Dynamic Performance Analysis of Precast Segment Column Reinforced with CFRP Subject to Vehicle Collision

Abstract

With the extensive use of a precast segment column in the field of engineering, impact resistance performance has gradually attracted attention, as many accidents have caused huge economic losses and casualties. This study explored the dynamic response and failure modes of a prefabricated segment column both with and without Carbon Fiber-Reinforced Polymers (CFRPs). Firstly, numerical models of a precast segment column and CFRP-wrapped steel column under impact loads were developed, and the modeling method’s accuracy was fully verified. Then, numerical models of a bridge precast segment column with and without CFRPs under vehicle collision were established, and the differences in the dynamic performances between the precast segment column with and without CFRPs are explored. Finally, the effects of impact velocity, concrete strength, and CFRP thickness on the dynamic performance of a precast segment column are considered. The results indicate that in the case of a vehicle collision, multiple cross-sectional positions form highly complex stress states. At 100 km/h, the differences in bending moment and shear force values between reinforced and unreinforced precast segment columns at the impact section are 7.6% and 7.1%, respectively. At this velocity, the peak impact force also increases by 15.8% as the local stiffness of the precast segment column increases after reinforcement with a CFRP. The bottom segment of the precast segment column with a CFRP is crushed, and the precast segment column experiences shear failure under vehicle collision.

1. Introduction

Recently, precast structures have aroused widespread interest owing to their advantages of less construction time, lower cost, high industrialization, environmental friendliness, improved working environment, etc. Precast structures are not only widely employed in residential buildings but also in bridge structures. Especially in the substructure of bridges, precast segment columns (PSCs) have recently been extensively adopted [1,2]. Among the methods of connection, many researchers confirmed that the method using an unbonded pre-stressing connection was very compatible, and it can provide effective self-centering to the PSC. Furthermore, the axial force applied by the unbonded pre-stressing connection can enhance the friction between concrete segments, which can reduce the relative slip between them [3]. During their service life, bridge structures may be subjected to earthquake loads, impact loads, blast loads, etc. Remarkably, the seismic behavior of the PSC has been extensively studied, while few studies have explored their dynamic response under impact loads [4,5,6]. As vehicle traffic grows, the risk of a bridge pier being damaged by a vehicle collision gradually increases, severely affecting the safety of the bridge [7,8].

Interestingly, the PSC demonstrated superior performance, with a self-centering capability, good energy consumption capacity, and less residual displacement and concrete damage under impact loads [5]. It should be mentioned that since the PSC is more flexible than a monolithic column, the PSC has a lower peak impact force under impact loads, and the duration of the impact force is longer compared to PSCs in a cast in situ column [5]. Zhang et al. [9] also suggested that the impact position had a significant influence on the PSC’s failure mode and response. For instance, the PSC experienced a flexural bending deformation when the impact location was in the middle of the column. When the impact was located in the base segment, the PSC experienced combined flexural bending and shear deformation. In addition, Do et al. [10] conducted a numerical analysis of a PSC subject to a collision with a Chevrolet S10 pickup, and the parameters of the initial levels of pre-stressing, quantity of segments, concrete strengths, and impact energies were studied. The findings show that while the number of segments and initial pre-stressing level had little effect on the impact force, they do have a major impact on residual displacement and column damage. In the PSC, increasing the initial pre-stressing level results in improved self-centering capacity and reduced displacement. Chung et al. [4] conducted a numerical analysis to reveal the dynamic responses and failure modes of a cast in situ column and PSC subjected to vehicle collision, and confirmed that prefabricated piers had a larger maximum displacement than monolithic piers, and the shear keys between segments had high stresses. However, it is important for the research of piers subjected to vehicle collisions to consider the superstructure of a bridge, and the internal force of PSC is clearly different between bridge piers with and without superstructures [11,12,13,14,15,16].

In general, many regulations suggest that the impact force created by a vehicle collision can be replaced by an equal static load [17,18], and this equal static load is incorporated by calculating the force that causes the same stress or strain [19]. However, the parameters of vehicle type, vehicle speed, impact angle, and structural characteristics have a noticeable effect on impact force, and it is unreasonable to employ a constant static force when designing the anti-impact performance of bridge piers [7,20]. Do et al. [15] considered that the shear force and bending moment of the pier was influenced by the impact force produced by vehicle collision, and it was difficult to accurately predict the failure mode due to the change in vehicle impact energy. In addition, Zhang et al. [5] conducted a test on piers subjected to impact loads, and found that bending cracks occurred at the impact position, and shear cracks formed at the bottom. Meanwhile, bridge piers subjected to vehicle collision need to be given more attention, and more research should be carried out to help make bridge structures safer. Zhang et al. [9] proposed using circular arc shear keys to limit the relative slip of PSC, but compared to trapezoidal shear keys, their effect is minimal. Do et al. [21] used steel pipes to reinforce the PSC, and selected mid-span and bottom segments as impact locations. Steel pipes limit the relative displacement between segments, but the damage to the PSC is more severe. In addition, Do et al. [21] also proposed embedded steel bars, and the results show a significant reduction in lateral displacement at the bottom segment.

On the other hand, fiber-reinforced polymer (FRP) composites are commonly used in civil engineering as they can significantly enhance the strength, stiffness, and ductility of concrete structures [22,23,24]. Zhang and Hao [25] conducted a study on a PSC strengthened with FRP composites under impact loads, and the effects of different impact locations were analyzed. The results show that the impact resistance of FRP-strengthened PSCs significantly improves as concrete spalling is prevented and the inelastic deformability of concrete is strengthened in the potential plastic region. Abdelkarim and EIGawady [26] investigated the dynamic response of hollow-core-reinforced polymer–concrete–steel columns subject to vehicle collision, and their research revealed that the impact resistance of this new type of column is mainly attributed to its inner steel pipe, and the calculation method of equivalent static load was proposed.

CFRP is utilized in this work to enhance the impact resistance of PSC. The failure modes and dynamic responses of PSC with and without CFRP under vehicle collision are investigated. Firstly, the bridge models of PSC with and without CFRP under vehicle collision were established, and the dynamic performances are analyzed in detail. Subsequently, this study was conducted on parameters such as concrete strength, impact velocity, and CFRP thickness to investigate the responses of the PSC strengthened with CFRP in a bridge under vehicle collision. After this introduction, the specific work arrangement is as follows. The finite element models of PSC and CFRP-strengthened steel columns are established in Section 2, and the results of the test and simulation are depicted in detail. Then, a typical three-span overpass bridge with PSC with and without CFRP was finely modelled, and the modeling process of the whole bridge is described in Section 3. Section 4 analyzes the failure modes, impact force, shear force, and bending moment of PSC with and without CFRP under vehicle collision. Additionally, Section 5 shows the outcomes of CFRP-strengthened PSC with various parameters. Finally, conclusions of this study are summarized in Section 6.

2. Numerical Model Validation

2.1. Precast Segment Column

In this section, the impact test [5] of PSC was used to calibrate the numerical model that was constructed. The construction method of this model has been described in detail; please refer to the literature [27,28] for details. The literature provides detailed descriptions, including material constitutive relations, strain rate effects, contact methods and prestressing application methods, etc. Figure 1 shows the specific finite element model created by the finite element software LS-DYNA 9.3.1 [29].

2.2. Steel Column Reinforced with CFRP

In a study, Kadhim et al. [30] conducted an impact test on CFRP-strengthened steel tubes. This article employs the findings of that experiment for the purposes of modelling and verification. In the test, an 850 mm steel column was employed, with a 40 mm × 40 mm × 3 mm steel section of Grade S355 cold-formed square hollow section (SHS) selected for the column section. In order to enhance the impact resistance of the steel column, the method of CFRP was employed in the course of the test. The thickness of the CFRP layer was 1.2 mm. Two plates, each measuring 150 mm in width, 150 mm in height, and 12 mm in thickness, were meticulously welded onto the extremities of the specimens. All degrees of freedom pertaining to the end plate on the left were constrained, while the Y-displacement of the end plate on the right was restrained throughout the course of the experiment. Furthermore, the impactor, weighing 150 kg, was propelled at a velocity of 4.9 m/s.

Figure 2 illustrates the detailed numerical model of a steel column that has been strengthened with CFRP in order to withstand impact loads. In this study, the steel tube and impactor were modelled using an eight-node constant stress solid element (Solid-164), while the CFRP was modelled with a four-node shell element (Shell-163) with 2 × 2 Gaussian quadrature integration. The mesh size convergence test revealed that the optimal mesh size for the steel column and CFRP was 5 mm. To enhance the efficiency of the calculation, the mesh size of the impactor was increased slightly in comparison to that of the steel column, with the impactor’s mesh size set at 10 mm. Furthermore, the interaction between the impactor and the CFRP-strengthened steel column was defined using the keyword “*AUTOMATIC_SURFACE_TO_SURFACE”.

The most frequently utilized adhesive for the purpose of affixing a CFRP sheet to a steel column is an epoxy adhesive. The contact relation between CFRP and the structure is typically represented in two ways in simulations. Youssf et al. [31] proposed a method for achieving perfect contact between the CFRP and the structure, which has since become a widely used approach [32,33,34,35]. It is, however, noteworthy that the bond strength between CFRP and concrete structures is susceptible to failure under impact loads, with the separation of CFRP being more pronounced in the impact area. Accordingly, Saini and Shafei [36] underscored the necessity of employing an automatic surface-to-surface algorithm with a tiebreak to ensure precise simulation of the interaction between the structure and CFRP.

In order to more accurately represent the contact effect between CFRP and the steel column, the methodology proposed by Saini and Shafei [36] was employed. This involved simulating the contact relation using the keyword *AUTOMATIC_SURFACE_TO_SURFACE_TIEBREAK. The criteria for defining contact failure between CFRP and the steel column were as follows:

$${({\displaystyle \frac{\left|{\sigma }_n\right|}{NFLS}})}^2 +{({\displaystyle \frac{\left|{\sigma }_s\right|}{SFLS}})}^2 \ge 1$$

(1)

where ${\sigma }_n$ and ${\sigma }_s$ represent normal and shear stress, respectively, at the interface between steel column and CFRP, and NFLS and SFLS are the tensile and shear failure stress of the epoxy adhesive, respectively.

Given that CFRP is an anisotropic material, it is not appropriate to express its mechanical properties using an elastic model. In this study, the mechanical properties of CFRP were simulated using the keyword *MAT_ENHANCED_COMPOSITE_DAMAGE (*MAT_054), which enabled the material model to control the direction of the CFRP-shell fibers [36]. The failure of the material can be regulated in accordance with the Chang-Chang laminate failure criteria. These criteria encompass tensile and compressive testing in both the longitudinal and transverse directions of each unidirectional ply.

Tensile failure in the longitudinal direction:

$$e_{f,t}^2={\left({\displaystyle \frac{{\sigma }_1}{X_T}}\right)}^2+\beta {\left({\displaystyle \frac{{\tau }_{12}}{S_C}}\right)}^2-1$$

(2)

Compressive failure in the longitudinal direction:

$$e_{f,c}^2={\left({\displaystyle \frac{{\sigma }_1}{X_C}}\right)}^2-1$$

(3)

Tensile failure in the transverse direction:

$$e_{m,t}^2={\left({\displaystyle \frac{{\sigma }_2}{Y_T}}\right)}^2+{\left({\displaystyle \frac{{\tau }_{12}}{S_C}}\right)}^2-1$$

(4)

Compressive failure in the transverse direction:

$$e_{m,c}^2={\left({\displaystyle \frac{{\sigma }_2}{{2S}_C}}\right)}^2+{\displaystyle \frac{{\sigma }_2}{Y_C}}\left({\displaystyle \frac{{Y_C}^2}{{{4S}_C}^2}}-1\right){\left({\displaystyle \frac{{\tau }_{12}}{S_C}}\right)}^2-1$$

(5)

In this context, $X_C$ and $X_T$ represent the longitudinally oriented compressive and tensile strength, respectively. The tensile and compressive strength in the transverse direction are expressed by $Y_C$ and $Y_T$, respectively. The stress in the longitudinal direction is represented by ${\sigma }_1$, while the stress in the transverse direction is represented by ${\sigma }_2$. Moreover, ${\tau }_{12}$ represents the in-plane shear stress, while $S_C$ denotes the shear strength of the CFRP sheet. The parameter $\beta$ is employed for the purpose of scaling the shear stress term that is defined for the fiber in the context of tensile failure.

2.3. Results and Validation

In order to verify the reliability of the methodology, two finite element models of PSC and CFRP-strengthened steel columns were established in this study. The results of the impact load tests on the PSC are presented in Figure 3 and Figure 4. Figure 3a illustrates the impact force time history curves of the simulation and the test. The peak impact force of the simulation and test are approximately 22.2 kN and 21.1 kN, respectively. In the numerical model, the contact surface is smooth and the influence of air is eliminated, which introduces some discrepancies between the test and simulation results. Four additional peak forces are observed in both the test and numerical simulation as a result of the vibration of the segment. Moreover, the impulses of the test and simulation are 537.4 N·s and 582.6 N·s, respectively. As illustrated in Figure 3b, the simulation exhibits a maximum mid-span displacement of 33.8 mm at 64.8 ms, while the corresponding value in the test is 32.9 mm at 62.1 ms. Given the PSC’s inherent self-centering capability, the residual displacements observed in the test and simulation are zero. Figure 4 illustrates the failure modes observed in the test and simulation under impact loads. A local failure at the impact position was observed in both the test and the simulation. The simulation and testing procedures revealed the existence of joint openings between segments 3 and 4, as well as a joint opening at the base segment.

The results of impact loads acting on a CFRP-strengthened steel column are illustrated in Figure 5 and Figure 6. As illustrated in Figure 5a, the peak impact forces observed in the test and simulation are 164 kN and 183 kN, respectively. This is due to the same reason as that which affects the finite element model of PSC. Furthermore, the greatest displacements observed in the test and simulation, respectively, were 34 mm and 35 mm, as illustrated in Figure 5b. Figure 6 illustrates the failure models observed in the experimental and simulation studies. In the simulation, the local failure of the CFRP and the local buckling of the steel column occur at the impact position, and the results of the simulation are consistent with the results of the test.

3. Numerical Model of Bridge under Vehicle Collision

3.1. Bridge Model

In this study, a conventional three-span overpass bridge numerical model with PSC was constructed, in accordance with the methodology outlined in [14,15,16], as illustrated in Figure 7. The superstructure, together with the pier and footing, are all included in the numerical model. The bridge has a total span of 15 m, with a PSC height of 7 m. The pier comprises five segments, with a height of 1.4 m. The four tendons, with a diameter of 70 mm, are used to link the segments, with a total section area of 15386 mm². The initial pre-stressing force is equivalent to 10% of the axial compressive capacity of the precast segmental pier. The present study investigates the structural form of PSC with and without CFRP in the context of vehicle collision. Moreover, the material model, strain rate effect, and modelling method of the bridge are identical to those employed in the verification model.

Typically, rubber or bearings are employed to fabricate the connecting components that are situated between the superstructure and the bent cap. As Tawil et al. [7] have demonstrated, the stiffness of the bearing pad has no discernible impact on the dynamic performance of the pier in the event of a vehicular collision. Accordingly, the elastic material was employed to model the bearing pad in the present study, and a coefficient of friction of 0.6 was utilized to simulate the contact mechanism [37]. The impact of soil–pier interaction has been excluded from the analysis to enhance the computational efficiency, in alignment with the methodologies employed in previous studies [14,15,16]. The convergence test indicates that a pier mesh size of 50 mm is sufficient, while the superstructure and footing require a larger mesh size to improve the efficiency of the calculation. Furthermore, the interaction between PSC and CFRP is based on the same validation model as that used for steel columns.

3.2. Vehicle Model

This study employed the vehicle model of a Ford reduced model single unit truck (SUT), comprising 35,353 elements, which is available for download from the National Crash Analysis Center (NCAC). This is illustrated in Figure 8. The reliability of the vehicle model was validated through collision testing, as documented in refs. [38,39]. The vehicle model has been extensively utilized in vehicle collision studies, as evidenced by [14,15,16]. The engine weight of the Ford reduced model single unit truck is 0.64 tons, while the additional mass is 2.8 tons, resulting in a total mass of 8.0 tons for the vehicle model. The contact method is consistent with that described in references [10,14,15,16,24].

Detailed research of the performance of a pier with and without carbon fiber-reinforced polymer (CFRP) under vehicle collision is presented. The present study examines the influence of impact velocity, concrete strength, and CFRP thickness on the outcome of the collision, as detailed in

Table 1. Parameters of precast segmental columns.

Case	Velocity of Vehicle (km/h)	Concrete Strength (MPa)	Thickness of CFRP (mm)	With or without CFRP
C1	60	30	-	without
C2	80	30	-	without
C3	100	30	-	without
C4	120	30	-	without
C5	60	30	2	with
C6	80	30	2	with
C7	100	30	2	with
C8	120	30	2	with
C9	100	50	2	with
C10	100	70	2	with
C11	100	30	4	with
C12	100	30	6	with

.

4. Results of PSC with and without CFRP

4.1. Impact Force

Figure 9 illustrates the impact force curves of PSC with and without CFRP in the event of a vehicle collision. It was observed that the peak impact force increased significantly with an increase in impact velocity. The peak force of PSC is 1968 kN at an impact velocity of 60 km/h. It is noteworthy that as the collision speed increases, the point of peak impact shifts from the bumper’s impact with the bridge pier to the engine’s impact with the bridge pier [14,15]. This transition is accompanied by a notable increase in the corresponding values, which rise from 4388 kN to 11,480 kN. Furthermore, the peak impact forces of CFRP-strengthened PSC are 1926 kN, 5917 kN, 10,571 kN, and 16,106 kN when the impact velocities range from 60 km/h to 120 km/h. The peak impact force of CFRP-strengthened PSC is observed to be larger than that of the unstrengthened PSC when the impact velocities exceed 80 km/h. This is due to the fact that the peak impact force is largely determined by the local stiffness of the piers, and the CFRP-strengthened PSC enhances this local stiffness. Notably, the difference in peak impact force between PSC with and without CFRP is minimal at 60 km/h. This is primarily due to the fact that the bumper’s local stiffness remains constant, and significant deformation of the bumper occurs to absorb energy.

4.2. Shear Force

The internal force of a structure subjected to impact loads is typically more complex than that under static loads due to the significant impact of the inertia force and strain rate effect on the internal force [40,41]. Figure 10 illustrates the shear force of PSC with and without CFRP at an impact velocity of 100 km/h. Both positive and negative shear forces are present in the same region, with the maximum shear occurring in section-2. It is important to note that the combined effect of inertia force, section shear force, and impact force is necessary to achieve a balance within the system [15]. The vibration of the structure, in turn, affects the value of the inertia force, which in turn affects the value of the shear force. The peak shear forces of the precast segment column with and without CFRP at section-2 are 5130 kN and 5486 kN, respectively.

Figure 11 illustrates the shear force dynamic responses of PSC with and without CFRP along the height. The area exhibiting the highest shear forces was primarily concentrated near the impact position, specifically in sections-1–3. Figure 12 illustrates the peak shear forces of the piers with and without CFRP in sections-2 and 3. It is evident that the shear force increases in direct proportion to the increase in collision impact velocity. As illustrated in Figure 12a, when the impact velocity of the vehicle increases from 60 km/h to 120 km/h, the peak shear forces of PSC in section-2 are 2361 kN, 3828 kN, 5130 kN, and 7184 kN, respectively. The corresponding values of PSC strengthened with CFRP are 2405 kN, 3960 kN, 5486 kN, and 7571 kN, respectively. This is due to the fact that the method of CFRP strengthening can markedly enhance the strength of the concrete [22,23,24]. Furthermore, the same outcomes can be seen in Figure 12b. The peak shear force of PSC with CFRP in section-3 is 1.15 times that of PSC without CFRP when the impact velocity is 120 km/h.

4.3. Bending Moment

Figure 13 illustrates the time history curves of bending moments at a speed of 100 km/h. The peak negative bending moment of the precast segment column is 2219 kN·m in section-3, while the corresponding value for the precast segment column with CFRP is 2388 kN·m. It is noteworthy that the bending moment in the top section (section-11) of the column is not zero due to the superstructure’s inertia effect, which prevents the free vibration of the PSC. Figure 14 illustrates the bending moment responses of the PSC with and without CFRP along its height. In contrast to the static load, a vehicle collision results in the PSC section experiencing both positive and negative bending moments. It can be observed that there are multiple sections which experience elevated bending moments as a result of the vehicle collision.

Figure 15 illustrates the bending moments of sections-1 and 3. The bending moment demonstrates a gradual increase in accordance with the rise in impact velocity. In section-1, the bending moments of PSC are, respectively, 1171 kN·m, 1544 kN·m, 2599 kN·m, and 3055 kN·m when the velocity of the vehicle is increased from 60 to 120 km/h. The bending moments of PSC with CFRP are 837 kN·m, 917 kN·m, 1379 kN·m, and 2231 kN·m, respectively, when the vehicle velocity is increased from 60 to 120 km/h. Moreover, the bending moments of PSC with CFRP in section-3 are greater than those of PSC under the same velocity. The peak bending moment of PSC with CFRP under 120 km/h is 3171 kN·m, with a corresponding bending moment of 3123 kN·m. It is notable that the bending moment of PSC with CFRP does not exceed that of PSC in any section. This is due to the fact that, in the event of a vehicle collision, it is highly unlikely that the bending moment in all sections will reach the maximum bearing capacity.

4.4. Failure Modes

This section provides a comprehensive account of the failure modes of the PSC in vehicle collisions, both with and without the presence of CFRP. The failure modes at different points in time are illustrated in Figure 16. Prior to the vehicle making contact with the pier (30 ms), the PSC is not compromised, as it is primarily responsible for resisting gravitational forces. Upon reaching approximately 45 ms, the first peak impact force results in slight damage to the piers at the impact position. At the instant of 58 ms, when the impact force reaches its second peak (i.e., the point of collision between the engine and the pier), the damage to the PSC, both with and without CFRP, increases, and slight damage occurs at the contact position between the segments. The final damage modes of PSC with and without CFRP are evidently disparate. The bottom segment of the PSC with CFRP is significantly damaged, whereas the bottom segment of the PSC is only slightly damaged. This can be attributed to the fact that CFRP can augment the overall stiffness of PSC, which subsequently reduces the deformation capacity. Consequently, the kinetic energy of the PSC is greater than that of the PSC with CFRP under vehicle collision, which results in less damage.

Figure 17 illustrates the failure modes of the PSC at varying velocities with and without CFRP. As the impact velocity increases, the damage to the piers gradually worsens. At an impact velocity of 80 km/h, shear cracks emerged in the bottom segment of the CFRP-strengthened PSC, while the PSC exhibited slight damage in the impact position. The bottom segment of the PSC with CFRP is severely damaged when the impact velocity reaches 120 km/h, with an oblique shear crack forming in the bottom segment of the PSC. Consequently, the damage to the PSC with CFRP is more significant than that of the PSC without CFRP. Additionally, the failure modes of CFRP are illustrated in Figure 18. Local failure of CFRP occurs at the impact position, and the damage intensifies gradually with an increase in impact velocity.

5. Results of CFRP-Strengthened Piers under Different Factors

5.1. Influence of Concrete Strength

The impact force of PSC with CFRP under different concrete strengths is illustrated in Figure 19. The maximum impact force demonstrates a slight increase in line with an increase in concrete strength. The peak impact forces of piers with 30 MPa, 50 MPa, and 70 MPa, respectively, are 10,571 kN, 11,201 kN, and 11,580 kN. The local contact stiffness is the determining factor in the impact force [5]. As a consequence of the enhanced concrete strength, the local contact stiffness demonstrates a progressive increase in line with the rising concrete modulus. Furthermore, it is important to acknowledge that the initial peak impact force experienced by the pier is to some extent influenced by the concrete strength. This is due to the fact that the contact stiffness of the vehicle’s bumper is less than that of the local contact stiffness of the pier, resulting in the bumper deforming in order to dissipate energy [14,15].

Conversely, as illustrated in Figure 20, the internal forces of the PSC with CFRP increase in line with the growth in concrete strength. Figure 20a and b illustrate the envelope curves of moment and shear force for a pier with varying concrete strengths. When the concrete strengths are within the range of 30 MPa to 70 MPa, the maximum shear forces are observed to be 5487 kN, 5989 kN, and 6153 kN, respectively, while the maximum bending moments are 2171 kN·m, 2703 kN·m, and 3129 kN·m, respectively. Furthermore, the damage degree of the PSC with CFRP decreases gradually with the increase in the concrete strength, as illustrated in Figure 21.

5.2. Influence of CFRP Thickness

Figure 22 illustrates the impact force of a pier reinforced with CFRP under different CFRP thicknesses. It is evident that an increase in CFRP thickness results in a slight increase in peak impact force. The CFRP thicknesses between 2 mm and 6 mm result in a gradual increase in local contact stiffness, which has a significant impact on the maximum impact force [5]. The peak impact forces of the pier with CFRP of thicknesses 2 mm, 4 mm, and 6 mm, respectively, are 10,571 kN, 11,153 kN, and 11,282 kN.

Figure 23 depicts the internal force of PSC with varying CFRP thicknesses. It can be observed that the peak shear force and bending moment exhibit a slight increase as the CFRP thickness is augmented. The peak shear forces of the pier with CFRP thicknesses of 2 mm, 4 mm, and 6 mm were found to be 5487 kN, 5531 kN, and 5659 kN, respectively. In comparison to the CFRP thickness of 2 mm, the peak shear force of PSC with a CFRP thickness of 6 mm has been observed to increase by 3.1%. Therefore, it can be concluded that increasing the thickness of CFRP does not yield significant results when the structural parameters remain fixed. It is, therefore, essential to consider the most effective strengthening scheme between the thickness of CFRP and the structural parameters in the design. The peak bending moment of PSC with CFRP thicknesses of 2 mm, 4 mm, and 6 mm, respectively, is 2388 kN·m, 2497 kN·m, and 2569 kN·m. Moreover, as the CFRP thickness increases, the damage degree of the PSC with CFRP decreases slightly, as illustrated in Figure 24.

6. Conclusions

The objective of this study was to investigate the failure modes and dynamic responses of PSC with and without CFRP in great detail. A numerical model of a multi-span bridge subjected to a vehicle collision was constructed, and the discrepancy in dynamic performance between PSC with and without CFRP was analyzed. Furthermore, the impact velocity, concrete strength, and thickness of CFRP were subjected to investigation. The following findings emerge from this study:

(1)

The use of a PSC with CFRP can result in a notable enhancement of the capacity to resist shear forces and bending moments. At a speed of 100 km/h, the PSC reinforced with CFRP demonstrated an increase in shear force and bending moment values in the impact area, with respective increases of 7.1% and 7.6%.

(2)

The predominant failure mode of the PSC with CFRP is the crushing of the bottom segment, whereas the PSC without CFRP exhibits a tendency towards shear failure. Furthermore, the maximum impact force of the PSC with CFRP is greater than that of the PSC without CFRP.

(3)

Enhancing the concrete strength of PSC has the effect of improving the bearing performance. In comparison with a maximum shear force and moment of 30 MPa, the PSC with 70 MPa demonstrates increases of 12.1% and 44.1%, respectively.

(4)

An increase in the thickness of CFRP has been observed to enhance the dynamic load-bearing capacity of PSC. Compared with the CFRP thickness of 2 mm, the maximum shear force and moment in the impact zone of PSC with a CFRP thickness of 6 mm, respectively, increased by 3.1% and 7.5%.

(5)

An increase in the thickness of the CFRP and the strength of the concrete can appropriately enhance the impact resistance of PSC. Furthermore, the degree of damage to the concrete will also be reduced.

In light of the discrepancy between the PSC with CFRP and those without CFRP, further research is required to enhance the strengthening methodology for mitigating the impact of high-speed vehicle collisions. Moreover, in light of the impact of factors such as pier structure, impact angle, and impact location, it is imperative to pursue continual optimization and investigation of the strengthening method of PSC.