Study on Impact Resistance of All-Lightweight Concrete Columns Based on Reinforcement Ratio and Stirrup Ratio

Abstract

All-lightweight concrete (ALWC), using non-sintered fly ash ceramic pellets and pottery sand as coarse and fine aggregates, is a novel energy-efficient and environmentally friendly building material that has emerged in recent years. However, its structural behavior under impact loading remains to be thoroughly studied. This paper examines the dynamic response of four ALWC columns with different longitudinal reinforcement ratios and stirrup ratios under lateral impact loading using drop hammer tests. The effect of stirrup densification on the impact resistance was analyzed, focusing on the failure modes, impact forces, acceleration, and midspan displacement time history curves. Results showed that increasing the reinforcement and stirrup ratios shifted the column failure mode from shear to flexural failure, significantly enhancing peak impact force and reducing both midspan and residual displacements. Densifying the stirrups in the column ends resulted in localized flexural failure, with first and second peak forces increasing by 7.43% and 55.98%, respectively, thereby improving impact energy absorption and reducing impact damage.

1. Introduction

In recent years, building structures and components have increasingly been subjected to accidental explosions, collisions, and other impact-related incidents, resulting in significant loss of life and property. Therefore, enhancing the impact resistance of structures has become a key research focus in civil engineering [1,2,3,4]. The fully lightweight concrete used in this study replaces conventional aggregates with non-sintered fly ash ceramic pellets and pottery sand, which not only reduces the structural weight but also facilitates the reuse of industrial solid waste, minimizing the energy consumption and carbon emissions associated with conventional sintered aggregates. To promote the application of fully lightweight concrete in engineering and ensure structural safety under accidental loads, this study investigates the impact resistance of fully lightweight concrete columns [5,6,7,8].

Current research on the impact resistance of concrete columns has been extensive, with many scholars employing experiments and numerical simulations to explore different aspects. Wang et al. [9] conducted lateral impact tests on all-lightweight concrete columns under different axial compression ratios. The results showed that as the axial compression ratio increased from 0.1 to 0.3, the failure mode changed from bending failure to shear failure. The peak values of the first impact force increased by 8.7% and 9.8%, respectively, while the peak values of the second impact increased by 3.2% and 213.3%, respectively, and the energy consumption of deformation increased by 12.37% and 104.32%, respectively. This provided a solid foundation for the design of axial compression ratios in this study. Thilakarathn [10] established numerical models to simulate the failure modes of concrete columns under transverse impact, identifying impact energy as a critical factor influencing damage. Huang [11] proposed using basalt fiber-reinforced polymer (BFRP) bars to reinforce geopolymer concrete (GPC), instead of ordinary steel-reinforced concrete (OPC). Their study of the impact response of these columns under lateral impact showed that the BFRP-GPC columns had different impact characteristics compared to conventional steel-reinforced concrete columns. Meng [12] investigated the dynamic behavior of lightweight ultra-high-performance concrete (L-UHPC) under high-speed impact, finding that changes in strain rate significantly affected L-UHPC, with higher strain rates leading to greater damage, higher peak stress, and increased energy absorption. Fan [13] conducted detailed experiments on three different types of ultra-high-performance fiber-reinforced concrete (UHPFRC) to enhance reinforced concrete (RC) columns. The performance of columns reinforced with UHPFRC at both ends (potential plastic hinge regions) was superior, with increased impact strength observed when UHPFRC was added in the contact zones. However, this reinforcement also led to a significant increase in impact force. Columns reinforced with UHPFRC at both the contact zones and both ends were found to be the least effective configuration, as the remaining RC section was more prone to shear (or punching) failure.

Longitudinal reinforcement and stirrups are crucial load-bearing components of reinforced concrete columns, and studying the influence of reinforcement and stirrup ratios on the impact resistance of concrete components is of great practical importance. Mohamed Esaker [14] established an experimental database of high-speed impact responses for concrete components, which helped identify critical failure modes and parameters affecting impact resistance. He highlighted a gap in current research on reinforcement types and ratios. Thong M. Pham [15] examined the effect of reinforcement ratio on the failure modes and impact resistance of GFRP-reinforced OPC columns under lateral impact. They found that the maximum compressive and tensile stresses of longitudinal GFRP bars were approximately 910 MPa (98% of fracture strength) and 125 MPa (14% of fracture strength), respectively, contributing significantly to the column’s load-bearing capacity. The impact resistance and failure mode of the columns were found to be significantly influenced by the longitudinal reinforcement ratio. H. Othman [16] conducted free-fall low-speed impact tests on five high-strength concrete slabs with varying reinforcement ratios (1.0%, 2.0%, 3.0%) and reinforcement layouts (single or double-layered slabs) and found that under the same impact load, crack patterns and failure modes depended largely on reinforcement layout. Zhong [17] used LS-DYNA software to numerically simulate reinforced concrete beams with different stirrup ratios, showing that at the same impact velocity, increasing the stirrup ratio changed the failure mode from localized punching shear to flexural failure.

All-lightweight concrete (ALWC) columns, made of non-sintered fly ash ceramic pellets and pottery sand, represent a new class of building materials, with limited research on their impact resistance. This study aims to address this gap by conducting drop hammer impact tests on ALWC columns with different reinforcement and stirrup ratios. An analysis was conducted on impact force, acceleration, and midspan time history curve, assessing their impact resistance and failure modes and providing a basis for improving the impact resistance of ALWC columns.

2. Experiment Program

Figure 1 represents a simple flowchart of this experiment.

2.1. Materials

The mix design for all-lightweight concrete followed JGJ/T12-2019 “Technical Standards for Lightweight Aggregate Concrete” [18]. The mix ratios for ALWC columns at LC25 grade is provided in

Table 1. ALWC proportioning detail.

Cement (kg/m3)	Fly Ash Ceramic Pellets (kg/m3)	Pottery Sand (kg/m3)	Fly Ash (kg/m3)	Water (kg/m3)	W/C	Water Reducing Admixture %
450	693	531	50	200	0.4	3.6

. The non-sintered fly ash ceramic pellets used had a particle size of 5–16 mm, and the pottery sand ranged from 3 to 4 mm in size, as shown in Figure 2. According to GB/T17431.2-2010 “Lightweight Aggregate and Its Test Methods” [19], the average bulk density of the ceramic pellets was 772 kg/m³, and the average compressive strength was 10.1 MPa. The mechanical properties of the non-sintered fly ash ceramic pellet lightweight concrete, such as compressive strength, axial compressive strength, and elastic modulus, were measured based on GB/T50081-2019 “Standard for Test Methods of Concrete Physical and Mechanical Properties” [20].

Table 2. Mechanical properties of ALWC.

Strength	Cube Compressive Strength MPa	Axial Compressive Strength MPa	Elastic Modulus MPa
LC25	26.3	20.8	3.02 × 104

presents the average basic mechanical properties of the lightweight concrete used in the experiment after 28 days of curing. The reinforcement strength grade was HRB400, and its mechanical properties were determined based on GB/T 228.1-2010 “Metallic Materials—Tensile Testing at Ambient Temperature” [21], as shown in

Table 3. Mechanical properties of steel.

Reinforcement Diameter mm	Yield Strength MPa	Ultimate Tensile Strength Mpa	Elongation %	Elastic Modulus GPa
14	492	679	17.6	201
12	489	661	18.9	204
8	462	647	20.7	195

.

2.2. Specimen Design

To examine the effects of longitudinal reinforcement ratio, stirrup ratio, and stirrup arrangement on the impact resistance of all-lightweight concrete columns, four specimens were designed, as specified in

Table 4. ALWC column design parameter details.

No.	Longitudinal Reinforcement Ratio	Stirrup Ratio	Longitudinal Reinforcement	Stirrup Spacing in Non-Densified Region
FACSC-1	0.72%	0.27%	4C12	C8@150
FACSC-2	0.98%	0.27%	4C14	C8@150
FACSC-3	0.72%	0.40%	4C12	C8@100
FACSC-4	0.72%	0.42%	4C12	C8@100

. The cross-section dimensions of the columns were 250 × 250 mm, with a total length of 2500 mm. One end of each column was embedded with four fixed anchor rods at a depth of 500 mm. To ensure an axial compression ratio of 0.2 for all specimens, a horizontal actuator was used to apply an axial force of 150 kN. Longitudinal reinforcements were symmetrically placed at the four corners, and the stirrups had a diameter of 8 mm, with spacings as detailed in Table 4, and the reinforcement layout is illustrated in Figure 3. The drop hammer used for the impact tests had a circular head with a diameter of 220 mm, weighing 237 kg, impacting from a height of 2.5 m, with an impact velocity of 7 m/s, resulting in an impact energy of 5807 J.

Specimens FACSC-1 to FACSC-2 were designed to study the effect of different longitudinal reinforcement ratios on the impact resistance of ALWC columns. Specimens FACSC-2 to FACSC-3 examined the impact resistance of ALWC columns with different stirrup ratios. Specimen FACSC-4, based on the reinforcement of FACSC-3, had an additional densified stirrup section of 250 mm at both ends, with a stirrup spacing of 50 mm in the densified sections, to investigate the effect of end stirrup densification on lateral impact resistance.

2.3. Drop Hammer Impact Test Procedure

2.3.1. Test Loading Setup

Figure 4 shows the drop hammer impact test setup. The setup consists of an axial loading system, a support restraint system, and a drop hammer impact system. In the axial loading system, the hydraulic actuator base was bolted to the left-side reaction frame, with the loading head applying an axial load to the left end of the specimen. The right end of the specimen had four fixed anchor rods embedded, passing through the right-side reaction frame and secured with nuts. In order to establish a self-balancing system that matches the thrust of the hydraulic actuator, the reaction frames on both sides were firmly fixed to the foundation using anchor points. Subsequently, the prestress applied by the actuator was used to initially apply tension to the four horizontal pull rods, ensuring the stability and appropriate deformation capacity of the rods. The column ends were fixed to the pedestal using four vertical pull rods for each end (fixed support). To ensure the horizontal alignment of the actuator, a supporting pedestal was placed under the loading end.

2.3.2. Measurement Plan

The impact test was conducted using a drop hammer test setup from Jilin University of Architecture, and data acquisition was performed using a NIPXI e-1006Q device from NI Corporation (Shanghai, China), with NI SignalExpresss2014 NI SignalExpresss2014, at a sampling rate of 1 MHz and temporal resolution of 1 µs. The layout of strain gauges, accelerometers, and displacement transducers is shown in Figure 5. The accelerometers and displacement transducers were used to measure the transverse acceleration and displacement at the midspan of the columns. The stirrup strain was measured using strain gauges S1 to S4, while longitudinal reinforcement strain at midspan was measured by D1 and D2, and strain at the quarter points of the midspan was measured by D3 and D4. Additionally, three concrete strain gauges, C1 to C3, were placed along the column height on the side surface at midspan to measure concrete strain at the impact location. The impact force was measured using a load cell located above the drop hammer. A high-speed camera was used to record the entire impact test process.

3. Results and Discussion

3.1. Impact Failure Process

The impact failure process of the columns could be divided into three stages: initial non-response, local response, and global response. The initial non-response stage was the phase in which kinetic energy was formed. During this stage, the drop hammer fell freely, and the decreased gravitational potential energy was converted into kinetic energy, without any contact between the hammer head and the column. In the local response stage, once the hammer head made contact with the column, the effect of boundary conditions on the column was minimal, with only the near end of the column responding to the impact load, while the far end remained unaffected and stationary. In the global response stage, the entire column was activated, undergoing deformation along its height, including the free vibration effect caused by long-term elastic–plastic deformation after impact [22,23].

All four specimens experienced the aforementioned three stages during the impact failure process. Taking specimen FACSC-1 as an example, its failure process is shown in Figure 6. Figure 6a shows the drop hammer descending, with the hammer above the specimen, not yet in contact. Figure 6b shows the moment of contact between the hammer and the specimen, with an indentation forming at the impact location and diagonal shear cracks appearing at the edges of the contact area. Short vertical cracks appeared at the bottom of the specimen, which widened and extended as time progressed. Figure 6c shows the drop hammer moving downward to the maximum displacement after contact, where the indentation depth and area at the impact location reached their maximum. One of the diagonal shear cracks developed into a critical crack, and vertical cracks at the bottom extended towards the impact point, forming diagonal cracks. Several diagonal cracks appeared parallel to each other near the midspan, with additional diagonal cracks forming away from the impact point. After the formation of the critical diagonal crack, it propagated through the column, leading to large-scale spalling of concrete at the bottom of the column. Figure 6d shows the moment when the hammer completely separated from the specimen, with the column moving upward under a deceleration equal to gravitational acceleration (g). Figure 6e shows the second contact between the hammer and the specimen, resulting in significant spalling of the concrete in the contact area and fragments splattering. Figure 6f shows the process of the hammer rebounding from the specimen and oscillating together with the specimen. The hammer fell onto the specimen for the second time, causing repeated up-and-down vibrations until they stopped. Ultimately, cracks on the specimen were radially distributed around the impact point, forming wedge-shaped cracks from the impact point to the bottom surface of the column, extending in a figure-eight shape to the top and bottom of the column. The column primarily exhibited shear failure, with localized punching failure. Damage to each column is shown in Figure 7.

For specimen FACSC-2, the damage was mainly concentrated at the top of the column at the impact location. During the early stage of contact between the hammer and the column, a few punching shear cracks formed, while vertical bending cracks appeared at the contact location and at the midspan bottom. The bottom cracks gradually extended towards the impact point, and their width increased as column deflection grew. Some bending cracks developed into longitudinal bending diagonal cracks. After the hammer and column experienced inertia-induced rebound, the movement tended to stop. The failure mode was predominantly bending, with localized punching failure. Compared to FACSC-1, specimen FACSC-2 did not exhibit cracks in the shear–bending region, and the number of bending cracks in the tensile region was reduced, with significantly shorter diagonal cracks. No through-punching diagonal cracks formed across the specimen, as seen in Figure 7b, and the bottom cracks were small without significant concrete spalling, while midspan deflection was minimal. Therefore, increasing the longitudinal reinforcement ratio enhanced the local punching shear resistance, and the overall failure mode transitioned from shear failure to bending failure, effectively improving the column’s lateral impact resistance.

For specimen FACSC-3, at the moment of contact between the hammer and the column, diagonal shear cracks appeared on both sides of the midspan, and minor vertical cracks appeared simultaneously in the tensile region, indicating bending failure. The impact face experienced penetration damage accompanied by partial concrete crushing and spalling. The bending cracks gradually widened and propagated into the compression region, with diagonal cracks forming on both sides of the midspan at the column base due to shear tension. As the impact load continued, column deformation reached its maximum, and two diagonal cracks on the right side of the midspan rapidly propagated towards the impact point, reaching their maximum width. The failure mode was characterized by bending failure and localized punching failure. Compared to FACSC-1, specimen FACSC-3 had a smaller damage area, with only a few bending cracks appearing in the pure bending section of the tensile region, and the crack width decreased, with an overall reduction in the number of cracks. As shown in Figure 7b,c, the bottom cracks of specimen FACSC-3 were not apparent, and the degree of damage to the penetration surface was reduced. Therefore, increasing the stirrup ratio effectively restrained the development of diagonal cracks and reduced the severity of punching failure. Compared to FACSC-2, specimen FACSC-3 had fewer vertical cracks in the tensile region, with smaller widths and an overall reduction in the damage area. Thus, increasing the stirrup ratio more effectively enhanced the impact resistance of the column.

For specimen FACSC-4, under the same impact load, minor shear cracks appeared at the impact point upon initial contact between the hammer and the column, and several minor vertical cracks appeared on the surface of the tensile region at midspan. When the midspan displacement reached its maximum, a diagonal crack on the right side of the midspan propagated to the top, but no diagonal cracks passed through the compression region. A clear diagonal crack formed at the interface between the densified stirrup region and the non-densified region due to the uneven strength at the interface. The indentation on the top of the column where the hammer made contact was not apparent, and minor concrete spalling occurred in the tensile region at the midspan bottom. The midspan deflection showed slight deformation, and the specimen primarily exhibited localized bending failure. Compared to specimen FACSC-3, the contact stiffness of FACSC-4 was improved, with no penetration damage occurring at the contact surface, and the crack width was reduced, with most bending cracks not continuing to propagate. From the perspective of the primary failure modes of the columns, it is observed that with the increase in longitudinal reinforcement and stirrup ratios, the failure mode gradually transitions from shear failure to flexural failure, while the degree of punching shear failure is significantly reduced. This phenomenon differs from the conclusion in reference [9], where shear failure was dominant under an axial compression ratio of 0.2. This indicates that under the same axial compression ratio, the failure mode of columns can be effectively controlled by rationally adjusting the reinforcement ratios of longitudinal bars and stirrups, thereby enhancing the ductility and load-bearing capacity of the structure. Furthermore, when densely spaced stirrups are adopted at both ends, only localized flexural failure occurs in the columns, which significantly improves their impact resistance .

3.2. Impact Force Time History Analysis

The impact force time histories for the columns are shown in Figure 8, Figure 9 and

Table 5. First and second peak forces of specimens.

No.	First Peak Forces	Second Peak Forces
FACSC-1	833.83	45.13
FACSC-2	862.51	72.42
FACSC-3	908.71	76.88
FACSC-4	976.21	119.92

. The impact force’s development can generally be divided into three stages: peak force, plateau, and unloading. Initially, when the drop hammer makes contact with the column, a large stress wave is generated, and the impact force rapidly reaches its maximum value, known as the peak force stage. After this, the impact force enters a relatively stable plateau stage, during which the internal forces in the column are nearly balanced, and additional energy dissipation occurs as the column interacts with the hammer. Finally, during the unloading stage, the accumulated potential energy is released, causing the column to vibrate. Upon the first contact between the ALWC column and the hammer, the stress wave from the impact is transmitted from the contact surface to the interior of the column. The transverse stress wave travels repeatedly along the height of the column, resulting in intense vibrations. During this period, the impact force rapidly increases to its peak, and the column rebounds after contact with the hammer, causing the impact force to decrease to a negative value due to the inertial resistance of the column. After the hammer bounces back and recontacts the column, the localized damage caused by the initial impact reduces the contact stiffness at the impact site, leading to a decreased peak value for the secondary impact. During this phase, the curve shows high-frequency oscillations due to the combined effects of stress wave propagation and impact-induced damage, lasting approximately 3 ms. Meanwhile, the relatively high strain rate experienced by the material under high-speed impact may cause the strength and equivalent stiffness of concrete and steel bars to increase temporarily within a short period of time. This dynamic enhancement effect, together with the action of stress waves, jointly shapes the fluctuating characteristics of the impact force. Eventually, the hammer remains in contact with the column and oscillates up and down, with the impact force gradually diminishing to the initial level. During this phase, the impact force curve exhibits a rebound due to the strain energy stored in the specimen in the form of elastic or plastic deformation, which is partially released, creating a rebound force and causing the specimen to deform and release energy again.

For all four ALWC columns, the impact force rapidly increased to its peak within approximately 0.5 ms after the impact and decreased around 8–10 ms after impact. The impact force is influenced not only by impact energy but also by the contact stiffness between the hammer and the column at the impact point. Severe damage was observed at the impact points and other critical regions after the first impact, leading to a reduction in the overall stiffness of the columns. Differences in impact force behavior were observed among the specimens with varying reinforcement and stirrup ratios. Figure 8 shows the peak values during the first two contacts between the hammer and the columns. As the reinforcement and stirrup ratios increased, the overall stiffness of the columns also increased. When the reinforcement ratio increased from 0.72% to 0.98%, the first peak impact force increased by 3.43%, while the second peak increased by 60.47%. When the stirrup ratio increased from 0.27% to 0.40%, the first and second peak impact forces increased by 8.98% and 70.35%, respectively. For FACSC-4, with densified stirrups at both ends compared to FACSC-3, the first and second peak forces increased by 7.43% and 55.98%, respectively. The results indicate that, under different conditions, the impact force time history curves exhibit similar trends, resembling triangular pulse shapes, with numerous small peaks following the primary peak. Increasing the reinforcement and stirrup ratios improved the initial stiffness of the ALWC columns, thereby increasing the impact force during the initial contact between the hammer and the specimen. The impact resistance of the columns positively correlated with the reinforcement and stirrup ratios, and densified stirrups effectively increased the local contact stiffness, enhancing impact resistance.

3.3. Acceleration Time History Analysis

Figure 10 presents the acceleration time history curves for the columns. At the initial stage, since the hammer had not yet made contact with the column, the acceleration remained at zero. After the impact, the acceleration responded and reached its first peak. As the column rebounded, the acceleration decreased, and the peak acceleration gradually reduced with successive contacts between the column and the hammer, following a trend similar to that of the impact force. After multiple oscillations, the acceleration eventually returned to zero. This trend is consistent with Bentur’s findings [24], which suggested that the impact force of the hammer is positively correlated with the inertial force generated by the acceleration of concrete components.

To better analyze the effects of reinforcement ratio, stirrup ratio, and stirrup densification on the dynamic response of ALWC columns, the peak acceleration values were compared. When the reinforcement ratio increased from 0.72% to 0.98%, the peak acceleration decreased by 7.61%. When the stirrup ratio increased from 0.27% to 0.40%, the peak acceleration decreased by 48.7%. The results show that increasing the reinforcement and stirrup ratios effectively improved the impact toughness of the specimens. In particular, increasing the reinforcement ratio enhanced the lateral compressive capacity and impact resistance, effectively suppressing the downward impact acceleration caused by the hammer. Compared to FACSC-3, FACSC-4 had a 40.55% higher peak acceleration due to the densified stirrups at both ends, which increased the compressive capacity at the ends and restricted vertical displacement. As a result, after the column experienced downward impact, a rapid downward displacement occurred in the middle, causing the acceleration to peak quickly and then drop sharply in a short period.

3.4. Midspan Displacement Time History Analysis

The midspan displacement time history curves for the ALWC columns are shown in Figure 11. Due to the severe oscillations near zero during the unloading phase, only the peak force and plateau phases were analyzed to examine the effects of reinforcement and stirrup ratios on midspan displacement. From Figure 8 and Figure 12, it can be seen that the peak impact force occurred before the maximum midspan displacement, indicating that the peak impact force mainly affected the localized deformation at the contact area, with minimal influence on the overall deformation of the column. After contact, the rapid propagation of the stress wave resulted in the maximum midspan displacement.

Figure 11 compares the maximum midspan displacement and residual displacement. The maximum midspan displacement refers to the maximum deformation of the specimen under impact loading. FACSC-1 had the largest maximum midspan displacement, because, after the column experienced impact, the concrete failed in tension, and the reinforcement quickly took on the load. Due to the relatively low reinforcement and stirrup ratios, the vertical displacement was significant. Compared to FACSC-1, the maximum midspan displacements of FACSC-2 and FACSC-3 decreased by 18.30% and 17.38%, respectively, indicating that increasing the reinforcement and stirrup ratios enhanced the confinement of the concrete, effectively reducing midspan displacement. In terms of damage, FACSC-1 sustained more severe damage than FACSC-2 and FACSC-3, with overall damage within the clear span, while FACSC-2 and FACSC-3 experienced localized damage. FACSC-4 had a 1% increase in maximum midspan displacement compared to FACSC-3 due to densified stirrups at both ends and an identical stirrup spacing in the midspan region, resulting in increased vertical displacement but approximately the same maximum midspan displacement. Therefore, densified stirrups at the ends had little effect on the maximum midspan displacement, while overall stirrup densification effectively limited vertical displacement and reduced midspan displacement. Residual displacement refers to the final displacement after the free vibration phase when the specimen, undergoing plastic deformation, dissipates the impact energy through inertia. Compared to FACSC-1, the residual displacements of FACSC-2 and FACSC-3 decreased by 24.88% and 30.38%, respectively, while FACSC-4 had a 55.17% reduction compared to FACSC-3. The results indicate that increasing the reinforcement and stirrup ratios and densifying stirrups at both ends effectively reduced both midspan and residual displacements, with localized stirrup densification having minimal influence on midspan displacement, suggesting that expanding the densification region could further reduce midspan displacement.

4. Finite Element Modeling

ABAQUS (version 2020), as a powerful finite element analysis software, is widely used in numerical simulation of impact resistance performance tests, enabling visual analysis of dynamic processes and the meeting of experimental requirements. This paper selects the FACSC-3 specimen as the simulation object. By adjusting the reinforcement ratio and introducing steel fibers for reinforcement (FACSC-5), the scope of the experimental research is expanded.

4.1. Finite Element Analysis of FSJ Concrete Columns Under Impact Loading

4.1.1. Material Model and Parameters

(1) Constitutive parameters of steel

The steel used in the experiment includes HRB400-grade reinforcing bars and low-carbon steel corrugated steel fibers. Their stress–strain relationship is described by a double-spline model as shown in Figure 13. This model follows the von Mises yield criterion and takes into account the strain hardening stage. The specific formulas are given in Equations (1) and (2).

$${\epsilon }_{true}=\ln \left(1+{\epsilon }_m\right)$$

(1)

$${\sigma }_{true}={\sigma }_m\left(1+{\epsilon }_m\right)$$

(2)

${\sigma }_m$—nominal stress,${\epsilon }_m$—nominal strain,${\sigma }_{true}$—true stress,${\epsilon }_{true}$—true strain.

Figure 13. Double broken line constitutive curve of reinforcement.

Figure 13. Double broken line constitutive curve of reinforcement.

(2) Concrete constitutive model and parameters

The impact resistance performance of FSJ concrete columns was analyzed through ABAQUS simulation. The constitutive model of FSJ concrete adopted a damage–plastic model [25]. At the same time, ABAQUS provided two model parts for plasticity [26] and damage [27].

The full stress–strain curve data of FSJ concrete was obtained from the stress–strain curve in Chapter 3. Referencing the single-axis tensile stress–strain relationship of lightweight aggregate concrete proposed in the literature [28], the stress–strain relationship equation is as shown in (3):

$$y=\left\{\begin{array}{c}{\displaystyle \frac{c_n+\left(d_n-1\right)x^2}{1+\left(c_n-2\right)x+d_n{x}^2}},x\le 1\\ {\displaystyle \frac{x}{b_n{\left(x-1\right)}^2+x}},x\ge 1\end{array}\right.$$

(3)

When n = 1, the lightweight aggregate concrete is in a uniaxial compression state. The values of various parameters in the uniaxial compression stress–strain relationship are as shown in (4)–(6):

$$c_1=1.68\times {10}^{-3}\rho {{\displaystyle f}}_{cu}^{-1/6}$$

(4)

$$d_1=1.6{\left(c_1-1\right)}^2$$

(5)

$$b_1=2.5\times {10}^{-5}{{\displaystyle f}}_{cu}^3$$

(6)

$$x=\epsilon /{\epsilon }_c,\mathrm{y}=\sigma /f_c;$$

• ${\epsilon }_c$—FSJ peak strain of single-axis compression of concrete;
• $f_c$—FSJ concrete axial compressive strength, (MPa);
• $\rho$—FSJ apparent density of concrete;
• $f_{cu}$—FSJ concrete cube compressive strength, (MPa).

When n = 2, the lightweight aggregate concrete is in a uniaxial tensile state. The values of various parameters in the uniaxial compression stress–strain relationship are as shown in (7) to (9):

$${\mathrm{c}}_2=1.5\times {10}^{-3}\rho {{\displaystyle f}}_{cu}^{-1/6}$$

(7)

$$d_2=1.6{\left(c_2-1\right)}^2$$

(8)

$${\mathrm{b}}_2=1+3.0\times {10}^{-4}{{\displaystyle f}}_{cu}^2$$

(9)

$$x=\epsilon /{\epsilon }_t,\mathrm{y}=\sigma /f_t$$

4.1.2. Geometric Model Establishment

The specific settings for each material’s attribute parameters are shown in

Table 6. List of material attribute parameters.

Name	Properties
Hammer head	ρ = 7800 kg/m3, E = 210 GPa, fy = 1000 MPa
FSJ concrete	ρ = 1674 kg/m3, E = 30.2 GPa, fc = 26.3 MPa
Rebar	ρ = 7800 kg/m3, E = 210 Gpa, fy = 428 MPa, 410 MPa (upper longitudinal reinforcement and lower) 335 MPa (stirrups)

.

4.1.3. Strain Rate Effect

The strain rate effects on concrete tensile strength were based on the study by Li et al. [29]. The strain rate model incorporates a correction to the local dynamic increase factor (DIF) in order to account for the influence of element mesh size.

For the strain rate effect on compressive strength, the definition of the difference index (DIF) used by Marwal and Crawford [30] for the difference between uniaxial compressive strength and uniaxial strain rate (ε_c) is adopted.

For the reinforcing bars, we refer to the Gordon R. Johnson [31] material model. Additionally, based on the corresponding research, the material model also takes into account the effect of strain rate.

4.2. Analysis of Injury Morphology

Figure 14, Figure 15 and Figure 16 present the finite element analysis results, including the stress damage cloud diagrams of specimens FACSC-3 and FACSC-5. The color changes from blue to red, with the red color indicating greater stress at this location and also reflecting that the failure pattern in this area is severely mapped to the dense distribution of FSJ concrete cracks at this position. As shown in Figure 6, Figure 7, Figure 8, Figure 9 and Figure 10, the irregularly distributed steel fibers in the simulated specimen FACSC-5 are more in line with the actual distribution of steel fibers in the specimen, and the simulation results are closer to the real test data.

From the damage stress cloud diagrams, it can be seen that at the moment of the hammer impacting the column, the FSJ concrete column begins to undergo bending deformation in the direction of the impact force. At 3 ms, concrete damage and failure occur at the contact surface between the hammer and the FSJ concrete, and the impact load expands downward from the impact point and is transmitted to the support. The bending fluctuation then spreads to both sides of the column, and the deformation of the column gradually increases. At 6 ms, symmetrical shear slant cracks begin to appear on both sides of the midspan bottom of the column and develop towards both ends. On the left side, due to the application of axial force, a slant crack extending to the support appears at this position. Between 6 ms and 10 ms, the slant cracks along the support to the midspan position further increase and widen. Due to the complete fixed constraint at the support, the shear cracks are generally closer to the midspan position. At 17 ms, the deformation of the column reaches its maximum, and the width of the slant crack at the midspan position further increases, and there is a significant concrete damage area in the column. From the damage cloud diagram, it can be seen that after the column is impacted, the midspan deflection deformation phenomenon of the column and the damage position on the surface can be observed, which is basically consistent with the crack development law of the column during the test.

By comparing and analyzing the simulation results with the test results using ABAQUS, it can be known that the development of the failure morphology in the simulation is slightly different from that obtained from the actual test, but the error is small and within a reasonable range. The failure of FSJ concrete in the simulation is basically consistent with the actual failure development.

By comparing the simulation results of specimen FACSC-3 and specimen FACSC-5, it can be seen from the damage change cloud map that the addition of steel fibers can significantly improve the stiffness of the specimen. The deflection deformation at the midspan of the specimen is smaller compared to specimen FACSC-3, which can effectively enhance the impact resistance performance.

4.3. Comparison Analysis of Impact Force Time History Curves

The comparison and analysis of the FACSC-3 simulation results with the actual test results are shown in Figure 17. Firstly, the impact force waveforms of both are basically consistent. Both consist of one main peak and two secondary peaks. The peak value of the simulated impact force reaches its maximum at 2 ms, and it is found through comparison that the peak value of the actual impact force also reaches its peak at 2 ms. In the simulation results of the impact force curve, the descending segment of the first peak section is smooth, while the descending segment of the test results shows a blockage. This is due to the presence of depressions on the surface of the drop hammer guide rail. In the 3–4 ms time period, the second peak section in the simulation results is basically consistent with the test results. The third peak section in the test results is at 6 ms, and there is a slight error compared to the simulation. Secondly, the maximum peak value in the test results is 908.71 KN, while the maximum peak value in the simulation results is 951 KN, with an error of 4.6%, and the error range is less than 5%. The peak values of the two secondary peaks in the simulation results are larger compared to the test results, which is due to the inevitable friction between the drop hammer and the guide rail.

4.4. Comparison Analysis of Midspan Displacement Time History Curves

As shown in Figure 18, the time history curves of the midspan displacements of specimens FACSC-3 and FACSC-5 were compared and analyzed, respectively, with the experimental results. The entire curves were captured within the time range of 0 to 0.06 s, from the moment the hammer head came into contact with the FSJ concrete specimen until the midspan displacement stabilized. Through the comparison and analysis, it was found that the wave patterns of the two curves were roughly the same, which also reflected the accuracy of the simulation results. Analyzing the trend of the curves in the simulation results, it can be seen that the peak segments of the simulation were caused by the flexural resistance of the FSJ concrete specimen, resulting in multiple wave-like trends. The time when the maximum peak occurred in both results was basically the same. For example, for specimen FACSC-3, both had the maximum peak around 0.015 s and then gradually stabilized and stopped changing as the impact load decayed. The maximum displacements and residual displacements between the simulation and the experiment were within a 5% difference, which is a very ideal result. Finally, through the comparison and analysis of the two, it can be concluded that the simulation results of the midspan displacement are in good agreement with the actual experimental results. The related simulation can be used to simulate related impact tests, and the simulation result has a good accuracy.

5. Conclusions

In this study, impact resistance tests were conducted on ALWC columns with reinforcement ratios of 0.72% and 0.98% and stirrup ratios of 0.27% and 0.40%. The effect of densifying stirrups at both ends of the columns was also investigated. Impact force, acceleration, and displacement time history curves were obtained, and the following conclusions were drawn based on an in-depth analysis of the experimental results:

(1)

From the main failure modes of the columns, it was observed that increasing the reinforcement and stirrup ratios gradually changed the failure mode from shear to flexural failure, and the degree of punching failure decreased. With densified stirrups at both ends, the columns experienced only localized flexural failure, significantly enhancing impact resistance.

(2)

When the reinforcement ratio increased from 0.72% to 0.98%, the first peak impact force increased by 3.43%, and the second peak increased by 60.47%. When the stirrup ratio increased from 0.27% to 0.40%, the first and second peak impact forces increased by 8.98% and 70.35%, respectively. For FACSC-4, with densified stirrups at both ends compared to FACSC-3, the first peak increased by 7.43%, and the second peak increased by 55.98%. The experimental results indicate that increasing the reinforcement and stirrup ratios and densifying stirrups at both ends improved the stiffness and damping of the specimens, reducing the amplitude of structural vibrations and enhancing the energy absorption capacity under impact loading.

(3)

Under impact loading, increasing the reinforcement and stirrup ratios effectively improved the impact toughness of the specimens. In particular, increasing the reinforcement ratio enhanced the lateral compressive capacity and impact resistance, effectively suppressing the downward impact acceleration caused by the hammer and reducing both midspan and residual displacements.

(4)

Densifying stirrups at both ends of the columns led to an increase in peak acceleration, with midspan displacement remaining almost the same as that of FACSC-3, while residual displacement was improved. The results suggest that densifying stirrups at both ends can enhance the impact resistance of the columns to some extent, and expanding the densified stirrup region could further improve the overall impact resistance of the columns.

(5)

For ALWC columns used in high seismic intensity zones, a minimum stirrup ratio of ≥0.4% is recommended to shift the failure mode to flexural failure and prevent sudden shear collapse. In areas subject to explosion or impact risks, a confined stirrup zone of 500 mm at both ends with a spacing of 50 mm should be employed, which can enhance the secondary peak load by 55.98% and significantly reduce progressive impact damage. The lightweight concrete columns reduce self-weight by 30%, making them suitable for seismic isolation floors in high-rise buildings.

(6)

The simulation results of the impact resistance performance of FSJ concrete columns conducted by ABAQUS show that in building structures, when designing FSJ concrete components, by increasing the longitudinal reinforcement ratio and hoop reinforcement ratio and adding 1% of wave-shaped steel fibers, the impact resistance performance can be significantly improved.