A novel UHPFRC-based protective structure for bridge columns against vehicle collisions: Experiment, simulation, and optimization

Engineering Structures 207 (2020) 110247

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A novel UHPFRC-based protective structure for bridge columns against vehicle collisions: Experiment, simulation, and optimization

T

Wei Fana,b, , Dongjie Shena, Zhiyong Zhanga, Xu Huangc, Xudong Shaoa,b ⁎

a

Key Laboratory for Wind and Bridge Engineering of Hunan Province, College of Civil Engineering, Hunan University, Changsha 410082, China Key Laboratory of Building Safety and Energy Efficiency of the Ministry of of Education, Hunan University, Changsha 410082, China c Department of Civil and Mineral Engineering, University of Toronto, ON M5S 1A4, Canada b

ARTICLE INFO

ABSTRACT

Keywords: Protective structure Vehicle collision Ultra-high performance fiber reinforced concrete (UHPFRC) Drop-hammer impact test FE modeling Multi-objective optimization

The paper aims to develop a new protective structure based on ultra-high performance fiber reinforced concrete (UHPFRC) to protect bridge columns against vehicle collisions and to reduce vehicle damage and casualties. The drop-hammer impact tests were performed to investigate the response of the composite structure composed of UHPFRC panels and the energy-absorbing member of corrugated steel tubes. For all test specimens, the expected damage modes were observed during impact testing. Specifically, the energy-absorbing member experienced large deformation to dissipate the kinetic energy of drop hammer, while slight damages occurred in the UHPFRC panels directly contacted with a drop hammer. Also, the impact tests showed that the impact force was more sensitive to the number of corrugated tubes than the tube thickness. On the contrary, increasing the tube thickness more effectively improved the energy dissipation capacity of the structure than adding the number of corrugated steel tubes. A finite element (FE) modeling method considering manufacturing process was proposed and demonstrated to be capable of capturing the impact-induced response of UHPFRC-based composite structures. Comparisons between the experimental data and the numerical results highlighted the importance of including the influence of the manufacturing process in modeling corrugated steel tubes. Using the validated FE modeling method, two types of UHPFRC-based protective structures were investigated and compared. Results showed that the protective structure with disconnection details between inner and outer panels was superior to that with connection details. The advantages of the former one included more effective reductions of the impact force and damage in UHPFRC panels for the reuse to improve the economy. Finally, a multi-objective optimization design procedure was presented to find the optimum configuration of the proposed protective structures under vehicle collisions.

1. Introduction Many vehicle-bridge collision accidents were documented around the world in recent years [1–5]. Among them, severe damage and even complete collapse of bridge structures often occurred in vehicle collisions with reinforced concrete (RC) bridge columns in a multiplecolumn bent, e.g., the Tancahua Street Bridge over IH-37 and the Bridge on 26½ Road over IH-70 in USA [3]. Just on May 15th, 2019, the catastrophic accident happened again for the overpass bridge with multiple-column bents located in Zhejiang Province in China. These disastrous accidents always warn the people to concern the protection of bridge columns against vehicle collisions seriously. Many studies have been devoted to exploring dynamic behaviors of bridge piers under vehicle collisions or to developing the corresponding

analysis or design methods [4–17]. However, little emphasis has been placed on investigating reasonable protective structures for bridge columns and their performances under vehicle collisions, in spite of the broad application of protection systems in practice. According to the stiffness characteristics, the protection systems of bridge columns against vehicle collisions can be categorized into two groups [5]: rigid protections (e.g., rigid concrete barrier [18]) and soft buffer structures (or energy absorbers) made of rubber, fiber-reinforced plastics (FRP), metallic material, or other plastic materials [19]. Because rigid protections cannot alleviate the collision severity, severe damage in vehicle and casualties cannot be avoided or reduced in accidents. Hence, bridges’ owners and designers in China usually give priority to flexible protective structures in recent years [5]. However, it was often observed from practice that the conventional flexible protection systems

⁎ Corresponding author at: Key Laboratory for Wind and Bridge Engineering of Hunan Province, College of Civil Engineering, Hunan University, Changsha 410082, China. E-mail address: [email protected] (W. Fan).

https://doi.org/10.1016/j.engstruct.2020.110247 Received 24 September 2019; Received in revised form 16 December 2019; Accepted 14 January 2020 0141-0296/ © 2020 Elsevier Ltd. All rights reserved.

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UHPFRC panel

280

150

Corrugated tube

40

Q235 steel plate

280

540

1700

540

310

350

1000 290

350

290

290

280

310

350

500

210

280

1000 440

1700

210

500

350

1700 (a) Dimensions of specimen (front view)

(b) Plan view (six corrugated tubes)

(c) Plan view (nine corrugated tubes)

(d) Front view of test specimen

(f) Fabrication of bottom panel

(e) Fabrication of top panel

Fig. 1. Dimensions of test specimen and details (Unit: mm).

were highly vulnerable to damage, although only minor or moderate collisions happened. Notably, the traditional face panels made of steel or FPR materials in these protective structures often exhibit low crashworthiness. Fan et al. [20] indicated that the steel face panel is easily penetrated under impact loading. Also, AASHTO [21] pointed out that steel face panels are susceptible to corrosion in aggressive environments and to fire (even explosion) due to metal-to-metal contact with steel-hulled vessels carrying flammable cargo. Similarly, Huo et al. [22] experimentally demonstrated that FRP panels are easily punched and could hardly distribute impact loads. Although FRP materials have high durability, the adhesive epoxy resin used to form the FRP laminated panel usually exhibits low durability (e.g., aging). Because of these intrinsic disadvantages of steel and FRP face panels, it seems

impossible to reuse these protective structures after a simple repair. Hence, the need is evident to develop a new protective structure with the functions of resilience and easy repair to overcome the limitations of the traditional protective structures and improve the economy. To achieve the goal of resilience and easy repair, it is essential to distinguish the roles of different members in protective structures. Two portions with different functions can be arranged in the protective structures [23,24]. Specifically, stiff guards can be reused after minor and moderate collisions, and energy-absorbing members can be replaced easily after accidents. Ultra-high performance fiber reinforced concrete (UHPFRC) has been widely demonstrated to be one of the promising civil engineering materials to resist impact and shock loadings [25–29]. Particularly, previous experimental studies [24] indicated 2

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impact tests to investigate the impact behavior of the CST-UHPFRC composite structures. As shown in Table 1, primary parameters varied during drophammer impact testing included the thickness of the corrugated tubes, the number of the corrugated steel tubes, impact energy, the type of the UHPFRC panels, and the shape of the hammer tips. Specifically, two different tube thicknesses (i.e., 1 mm and 1.5 mm) were considered to investigate the influence of the stiffness of corrugated tubes on the impact response. Six and nine corrugated steel tubes were arranged to study the impact of the distribution of corrugated steel tubes. Two impact energies were considered by changing drop heights. Two different shapes (i.e., flat and round) of drop hammers were considered to represent different impactors. Also, two types of UHPFRC panels (i.e., with and without ribs) were studied. For brevity, an identification code (e.g., 1-6-1-N-F) was assigned for each impact case. The first three numbers were used to represent the thickness of corrugated steel tubes, the number of corrugated tubes, and the drop height, respectively. The subsequent letter (“Y” or “N”) denotes the UHPFRC panel with or without ribs, while the last letter (“F” or “R”) indicates the shape of hammer tip (flat or round).

that UHPFRC panels have excellent crashworthiness under impact loading in comparison with conventional reinforced concrete (RC) panels. In addition to the high crashworthiness and low damage under impact loading, UHPFRC materials have been experimentally demonstrated to possess excellent durability [30,31]. It is attributed to the fact that UHPFRC materials are extremely dense and compact [32]. Compared to any other materials, this advantage provides a basis for realizing the desired goals of high resilience and easy repair after collisions. For this reason, UHPFRC panels have been considered as a stiff guard in the new protective structure to distribute the impact loading. Many types of energy-absorbing members (e.g., thin-walled tubes, foams, etc.) can be chosen as the energy-absorbing members to fill the gap between the inner and outer UHPFRC panels. Accordingly, UHPFRC-based protective structures are worth investigating for bridge column protections in vehicle collisions. The purpose of this paper is to address the performance of a new UHPFRC-based protective structure under vehicle collisions through physical experiments and numerical simulations. Drop-hammer impact tests were performed to investigate the impact behaviors of UHPFRCbased composite structures. Numerous studies [14,33,34] indicated that corrugated tubes not only are low cost, ease of fabrication and excellent energy absorption efficiency, but also can improve stabilization of the crushing process and reduce initial peak load in comparison with straight tubes. Hence, corrugated steel tubes were used as the primary energy absorber in the proposed protection. Based on the experimental data, a detailed FE modeling method was developed and validated to simulate UHPFRC-based protective structures under impact loading. Using the validated FE modeling method, the performance of UHPFRC-based protective structures under vehicle collisions was examined in detail. The suitable configurations of UHPFRC-based protective structures were presented. For the proposed protection, a multiobjective optimization design was performed to develop the design method, to determine the sensitive factors of the proposed protective structures, and to seek the optimum results.

2.2. Materials and properties Since the main purpose of this study is to develop a new UHPFRCbased protective structure for bridge protection, a typical UHPFRC rather than a specially-design UHPFRC was recommended to be used. The more normal the UHPFRC is, the more feasible the proposed protection is in practical application [24]. For the UHPFRC material used in the impact tests, the dry mixture was provided by the Xing Gu Li (XGL) company in China. The dry mixture of the UHPFRC was designed and optimized based on packing density theory without coarse aggregate, and it was consisted of steel fibers, Portland cement, silica fume, quartz sand and very fine powder mainly composed of quartz as the mineral admixture. Hooked-end steel fiber with 13 mm long and 0.2 mm diameter were employed in the UHPFRC, and 2% in volume were used to improve the ductility of UHPFRC materials. The steel fibers and the other dry materials were well mixed by the XGL company. Just water was needed in the laboratory to produce the hardened UHPFRC. Table 2 lists the typical mix proportions of UHPFRC materials that were used to cast the top and bottom panels of the test specimens. Multiple UHPFRC cubes with a side length of 100 mm were cast and cured under the conditions the same as the UHPFRC panels to determine the compressive strength. The standard, manufacturer-recommended steam curing was employed for the UHPFRC cubes and panels. According to the uniaxial compressive testing, the average compressive strength of UHPFRC was 167.29 MPa. Also, the tensile properties of UHPFRC were estimated by the standard four-point bending tests on 400 mm long prism specimens with a side length of 100 mm. The average tensile strength of UHPFRC was about 8.30 MPa in accordance with the data processing method provided in AFGC/SETRA [32] and the measured data. HRB400 steel bars were embedded in the top and bottom UHPFRC panels. Typical Q235 carbon steel materials were used in the top and bottom steel plates for the connections. The corrugated tubes (1.0 mm and 1.5 mm in thickness) were thin, which cannot be usually

2. Impact test procedures The test specimens combined with both corrugated steel tubes (CST) and UHPFRC panels are first introduced in this section. Also, the material properties of steel and UHPFRC used in the tests and the drophammer impact test setup are given for the UHPFRC-based composite structures. 2.1. Impact test specimens and matrix Fig. 1 shows the typical configuration of the CST-UHPFRC composite structure that was subjected to drop-hammer impact testing. Each specimen included corrugated steel tubes, steel plates and UHPFRC panels reinforced by steel bars. For each specimen, the UHPFRC panels were 1700 mm in length and 1000 mm in width. Each corrugated steel tube had a 150-mm diameter and a 280-mm height, and the identical corrugation details, i.e., a wavelength of 30 mm and corrugation depth of 20 mm. Similar to the previous study [24], 10-mm-diameter steel bars were placed in the UHPFRC panels with a spacing of 100 mm. A total of six specimens (see Table 1) were fabricated for drop-hammer Table 1 Summary of test specimens. No.

Impact case

Thickness of tube t (mm)

Number of tube

Drop height h(m)

Impact energy (kJ)

Type of UHPC panel

Shape of hammer tip

1 2 3 4 5 6

1-6-1-N-F 1.5-6-1.5-N-F 1-9-1.5-N-F 1-6-1.5-N-F 1-6-1.5-Y-R 1-6-1.5-N-R

1.0 1.5 1.0 1.0 1.0 1.0

6 6 9 6 6 6

1.0 1.5 1.5 1.5 1.5 1.5

8.01 12.01 12.01 12.01 12.22 12.22

Without rib Without rib Without rib Without rib With rib Without rib

Flat Flat Flat Flat Round Round

3

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densification) phase (e.g., the line D-E in Fig. 3(a)). Nonlinear unloading behaviors were observed for the hardening (or densification) phase.

Table 2 Mix proportions of UHPFRC. Relative weight ratios to cement Cement

Water

1.0

18%

Steel fiber volume fraction Vf (%)

Compressive strength (MPa)

Tensile strength (MPa)

2

167.29

8.3

2.3. Drop-hammer impact test setup The setup of the drop-hammer impact tests in this study is illustrated in Fig. 4. Generally, the test setup included the specimen, the drop-hammer impact testing system, the supporting system, and the measuring system (i.e., the data acquisition and transducer). The highperformance drop-hammer impact testing system at Hunan University was employed in this study to carry out the impact tests on the UHPFRC-based protective structures. This impact testing system has been widely used and shown to be suitable for impact testing [12,24,26]. As mentioned above, two types of hammer tips (i.e., flat and round) were considered to investigate their influences on impactinduced responses. Since the round hammer tip was slightly heavier than the flat one, the total mass (831.4 kg) of the drop hammer with a round hammer tip was slightly greater than that (817.2 kg) with a flat hammer tip. During impact testing, the hammer freely falling at a given height was used to hit the center of the CST-UHPFRC composite structure. The supporting system consisted of the trough-type steel structures, 20 mm-thick steel shim, and four high-strength bolts that were distributed in four corners to further fix the specimen. A load cell placed inside the drop hammer was used to measure impact forces between the drop hammer and the test specimen, while vertical displacement data were measured by displacement transducers (see Fig. 4). A high-frequency data acquisition system manufactured by NI Company was used to record impact forces and displacements with a sampling frequency of 500 kHz during impact testing. Also, each impact test was visually recorded using a high-speed camera with the frame per second (FPS) of 3000.

manufactured from Q235 carbon steel materials. Hence, 304 stainless steel materials widely used in China were employed to fabricate the corrugated tubes in this study. The tensile properties of these steel materials were determined from the standard quasi-static uniaxial tension tests recommended by GB/T 228.1-2010 [35]. Fig. 2(a) plots the stress versus strain relationships of these steel materials recorded by a SANS electromechanical testing system. The manufacture of the corrugated steel tubes included two main procedures in this study: cold processing to form the groove and roll into a round shape, and welding to form a whole tube. As a result of these treatments (e.g., cold processing), the mechanical properties of the corrugated steel tubes were significantly different from those of the raw 304 stainless steel materials. As shown in Fig. 2(b), the tensile strength of the 304 stainless steel plate that experienced the first loading-unloading action was significantly higher than that without any treatments. Hence, in addition to the material tests of 304 stainless steel, it is necessary to obtain the mechanical properties of the corrugated steel tubes. Therefore, quasi-static uniaxial compression tests on single corrugated steel tubes were performed. Fig. 3(a) shows the force versus deformation curves of the corrugated tube (t = 1.0 mm ) measured from the uniaxial compression tests. Unlike the straight tube investigated by the previous study [36], the peak crushing force did not occur in the initial stage. Generally, the excellent uniformity was observed in the measured force-deformation curves, which is one of the favorable characteristics for an energy absorber. In addition to the force-deformation curves, the deformation evolutions of the corrugated tubes under compressive loading are shown in Fig. 3(a) at various deformations. Specifically, the corrugated portion yielded at point A. The straight portions at the ends began to yield after all the grooves were compacted thoroughly. The stiffness of the corrugated tube significantly increased when the straight parts were also crushed (e.g., the line D-E in Fig. 3(a)). Meanwhile, the cyclic behaviors of the corrugated steel tubes were also investigated, as shown in Fig. 3(b). The unloading stiffness was consistent with the initial loading stiffness of the corrugated steel tube before the hardening (or

3. Test results and discussions Drop-hammer impact tests were performed for all the specimens listed in Table 1. Impact responses (e.g., failure mode and damage, impact force and displacement) were discussed in this section to address the behaviors of the CST-UHPFRC composite structures subjected to impact loading.

800

600

(b) 800

Reinforcing bar

Engineering stress(MPa)

Engineering stress (MPa)

700

1000

(a)

500 Q235 steel plate

400 300

304 stainless steel

200

304 stainless steel plate after cold processing 600 Raw 304 stainless steel plate 400

200

100 0 0.0

0.1

0.2

0.3

0 0.00

0.4

Engineering strain (mm/mm)

0.02

0.04

0.06

0.08

0.10

Engineering strain (mm/mm)

Fig. 2. Properties of steel materials measured from tension tests: (a) uniaxial tension; (b) the influence of loading history. 4

0.12

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40 35 30

Force (KN)

(b)

Sample1 Sample2 Sample3 MAT24 with the raw data of material test MAT03 with the equivalent curve (yield stress=270MPa) MAT24 with yield stress of 550 MPa MAT03 with yield stress of 550 MPa MAT24 with yield stress of 550 MPa(ELFORM=2)

E

Sample1 Sample2

30

D

25 20

25 20 15

15 10

C

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A

10 5

5 0

40 35

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(a)

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Fig. 3. Force versus displacement curves of single corrugated tube (t = 1 mm ) (a) uniaxial compression; (b) uniaxial cyclic loading.

Anchor bolt

slighter than that of the energy-dissipating corrugated tube. It implies that the UHPFRC panel has excellent crashworthiness and can be used as a stiff guard to distribute impact loading in practical applications. Case 1-6-1-N-F was compared with case 1-6-1.5-N-F to investigate the influence of impact energy on impact responses, as shown in Fig. 5(a) and (d). Expect the deformation amount of the corrugated tube, similar damage evolution and modes were observed in these two cases. It indicates that the damage mode of the CST-UHPFR composite structure is stable to the extent of impact energy. Comparisons between the impact cases of 1-6-1.5-N-F and 1-9-1.5-N-F in Fig. 5 demonstrate that the number of corrugated steel tube has a limited influence on the damage evolution and modes. On the contrary, the uneven stiffness of corrugated tubes had an impact on the damage modes. Different from other impact cases, a slope (see Fig. 5(b)) can be observed in impact case 1.5-6-1.5-N-F. It is because all energy-dissipating tubes were thickened to 1.5 mm except the one located at the right corner, which had a thickness of 1.0 mm. Compared with impact case 1-6-1.5-N-F, a hemispherical pit (Fig. 6(e) and (f)) was observed at the impact point of the outer UHPFRC panel in 1-6-1.5-N-R. This implies different effects of the type of hammer tip on the damage modes of the UHPFRC panels. In addition, the local damage (i.e., hemispherical pit) of the outer UHPFRC panel in impact case 1-6-1.5-Y-R decreases apparently in comparison with impact case 1-6-1.5-N-R. It is attributed to the fact that the inclusion of the ribs improves the local stiffness and integrity of the UHPFRC panel.

Anchor rod

3.2. Impact force time history

Guide rod

Specimen

Disp. gauge Steel support (a) Front view

Load cell Hammer tip

Fig. 7 plots the time histories of impact forces recorded by the load cell embedded in the drop hammer. Generally, some individual interaction phases (i.e., some individual impact-force waves) can be observed from the measured impact force-time histories. In the first phase, the peak impact force occurred in the initial contact of the drop hammer and the UHPFRC panel. Under the drop-hammer impact loading, the CST-UHPFRC composite structure accelerated quickly during the initial contact phase because of the relatively low stiffness of the corrugated steel tubes. It can be inferred that the velocity of the outer panel exceeded the falling speed of the drop hammer at the end of the initial contact phase according to the interaction analysis method given in [26]. As a result, no impact force like a gap exhibited after the first interaction phase, meaning the occurrence of the separation between the drop hammer and the UHPFRC panel. After the separation,

(b) Side view

Fig. 4. Setup of drop-hammer impact tests on CST-UHPFRC composite structures.

3.1. Impact-induced damage mode of CST-UHPFRC composite structures Figs. 5 and 6 show the damage modes of the CST-UHPFRC composite structures subjected to different impact events. All the specimens showed similar damage modes, particularly for the specimens subjected to impacts with a flat hammer. As expected, the damage in the outer UHPFRC panel that was directly impacted by a drop hammer was much 5

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Drop-hammer impact tests

Numerical simulations

(a)1-6-1-N-F

(b)1.5-6-1.5-N-F

(g)1-6-1-N-F

(h)1.5-6-1.5-N-F

Slope

(c)1-9-1.5-N-F

(i)1-9-1.5-N-F

(d)1-6-1.5-N-F

(j)1-6-1.5-N-F

(e)1-6-1.5-Y- R

(k)1-6-1.5-Y- R

(f)1-6-1.5-N-R

(m)1-6-1.5-N-R

Fig. 5. Global damage of CST-UHPC composite structures obtained from impact tests and FE simulations.

the composite structures decelerated because the imposed energy was gradually dissipated by the corrugated tubes, and there is no external energy input in this phase. As a result, the second contact (interaction) between the drop hammer and the outer panel occurred when the velocity of the top panel became less than that of the drop hammer. The local peak impact forces observed in the subsequent contacts were always less than the peak forces that occurred in the first interaction phase. The impact forces of case 1-6-1-N-F were not recorded because the cable for data recording was accidentally pulled off during drop hammer impact testing. As shown in Fig. 7(b) and (d), no apparent differences in peak impact forces (i.e., 476.1 kN and 477.2 kN) were observed when the thickness of corrugated tubes increased from 1.0 mm to 1.5 mm. In contrast, the peak forces were raised by a relatively large amount when the number of corrugated tubes was increased (see Fig. 7(c) and (d)). As mentioned above, these peak impact forces always appeared in the initial contact of the drop hammer and the UHPFRC panel. They were primarily dependent upon the initial stiffness of the UHPFRC panels that were in direct contact with the drop hammer [24,26]. Compared with the increase in the tube thickness, the addition of corrugated steel tubes not only provides additional vertical stiffness but also changes the boundary condition of the UHPFRC panel, as shown in Fig. 1(b) and (c). Hence, the initial contact stiffness was more significantly improved by adding steel tubes. More importantly, it was found that the shape of the hammer tip had a significant influence on peak impact forces. As shown in Fig. 7(d) and (e), the peak impact force was reduced by approximately 44% after replacing the flat hammer tip with the round one. Such reduction is due to the decrease of the contact interface between the drop hammer with a round tip and the UHPFRC panel [24,37,38]. Also, the presence of ribs in UHPFRC panels led to the increase in impact force because of the stiffness improvement of the UHPFRC panels.

specimens are presented in Fig. 8. Three different phases (i.e., loading, unloading, and free vibration) can be identified from the measured impact-induced displacement data. According to the data measured from impact cases 1-6-1-N-F (Fig. 8(a)) and 1.5-6-1-N-F (Fig. 8(d)), it is evident that the impact-induced displacements increased with the increase of impact energy. As mentioned above, the peak impact force is more sensitive to the number of corrugated tubes than their thickness. On the other hand, for reducing the impact-induced displacement, increasing the tube thickness was more effective than adding the number of tubs. Compared to impact case 1-6-1.5-N-F, 31.3% reduction in the maximum displacement was observed after increasing the tube thickness from 1.0 mm to 1.5 mm (Fig. 8(b)). On the contrary, only 14.5% drop was obtained by adding the number of corrugated tubes (see Fig. 8(c)). Ideally, the increase in the energy dissipation capacity should be similar for increasing the tube thickness from 1.0 mm to 1.5 mm (i.e., 6 × 50% = 3) and adding three tubes. The deduction is based on the assumption that the UHPFRC panel behaves as a complete rigid plate and all the corrugated steel tubes have the identical deformations under a localized impact load. The premise is unrealistic for the composite structure subjected to a localized impact. As shown in Fig. 1(b) and (c), six edge tubes of the nine-tube specimen were farther away from the impact point than those of the six-tube. The efficiency of the nine-tube specimen to resist impact loading was lower than that with six tubes. It was also observed from the experiments that the six-tube specimen had more uniform deformation compared with that with nine tubes. The above observations indicate that increasing the tube thickness is superior to adding the number of corrugated tubes for the crashworthiness improvement of UHPFRC-based composite structures. The former treatment achieves better energy dissipation efficiency (i.e., higher energy dissipation capacity and lower mass) without significantly increasing the impact force. Unlike the influence on the peak impact force, the shape of the hammer tip has a limited impact on the overall displacement of the CST-UHPFRC composite structures. In addition, the midspan displacement of impact case 1-6-1.5-Y-R (Fig. 8(e)) was less than that of impact case 1-6-1.5-N-R (Fig. 8(f)). It is because

3.3. Impact-induced displacement results The vertical mid-span displacements of the composite structure 6

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Numerical simulations

Drop-hammer impact tests (a) 1-6-1-N-F

(b) 1.5-6-1.5-N-F

(c) 1-9-1.5-N-F

(d) 1-6-1.5-N-F

(e) 1-6-1.5-Y-R

(f) 1-6-1.5-N-R

Fig. 6. Damage of outer UHPFRC panels obtained from impact tests and FE simulations.

the presence of the ribs improves the integrity of the composite structure so that each corrugated tube yields identical displacement. In short, the most sensitive factor influencing the overall deformation of a CST-UHPFRC composite structure is the tube thickness.

4. FE modeling method Detailed FE models of CST-UHPFRC composite structures under impact loading were developed in this section. The models were validated against the aforementioned experimental results.

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(a) 1-6-1-N-F

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(b) 1.5-6-1.5-N-F

Impact force (kN)

Impact force (kN)

600

Yield stress=270MPa

0.16

0.20

Time (s)

Yield stress=550MPa,ELFORM=2.-

Yield stress=550MPa,C=40.4, P=5

Fig. 7. Impact force time histories obtained from impact tests and FE simulations.

140 120 100 80 60 40 20

120 100 80 60 40

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0.20

Time (s) Yield stress=550MPa,C=40.4, P=5

Fig. 8. Midspan displacements obtained from impact tests and FE simulations.

4.1. FE modeling

minor details such as the shear stud and the weld seam had little effect on the FE results. Therefore, similar simplifications of the minor details were employed in this study. Specifically, ideal bonds among the UHPFRC panels, the steel plates, and the corrugated tubes were defined by sharing common nodes. The keyword CONSTRAINED_LAGRANGE _IN_SOLID in LS-DYNA [39] was used to describe the bond between the UHPFRC panels and the steel bars embedded. The keyword CONTACT_AUTO_SURFACE_TO_SURFACE was employed for the contact

Fig. 9 presents the detailed FE models corresponding to the above drop-hammer impact tests. In the FE models, the UHPFRC panels and the drop hammer were modeled by solid elements. Belytschko-Tsay shell elements and Hughes-Liu beam elements were used to simulate the steel plates and the steel bars distributed in the UHPFRC panels, respectively. As addressed in a previous study by the authors [24], 8

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Drop hammer

Reinforcing bar

Steel plate

UHPFRC panels Corrugated tube Fig. 9. Detailed FE model of CST-UHPFRC composite structures under drop-hammer impacts.

between the drop hammer and the tested specimen, while the contact type CONTACT_SINGLE_SURFACE were defined for the internal contacts after the test specimen deformed under impact loading.

indicating that the material models have a limited influence on the FE results. Hence, the model MAT_PLASTIC_KINEMATIC, which is very computationally efficient, was used to describe the material behavior of the corrugated steel tubes in the subsequent impact simulations. As mentioned above (Section 2.2), the mechanical properties of corrugated steel tube differ from those of the original material because of the cold processing and welding during the form of the corrugated steel tube. As illustrated in Fig. 2(b), the yield stress of 304 stainless steel was significantly increased due to these treatments (e.g., cold processing and welding). Consider the difficulty in directly retrieving the realistic mechanical properties of the corrugated steel tubes, a set of trial simulations was used to estimate the mechanical properties of 304 stainless steel for modeling the corrugated steel tubes. After increasing the yield stress of 304 stainless steel from 270 MPa to 550 MPa (Fig. 10(b)), good agreements between the numerical and experimental force-deformation curves were observed, as shown in Fig. 3(a). In addition to the force-deformation curves, the failure mode predicted by the numerical model agreed well with the experimental data, as shown in Fig. 10(c) and (d). Also, the yield stress of 550 MPa obtained from the trial simulations was consistent with the uniaxial tension test result (530 MPa) of 304 stainless steel plate after cold processing, as shown in Fig. 10(b). Based on the above observations, the calibrated material model of 304 stainless steel was used in the subsequent FE simulations of the CST-UHPFRC composite structures under impact loading. The previous experimental studies [40–42] indicated that the behavior of 304 stainless steel materials under rapid loading was sensitive to strain-rate effects. Hence, the strain-rate effects of the 304 stainless steel material were taken into account in the impact simulations. The Cowper-Symonds model was used in this study to account for the strainrate effects as follows:

4.1.1. Modeling of corrugated steel tubes The experimental results in Section 3 indicate that large deformations of the CST-UHPFRC composite structures (i.e., high nonlinear behavior) mainly occurred in the corrugated steel tubes. Therefore, it is of importance to capture the mechanical behavior of the corrugated steel tubes to ensure the rationality of the FE model of the CST-UHPFRC composite structure subjected to impact loading. Compared to other components in the CST-UHPFRC composite structure, more details about the modeling of the corrugated steel tubes were presented in the following. It is essential to examine the quasi-static behavior of the corrugated steel tubes under compressive loading before the FE simulation of CSTUHPFRC composite structures subjected to drop-hammer impact loading. Fig. 10 illustrates the high-resolution FE model of the corrugated steel tube for quasi-static compressive tests. Full integrated shell elements were employed to simulate the corrugated steel tubes. Solid elements with rigid steel material model (i.e., MAT_RIGID in LS-DYNA) were used to model the rigid top plate of the uniaxial compression testing machine. The bottom nodes of the corrugated steel tubes were fixed. Then, the rigid steel plate imposed the compressive force to the corrugated steel tube through displacement-based control. The same contact definitions as the above impact model were adopted for the contact between the rigid plate and the corrugated steel tube and the self-contact of corrugated steel tube. To investigate the influence of different material models, the models MAT_PIECEWISE_ LINEAR_PLASTICITY (MAT_24) and MAT_PLASTIC_KINEMATIC (MAT_03) were employed to simulate corrugated steel tubes. The raw stress versus strain curves obtained from the material test data of 304 stainless steel (see Fig. 2) and the equivalent bilinear curve with the yield strength of 270 MPa were used to define the material models, respectively. Fig. 3(a) presents the compression simulation results of the corrugated steel tube along with the experimental data measured from the quasi-static uniaxial compression test. The shape of the numericallyobtained force-deformation curve was similar to the experimental result. However, the numerically-estimated strength (~4.0 kN) in the plateau phase was much lower than the experimental data (~7.0 kN) when the raw stress-strain data obtained from uniaxial tension tests of 304 stainless steel plates (Fig. 2(b)) were adopted in the compression simulations. Moreover, the FE results obtained using MAT_03 are consistent with those using the advanced material model (MAT_24),

y

= [1 + ( C )1 P ]

0

(1)

where y is the dynamic strength of the material with strain-rate effects; is 0 is the static strength of the material without strain-rate effects; the strain rate; C and P are the strain-rate parameters in the CowperSymonds model. To our knowledge, none of the previous studies determined the strain-rate parameters (i.e., C and P ) that could be widely used for stainless steel. Rodríguez-Martínez et al. [40] experimentally investigated the dynamic increase factor (DIF ) with the strain rates from 0.001 s−1 to 1000 s−1, and the physical experiments with the strain rates from 0.001 s−1 to 0.1 s−1 were also performed by Kundu and Chakraborti [41], as shown in Fig. 11. These experimental data were used in this study to determine the strain-rate parameters C and P . Because of a lack of the static strengths in [40,41], the minimum strain rate of 0.001 s−1 was taken as the benchmark, and the following 9

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8×30=240

20

Steel plate

(b) 1000

Corrugated tube

600

20

Node fixed

20

304 stainless steel plate after cold processing

400 200

Unit: mm

FE simulation used

800

True stress (MPa)

150

(a)

0 0.00

Raw 304 stainless steel plate

0.02

0.04

0.06

0.08

0.10

0.12

True strain (mm/mm)

(c)

(d)

Fig. 10. FE simulations of corrugated tubes under uniaxial compression: (a) High-resolution FE model; (b) True stress versus strain relationship; (c) deformation mode observed from compression test; (d) deformation mode predicted by FE simulations.

2.0

180

Experimental data[36] Experimental data[35] Fitting curve

160 140

Displacement (mm)

1.6

DIF

1.2

0.8

R2=0.94 C=1.434e5, P=6.502

0.4

120 100

Mesh size=5mm Mesh size=3mm Mesh size=2mm

80 60 40 20

0.0 0.001

0.01

0.1

1

Strain rate (s-1)

10

100

0 0.04

1000

y

=

0.20

structure, mesh convergence tests of the corrugated steel tubes were carried out for impact simulations. Take the impact case 1-6-1.5-N-F as an example. Fig. 12 presents the predicted impact results from three different mesh sizes of the corrugated steel tubes (i.e., 2 mm, 3 mm, 5 mm). Generally, the mesh size had a minor effect on the impact-induced responses of the corrugated steel tubes, particularly in the loading phase. Although the unloading behavior of the tubs was affected by the mesh size, similar responses were observed for the cases using the mesh sizes of 2 mm and 3 mm. Therefore, 3 mm mesh size was adopted in the impact simulation of the CST-UHPFRC composite structures.

C )1 P ]

[1 + ( [1 + ( 0 C )1 P ]

0.16

Fig. 12. The influence of mesh size on impact-induced response.

equation was used to estimate the strain-rate parameters:

y0 | 0 = 0.001

0.12

Time (s)

Fig. 11. Strain rate effects of 304 stainless steel.

DIFr =

0.08

(2)

where DIFr is the strength ratio of the dynamic strength ( y ) to the strength ( y0 ) with a strain rate of 0.001 s−1. Based on the data points shown in Fig. 11, the strain-rate parameters (C = 1.435 × 105 s−1 and P = 6.502 ) were estimated by the least square method. Proper fitting with the coefficients of determination (R2 ) of 0.94 can be observed in Fig. 11 for the estimated values of C and P, which were used for the impact simulations in this study. In addition, as the primary member in the CST-UHPFRC composite 10

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1000

5000

1000

8000

1650

3500

350 0 6400

1950 UHPFRC panels

1950 Baffle plate made of wood or plastics

Corrugated tubes

PU-foam filled

3390

1650

t3

t1

Type-B UHPFRC-based protective structure

Type-A UHPFRC-based protective structure

t2

t4

Fig. 13. UHPFRC-based protective structure for bridge columns against vehicle collisions (Unit: mm).

4.1.2. UHPFRC and steel material models The software package LS-DYNA [39] provided many material models (e.g., the Karagozian & Case (KCC) model, and the continuous surface cap (CSC) model) to capture the behavior of normal concrete under shock and impact loading. Compared to other material models (e.g., KCC model), the CSC model has been demonstrated to be more suitable for simulating the low-velocity impact behavior of normal concrete materials [4,12,24,43]. However, since the mechanical properties (e.g., tensile and compressive strengths, tensile strain-hardening behavior) of UHPFRC were significantly different from that of normal concrete, the CSC material model cannot be directly used to simulate UHPFRC under impact loading. Based on the constitutive model theory and the existing experimental data, Guo et al. [43] modified the CSC model to reasonably simulating UHPFRC materials under impact loading. Much research indicated that the modified CSC model provided good accuracy for impact simulations of UHPFRC-based members [4,12,24,26,43]. Therefore, the modified CSC model was employed in this study to model the UHPFRC panels of composite structures. For the UHPFRC material used in the CST-UHPFRC composite structures, Zhang [44] experimentally investigated the tensile behaviors in detail. Based on the material properties from Table 1 and Zhang [44], the model parameters of the UHPFRC in FE simulations were generated according to the method provided in [43]. Like the previous studies [4,12,24,43], the empirical formulas obtained from the physical experiments performed by Fujikake et al. [45] and [46] were used to account for the strain-rate effects of UHPFRC. More details about the material model of

UHPFRC can be found in Guo et al. [43]. Expect the corrugated steel tubes, the steel bars and plates were simulated by the material model MAT_PIECEWISE_LINEAR_ PLASTICITY. The experimentally-measured stress versus strain curves shown in Fig. 2(a) were employed to determine the parameters of these steel material models. For shell elements of the steel plates shown in Fig. 9, the engineering stress-strain curves were converted based on the “combined material relation” to the corresponding true stress-strain curves for the definition of the material model. Similar to the previous study [43], the following equation suggested by [47] was used to consider the strain-rate effects of the steel bars and plates:

DIFst = 1.202 + 0.040 × log10

1.0

(3)

where DIFst is the dynamic increase factor of steel materials. Because of the difference in formula form between Eq. (4) and the Cowper-Symonds model for steel materials, the formulas conversion were conducted to determine the strain-rate parameters [43]. 4.2. Validation of FE model and discussions Figs. 5–8 present the numerically-predicted impact forces, displacements, and damage distributions of the CST-UHPFRC composite structures under various impact events, along with the corresponding experimental data. In addition to the above-calibrated model of the corrugated steel tube in compression simulations, the influences of other parameters, such as element types, strain-rate parameters, yield 11

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Multi-column bent Vehicle

UHPFRC-based protective structure

(a) Entire FE model PU foam Rubber

(b) Overall model of UHPFRC-based protection

Distributed rebars

Corrugated steel tube

UHPFRC panel

(c) FE mesh of UHPFRC-based protection

(d) FE model without UHPFRC panels

Fig. 14. UHPFRC-based protective structure for bridge columns against vehicle collisions.

4

(a)

(c)

(b)

Strength (MPa)

3

2

1

0 0.0

0.2

0.4

0.6

Volumetric strain

0.8

1.0

Fig. 15. Compression tests on PU foam: (a) Initial state; (b) compact state; (c) stress versus strain relationship.

strength of corrugated steel tubes, were further investigated and discussed in the following. As shown in Fig. 7, the developed FE model exhibited a good accuracy in the prediction of the peak impact force and interaction phases. The influence of the parameters related to the corrugated steel tubes on the peak impact force was not pronounced. This is because

these parameters mainly affect the overall behavior of the composite structures, and the peak impact force is typically dependent upon the initial contact stiffness. Guo et al. [43] pointed out that the contact condition between the flat hammer and the top panel had a significant influence on peak impact forces. Thus, the tiny inclination between the hammer surface and the UHPFRC panel surface measured from the 12

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Table 3 Material parameters in FE simulations of UHPFRC-based protective structures. Member

Material model

Parameter

Magnitude

Corrugated tube

MAT_PLASTIC_KINEMATIC

Mass density Young’s modulus Poisson’s ratio Yield stress ETAN Failure strain Strain rate parameter Strain rate parameter Mass density Young’s modulus Poisson’s ratio Yield stress ETAN Failure strain Strain rate parameter Strain rate parameter Mass density Poisson’s ratio A B Mass density Young’s modulus Poisson’s ratio

7.93 × 10−9t/mm3 1.93 × 105 MPa 0.29 550 MPa 3100 MPa 0.4 1.434 × 105 6.502 7.85 × 10−9t/mm3 2.0 × 105 MPa 0.30 400 MPa 700 MPa 0.2 7.274 × 107 11.22 1.15 × 10−9 t/mm3 0.499 0.4305 0.0756 9.13 × 10−11 t/mm3 30.6 MPa 0.3

Steel bar

MAT_PLASTIC_KINEMATIC

Rubber

MAT_MOONEY_RIVLIN_RUBBER

Foam

MAT_CRUSHABLE_FOAM

experiments were taken into account in the impact simulations in this study. When omitting the influence in the flat-hammer impact, the peak impact forces obtained from the FE simulations would be significantly higher than the experimentally-measured data [43]. Distinct to the impact forces, the impact-induced displacements are very sensitive to the parameters related to the corrugated steel tubes, as shown in Fig. 8. The numerically-obtained deformations were larger than the experimental results when directly using the material properties (yield strength = 270 MPa) measured from the tension tests of 304 stainless steel plates. It further indicates that using the original mechanical properties of 304 stainless steel plate was not reasonable in modeling the corrugated steel tubes. Good agreements were achieved between the experimental and numerical results for all impact events after using the calibrated material parameters (yield strength = 550 MPa) in the simulations of the corrugated steel tubes. Besides, it was found that the strain-rate parameters had a significant influence on the impact-induced displacements. As shown in Fig. 8, using the strain-rate parameters (C = 40.4 s 1 and P = 5.0 ) suggested in reference [48] underestimated the structural deformation and overestimated the energy dissipation capability. The strain-rate parameters determined in Section 4.1.1 were demonstrated to be reasonable. The influence of shell element types (i.e., reduced and full integration) of the corrugated steel tubes was investigated as well. Compared with shell elements with reduced integration (ELFORM = 2), shell elements with full integration (ELFORM = 16) provided much better predictions of the impact-induced responses. Overall, when the calibrated model of the corrugated steel tubes was used, the impact forces, displacements, and damage modes obtained from FE simulations were in good agreement with the experimental results. The rationality of the proposed FE modeling method was demonstrated for the CST-UHPFRC composite structures under impact loading. The modeling method was also used in the following simulations of UHPFRC-based protective structures subjected to vehicle collisions.

C P

C P

vehicle collisions. Compared with the traditional rigid measures (e.g., an artificial island, rigid concrete barrier), the proposed protective structure can decrease vehicle damage and reduce casualties. On the other hand, it has been observed that the traditional buffers (e.g., FRPbased protections) were vulnerable to damage during minor and moderate collisions. Hence, they are hard to reuse in engineering practices. Since the UHPFRC panel has excellent crashworthiness, the UHPFRC panel can be reused after minor and moderate impacts and the protective structures can be renewed quickly. The limitations in the traditional buffers may be overcome through the thoughtful design of the proposed composite structure. For this purpose, two types (referred to as Type A and Type B) of different composite protective structures were investigated in this section, as illustrated in Fig. 13. In these two types of protective structures, the outer and inner UHPFRC panels were designed as a stiff guard to distribute the impact loads. In addition to the corrugated steel tubes as the energy-dissipating member, the PU foam was filled in the gap between the outer and inner UHPFRC panels to further increase the energy dissipation capacity. Some D-shape rubbers were suggested to attach to the inner UHPFRC panel to reduce the impact force on the bridge column during low-energy impact events. The differences between Type A and Type B are the connection details between the outer panel and the inner panel, as shown in Fig. 13. Specifically, the complete connection and the disconnection were arranged in Type A and Type B protections, respectively. 5.1. FE modeling for vehicle-protection-bridge collision Vehicle collision accidents indicated that bridge structures with multiple-column bents are susceptible to substantial damage and even collapse compared with other types of bridge structures. Hence, a typical three-span bridge structure with multiple column bents was chosen to investigate the performance of the proposed protective structures under vehicle collisions. The vehicle-impact resistant performance of the bridge structures without protections had been carefully examined in the previous study [4]. The detailed FE models were developed and validated for simulating vehicle collisions on the bridge structures. The whole bridge structures, including pier columns, bent caps, footings, bridge girders, and abutments as well as bearings, were first modeled in [4]. The previous study [4] also examined three different simplified models, i.e., two single-column models with different boundaries and one pier-bent model to improve computational

5. Composite structures for bridge protection The proposed UHPFRC-based composite structures can be designed to buffer bridges from vehicle and vessel collisions. In this study, the emphasis was placed on the application of the proposed composite structures into the protective structure for bridge structure against 13

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Impact force (MN)

2.5 2.0

18

Without protection Type A protection Type A protection without rubber Type B protection Type B protection without rubber

(a)

45%

Column disp. at impact point (mm)

3.0

64%

1.5 1.0 0.5 0.0 0.05

0.10

0.15

0.20

0.25

0.30

Without protection Type A protection Type A protection without rubber Type B protection Type B protection without rubber

(b)

15

10%

12

42%

9 6 3 0 0.05

0.10

0.15

0.20

Time

Time

Type A protection

Type B protection

0.25

0.30

(c)

100 Energy dissipation (MJ)

250

(d) Type A protection

80 60

PU foam UHPFRC Corrugated steel tube Steel bars Rubber PU foam (without rubber) UHPFRC (without rubber) Corrugated steel tube (without rubber) Steel bars (without rubber)

40

150

PU foam UHPFRC Corrugated steel tube Steel bar Rubber PU foam (without rubber) UHPFRC (without rubber) Corrugated steel tube (without rubber) Steel bars (without rubber)

100

50

20 0 0.00

(e) Type B protection

200 Energy dissipation (MJ)

120

0.05

0.10

0.15 Time (s)

0.20

0.25

0 0.00

0.30

0.05

0.10

0.15 Time (s)

0.20

0.25

0.30

Fig. 16. Comparisons of different UHPFRC-based protective structures: (a) Impact force; (b) displacement at impact point; (c) damage in UHPFRC panels; (d) energy absorbed by each part in Type A protection; (e) energy absorbed by each part in Type B protection.

efficiency. Both single-columns models were shown to inaccurately predict vehicle-impact responses, while the pier-bent model with the influence of the superstructure gravity exhibited high accuracy. For this reason, the pier-bent model developed in the previous study was used to discuss the effectiveness of the proposed protection. As shown in Fig. 14, solid elements were utilized to simulate the pier columns, bent caps, footings, and bearing pads as well as the equivalent superstructure mass. Beam elements were employed to explicitly model the longitudinal and transverse reinforcement embedded in pier columns. The calibrated CSC model and the elastic-plastic model (MAT_PLASTIC_KINEMATIC) were used to describe the mechanical properties of column concrete and steel materials under impact loading, respectively. Similar to the previous studies [9,49], the FE model of a Ford F800 Single Unit Truck (SUT) developed by the FHWA/NHTSA National Crash Analysis Center (NCAC) at the George Washington

University [49] was used as the aberrant vehicle in this section. The vehicle model has been widely used to investigate the infrastructure performances under vehicle collisions [9,49,50]. Not only the vehicle model had been validated in current studies [49], but also its rationality of the vehicle model was confirmed again in the previous study [4]. In vehicle impact simulations, the keyword *CONTACT_AUTO_SURFACE_TO _SURFACE [39] was used to define the contacts among the vehicle, the protective structure, and the bridge structure. Internal contacts after the protective structures and the vehicle deformed were simulated by using the *CONTACT_SINGLE_SURFACE. Also, the mesh sensitivity analysis of the bridge column performed in the previous study [4] indicated that 35-mm mesh should be used to model the bridge column in this study. Detailed modeling and validation of the bridge structure model under impact loading can be found in [4]. 14

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with Type B protection. Compared to the impact forces, similar levels of reduction in the contact-point displacements of the bridge columns with two types of protective structures were predicted. Fig. 16(c) shows damage in the UHPFRC panels. Severe damage was observed in the UHPFRC panels of Type A protection. On the contrary, relatively slight damage occurred in the UHPFRC panels of Type B protection with the disconnection details of inner and outer panels. Fig. 16(d) and (e) present the impact energy absorbed by each part for two types of the protective structures, respectively. It can be found that different configurations of the UHPFRC-based protections exhibited various energy absorption characteristics. For the Type A protection, the impact energy was primarily dissipated by the UHPFRC panels, the energy-dissipating members (i.e., corrugated steel tubes and PU foam, and the steel bars distributed in the UHPFRC panels. In contrast, most of the impact energy was absorbed by the designed energy-dissipating members (i.e., corrugated steel tubes and PU foam) for the Type B protection, as shown in Fig. 16(e). Relatively little energy was dissipated by the other parts (e.g., UHPFRC panels, steel bars distributed in UHPFRC panels, and rubber). These results indicate that the presence of the disconnection details facilitates the realization of the expected goals (e.g., reducing the impact force and impact-induced response of the protected column, and reutilizing the UHPFRC panels to improve the resilience and economy) of the proposed protective structure. Overall, the performance of the Type B protection was superior to that of the Type A. Compared with the CST-UHPFRC composite structure in the impact tests, the presence of the PU foam can significantly increase the energy dissipation capacity (Fig. 16(e)), which was essential for the proposed protective structure. Unlike the PU foam, the D-shape rubbers had a limited influence on the energy dissipation of the protective structure, as shown in Fig. 16(d) and (e). However, it was observed from Fig. 16(a) that the presence of the D-shape rubber can considerably reduce the impact force and impact-induced responses of the bridge column. This is attributed to the fact that the D-shape rubbers greatly decrease the contact stiffness in comparison with the direct contact between the UHPFRC panel and the bridge column. Hence, the D-shape rubber was arranged in the proposed protective structure.

Table 4 Independent variable and levels in design of experiments (DOE). (Unit: mm) Independent variable

Symbol

Range

BBD level

Thickness of inner panel Thickness of outer panel Depth of energy-dissipating layer Thickness of corrugated tube

t1 t2 t3 t4

100–200 100–200 500–1000 0.8–2.0

100, 150, 200 100, 150, 200 500, 750, 1000 0.8, 1.4, 2.0

For the proposed protective structures (Fig. 14), the FE modeling method developed for the drop-hammer impact simulations in Section 4 was employed to model the corrugated steel tubes and the inner and outer UHPFRC panels. The thicknesses of both the inner and outer UHPFRC panels were 150 mm in the protective structures. The trial simulation indicated that the relatively high strength of UHPFRC would be beneficial for the UHPFRC panels acting as the stiff guard. Hence, the 190 MPa strength grad UHPFRC described in [43] was used in the vehicle impact simulations. The UHPFRC panels had distributed HRB400 steel bars with a space of 100 mm. The material properties of these steel bars were determined in accordance with China’s design specification [51]. Like the test specimens in Section 2, the corrugated steel tubes were made of 304 stainless steel materials for durability consideration. Solid elements were used to model the D-shape rubber and the PU foam in the protective structures. The material model MAT_CRUSHABLE_FOAM was chosen to describe the mechanical behavior of the PU foam. Fig. 15 shows the yield stress versus volumetric strain results measured from the physical experiments that were used in the definition of the material model of the PU foam. Similar to the previous studies [20,24], the material model MAT_MOONEY-RIVLIN_RUBBER in LS-DYNA was used for modeling the D-shape rubber [20]. Table 3 lists the material parameters of the primary members in the protective structures. 5.2. Effectiveness of the proposed protective structure Using the above FE models, two types (Type A and Type B) of the protective structures were evaluated under a vehicle collision with an initial impact velocity of 50 km/h. Fig. 16 presents the impact forces and impact-induced displacements obtained from the numerical simulations. As shown in Fig. 16(a), the impact forces on bridge columns were significantly reduced with the use of the protective structures. Moreover, the impact forces on bridge columns with Type B protection were smaller than those with Type A protection. It is attributed to the fact that the protective structure with the connection details of the inner and outer UHPFRC panels exhibited higher stiffness than the Type B protection. Also, the impact-induced displacements of the bridge column with Type A protection were significantly higher than those with Type B protection, as shown in Fig. 16(b). It implies that vehicle damage and injury with Type A protection significantly exceed those 1.4

24

(a) Impact force

5.3. Multi-objective optimization Multi-objective optimizations were performed for the Type B protection. This section first presented the surrogate models and discussed the sensitivity of design parameters. Then, the design optimization problem was defined. Finally, the multi-objective optimization results of the proposed UHPFRC-based protective structures were provided. 5.3.1. Surrogate model and sensitive analysis To begin with the optimal design of the proposed protective structure, the criteria to evaluate the performance of the protective structure should be determined. Considering the primary functions of the 22

(b) Displacement

1.0 0.8

2

R =0.96 IARE=3.5%

0.6 0.6

0.8

1.0 Actual value

1.2

1.4

18 Predicted value

Predicted value

Predicted value

20 1.2

16 12 R2=0.93 IARE=7.73%

8 4

(c) REP

20

4

8

12

16

Actual value

20

16 14 12 10

R2=0.99 IARE=1.98%

8 24

6

6

8

10

12

14

16

18

20

22

Actual value

Fig. 17. Comparisons between FE results and the results predicted from response surface models: (a) Impact force; (b) displacement at impact point; (c) REC. 15

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Fig. 18. Influences of design parameters on PIF.

protective structure in this study, the optimization of this study could consider the following indicators: (1) the peak impact force (PIF ) on bridge columns that reflects the collision severity related to shear or local damage in columns, damage in vehicle structure, and the casualties, (2) the maximum displacement (MDIS ) at the impact point of bridge columns that relates to the overall damage of the protected bridge columns, and (3) the ratio of energy absorption to total cost of the protective structure (REC), which can be written as:

REC = EA Ct

models (e.g., response surface model (RSM), and artificial neural network (ANN)) have been widely used in crashworthiness optimization designs to reduce the number of required FE simulations and to improve the computational efficiency. According to [52–54], the response surface method was employed in this study to construct the surrogate models for the performance indicators of PIF, MDIS, and REC of the protective structures under vehicle collisions. If a full factorial design is used for four parameters with three levels, a total of 34 = 81 models have to be performed. To improve the computational efficiency, the Box-Behnken design (BBD) was proposed by Box and Behnken [55] to fit response surfaces using fewer required runs than a normal factorial technique. The Box-Behnken design was implemented by combining 2 k factorials with incomplete block designs, where the treatment combinations are at the midpoints of the edges of the cube and at the center [55]. BBD has been widely used to suppress required runs and to maintain the higher order surface definition [4,56]. By using the BBD, the number of the required FE simulation runs were reduced to 29 in this study. Table 4 lists three levels of all varying parameters in BBD. A total of 29 sampling points were created and simulated by detailed FE model to construct the response surface models of PIF, MDIS, and REC as follows:

(4)

where EA is the total strain energy absorbed during the deformation of the protective structure; Ct is the total cost of the protective structure. Apparently, the combined index REC is different from SEA in vehicular energy-absorbing member design. It is because structural weight related to fuel consumption is an essential factor in vehicle design, while the cost is much more critical for the protective structure in this study. Based on the prices provided by the manufacturers in China, the general expenses of UHPFRC, PU foam, and corrugated steel tube are about 1 × 104 RMB/m3, 450 RMB/m3, and 50 RMB/kg, respectively, which were used in the following analysis. The primary geometric parameters chosen as design variables included the thickness of the inner UHPFRC panel (t1), the depth of the outer UHPFRC panel (t2 ), the width of the energy-dissipating layer (t3 ), and the thickness of corrugated steel tubes (t4 ). These parameters (t1 to t 4 ) are illustrated in Fig. 13. Since the energy-dissipating layer consists of the corrugated steel tubes and the filled PU foam, the parameter t3 not only denotes the width of the filled PU foam, but also represents the total height of the corrugated steel tube. Due to the high computational cost for vehicle-bridge-protection collision simulations, the detailed FE simulations were limited in the context of the multi-objective optimization design. Various surrogate

PIF = 3.2374 + 2.92 × 10 3t1

3.5333 × 10 3t2

2.7523 × 10 3t3

1.1651t4 + 1.72 × 10 5t1·t2 + 2.72 × 10 6t1·t3 + 3.275 × 10 3t1·t4 + 1.4 × 10 7t2·t3 + 1.9167 × 10 3t2· t4 + 8.1167 × 10 4t3· t4 + 1.1267 × 10 7t32

3.5833 × 10 5t12

1.0433 × 10 5t2 2

3.044 × 10 2t4 2 (5)

16

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Fig. 19. Influences of design parameters on MDIS.

resolution FE simulation was run on the computer with Intel i7-6700 k processors (CPUs). However, once the response surface models (i.e., Eqs. (6)–(8)) are developed, a simple hand calculation can be used to predict the primary impact-induced responses. Hence, the computational efficiency can be significantly improved by the use of the developed response surface models. Figs. 18–20 present the 3D plots of the performance indicators for pairs of varying design parameters. It was found that PIFs were more sensitive to the width of the energy-dissipating layer and the thickness of the inner UHPFRC panel compared with the depths of the outer panel and the corrugated tube (Fig. 18). Specifically, the peak impact force increased with increasing the thickness of the inner UHPFRC panel. It is because that the increase in the inner UHPFRC panel led to the rise of the contact stiffness between the impacted column and the UHPFRC panel. In contrast, the whole stiffness of the protective structure decreased with the increase of the width of the energy-dissipating layer. Hence, the peak impact force significantly reduced with increasing the width of the energy-dissipating layer. Similar observations can be found in Fig. 19 for the maximum displacements of the bridge columns because the impact-induced responses mainly depend on the impact forces. Accordingly, three objectives can be simplified two objectives (i.e., maximum REC and minimum PIF). In contrast, it was observed from Fig. 20 that the REC of the protective structures significantly reduced with the increases in the thicknesses of the inner and outer UHPFRC panels. It is because that the UHPFRC materials have a relatively high cost compared with the conventional materials, and the UHPFRC panels were functioned as the stiff guard other than the energy absorber. The REC slightly reduced with the width of the energy-dissipating layer because the PU foam in the two lateral sides led to a high cost but a low energy absorption contribution under head-on collision. On the contrary, a balance between energy absorption and the price

MDIS = 5.0604 × 101 + 6.255 × 10 2t1 + 3.9167 × 10 3t2 6.2173 × 10 + 5.04 × 10 4t1· t2

2t 3

101t

1.9382 ×

4

2.02 × 10 5t1·t3 + 2.9083 × 10 2t1· t4

+ 1.62 × 10 5t2·t3 + 1.3583 × 10 2t2· t4 + 1.8183 × 10 2t3· t4

4.9417 × 10 4t12

+ 1.2813 × 10 5t32 REC =

4.3217 × 10 4t2 2

3.8657 × 10 1t4 2

(6)

3.8788 × 101 + 9.206 × 10 2t1 + 1.4368 × 10 1t2 1.9658 × 10 2t3 + 9.142t4

2.329 × 10 4t1·t2 + 6.522 × 10 6t1· t3 + 3.853 × 10

5t ·t 2 3

+ 5.4614 × 10 4t3· t4 + 9.699 × 10

6t 2 3

1.568 × 10

6.881 × 10 5t12 3.8225 × 10

1.32 × 10 2t1·t4 2t ·t 2 4

1.8211 × 10 4t22 1t 2 4

(7)

It was of importance to examine the accuracy of the above response surface models of PIF, MDIS, and REC before their application in the optimization design. Relative error (RE), and the coefficient of multiple determination (R2 ) were used in this study to evaluate the accuracy of these surrogate models. Fig. 17 shows the data pairs (i.e., the dots) of PIF, MDIS, and REC obtained from the high-resolution FE simulations and the developed response surface models, respectively. The expected line y = x is also plotted in Fig. 17 to show the consistency between the values predicted by the developed response surface models and the FE models. As shown in Fig. 17, the values of R2 were approximate to 1.0 for all three responses surface models, and the average RE values were 3.50%, 7.73%, and 1.98% for the response surface models of PIF, MDIS, and REC, respectively. Hence, the rationality of the response surface models was confirmed. The total wall-clock time required to simulate the 0.3-second vehicle impact event was about 17.5 h when the high17

Engineering Structures 207 (2020) 110247

REC(J/RMB) REC(J/RMB)

REC(J/RMB)

REC(J/RMB)

REC(J/RMB)

REC(J/RMB)

W. Fan, et al.

Fig. 20. Influences of design parameters on REC.

was achieved by changing the thickness of corrugated steel tubes. Contradictions were found for achieving the expected objectives, which highlights the necessity of conducting the multi-objective optimization design of the proposed protective structure.

-12

-REC (J/RMB)

-13 -14

5.3.2. Problem definition As an energy absorber, the protective structure is expected to minimize PIF and maximize REC, which was defined as the two objectives in the optimization design process. Without considering the cost of the protective structure, the designer can obtain the optimal solution with the lowest impact force on bridge column by increasing the width of the energy-dissipating layer. On the contrary, the designer can get the protective structure with the highest REC for the bridge column. Hence, the two-objective optimization problem cannot be considered as the two independent optimization problems. Also, unlike the single-objective optimization problem that provides only a sole optimal solution, the task in a multi-objective optimization is to find a cloud of best trade-off solutions (called “Pareto-optimal solutions” or “Pareto-optimal front”) of the conflicting objectives [57–59]. Once the Pareto-optimal solutions are obtained, the designers (or owner) can

-15 -16 -17 0.7

0.8

0.9

1.0

1.1

1.2

PIF (MN) Fig. 21. Pareto Solution.

Table 5 Optimal design results and comparisons with FE results. No.

1 2 3 4

Parameters (mm)

PIF (MN)

REC (J/RMB)

t1

t2

t3

t4

Predicted

FE result

Error(%)

Predicted

FE result

Error(%)

132 125 128 126

173 125 144 132

839 697 839 830

1.02 1.00 1.02 1.02

0.813 1.111 0.879 0.913

0.808 1.05 0.805 0.833

0.6 5.8 9.2 9.6

12.249 16.415 14.454 15.512

12.025 16.245 15.036 14.563

1.9 1.0 3.9 6.5

18

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Without protection (50km/h) With protection (50km/h) Without protection (80km/h) With protection (80km/h)

(a)

Impact force (MN)

5 4 3

71%

2 46%

1 0 0.0

0.1

0.2

80 Column disp. at impact point (mm)

6

60

15% 40

20 37% 0 0.00

0.3

Time (s)

Without protection (50km/h) With protection (50km/h) Without protection (80km/h) With protection (80km/h)

(b)

0.05

0.10

0.15

0.20

0.25

0.30

Time (s)

Fig. 22. Response of optimized UHPFRC-based protective structures under vehicle collisions (a) impact force; (b) column displacement at impact point.

make further decisions according to their subjective preferences [57–59]. Accordingly, the multi-objective optimization design (MOD) problem of the proposed protective structure under vehicle collisions can be defined as follows:

min{PIF (t1, t2, t3, t4 ), REC (t1, t2, t3, t4 )} s.t. 100 mm < t1 < 200 mm 100 mm < t2 <200 mm 500 mm< t3 <1000 mm 0.8 mm< t4 <2 mm

algorithm (called NSGA-II) is rather useful in searching for widelydistributed Pareto-optimal solutions with conflicting objectives. For this reason, NSGA-II were employed in this study to obtain the Pareto designs of the formulated MOD problems of the proposed protection. Fig. 21 shows the Pareto fronts of REC versus PIF under the given vehicle collision, which were derived through NSGA-II iterations of 202 generations. As shown in Fig. 21, the simplified two objectives conflict with each other, which means an increase in REC always leads to an undesirable rise in PIF. According to the obtained Pareto set, the large value of the width of the energy-dissipating layer were recommended. The relatively thick (over 125 mm) outer UHPFRC panel was suggested with the purpose of the reutilization. Table 5 lists four typical optimization results for the proposed protection under vehicle collisions. The detailed FE simulations were performed to examine the optimization results. The corresponding FE results are presented in Table 5. Good agreements were achieved between the optimization results and the FE results. As shown in Figs. 22 to 23, the impact forces and responses were significantly reduced when adopting the proposed protection with the optimal design parameters (i.e., the first option in Table 5). More importantly, the damage in the impacting vehicle was decreased considerably to reduce the risk of severe injury or death of the vehicle’s driver.

(8)

5.3.3. Multi-objective optimization results and discussions The MOD design task is to obtain a cloud of best trade-off solutions (called “Pareto front”) in the design space [60]. Based on the obtained Pareto front, the designer can make further decisions according to their subjective preferences. In the MOD of the proposed protection under vehicle collisions, the validated response surface models instead of detailed FE models were used to estimate the values of PIF and REC under various design parameters (i.e., t1 to t4 ). Much research [59,61,62] pointed out that the non-dominated sorting genetic

Fig. 23. Influence of UHPFRC-based protective structures on damage in vehicle. 19

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6. Conclusions

Appendix A. Supplementary material

A new UHPFRC-based protective structure was proposed in this study to protect bridge columns from vehicle collisions and to reduce the damage of vehicles and casualties. Drop-hammer impact tests were performed for the proposed CST-UHPFRC composite structures. Detailed FE modeling methods were developed and validated against the drop hammer impact tests. Also, the performance of the proposed protective structures under vehicle collisions was carefully examined. Based on the experiments and FE analysis, the main conclusions can be drawn as follows:

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(1) The drop-hammer impact tests confirmed that the UHPFRC panel in the propose composite structure has excellent crashworthiness to be capable of acting as a stiff guard to distribute impact loads. (2) The impact forces were more sensitive to the number of corrugated steel tubes than the thickness and thickening the corrugated steel tubes was superior to adding the number for the crashworthiness improvement. (3) The overall displacement of the tested specimens could be reduced by adding ribs in the UHPFRC panel because the presence of ribs can improve the integrity of the composite structure. (4) An FE modeling method was proposed to predict the responses of corrugated steel tube-UHPFRC composite structures under impact loading. Notably, a calibrated approach was developed to model the corrugated steel tubes including the influence of manufacture process. Numerical results obtained using the proposed FE modeling method were in good agreement with the experimental results. (5) Numerical results show that the protective structure (Type B) with the disconnected details between the inner panel and the outer panel is superior to that (Type A) with the connection details. Type B protective structure reduced the impact force as well as damage in the UHPFRC panels for reutilization (i.e., resilient performance). (6) A multi-objective optimization design (MOD) procedure was presented for the protective structure under a given vehicle collision. Response surface models were developed and were demonstrated to be capable of predicting PIF and REC under various design parameters. The Pareto front obtained using NSGA-II shows that two objectives (i.e., minimizing PIF and maximize REC) conflict with each other, preventing simultaneous optimums from being reached. Some typical optimum results were examined and confirmed through high-resolution FE simulations. CRediT authorship contribution statement Wei Fan: Conceptualization, Validation, Writing - original draft. Dongjie Shen: Methodology, Data curation. Zhiyong Zhang: Investigation, Visualization. Xu Huang: Writing - review & editing. Xudong Shao: Supervision. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This research is supported by the National Key Research and Development Program of China (Grant Number: 2018YFC0705400), the National Natural Science Foundation of China (Grant Number: 51978258), the Major Program of Science and Technology of Hunan Province (Grant Number: 2017SK1010), and the Science and Technology Base and Talent Special Project of Guangxi Province (Grant Number: 2019AC20136). 20

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