the RC members was significantly degraded during the earlier impact stage.

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To investigate RC members' impact resistance under the increment impact energy with a different combination of impact height and impact mass, two impact energy were chosen from the results: (1962.5, 2942.9) j, as shown in Fig.15.

Figure.15 Impact force comparison of RC members with different impact energy.

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It can be seen that the differences between the first and second peaks increase as the impact height increases under the same impact energy. That is because the contact region's serious damage causes a rapid loss of RC member's stiffness [31]. Besides, under the same impact energy with the employment of larger impactor mass but smaller impact height, the duration of impact force is longer, indicating longer interaction between the impactor and the RC members. This trend is consistent with Zhang et al.'s study [32], which found that the impact duration expands with the increase of impactor mass and becomes short with the increase of impact height. Moreover, under these two impact

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energies, regression analyses were performed to measure the influences of impactor mass and impact height on RC members' performance. Referring to the influences of impactor mass and impactheight on the deflection of RC members undergoing impact load, Fig.18 illustrates the maximum members' deflections at different impact heights and various impactor mass. It can be clearly evidenced that hammer mass has a noticeable influence on the maximum unequal span deflection.

Figure.18 Comparison of the simulated maximum deflection of the RC members havingdifferent hammer mass.

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To quantify the combined effects of height and mass on the deformation level under identical impact energy. The same input impact energies mentioned before were employed herein (1962.5, 2942.9) j. At a similar impact energy scenario, the slope of the ascending portion of the deflection curve for the members with larger impact velocity is steeper than that for members with low impact velocity, indicating a higher loading rate of deformation, as shown in Fig.19. More remarkably, the utilization of small impact velocity with a heavy impact mass results in higher deformation except for the member with small impact energy. The time required to achieve the maximum value rises as the impact mass increases, implying that the specimen's deflection is affected by the degree of impact force and the drop weight's interaction with the RC member.

Figure.19 Time history of deflection at two different impact energy

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As a result, the degree of deformation of RC members susceptible to unequal impact load conditions is primarily dictated by the impact loadings' impulse. In the meantime, the impulse increases with increment impact mass. It has an inverse relationship regarding velocity under the same impact energy. Therefore, it can be concluded that the influences of impactor mass and its velocity on RC member's deformation could be extracted indirectly.

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8.1 Conclusion

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In the present work, an experimental and numerical study of reinforced concrete members was performed to investigate the effect of unequal impact force. Therefore, the conclusion can be summarized as follows:1.5

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The typical failure modes of RC members under unequal impact are obtained. Several oblique cracks occur in the RC member's concrete right span, and the shear failures were dominated.

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There is a big difference in the members' peak impact force. The energy consumption is stronger before entering the falling stage. Still, due to the longitudinal reinforcement fracture, the failure section has a short duration. The impact performance drops rapidly after entering the descending stage. The impact force was reduced, and the energy consumption capacity was weakened.

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The numerical model demonstrated superior agreement with the experimental findings regarding impact and deflection time history, confirming the model's and parametric studies' validity.

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The impact position as a ratio (α) from right support to mid-span was varied from 0.44 to 1.0. It was found that δmax of the members decreased significantly when α increases from 0.44 to1. The reason would be the concrete's brittle nature increases the opportunity of the shear failure occurrence near the fixed supports, which leads to disperse the wave velocity under impact loading conditions. This trend decreases when the hammer's position moves away from the support, indicating a change in failure mode from brittle shear to a more ductile one. Consequently, it reduces the maximum deflection of the member.

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Independent of the impactor mass, the peak impact force increases as the impact height rise under the same contact surfaces. That means the members' inertial force when the impact force enters peak value is greater than those impacted at a lower height.

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According to the current analysis, RC members' maximum deflection is primarily influenced by the impact mass and impact height. The numerical results revealed that, under identical input impact energy, collisions characterized by massive masses with low height result in greater deflection of the member; the opposite is true. Therefore, the maximum deflection of the members exposed to similar impact energy is indirectly dictated by the impact force's impulse before maximum deformation.

9.32 Acknowledgement

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The authors wish to express their gratitude and sincere appreciation to the authority of The National Natural Science Foundation of China (Grant no. 51378427), the National Key Research and Development Program of China (Grant no. 2016YFC0802205-9), for financing this research, work andalso several on-going research projects related to the durability of concrete structures.

10.37 REFERENCES

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4243[2] F. L. Flager, “The Design of Building Structures for Improved Life-Cycle Performance,”

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[3] “Accidental Load - an overview (pdf) | ScienceDirect Topics,” 2015. https://www.sciencedirect.com/topics/engineering/accidental-load/pdf (accessed Mar. 19, 2021).

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[4] E. Noroozieh and A. Mansouri, “Lateral strength and ductility of reinforced concrete columnsstrengthened with NSM FRP rebars and FRP jacket,” International Journal of Advanced Structural Engineering, vol. 11, no. 2, pp. 195–209, Jun. 2019, doi: 10.1007/s40091-019-0225-5.

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