Dynamic response of precast segmental bridge columns under heavy truck impact

Abstract

Considering the wide application of precast segmental bridge columns (PSBCs) in engineering practice, impact-resistant performance has gained significant attention. However, few studies have focused on PSBCs subjected to high-energy impacts caused by heavy truck collisions. Therefore, the behavior of PSBCs under a heavy truck impact was investigated in this study using high-fidelity finite element (FE) models. The detailed FE modeling methods of the PSBCs and heavy trucks were validated against experimental tests. The validated modeling methods were employed to simulate collisions between PSBCs and heavy trucks. The simulation results demonstrated that the engine and cargo caused two major peak impact forces during collision. Subsequently, the impact force, failure mode, displacement, and internal force of the PSBCs under heavy truck impacts were scrutinized. An extensive study was performed to assess the influence of the section size, truck weight, impact velocity, and number of precast segments on the impact responses. The truck weight was found to have a minor effect on the engine impact force. Damage was found to be localized at the bottom of the three segments, with the top remaining primarily undamaged. This parametric study demonstrated that larger cross-sections may be a preferred option to protect PSBCs against the impact of heavy trucks.

Graphical abstract

Keywords

precast segmental bridge columns / heavy truck / collision / dynamic response

1 Introduction

Precast segmental bridge columns (PSBCs) have been increasingly applied in practical engineering in recent years owing to their many advantages over cast-in-place reinforced concrete (RC) piers [1,2]. These include shortening the construction stage, improving structural quality, and reducing the negative impact on the environment and economic costs [3,4]. With the acceleration of bridge construction and the development of three-dimensional transportation, the threat of vehicle collisions is becoming more severe. Harik et al. [5] identified 114 bridge failures in the United States between 1951 and 1988, 14% of which were related to vehicle impacts. Wardhana and Hadipriono [6] investigated 503 bridge failures from 1989 to 2000 and found 14 of those were due to vehicle impact. In 85 bridge collapse accidents in China that occurred from 2000 to 2010, excluding earthquakes, Ji and Fu [7] found that overload and vehicle collisions accounted for 28% of the collapses, followed by poor construction (41%). Vehicle-pier collisions may lead to severe accidents, including human casualties and traffic blockages, particularly when heavy trucks are the source of impact [8]. Therefore, the behavior of PSBCs subjected to vehicle impact requires further investigation to enable the effective design of these structures against collisions.

Studies regarding the vehicle impact resistance of cast-in-place RC piers have been conducted. El-Tawil et al. [9] adopted an F800 medium-weight truck model to simulate collisions with RC piers. The authors analyzed the impact force for speeds ranging from 55 to 135 km/h and reported the equivalent static force by AASHTO-LRFD [10] as non-conservative for the design of piers against a medium-weight truck impact. Zhang et al. [11] proposed an energy-based method for calculating the equivalent static force for a vehicle colliding with bridge piers. This method allowed the static equivalent force to be directly obtained from the initial conditions of the problem without advanced simulations and experimental testing. Chen et al. [12,13] proposed a simplified coupled mass-spring-damper model to predict the behavior of a vehicle-pier system, including a medium-weight truck. Subsequently, the authors developed a response-spectrum-based method to calculate the impact force. Fan et al. [14] proposed a novel protective structure using ultra-high-performance fiber-reinforced concrete (UHPFRC) to protect bridge columns from vehicle collisions. Do et al. [15] numerically investigated the failure modes of piers with four superstructures having different geometries under impact loads. The results indicated that shear failure was the primary mechanism, with the corresponding force distributed at the bottom of the piers. Fan et al. [16,17] numerically investigated the performance of bridge piers subject to vehicle impact and developed response surface models that can reduce the time required to predict the vehicle-impact-induced response. Cao et al. [18] adopted a tractor-semitrailers model weighing 36 t to analyze the impact force distribution along the height of the pier and decomposed the impact force-time history into three triangular load pulses. These were applied at different pier heights to approximate the effects of the original impact force. Note, full-scale tests of vehicle collisions with piers are scarce. Chen et al. [19] conducted a full-scale test of a medium-weight truck impacting an RC pier, where concrete spalling and shear cracks were observed at the impact area. The engine was observed to have a major contribution to the impact force.

Considering the wider practical application of PSBCs, their impact resistance to vehicle collisions requires attention. Previous studies have targeted seismic performance [20–23]; however, studies directly focusing on vehicle collisions are required. Wu et al. [24] investigated the dynamic response of PSBCs under the impact of medium trucks and considered that the relative displacement between precast segments should be considered in an anti-collision design. Zhang et al. [25] conducted drop-hammer tests on scaled precast segmental columns and found that the columns freely vibrated around the initial position under lateral impact. The segmental columns can achieve a smaller residual displacement and impact force compared to the monolithic columns. Do et al. [26] developed a detailed finite element (FE) model to investigate the response of PSBCs subject to vehicle impacts. In a subsequent numerical study, Do et al. [27] investigated and compared the dynamic behavior of PSBCs under medium truck impacts with a corresponding monolithic column and proposed an analytical method for evaluating the bending moment capacities of PSBCs. The authors indicated that the initial prestress level and segment number significantly affected the residual displacement, and the impact force was only slightly different when the concrete strength was changed from 20 to 80 MPa. Notably, the peak impact force did not always increase with the impact velocity in this study.

The previous aforementioned studies focused on light- and medium-weight vehicle collisions with PSBCs. The impact energy of heavy trucks is significantly greater than that of light vehicles, which may cause increasingly critical damage to PSBCs or cause them to collapse. Therefore, this study aims to investigate the behavior of PSBCs under heavy truck impacts. A detailed FE model of the PSBCs and heavy trucks was built in LS-DYNA, which was validated against experimental data. The validated model was then used to conduct a series of parametric studies targeting the role of the section size, truck weight, impact velocity, and number of precast segments on the impact response of the PSBCs.

2 Research significance

The trucks were classified by total mass (m) as follows: heavy trucks (m > 12000 kg), medium trucks (4500 kg < m ≤ 12000 kg), and light trucks (m ≤ 4500 kg) in Chinese standard “GA 802-2014” [28]. Note that, 12000 kg is generally used as the lower limit of the heavy truck category [29]. Compared to light and medium trucks, the impact force caused by heavy trucks usually has a larger peak value and a longer duration, and the shear effect on bridge piers caused by heavy trucks is generally more pronounced, which makes them more prone to shear failure than bending failure [30]. Do et al. [27] compared the performance of PSBCs and a corresponding monolithic column under normal truck impacts. The simulation results demonstrated that the bending moment of the PSBCs was apparently smaller than that of the monolithic column subject to the truck impact owing to the joint opening and shear slippage of the PSBC segments. Damage to the PSBCs mainly occurred at the two bottom segments, while damage to the monolithic column was widely distributed in multiple column sections [19,27]. However, the cause of the difference in the performance of PSBCs under heavy truck collisions from that of conventional bridge columns is unclear. High-energy impacts on PSBCs owing to heavy truck collisions can cause severe damage including the collapse of the structural members. Previous studies have not focused on this relevant issue; therefore, this study presents an investigation of the dynamic behavior of PSBCs under a heavy truck impact through high-fidelity FE analyses. A full-scale collision model between PSBCs and tractor−semitrailers was developed after validating the PSBC and tractor-semitrailer models against experimental tests. The collision process between the tractor-semitrailer and the PSBC was divided into the following three phases: engine impact, cab crushing, and cargo impact. These are different from what is known about the collisions of light- or medium-weight vehicles. The evolution of the impact force, internal force, and damage mode of the PSBC during the three phases of the collision was thoroughly assessed. An extensive study was performed to evaluate the influences of the section size, truck weight, impact velocity, and number of precast segments on the impact responses of PSBCs. The initial impact velocity, rather than the truck weight, was found to have a significant influence on the peak impact force and impact-induced response. Two recommendations for the design parameters of PSBCs related to the cross-section and number of segments can be provided to improve the impact-resistance performance against a heavy truck impact. Thus, this study presents the dynamic response mechanism of PSBCs under a heavy truck impact and suggestions for improving their anti-impact resistance, which can be used for the future impact-resistant design of PSBCs and for improving their structural safety under the impact of heavy trucks.

3 Modeling approach and validation

This section presents the modeling approach, including the definition of the parameter settings for the PSBCs and heavy trucks. The material models, strain rate effects, and contact definitions are also addressed. Finally, the numerical models were compared to experimental tests.

3.1 Precast segmental bridge columns model

The drop hammer tests on precast segmental columns conducted by Zhang et al. [25] were adopted to validate the PSBC model, as illustrated in Fig.1. The test column was composed of five concrete segments, each with dimensions of 100 mm × 100 mm × 160 mm (length × width × height). A foundation with dimensions of 400 mm × 400 mm × 140 mm (length × width × height) was clamped onto the floor to support the segments. A concrete block of 400 mm × 400 mm × 450 mm was placed on top of the column along with five 23 kg steel plates, providing a total weight of 288 kg. A hole with a diameter of 15 mm was left at the center of each segment to accommodate the 9.3 mm prestressing tendon passing through the column. The tendon was anchored at the bottom of the foundation and top of the steel plates.

The reinforcement cage consisted of four 6 mm diameter longitudinal rebars (f_{\mathrm{y}} = 500 MPa) and 4 mm diameter stirrups (f_{\mathrm{y}} = 300 MPa). The other steel rebars had no continuity across the segments, except for the prestressing tendon. The foundation and base segments were connected by two starter bars that were 6 mm in diameter. A self-compacting concrete block with a compressive strength of 34 MPa and maximum aggregate size of 10 mm was used in the test. After building the precast segmental column, a 30 kN axial force was applied by the prestressing tendon. The tendon was composed of seven-wire strands with a yield strength of 1860 MPa. The steel impactor weighed 300 kg and was lifted and released at a specific angle for the impact at the center of the column to have a velocity of 1.37 m/s.

The numerical model was based on hexahedral elements with eight nodes and reduced integration to simulate the concrete elements, steel plates, and the impactor. In addition, the steel bars were represented by beam elements using the Hughes−Liu formulation and 2 × 2 Gauss quadrature integration. The mesh size of the segments and steel bars was 5 mm, whereas that of the foundation, concrete block, and impactor was 20 mm. Furthermore, the contact area between the impactor and segments had an identical mesh size of 5 mm. A total of 90148 solid elements and 2003 beam elements were used in the simulations.

The behavior of concrete can be represented using different constitutive models [31]. However, the material model *MAT_CSCM (*MAT_159) was employed in this study because it includes strain rate and softening [32]. *MAT_159 was validated multiple times in previous existing studies to yield reliable results for concrete structures under impact loading [33,34]. In *MAT_159, the user can input the compressive strength of the concrete, and other parameters are automatically calculated using LS-DYNA, or can be manually input. Among these parameters, the uniaxial tensile fracture energy (G_{\mathrm{f}\mathrm{t}}), pure shear fracture energy (G_{\mathrm{f}\mathrm{s}}), and uniaxial compressive fracture energy (G_{\mathrm{f}\mathrm{c}}) significantly influence the failure modes of the material. According to Agrawal et al. [35], the optimal values of G_{\mathrm{f}\mathrm{t}}, G_{\mathrm{f}\mathrm{s}}, and G_{\mathrm{f}\mathrm{c}} were determined to be 0.4, 0.4, and 1.0 times that of the default values calculated by using LS-DYNA, respectively. The parameters are optimal for normal-strength concrete with compressive strengths ranging between approximately 28 and 58 MPa [32]; the concrete adopted in this study falls within this range.

In addition, the steel reinforcement was simulated using the material model *MAT_PLASTIC_KINEMATIC (*MAT_003), which includes the effects of both the strain rate and kinematic hardening plasticity. The prestressing tendon was modeled using the temperature-dependent model *MAT_ELASTIC_PLASTIC_THERMAL (*MAT_004). Finally, the elastic model *MAT_ELASTIC (*MAT_001) was adopted to simulate the impactor, steel plates, and anchor. The material models and input parameters are presented in Tab.1. A prestressing load was applied by reducing the temperature of the tendon according to the following equation [36]:

(1)\mathrm{\Delta }T=\frac{F}{\alpha }\left(\frac{1}{A_{\mathrm{T}}{E}_{\mathrm{T}}}+\frac{1}{A_{\mathrm{C}}{E}_{\mathrm{C}}}\right),

where F is the prestressing load at the tendons, A_{\mathrm{T}} and A_{\mathrm{C}} are the cross-sectional areas of the tendon and concrete block, respectively, E_{\mathrm{T}} and E_{\mathrm{C}} are the Young’s modulus of the tendon and concrete, respectively, α is the thermal expansion coefficient of the tendon, and \mathrm{\Delta }T is the change in temperature. For a prestressing force of 30 kN, based on the material properties listed in Tab.1, the reduction in temperature to be applied to the tendon was 29.4 °C. Stress initialization was performed in the dynamic relaxation phase (*CONTROL_DYNAMIC_RELAXATION) and a convergence tolerance of 0.001 was adopted to achieve the convergence result.

The effect of the dynamic load on the mechanical properties of the materials was considered by using a dynamic increase factor (DIF) associated with the strain rate [37,38]. For concrete, the relationship proposed by Murray [32] was adopted as follows:

(2)CDIF=1+\frac{E\dot{\epsilon }\eta }{f_{\mathrm{c}}^{\prime }},

where CDIF is the DIF of the compressive strength, E is the elastic modulus, \dot{\epsilon } is the effective strain rate, η is the rate-effect fluidity parameter, and f_{\mathrm{c}}^{\prime } is the unconfined compression strength of concrete.

Similarly, the DIF for the tensile strength was as follows:

(3)TDIF=1+\frac{E\dot{\epsilon }\eta }{f_{\mathrm{T}}^{\prime }},

where TDIF is the DIF of the tensile strength and f_{\mathrm{T}}^{\prime } is the unconfined tensile strength of the concrete. The DIF was considered in *MAT_CSCM, and the relevant parameters were automatically calculated based on the unconfined compression strength.

For steel reinforcement, the strain rate effect was represented by the Cowper and Symonds model, which scales the compressive and tensile strengths with the following factor [39]:

(4)DIF=1+{\left(\frac{\dot{\epsilon }}{C}\right)}^{1/P},

where C and P are the strain rate parameters for the Cowper and Symonds models, respectively. In this study, the strain rate parameters were set to 40 (C) and 5 (P), as suggested by Jones [40] and Do et al. [41].

The erosion criterion was also included in the material models of the concrete and steel reinforcements. The principal strain was used as an index of material failure. When the principal strain reached the maximum threshold, the element was removed from the numerical model. The thresholds were 0.1 and 0.2 for the maximum principal strain of concrete and steel reinforcements, respectively [11].

The sliding and impact between the interfaces in the model are critical for achieving reliable results. The penalty method was used to simulate the contact behavior [42], which is defined as *AUTOMATIC_SURFACE_TO_SURFACE (ASTS), where the bulk modulus of the element determines the contact stiffness. As suggested by Do et al. [26], a default penalty scale factor of 1.0 was adopted for the contact definition between concrete segments, and 0.1 between the impactor and concrete segments. A scale factor of 0.1 between the steel impactor and concrete segments was used to match the stiffness of the two materials [26]. The coefficient of friction between the concrete segments was considered as 0.6, as described in Ref. [27]. In addition, a perfect bond between the steel reinforcements and concrete was assumed. The contact definitions in the current model are listed in Tab.2.

3.2 Heavy truck model

A detailed FE model of a tractor−semitrailer weighing approximately 36 t was adopted in this study, as illustrated in Fig.2. The original tractor-semitrailer model was developed by Miele et al. [43] to investigate collision events between trucks and concrete barriers. The tractor−semitrailer consists of a tractor, trailer, and cargo, which represents a typical tractor−semitrailer with dimensions of 20 m × 3 m × 4 m (length × width × height), such as the 1991 White GMC tractor with a 1988 Pines semitrailer. The original tractor−semitrailer model was validated to accurately predict the eccentric impact with the barriers. However, the collision between the vehicle and pier was more intense and the original model was not applicable.

Therefore, further modifications were made to the original tractor−semitrailer model to match a real truck used in the full-scale test performed by Buth et al. [44]. These modifications included defining the failure criteria for steel material, updating the material connecting the tractor and trailer, remeshing the irregular elements in front of the tractor, and removing certain components that do not exist in a real truck. However, the weight of the engine was not reported in the test, which was set to 1.4 t in the truck model and is the typical weight of a heavy truck engine, such as the Detroit DD15 14.8-L engine [31]. The total weight of the heavy truck was modified by changing the cargo density. There were 349740 elements in the modified tractor−semitrailer model, among which 303306 elements were deformable and the remaining 46434 elements that were used to simulate the hubs of the wheels were rigid.

3.3 Model validation

3.3.1 Precast segmental bridge columns model validation

To verify the suitability of the PSBCs model for predicting the dynamic response under impact loading, the simulation results were compared to the experimental test performed by Zhang et al. [25]. Fig.3(a) presents the impact force−time history curves for the simulation and test, where five peak impact forces can be identified in both cases. The first peak impact force was 20.62 kN at 2 ms in the simulation, which was consistent with 20.91 kN found within 3.1 ms of testing. The first peak impact force was caused by the initial contact between the impactor and column, and the column was hardly in motion at this moment owing to inertia. After the initial contact, the column began to vibrate around the symmetry axis, which caused the following four peaks. According to the impact force−time history curves, the column had a vibration period of approximately 20 ms in both the simulation and the experiment. The displacements at the middle height of the column are compared in Fig.3(b). The maximum displacement in the simulation was 32.7 mm at 55 ms. Correspondingly, the maximum displacement in the test was 32.8 mm at 61 ms. After the impact, the residual displacements in the simulation and test were 3 and 4 mm, respectively.

The impact area of the column was significantly damaged, as shown in Fig.3(c). The concrete elements at the top of the impact area were eroded in the simulation, which corresponded to concrete spalling in the test. The joint opening and shear slip between segments 3 and 4 were sufficiently represented in the numerical model. In addition, the joint openings between the base segment and foundation in the simulation and test were significantly similar.

Based on the aforementioned analysis and observations, the numerical model can accurately predict the dynamic response of PSBCs under impact loads and capture the impact force, displacement, failure modes, and deformation of PSBCs.

3.3.2 Heavy truck model validation

In a test performed by Buth et al. [44], a truck head-on was impacted with a rigid pier at a speed of 80 km/h. The rigid pier was 4.28 m in height and 0.91 m in diameter, was supported by a steel frame and fixed at both ends. The bottom of the steel frame was completely fixed deeply underground. To validate the heavy truck model, the parameters were set identical to those of the full-scale test, including the truck size, truck weight, truck speed, and column size. The main parameters of the truck are shown in Subsection 3.2, while the more specific parameters are not provided owing to space limitations of this study but can be found in Ref. [44].

There were two major peak impact forces during the truck−pier collision, as depicted in Fig.4. The engine impact force provided by the model was 4447 kN, whereas the test value was 4200 kN, representing a difference of approximately 6%. The emergence time of the engine impact was significantly close, occurring at 0.028 and 0.03 s, respectively. After the tractor was crushed, the trailer began to impact the pier, as illustrated in Fig.5. This caused a second major peak impact force of 2724 kN in the FEM model, whereas the test value was approximately 2420 kN. The emergence time of the cargo impact did not sufficiently match; however, the difference was considered insignificant when the cargo hit the pier earlier in the simulation. The impulses of the simulation and test were 649 and 578 kN·s, respectively. The deformation of the truck during the collision is plotted in Fig.5. The tractor was completely crushed in the simulation, which was similar to what was observed during the test. The trailer was disconnected from the tractor and collided with the pier in both the simulation and the test.

Owing to the complexity of the tractor−semitrailer, the impact force and deformation of the truck can be regarded as well-matched. Therefore, the modified tractor−semitrailer model can be deployed to simulate truck−pier collision events and yield reliable results.

4 Collision model of precast segmental bridge columns and heavy truck

In this section, the same modeling approach validated in the previous section is deployed to build full-scale models of PSBCs, including a heavy truck collision. Three types of PSBC cross-sections were considered, as plotted in Fig.6: D600, D800, and D1000, where the numbers represent the length of the edges of the cross-section in ‘mm’. The arrangement of the steel reinforcements refers to the piers designed by Liu [45] for different earthquake regions in the United States, as illustrated in Tab.3. There were 12 longitudinal reinforcements in the segment; each side of the cross-section had four longitudinal reinforcements. The spacing between the stirrups was 160 mm, and the concrete cover depth was 40 mm. The yield strengths of the longitudinal reinforcements and stirrups were 400 and 335 MPa, respectively.

The entire FE model of the PSBC with sectional dimension of 1000 × 1000 was illustrated in Fig.7. In this model, there were five segments with a total height of 6000 mm, with each segment being 1200 mm in height. The foundation was 2600 mm wide, 2600 mm deep, and 960 mm high. The cap beam was 3800 mm in width, 800 mm in depth, and 1000 mm in height. There were four prestressing tendons in the segments at each of the four corners of the cross-section, and the prestressing tendon was 30 mm in diameter. Note that, a steel duct that was 35 mm in diameter and 4 mm in thickness was embedded in each corner for the prestressing tendons to pass across the segments. A total prestressing force of 3200 kN was applied to the PSBC, which is equivalent to 10% of the axial load capacity of the pier. The axial load capacity can be simply calculated by f_{\mathrm{c}}^{\prime }{A}_{\mathrm{c}}, where f_{\mathrm{c}}^{\prime } is the compression strength of the concrete and A_{\mathrm{c}} is the cross-sectional area of the segments. The axial load capacity of the PSBCs with different cross-sectional dimensions can vary; however, for comparison purposes, the prestressing force was unchanged and equivalent to 0.1f_{\mathrm{c}}^{\prime }{A}_{\mathrm{c}}, as noted in Tab.3. In addition, the compression strength of concrete was 32.4 MPa, and the yield strength of the prestressing tendon was 1860 MPa. The total weight of a heavy truck can be modified by changing the cargo density.

The contact definition within the PSBC was consistent with that of the model above. A perfect bond was assumed between the steel reinforcements and concrete. The contact definition between the truck and PSBC uses the keyword *AUTOMATIC_SURFACE_TO_SURFACE (ASTS), with a coefficient of friction of 0.3. According to the convergence test, the mesh size of the segments and steel reinforcements in the model was selected to be 40 mm. Because the foundation and cap beam were not directly subjected to vehicle collisions, the mesh size of the foundation and cap beam could be increased to achieve a faster calculation efficiency. A total of 465904 elements were included in the full-scale FE model.

The boundary conditions of piers can be complex owing to the existence of the superstructure. Agrawal et al. [35], Liu [45], and Xu [46] conducted extensive sensitivity studies and concluded that the bridge system can be simplified to a more convenient model, as illustrated in Fig.7. The superstructures can sufficiently limit the displacement of the pier top. Similar to these previous studies, the cap beam was fixed in the horizontal direction, and the bottom of the foundation was also fixed.

5 Analysis of impact process

This section investigates the behavior of PSBCs under heavy truck impacts. A full-scale FE model was deployed to simulate a 30 t truck collision with a D1000 PSBC at a speed of 80 km/h. The failure mode, impact force, displacement, and internal force of the PSBC were assessed during impact.

5.1 Failure mode

Fig.8 depicts the truck deformation and PSBC damage during collision. The impact process can be divided into the following three phases: engine impact (phase 1, 0–0.082 s), cab crushing (phase 2, 0.082–0.257 s), and cargo impact (phase 3, 0.257–0.500 s). In phase 1, which occurred while the bumper was impacting, the location of the plastic strain was reduced to the edge of the impact side. The damaged area expanded owing to the higher intensity of the impact of the engine. In addition, minor concrete spalling was identified at the edge of the contact area. In phase 2, with cab crushing, the contact area extended further along the height of the PSBC. The onset of the cargo collision with the PSBC occurred in phase 3, with extensive spalling on the impact side, and the contact area extended over the three bottom segments. Therefore, these components play critical roles in impact protection and resistance.

The concrete was mainly damaged at the edges of the contact area. This is because the truck is wider than the PSBC, and the segments can be wrapped by the crushing truck, which does not entirely conform to the curvature of the segments. Shear slips and joint openings were also observed between the segments during impact. Notably, approximately 90% of the kinetic energy was converted into internal energy during the collision, as shown in Fig.9. Approximately 60% of the kinetic energy was transformed into phases 1–2, which was essentially absorbed by the deformation of the cab. Fig.9 demonstrates that there was a sudden shift in the energy exchange at approximately 0.2 s owing to the increase in the interface slip energy in the contact region. At that moment, the cab began to crush, causing several shell elements to contact one another, suddenly increasing the interface slip energy. It is difficult to avoid interface slip energy with hundreds of contacts defined in the model. However, this issue only affects a small part of the system energy and has a minimal effect on the simulation results [39].

5.2 Impact force

The impact force significantly varied during the collision, as shown in Fig.10. There were two critical peaks corresponding to the engine impact (4586 kN at 0.027 s) and cargo impact (4012 kN at 0.363 s). Notably, the cargo impact force is highly related to the type of cargo [8]; however, this is not discussed in this study owing to the various types of cargo. Although the maximum occurred during the former, its duration was significantly short, similar to a pulse, particularly when compared to the cargo impact. The resulting shear force indicated in Section 1 is plotted in the same figure, which demonstrates that the shear force is clearly less than the impact force because the inertial force partially carries the impact force. The evolution process of the shear force is nearly consistent with the impact force, which can be understood because the distance between cross-section 1 and the impact point is close, and the internal force state of the two positions is similar. This also indicates that the bottom of the pier has a significant impact resistance to a truck impact.

Fig.11 depicts the impact force distribution along the height of the PSBC over time, which indicates that the impact force presents the form of an impulsive load, and frequently appears during the collision. In addition, the impact force gradually increased from 600 to 1800 mm of the PSBC height during the collision.

5.3 Lateral displacement

Fig.12 demonstrates the lateral displacement along the PSBC, which can be used to identify the localized shear slip between the segments. This slip was most significant at the bottom of the PSBC and progressively grew during the collision phases. Notably, the relative displacement at a height of 1.2 m was not significantly apparent because the impact area covered both S1 and S2, making them closely stick to the truck. The displacement–time history curves at different heights of the PSBC are plotted in Fig.13. The displacement namely consisted of the following two growth stages: after the engine and cargo impact. Nevertheless, the maximum displacement was caused by the cargo, which was 144 mm at 0.406 s at the PSBC center. Then, the displacement at the impact point and center sprung back owing to the self-centering capacity of the PSBC. The displacement demonstrated negligible oscillations during cab crushing and hardly increased. The top of the PSBC had a minimum displacement of 8 mm.

5.4 Internal force

Fig.14 demonstrates that the section forces can be positive or negative; however, all the sections had a gradually growing internal force immediately after the cargo impact. A maximum shear force of 2437 kN occurred at cross-section 2, and the maximum bending moment of 5977 kN·m occurred at cross-section 6. The internal forces along the height of the PSBC at 1 ms intervals (500 ms in total) are plotted in Fig.15. The base and top segments have the most significant internal forces, which should be sufficiently designed in engineering practice.

Fig.16 demonstrates the prestressing force in the tendons during the collision. Apparently, the prestressing force in each tendon demonstrated a similar trend at the same position but was not uniformly distributed along the length of the tendon. The tendons were divided into several regions by the segments, and the tendons only uniformly deformed within the length of each segment owing to the shear slip and joint opening. The prestressing force at the top of the tendons gradually increased and yielded under the heavy truck impact and then recovered to the initial level. At the bottom of the tendons, they remained in a yielding state because the displacement of the base segment could not be restored.

6 Parametric study of precast segmental bridge columns

To further investigate the dynamic response of the PSBC under a heavy truck impact, a series of simulations were conducted to assess the parameters with the most significant effect on the response of the PSBC, as presented in Tab.4. These parameters include the section size, truck weight, impact velocity, and segment number because the structural response is generally related to the vehicle energy and structural characteristics.

6.1 Section size

To investigate the effect of the cross-sectional size of the PSBCs upon a heavy truck impact, piers D600 (C1), D800 (C2), and D1000 (C3) were analyzed. Fig.17 demonstrates that the change in the engine impact forces was significant, having values of 2902, 4030, and 4773 kN, which correspond to section sizes D600, D800, and D1000, respectively. In general, the impact force was influenced by the shear stiffness and contact area, both of which increased when the section increased. However, the cargo impact forces for the larger cross-sections D800 and D1000 were 2472 and 3021 kN, respectively. Note that, the PSBC with a section size of D600 lost its carrying capacity owing to the excessive deformation during cargo impact.

The plastic strains of the PSBCs for the different cross-sections are shown in Fig.18, which indicates that the section size had a significant effect on the impact resistance of the PSBCs. The column with section size D600 exhibited the worst performance in terms of crash resistance, with concrete failure and joint openings resulting in significant lateral deflection. Meanwhile, plastic damage developed along the entire PSBC height, and nearly all of the concrete cover on the impact side of the base segments spalled. The concrete damage decreased as the size of the section increased. The plastic strain at the top segment also significantly decreased with an increasing cross-section. Therefore, PSBCs with small sections, similar to D600, may not be suitable for withstanding the impact of heavy trucks in bridge designs.

Fig.19 presents the shear force presented in Section 2 and the bending moment in Section 6. As previously indicated, a larger section size results in a higher impact force, which also induces an increase in the internal forces. Note that, the internal force response to the D600 PSBC had a steady variation because the PSBC prematurely reached the limit of the internal force owing to an insufficient impact resistance.

Based on the simulation results of PSBCs with different section sizes, increasing the section size can effectively improve the impact resistance of PSBCs against heavy truck impacts. Thus, the section size of PSBCs should be increased if possible, to increase the anti-impact resistance of PSBCs under a heavy truck impact.

6.2 Truck weight

The behavior of PSBCs in response to heavy trucks with weights of 20 (C3), 30 (C4), and 40 t (C5) was studied in this section. Note that, the truck weight was basically changed by modifying the density of the cargo. A pin joint connects the tractor and trailer, thus the density of the cargo would not change the structure of the tractor but only move the center of gravity of the truck toward the rear. As shown in Fig.20(a), the impact force undergoes nearly the same time history under the engine impact before 0.1 s. The truck weight only had a slight influence on the engine impact forces, which were 4773, 4586, and 4447 kN for the 20, 30, and 40 t trucks, respectively. The cargo impact force significantly varied under a heavy truck impact with different vehicle weights, and increased from 3022 to 4011 and 5227 kN, with the truck weight changing from 20, 30, and 40 t, respectively. Moreover, the instant corresponding to the cargo impact force shifted to an earlier time, that is, 0.393, 0.363, and 0.324 s, respectively. The impulse was nearly proportional to the truck weight, as shown in Fig.20(b).

The damage to PSBCs under the impact of trucks with different weights can be captured more significantly in the overall deformation rather than in the plastic strain, as shown in Fig.21. The plastic strain of the concrete on the impact side was similar in each case and covered the three bottom segments. However, the deformation of the PSBCs was significantly different as the truck weight changed. There was no joint opening when the 20 t truck impacted the PSBCs. When the truck weight was 30 t, joint opening occurred between segments 2 and 3, and the PSBC had a small deflection at the pier center. As the truck weight increased to 40 t, the joint opening angle and center deflection further increased, which led to the crushing failure of the concrete in the local compression zone between segments 2 and 3.

Under the heavy truck impact, the variation law of the displacement at each position was similar, as illustrated in Fig.22. The displacement entered the first growth stage under the engine impact, then tended to be stable during cab crushing, and finally entered the second growth stage under the cargo impact. Note that, the displacement partially rebounded after it reached the maximum value owing to the self-centering capacity of the PSBCs. The recovery of the displacement at the bottom of the column was not apparent owing to the shear slip that contributed the most to the displacement, and this component was not recoverable. Moreover, prestressing tendons may be cut off under extreme impacts. This feature is difficult to capture by the simulation method in this study, and is worthy of further study.

Notably, when the truck weight changed from 20, 30, to 40 t, the effect on the internal force was not significant, as shown in Fig.23. The shear force envelope curves remained nearly unchanged, except that the shear force at the bottom clearly increased from 760 to 1877 and 2783 kN, respectively. The bending moment envelope curves only slightly widened with the truck weight because the PSBCs entered the yielding state and the internal force evolution was stable.

6.3 Impact velocity

The effects of the 80 (C4), 60 (C6), and 40 km/h (C7) impact velocities on the response of PSBCs were studied. The impact force rapidly increased with the impact velocity, as shown in Fig.24(a), and the occurrence time of the engine impact also advanced. Different patterns of the impact force with velocity can be clearly observed in Fig.25. No cargo impact force occurred at an impact velocity of 40 km/h because the kinetic energy of the vehicle was exhausted while crushing the cab, in which case the cargo could not progress to contact the pier. Most of the kinetic energy was converted into internal energy during the collision, as shown in Fig.24(b). Therefore, an effective way to contribute to the enhanced performance of bridge piers against collisions can be to reduce the structural damage by increasing the energy consumption.

The impact velocity has a noticeable effect on the damage level of the PSBCs, as shown in Fig.26. As the impact velocity increased from 40 to 60 and 80 km/h, the failure mode of the PSBC changed from predominantly local to global damage. The damaged area on the impact side also gradually expanded upward. The increasing impact velocity not only expanded the concrete damage but also forced the joint opening between the segments, as shown in Fig.26(a). Moreover, the joint opening caused local compression in the sections and led to concrete failure in the compression area.

The displacement significantly increased with the impact velocity, as shown in Fig.27. As previously indicated, the displacement has two main contributions and stages of growth: the first corresponds to the engine and the other to the cargo impact. These two stages can only be observed in the case of C4. Despite the cargo reaching the pier in C6, there was no corresponding growth stage in the displacement curve. This can be explained by the combination of the impact force of the cargo and the duration, which were small, particularly when compared to the engine impact force in C6. Specifically, the impulse of the engine impact was 236 kN·s, whereas that of the cargo impact was 57 kN·s. Therefore, the impact velocity affected whether the cargo was relevant during the impact. More importantly, it determined whether further displacements or deformation can be reached after the collision.

Fig.28 presents the internal force envelope curves of the PSBCs under different impact velocities. The shear force increased with the impact velocity, particularly near the bottom of the pier. At an impact velocity of 80 km/h, the shear force reached a maximum value of 2601 kN at the base segment. In contrast to the shear force, the bending moment reached the maximum value at the top of the pier, which was 5997 kN·m under an impact velocity of 80 km/h.

6.4 Number of segments

To study the effect of the number of segments on the PSBCs under a heavy truck impact, columns of five segments (C4), four segments (C8), and three segments (C9) were considered for the same total height of the pier. As presented in Fig.29, there was only a small difference in the impact force−time histories of those columns before 0.1 s, after which the differences became evident. At the initial impact stage, the impact force was controlled by the engine impact, and the effect of the structural stiffness was limited owing to the significantly small displacement produced in the PSBC. Therefore, the impact force−time history was similar in the initial stage. With the development of the collision process, the PSBC exhibits a large lateral displacement, and the lateral stiffness plays an important role in the variation of the impact force. Changing the number of segments also changes the lateral stiffness of the PSBC.

The plastic strains of PSBCs with different segment numbers are compared in Fig.30. Greater extended damage was found on the impact side as the number of segments increased. For example, a column with five segments exhibited extensive concrete spalling and a maximum area of plastic damage distributed on the impact sides. In contrast, the damage to the 3-segment column was lighter, and the concrete damage was concentrated on the edge of the segment.

There is a close relationship between the displacement and segment number, as shown in Fig.31. The maximum displacements at the impact point corresponding to the 3-, 4-, and 5-segment columns were 121, 166 and 80 mm, respectively. At the center of the column, the maximum values were 144, 133, and 61 mm, respectively. The displacement time history of the three-segment column only had one apparent growth stage, and the recovery of the displacement after the cargo impact was not observed owing to the shear-slip-dominated segmental drift in this case.

Under the same PSBC height, reducing the number of segments can ease the amount of displacement, and the magnitude of the displacement variation during the collision would also be smaller. Without affecting the convenience of assembly, it is recommended to appropriately reduce the number of segments to decrease the damage of PSBCs subject to heavy truck collisions.

7 Conclusions

The dynamic response of PSBCs under a heavy truck impact was numerically investigated in this study. An extensive parametric study including nine collision scenarios was conducted to reveal the influences of different parameters on the vehicle impact-resistance performance. The main conclusions are summarized as follows.

1) The impact simulation results are in agreement with the experimental results, including the force−displacement curves and damage modes, which indicates that the FE modeling method used in this study can adequately capture the behavior of PSBCs under a heavy truck impact.

2) The damage characteristics of PSBCs under heavy truck impacts were revealed through high-fidelity FE simulations. The damage to the PSBCs under heavy truck impacts mainly includes concrete spalling on the impact side and concrete crushing at the joint. In addition, the shear slippage and joint opening between segments were significant, and the tendons were therefore divided into several regions with a non-uniform distribution of the prestressing force.

3) Increasing the cross-section of PSBCs can considerably improve the impact-resistance performance against a heavy truck impact. Because the peak impact force is primarily dependent on the resistance of the impacting truck, a slight increase in the peak impact force was induced by increasing the section size. Moreover, under a heavy truck impact of 20 t at 80 km/h, a PSBC with dimensions of 600 mm × 600 mm loses its function owing to the large deformation.

4) The weight of the truck was found to have only a minor effect on the engine impact force because it was changed by modifying the density of the cargo. In contrast, the initial impact velocity significantly influenced the peak impact force and impact-induced response (e.g., damage, displacement, and internal forces). For example, when the impact velocity increased from 40 to 80 km/h, the corresponding maximum impact forces were 2061 and 4586 kN, respectively.

5) For the same total height, reducing the number of segments can increase the lateral stiffness of the PSBCs, which helps reduce the displacement and variation magnitude of the PSBCs. It is recommended that the number of PSBC segments be appropriately reduced to improve the impact resistance under heavy truck impacts.

Further studies are worth investigating to compare the performance of PSBCs and their counterpart monolithic bridge columns under heavy truck impacts.

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