Experimental and Numerical Analysis of Reinforced Concrete Columns under Lateral Impact Loading

Abstract

Reinforced concrete bridge columns (RCCs) are vulnerable to collisions with vehicles or vessels. To assess the performance of RCCs under lateral impact loading and to guide the impact-resistant design of RCCs, scaled model tests and numerical simulations were carried out in this study. An experimental facility was designed, and three sets of RCC specimens were tested. The specimens were available in three sizes: 60 cm × 14 cm × 14 cm, 80 cm × 14 cm × 14 cm, and 80 cm × 20 cm × 20 cm. Finite element models of RCCs were created in LS-DYNA, and parametric studies were carried out to investigate the variables influencing the impact resistance of RCCs. According to the findings, the impact mass and velocity had a positive correlation with the extreme value of dynamic strain. When the mass of a model car increased by 22.8% and 45.6% during the impact test, the extreme concrete strain at the same position increased by 22.5% and 42.3%, respectively. In addition, as the longitudinal reinforcement ratio increased, RCCs exhibited significantly less plastic deformation and damage. The findings of this study aided in the formulation of several recommendations for future research.

1. Introduction

Reinforced concrete columns (RCCs) play an important role in bridges by supporting vertical loads from upper structures. They are also vulnerable to lateral impact loads caused by vehicle or vessel collisions. Figure 1 shows the damage to a bridge pier on IH-37 in Texas caused by a truck–tractor collision on 14 May 2004 [1]. On 15 June 2007, a vessel collided with the Jiujiang Bridge in China [2]. After two nearby piers collapsed, the bridge deck fell into the river (Figure 2).

The response of RCCs to transient impact loads differs significantly from that of traditional static loads. Since Abrams [3] discovered that the compressive strength of concrete is rate-sensitive in material dynamics experiments, numerous studies on the rate-related behavior of concrete materials have been conducted. It has been discovered that strain rate affects the mechanical behavior of concrete in a wide range of situations [4,5,6,7,8]. According to these studies, as the strain rate increases, the dynamic load strength of concrete specimens increases nonlinearly.

A variety of research methods, including experimental, analytical, and numerical investigations, have been used to investigate the behavior of reinforced concrete components under impact loads. Most previous experiments in the field have used drop hammer impact to investigate the dynamic responses of reinforced concrete structural members, such as beams, slabs, and columns [9,10,11,12]. Due to the difficulty of carrying out impact tests, numerical simulation has emerged as an important tool for analysis [13,14]. When RCCs are impacted in various locations, they can experience localized failure modes and damage, such as brittle spalling, scabbing, perforation, and punching shear failure, as well as overall flexural failure modes [15,16,17,18,19,20,21,22]. The impact-resistant behaviors of columns differ from those of the beams due to axial load. Previous research has found that the failure modes of RCCs with axial loads are not thoroughly explained, and more research is required to understand the mechanism underlying it.

In this study, an experimental facility was designed to facilitate the application of axial pressure on RCCs. This paper aims to first clarify the failure mechanism of RCCs under lateral impact loading through experimental and numerical research and then to evaluate the key factors affecting the impact resistance of RCCs by a parametric analysis. Firstly, an experimental facility is designed, and three sets of RCC specimens are tested. An analysis is conducted on how the response of RCCs under lateral impact loading is affected by impact energy, boundary conditions, and axial pressure. Secondly, finite element models of the RCCs are created in LS-DYNA. By contrasting simulation results with experimental data, the validity of the numerical simulation method and constitutive material model are established. Finally, parametric studies are carried out to investigate the variables influencing the impact resistance of RCCs.

2. Impact Test

2.1. Experimental Facility

When studying lateral impact, the drop hammer device is a common test device used in the medium- and low-strain-rate ranges. However, providing the initial axial pressure, which is significantly correlated with failure mode and impact resistance, proves difficult. In this study, an experimental facility (Figure 3 and Figure 4) was designed to facilitate the application of axial pressure, and a scaled model experiment was conducted.

To obtain different impact velocities, a model car was released at various heights along the track. The track was made of U-shaped aluminum alloy and measured 200 cm in height and 380 cm in horizontal length. It was made up of three sections: a linear acceleration section, a horizontal straight section, and an arc transition section. Steel plate and roller bearings were used to construct the model car. An aluminum block for impact was fixed on the head of the car. The weight of the empty car was 17.55 kg, which could be added to with the car’s fixing screw. An MTS hydraulic loading device was used to load the axial pressure of the column. A reinforced concrete cap was designed at the bottom of the model column and fastened to the laboratory reaction floor via designated anchor holes. Two strain gauges were pre-buried at the same measuring point in case either of them failed to function during the concrete-pouring and maintenance process. For signal acquisition, an HBM MX1601B data collector was used.

2.2. Reinforced Concrete Column Specimens

Three RCC specimens were manufactured and tested in this study (Figure 5). The dimensions of C_1 were 60 cm by 14 cm by 14 cm. The dimensions of C_2 were 80 cm by 14 cm by 14 cm. The dimensions of C_3 were 80 cm by 20 cm by 20 cm. C30 concrete was used, and four Φ8 steel bars were arranged longitudinally. HPB235 stirrups were arranged as Φ6@5 cm. A BX120-5AA strain gauge was affixed to the longitudinal rebar and covered with a waterproof layer, and a BX120-50AA strain gauge was affixed to the concrete. With four anchor holes set aside, the reinforced concrete cap had dimensions of 65 cm by 65 cm by 10 cm. The three concrete standard test blocks were simultaneously conserved in order to determine the mechanical characteristics of the concrete material. The strengths of the test blocks were 34.2 MPa, 35.8 MPa, and 37.3 MPa.

During the experiment, the following measurements were collected: (1) the concrete vertical and transverse strains on the backside of the impact location; (2) the rebar vertical strain on the backside of the impact location; and (3) the concrete and rebar vertical strains at the bottom. The validity of the strain gauge at the measuring point was checked before the experiment.

2.3. Experimental Procedure

In the impact test, the model car was dropped and accelerated from four different heights to hit the fixed model column in the straight section of the track. A dynamic data collector was used to collect the strain data of the rebar and concrete. The impact velocity was calculated by referring to the video recorded.

To investigate the typical failure modes of RCCs under lateral impact loads and the critical variables influencing the transition to failure mode, two sets of cantilever column impact tests were carried out. Due to the high risk of failure under large axial pressure, the degree of damage to the model column at the maximum impact energy was previously examined using numerical simulation to ensure the experiment’s safety.

The model column section, impact kinetic energy, and axial pressure were considered to determine the experimental conditions, which are shown in

Table 1. Lateral impact experimental conditions.

Column Number	Test Number	Impact Mass (kg)	Drop Heights (cm)	Axial Pressure
C_1	1-1	17.55	30, 80, 150, 200	None
	1-2	21.55	30, 80, 150, 200	None
	1-3	25.55	30, 80, 150, 200	None
C_2	2-1	17.55	30, 80, 150, 200	None
	2-2	21.55	30, 80, 150, 200	None
	2-3	25.55	30, 80, 150, 200	None
C_3	3-1	17.55	30, 80, 150, 200	None
	3-2	17.55	30, 80, 150, 200	20% Pu
	3-3	17.55	30, 80, 150, 200	40% Pu
	3-4	17.55	30, 80, 150, 200	60% Pu
	3-5	17.55	30, 80, 150, 200	80% Pu

. Specimens C_1 and C_2 were subjected to the failure test. The influence of axial pressure was tested by adding an axial load on C_3. The mass of the model car was set as 17.55 kg, 21.55 kg, and 25.55 kg. The drop heights of the model car were set as 30 cm, 80 cm, 150 cm, and 200 cm.

3. Results of the Impact Test

3.1. Failure Mode

Local and integral failure are possible failure modes for RCCs subjected to lateral impact loading. Furthermore, the failure mode is affected by the impact body properties, RCC parameters, and boundary conditions. Local failure refers to damage caused by an instantaneous impact force that manifests as concrete crushing in the contact area and concrete cracking and spalling in the adjacent area. The type of impact load has the greatest influence on integral failure. When subjected to an impulse load with a high peak and low holding, a component’s shear stress quickly reaches failure stress, and bending deformation does not develop significantly, indicating that shear failure is the most likely mode. When a quasistatic load has a low peak and high holding, the bending failure mode is preferred because it allows a component to deform effectively.

There are several explanations for the distinction between RCC impact failure mode and static load failure mode. According to the inertial effect theory, the main reason for the change in failure mode is the inertia response hysteresis of the adjacent impact region under the impact. Another theory proposes that changing failure mode is caused by the uncoordinated effect of strain rate enhancement on cross-section bending capacity and shear resistance under impact loading.

In this impact test, the damage area of C_1 is shown in Figure 6. The following stages of the C_1 failure process were identified through a video-recording analysis: (1) local concrete fell off; (2) cracking occurred in the tension zone of the model column bottom and in the impact contact position locally; (3) cracking occurred on the backside of the impact position; (4) and, in the bottom tension zone, cracks developed and penetrated to form a plastic hinge. Although the impact process of C_1 showed local damage in the impact contact area, the ultimate failure mode was the crack penetration of the bottom tension zone, which was an integral failure.

The damage area of C_2 is shown in Figure 7. The following are brief explanations of the failure process: (1) the concrete fell off in the impact contact zone; (2) cracks in the contact zone and the tension zone at the column bottom were developed; and (3) cracks in the contact zone developed to produce plastic hinges. Despite the development of cracks in the tension area at the bottom, the final failure mode was the formation of a plastic hinge via the local fracture.

3.2. Strain Response

The primary factor affecting the model columns’ strain response was the impact energy. The strain time history of the rebar and concrete of C_1, along with various drop heights, is shown in Figure 8. The contact between the car and the RCC was very brief, as can be seen from the strain time history. Then, the model car rebounded, and the model column oscillated freely to absorb the impact energy. The strain time history demonstrated that the concrete’s strain peak was positively connected with the model car’s drop height. The strain peak of the rebar grew as the drop height increased.

The inertia effect, stress wave propagation effect, and dynamic behavior of the materials were three factors that needed to be considered in the impact problem. Due to the inertia effect, the deformation and force mode of the reinforced concrete column under impact were significantly different from the static effect. At the beginning of the impact, the rebar and concrete deformation were not coordinated. The instantaneous contact between the rebar and concrete was in an inertial constraint relationship due to the inertia effect and the bonding effect between the rebar and concrete. The highest strain of the rebar trailed the peak strain of the concrete. Eventually, when the impact energy steadily decreased, the deformation of the concrete and rebar began to cooperate. The strain time history of the concrete and rebar at the same location in C_1 is shown in Figure 9. As the drop height rose, the stress on the rebar and concrete grew.

The impact mass was modified by adding weight to the model car, with a single ballast weighing 2 kg. The strain time history of the concrete when the drop height was 1.5 m is shown in Figure 10. As can be seen from the picture, when the mass of the model car increased by 22.8% and 45.6%, the extreme concrete strain at the same position increased by 22.5% and 42.3%, respectively.

Additionally, the effect of axial pressure on RCC lateral impact performance was investigated. Prior to the impact test, a pre-load of 50 kN of axial force was applied. After the load was stabilized, the car was gently pushed to hit the model column to test the effectiveness of the acquisition channel.

The strain time history of the concrete of C_3 under no axial pressure is shown in Figure 11. The peak strain rose as the drop height increased. Figure 12 depicts the strain time history of the concrete of C_3 when the axial compression ratio was equal to 0.2. The overall tendency was that, as the drop height grew, so did the strain response of the concrete. Unfortunately, no damaging load was applied due to safety concerns. The axial compression ratio was studied using numerical modeling to see how it influenced the lateral impact failure mechanism of RCCs.

These test results demonstrate how the response and failure mode of RCCs under lateral impact loading was affected by impact velocity, impact mass, and axial pressure. Further analysis was performed next using numerical simulation methods for additional parametric research.

4. Nonlinear Numerical Simulation

4.1. Finite Element Model

The present impact test data of the reinforced concrete members is still scarce since the impact test had a high need for the collecting device, a high safety risk, and high expense. High-precision modeling of the failure processes of reinforced concrete structures under impact is now achievable due to the development of contact algorithms and constitutive material damage models. The impact response and damage failure process analyses of complex structures are often carried out using a numerical technique once the reliability of a numerical simulation tool has been confirmed by a limited number of tests. The finite element method is gradually becoming an important aid to study impact on reinforced concrete structures.

A face-to-face contact algorithm based on a penalty function was used to simulate the impact process between the car and RCCs in this study. The bond slip between the concrete and rebar during the impact process was ignored. The finite element model of a specimen is shown in Figure 13. The constraints in the experiments were modeled by constraining the freedom of the concrete caps, and progressive grid density was used to discretize the concrete cap element. The model car was simplified in the finite element model. Since the impact contact process lasted for a short time, the effects of the car tires and track friction on the impact process were not considered.

The material model of the column and the concrete cap used in the simulation was an elastoplastic damage continuous face cap model [23,24,25]. In the absence of detailed meridian strength parameters, cap parameters, position parameters, and material damage parameters, the model parameters were interpolated values corresponding to the strength of the concrete in the experiment. The material model of the rebar was an elastoplastic follow-up strengthening model, and the steel yield stress rate correlation was considered using the Cowper–Symonds formula [26].

4.2. Results and Discussions

The boundary conditions and local contact conditions were improved to reproduce the impact test conditions. By contrasting the strain time history in the simulation with the experimental data, the reasonability and accuracy of the numerical simulation approach were confirmed. Figure 14 and Figure 15 show the simulation and experimental results of the strain data of C_1 under different drop heights. Regardless of the changing model boundary conditions and damping parameters of the impact system, the numerical simulation values of strain could be well-matched with the experimental results in the curve waveform characteristics and the attenuation law. The cause of the strain peak difference may be the transient edge contact conditions in the experiment.

In the impact test, two different types of failure modes occurred in RCC specimens with different slenderness ratios. The dominant failure mode of C_1 was that the bottom was subjected to tensile cracking and the entire model column was rotated around the bottom, which was an overall failure mode. The dominant failure mode of C_2 was that the local crack in the contact position formed a plastic hinge that penetrated through the contact position, which was a local failure mode. The numerical calculations of the RCC failure process and the outcomes of the experiments were identical.

The comparison of the final deformation of the RCCs is shown in Figure 16. The impact deflection of the two model columns was different under the same drop height. The deflection curve of C_1 showed that there was a plastic hinge around the bottom. The deflection curve of C_2 showed deformation in the area adjacent to the impact position. In addition, due to the reverse displacement of the top of the model column, the impact area was formed on the backside of the model column. The failure modes of the columns obtained by numerical simulation agreed well with the experimental results.

5. Parametric Analysis

5.1. Effect of Impact Energy

By altering the model car’s mass and drop height, the effect of impact energy was evaluated. Figure 17 shows damage cloud maps of model columns at different impact speeds. The main damage areas were the backside inertial tension area and the bottom area. As the impact speed increased, the damage area expanded significantly.

Impact body mass and impact velocity are the two most important factors affecting the contact interface force [27]. Equivalent static impact loads are expressed mostly as a the function of impact mass and impact velocity [1]. Figure 18 shows the relationships among peak contact interface force, impact velocity, and impact mass.

As impact mass and velocity rose, so did impact impulse and peak contact interface force. The link between the contact interface force peak and impact mass could best be matched by a quadratic polynomial in the set of data points examined in this study, whereas the relationship between the contact interface force peak and impact velocity was best-suited by a cubic polynomial.

5.2. Effect of Reinforcement Ratio

To investigate the effects of various reinforcement ratios on the performance of RCCs under lateral impact loading, the longitudinal reinforcement and stirrup diameters were altered.

Along with an increase in longitudinal reinforcement diameter, there was a change in local contact stiffness and an increase in peak contact interface force. Peak horizontal displacement and residual column top displacement decreased with an increase in the longitudinal reinforcement ratio. Figure 19 shows the comparison of the damage to model columns using different longitudinal rebars under the same impact energy (m = 17.55 kg, v = 3.960 m/s). The impact damage zone was the impact backside inertia effect tension zone, and the increase in longitudinal reinforcement size significantly reduced the impact damage.

The local contact stiffness rose with the stirrups’ increasing diameter. The increase in stirrup diameter could significantly reduce the impact deformation of the RCCs. Figure 20 compares the displacement of column tops with various reinforcing ratios. As the diameter of the stirrup increased, the maximum displacement and the residual deformation of the RCCs were reduced. The lateral impact resistance of the RCCs could be increased by increasing the stirrup reinforcement ratio.

5.3. Effect of Concrete Strength Grade

Two factors needed to be taken into account when analyzing how the increase in axial compressive strength affected RCC impact resistance. To begin, the model column entered the plastic damage region at the same load level as the concrete strength rose, somewhat enhancing the model column’s impact resistance. For instance, the dynamic yield strength of the concrete under the impact load was somewhat increased as a result of the correlation with concrete strength rate under the impact load. The relationship between the concrete strength grade and the concrete strength increase coefficient showed that lower strength concrete had a larger power increase coefficient. Figure 21 shows the relationship between impact deflection of model columns and concrete strength.

Figure 22 is an equivalent damage cloud diagram of the continuous face cap model of RCC. The impact damage area of the RCC only slightly lowered as concrete strength grade rose. Due to the correlation between the dynamic strain rate effect of concrete and concrete strength grade, the improvement in concrete strength grade under the analysis conditions of this paper limited the improvement in the lateral impact resistance of the model column from the perspectives of overall impact and local damage.

5.4. Effect of Slenderness Ratio

The influence of the slenderness ratio of RCCs on the impact effect was evaluated using columns with different heights. The heights of the three models were 0.6 m, 0.8 m, and 1.0 m respectively. The boundary of the models was the lower end consolidation, and the top was unconstrained. The fine ratios were 29.7, 39.6, and 49.5, respectively. The impact position was the midpoint of the column. The impact body mass was 17.55 kg, and the impact contact instantaneous velocity was 3.960 m/s. The model column sections and reinforcement were the same as C_1. The finite element models are shown in Figure 23. The constitutive structures of the concrete and rebar were the same as in the previous analysis. The coupling degree of gravity was used to simulate the co-deformation relationship between rebar and concrete. The initial stress of gravity was pre-added using the dynamic relaxation method, and the influence of gravity was simulated with body acceleration.

As column height increased, the maximum contact interface force also increased. The corresponding peaks were 16.134 kN, 17.197 kN, and 18.192 kN, respectively. Figure 24 shows the comparison of the displacement angles of RCCs with different slenderness ratios. The top displacement extreme value was positively correlated with the column height. The maximum lateral displacements of the column tops were 7.6 cm, 13.1 cm, and 22.2 cm, respectively. Under the condition of midpoint impact of the RCCs, the displacement angle was positively correlated with the slenderness ratios of the RCCs.

5.5. Effect of Axial Compression Ratio

Two perspectives can be used to analyze how the axial compression ratio affects the impact resistance of RCCs. On the one hand, the impact resistance and damage failure mode of a column section are impacted by the second-order effect of axial force. On the other hand, the contact interface force time history is somewhat impacted by variations in the axial compression ratio and the contact stiffness between the impact body and the column impact contact area. However, there are differences in existing research conclusions. He Su et al. [28] used an MTS dynamic-loading device to carry out the multipoint loading of RCC lateral impact loads and studied the effect of the axial compression ratio. The specimen lateral displacement increased with increase in the axial compression ratio at the same loading rate. Huijia Wang [29] conducted a shear failure test of 30 reinforced concrete beams. It was concluded that the shear resistance varied with the axial compression ratio. When the axial compression ratio was less than 0.4–0.5, the axial pressure improved the shearing capacity. Xiaozhen Zhou [30] conducted a shear failure test of 18 RCCs. The findings showed that the shear strength rose with an increase in the axial compression ratio when the ratio was smaller than 0.8. The current design standards do not harmonize axial force and section shear capacity. In conclusion, different studies have reached different results about the relationship between the axial compression ratio and the lateral impact behavior of RCCs.

This section compares how the axial compression ratio affected RCC behavior under lateral impact loading. The column size was 80 cm × 14 cm × 14 cm (Figure 25). The axial compression ratios were 0, 0.2, 0.4, 0.6, and 0.8. In the five working conditions, the impact mass of the model car was 17.55 kg, and the impact velocity analyses of impact strength were 2 m/s and 4 m/s. The axial initial pressure in the analysis was loaded using the dynamic relaxation method.

The relationship between peak contact force and axial pressure ratio is given in Figure 26. The peak contact interface force increased with the increase in the axial compression ratio under the same impact energy. In addition, the peak contact interface force at the same axial pressure ratio and the contact holding time increased with the increase in the impact speed.

The relationship between column top displacement and axial pressure ratio is given in Figure 27. With an increase in the axial compression ratio, the column top displacement decreased. With an increase in the axial compression ratio in the scenario of higher impact velocity, the displacement of the top of the column increased more quickly. The damage area and failure mode of the impact scenario model did not differ noticeably, and the damage area of the model column was primarily on the collision side of the root. The peak contact interface force increased to a certain extent due to the stress stiffness caused by the increased axial compression ratio, which also reduced the impact deformation of the RCCs.

6. Conclusions

Experimental and numerical studies were conducted to investigate the performance and failure mode of RCCs under lateral impact loading. The findings of this study led to the following conclusions:

1. The findings of the impact test revealed that the impact mass and velocity were the most important elements influencing the dynamic strain response of the model columns. When the mass of the model car increased by 22.8% and 45.6%, the extreme concrete strain at the same position increased by 22.5% and 42.3%, respectively. The extreme value of dynamic strain was positively correlated with the impact mass and impact velocity.

2. The results indicated that the plastic deformation and the impact damage of the model columns significantly reduced as the longitudinal reinforcement ratio increased. The impact deformation increased with the increase in column height, and the energy conversion time was extended during the contact process.

3. Since the strength increase coefficient (DIF) of the concrete material was related to the strength grade of the concrete, concrete with a lower strength grade could have greater dynamic load strength under the same strain rate. Raising the concrete strength at the experimental impact strain rate improved a model column’s impact resistance only marginally. As the slenderness ratio of the model column increased (the section was constant and the column height increased), the lateral impact failure mode of the model column did not change significantly.

4. The effect of the axial pressure ratio on the model column lateral impact resistance must be examined by integrating the model column action–resistance relationship and deformation capacity. The enhanced axial pressure ratio’s stress stiffness minimized the impact deformation of the model columns while simultaneously increasing the peak contact interface force to some extent.

These research results can provide a reference for impact-resistant design and make it easier to more accurately evaluate the performance of RCCs under lateral impact loading.

Although RCCs with axial forces under lateral impact loading were studied in this work using a self-designed experimental facility, the mechanism of the influence of axial forces on the impact-bearing capacity of RCCs remains uncertain. The authors recommend that extensive experimental work should be conducted when conditions allow, as present relevant experimental data are still scant. Micro-level concrete mechanism studies can assist in understanding the influence of axial forces on the lateral impact behavior of RCCs. Investigations were only performed at the member level in this study, but further studies at the structural level can be conducted in the future.