Experimental and numerical analysis of the modified TB32 crash tests of the cable barrier system

Engineering Failure Analysis 104 (2019) 227–246

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Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal

Experimental and numerical analysis of the modified TB32 crash tests of the cable barrier system

T

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Dawid Bruskia, , Stanisław Burzyńskia, Jacek Chróścielewskia, Kazimierz Jamrozb, Łukasz Pachockia, Wojciech Witkowskia, Krzysztof Wildea a

Gdańsk University of Technology, Faculty of Civil and Environmental Engineering, Department of Mechanics of Materials and Structures, ul. Gabriela Narutowicza 11/12, 80-233 Gdańsk, Poland b Gdańsk University of Technology, Faculty of Civil and Environmental Engineering, Highway and Transportation Engineering Department, ul. Gabriela Narutowicza 11/12, 80-233 Gdańsk, Poland

A R T IC LE I N F O

ABS TRA CT

Keywords: Road safety equipment Cable barrier Crash tests Finite element method LS-DYNA Numerical simulations Explicit dynamics

Road restraint systems, including safety barriers, are one of the means used to improve road safety. Currently, they can be allowed to general use after passing the specific crash tests. However, it is always important and desirable to evaluate their performance under various realistic conditions, which can happen on the roads. In this study, the behaviour of the cable barrier system in impact conditions different than assumed by EN 1317 standard was analysed. For this purpose, a full-scale crash test was performed and on the basis of this the validation process of numerical simulations was carried out. Correctly and carefully developed numerical simulations give unique insight into the impact mechanism and allows for comprehensive understanding of barrier responses. The accuracy of the numerical models was assessed by comparing the results of the simulation with the crash test. The research showed that the analysed barrier work correctly, it contained and then properly redirected 1500 kg car back onto the road and ensured safety for the vehicle occupants at the same time.

1. Introduction 1.1. General description of road safety equipment Every day on roads and motorways, many different scenarios of accident occur, in which safety equipment has to minimize their negative consequences [1,2]. Reasonably and responsibly designed safety equipment installed at roads could minimize chances of vehicle occupants' injury or fatality [3], so an accident can end up with only damaged vehicle. Road safety equipment can be divided into passive and active devices [4]. Passive road safety equipment means such devices which the vehicle does not come in direct contact but are used only for the organization and management of traffic (e.g. road signs, traffic lights). Active road safety devices comprise structures which the vehicle comes into direct contact during unintentional events (e.g. safety barriers, energy absorbing crash cushions) [5]. The main purpose of using safety barriers is to prevent the vehicle from uncontrolled getting off the road in hazardous places and to prevent getting the vehicle to the opposing lane, where it can collide with oncoming vehicles which is particularly dangerous (socalled cross-median crashes [6]). Barriers are used on roads, bridges and where obstacles such as trees or bridge abutments are close

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Corresponding author. E-mail address: [email protected] (D. Bruski).

https://doi.org/10.1016/j.engfailanal.2019.05.023 Received 26 November 2018; Received in revised form 13 April 2019; Accepted 29 May 2019 Available online 30 May 2019 1350-6307/ © 2019 Elsevier Ltd. All rights reserved.

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to the road. Their additional advantage is that they clearly mark the road's edges, increasing the confidence of vehicle's motion, which is especially useful at night or when visibility is poor e.g. fog or snow [7]. The barrier should ensure safe conditions of the collision for vehicle occupants and redirect the errant vehicle back on the travelled lane so that it can continue its motion approximately parallel to the barrier's face. Barriers are not neutral devices and do not eliminate road accidents, however when properly used, they mitigate their negative effects. Thus, barriers should be used only in places where the anticipated consequences of a road accident will be more serious than the results of the vehicle impact into the barrier [8]. The most basic classification of safety barriers is due to the used material (steel, cable and concrete barriers) and due to the place of application (road and bridge barriers). A special feature of safety barrier is that they cannot be designed using only standard methods of calculations, like static or dynamic, linear or nonlinear analysis. The correctness of their response and their effectiveness must be checked in full-scale crash tests [9–11]. In everyday life many cases of vehicle's impacts into the barrier may occur e.g.: different vehicles (cars, trucks), different impact speeds or different impact angles. To cover these situations and ensure an adequate level of safety on roads, European standard EN 1317 [12,13] has been stablished, describing requirements that safety barriers must obey. Nevertheless, there is always a probability of hitting the barrier under different conditions than anticipated by EN 1317. Yet, due to the high costs of crash tests, EN 1317 standard tests are usually carried out leaving nonstandard cases not studied. As per EN 1317 the TB32 crash test assumes the impact of a typical 1500 kg passenger car into a barrier at a speed of 110 km/h at an angle of 20°. However, at a speed of 110 km/h, impacts at a lower angle are more often observed [14]. In this study, the impact of a 1500 kg BMW e34 into the cable barrier (speed 110 km/h, angle 7°) is analysed experimentally and numerically. To the best authors' knowledge, there is a lack of papers dedicated to cable barrier studies showing the results of collisions in other than standard configurations. Hence, it was decided to examine a non-standard case in this work. Additionally, validation of numerical simulations of cable barrier performance is seldom presented in papers, without details of modelling techniques given for further comparison. The aim of present study is to derive a detailed numerical model (in LS-DYNA FEM explicit dynamics software) and validate it with respect to data collected in own, full scale test. Then, further studies are conducted: description of the response of the cable barrier and the vehicle trajectory, determination of indicators according to the EN 1317 standard, and to assess the damage of the safety system in detail. The obtained results enable to follow the behaviour of the barrier system during the accident and allow the better understanding of the phenomena occurring whilst the impact. Roadside hardware simulations are more and more used, and for this reason this paper also points at some existing legal conditions for their use during the barrier certification process, which significantly increases their importance. The paper is organized as follows. Section 1.2 contains a general description of cable barriers and their features. Section 2 describes the most important information about the EN 1317 standard concerning crash tests. It also depicts the possibility of using numerical simulations to analyse barriers' behaviour during vehicle impact and to certify modified barrier system. The overview of the basics of used LS-DYNA software is included in Section 3. Section 4 presents a numerical model and a full-scale crash test scenario involving a cable barrier and a BMW vehicle. The results of the numerical simulation and a detailed comparison with the results from the crash test are shown in Section 5. Section 6 is discussion of the results and the last section presents general conclusions. 1.2. Cable barriers Cable barriers have been used in USA since 1910 [8], at that time they were used to secure road edges on steep slopes and high embankments. Their importance as a road safety equipment was noticed sometime between 1920 and 1930 [6,8], earlier than in the case of steel barriers. And at that time they were subjected to the first crash tests. In the initial period of use, the wire ropes were used without any pre-stressing (tension force in cables). However, the crash tests and practical experience on the roads have shown that the barriers are not very effective. Therefore, nowadays almost only cable barrier which are prestressed are used. In Europe, cable barriers have been used since the 1950s [8]. Currently there are various structures of cable barriers e.g. 3-cable guardrail, 4-cable guardrail, which are commonly used on roads, for instance on the highways as well as on the city roads, as shown in Fig. 1. In contemporary cable barriers, easily deformable posts are used, which can easily bend due to the impact, thus neither causing significant damage to the vehicle nor change its velocity or motion direction. The mounting of the wire ropes to the posts is usually designed to easily detach from the post when the vehicle strikes [6,8,15]. The wire ropes during impact deform significantly the vehicle bodywork, which makes it possible to keep the ropes at the desired height and do not allow ropes to pass over or under vehicle. This decides about the effectiveness of containing and departure of the vehicle, even when the number of the posts damaged during the collision is significant [8]. Cable barriers are the structures, that are relatively inexpensive, easy to install, maintenance and repair after impact. They reduce snow buildup and do not impede snow ploughing operations in comparison to the steel and concrete barriers. In addition, they slightly limit visibility from the road and provide good “see-through” appearance. Cable barriers are generally beneficial structures in terms of safety of vehicle occupants, because unlike the steel or concrete barriers, they usually provide smaller accelerations for people inside the vehicle during the collision. Properties of cable barriers cause that the number of collision with low severity, where people are not seriously injured and the vehicle can often continue to drive, is higher than in the case of other types of barriers [6,8]. Installation of cable barrier on medians can be very effective method for reducing the fatal cross-median crash rates, as was shown in [16], and may contribute to the improvement of the road safety. It should be clearly emphasized that the cable barriers are not universal devices, the same concerns the steel and concrete barriers, but they are a complementary solution to the other types of barriers. This means that in some situations the cable barrier will be the best choice, and in the other better solution might be to use the different type of barriers, when, for example, at a short distance 228

Fig. 1. Barrier installed a) on a roadside, b) on a median, c) in the city centre.

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Fig. 2. Impact energy depending on the crash test and the containment level.

behind the barrier are obstacles such as a road sign gantry [8]. 2. Testing of safety barriers 2.1. EN 1317 standard In most European countries requirements for safety barriers are regulated by EN 1317 European standard [12,13], which was established in 1998 and then revised in 2010. This standard defines the crash testing procedures and their acceptance criteria. Based on the results of impact tests, levels of performance for barriers are determined. It is important to point out that the EN 1317 standard does not specify the dimensions, geometry or materials for safety barriers. It also does not states what barriers are to be used on what roads, leaving these decisions to national and local road authorities [17]. EN 1317 standard introduces three main criteria on the basis of which the levels of barrier performance are established:

• Containment level – indicates the ability of a barrier to contain an impacting vehicle. The standard distinguishes four contain-

ment, named as low, normal, higher and very high. Fig. 2 shows the kinetic energy of the vehicle before the impact, depending on the standard crash tests and the containment level. The horizontal and perpendicular to the barrier's face component of the vehicle velocity is taken into account. Below the horizontal axis, in the first row, the standard names of the crash tests are given, and under them the names of the subsequent tests are shown. These are the tests which the barrier must pass, to assign it one of the containment level. For instance, the containment level of H1 will be assigned to a barrier that successfully pass TB42 test (velocity 70 km/h, angle 15°, vehicle's mass 10,000 kg) and TB11 test (100 km/h, 20°, 900 kg).

Fig. 3. Working width measured values. 230

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• Working width – is a measure of the barrier's capacity to deform during a collision. It is defined as the maximum lateral distance •

between the face of the barrier from traffic side before the impact and the maximum dynamic position of any part of the barrier (Fig. 3a) or vehicle (if vehicle body deforms around the barrier, Fig. 3b) during the impact. The working width is divided into 8 classes (from W1 to W8), according to the growing deformation of the safety system. This distance allows to establish what space behind the barrier needs to remain free of obstacles in order for the safety system to operates in smooth manner. Impact severity level – allows to assess the effects of collision on people inside the vehicle on the basis of two indicators: the acceleration severity index (ASI) and the theoretical head impact velocity (THIV). The acceleration severity index (ASI) is a nondimensional function of time, computed using the following formula: 2

ASI (t ) =

2

2 ⎛ Ax ⎞ + ⎜⎛ Ay ⎟⎞ + ⎜⎛ Az ⎟⎞ ⎝ ax̂ ⎠ ⎝ aẑ ⎠ ⎝ a ŷ ⎠ ⎜

⎟

(1)

where Ax , Ay , Az are the time dependent functions of components of the acceleration along the axes x, y and z recorded at the vehicle's centre of gravity, which are filtered with a four-pole phaseless Butterworth low-pass digital filter with the cut-off frequency of 13 Hz, a x̂ = 12g , a ŷ = 9g , aẑ = 10g are limit values for the acceleration components along the body axes x, y and z (g = 9.81m/s2). The maximum value of the ASI during collision is assumed as a measure of severity. ASI is one of the most important indices of the safety barrier. The second indicator, theoretical head impact velocity (THIV) denotes an impact speed of the theoretical head at the moment of contact with a theoretical vehicle cabin. In previous versions of the EN 1317 standard there was also PHD indicator (postimpact head deceleration) defining the theoretical head deceleration after impact. This parameter, along with ASI and THIV, was used to determine the impact severity level, however, in current versions of the standard [12,13], the obligation to determine PHD was waived. Impact severity level A (ASI ≤ 1.0) affords a greater level of safety for vehicle occupants than level B (1.0 < ASI ≤ 1.4), and level B is safer than level C (1.4 < ASI ≤ 1.9). Classification to any of listed levels is possible if THIV ≤ 33km/h is obtained in test. 2.2. Numerical simulations of crash test Nowadays, the continuous development of numerical methods allows to use them to study the properties of safety barriers [18,19]. As the standard [20] states, computer simulation (…) are powerful and fast developing design tools. They are used as a supplement to expensive real crash test to assess the crashworthiness of road safety equipment. Additionally, numerical methods are also applicable to study the cases that are not included in the standards like e.g. impact into a damaged barrier. Numerical simulations of crash tests are the subject of many scientific and research works [21–25]. Numerous publications presenting the results of numerical research confirm their suitability to support the road safety devices design, their assessment and also to provide guidelines for devices' installation and maintenance [26–28]. The possibilities of using numerical simulations to study the effectiveness of safety barriers and the methodology of creating a computational model is described in the article [29]. In [30] a steel road safety barrier was analysed. Experimental crash test and numerical simulations of the TB11 test were carried out. Results from computational simulation were compared with the results of the full-scale crash test and very good compatibility was obtained. Another papers considering steel barriers are works by Gutowski et al. [31,32]. In [31] the researches evaluated the performance of single-faced and double-faced W-beam guardrails installed on sloped median, to investigate the possibility of replacing the two lines of guardrails with a single line of a double-faced guardrail. In [32] authors examined the influence of W-beam guardrail heights placement and the distance between the barrier and the curb for Dodge Neon and Ford F250 vehicles impacting the barrier at 15° and 25°. In the two above works, the numerical model of the barrier developed by NCAC [33] was used and then adapted for the needs of this studies. An example of analysing crash tests deviating from the requirements of the EN 1317 standard for testing the straight section of the barrier, are works [34–36]. In this papers the steel road barrier installed on a horizontal concave arc was considered. It was shown that, in order to meet the criteria of the vehicle motion in the exit box, the barrier had to be equipped with an additional composite-foam protective overlay. The cable barrier was considered at work [37]. The authors performed a number of numerical simulations using validated Dodge Neon car and cable median barrier (CMB) models. Several CMB designs were analysed, including different impact velocities and angles. A major finding of this work is that the heights of the wire ropes strongly affect cable-vehicle interaction and the redirection of impacting vehicles. In [38] the numerical simulations of cable barrier crash tests that involved 900 kg car (TB11 test) and 13,000 kg bus (TB51 test) were carried out. The ASI, THIV, working width and the length of contact from TB51 numerical calculation were compared with the results obtained from full-scale crash test. The reports [39,40] and the article [41] describe in detail the methods of modelling the wire rope. The concrete barrier was a subject to analysis in the paper [42]. The study shows the results of the numerical simulation of the TB11 and TB32 crash tests. Two types of barriers were examined: barrier, which can move on the ground, and the fixed rigid barrier. The results indicate a significant effect of the barrier installation method on collision course and dynamic loads affecting the car passengers. Bridge barrier was consider in e.g. [43] where analysing and testing of a new high containment level bridge rail was shown. This barrier was subjected to full-scale crash testing in accordance with EN 1317 standard and the results were used to check the numerical simulations. In the study [44] the problem regarding bridge barrier placement as relative to the curb was analysed. A series of numerical tests included 13,000 kg bus was conducted. Results reveal that the distance between barrier and the curb affects a little on the working width but it influences the course of the crash event. In all above mentioned works concerning numerical studies of the road and bridge barriers behaviour, the explicit finite element code LS-DYNA was applied. 231

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Table 1 Categories of modifications of vehicle restraint system (VRS) in accordance with [20]. Category

Change

Description and an example

A B

Slight Moderate

C

Significant

Modifications requiring no mechanical changes to the VRS. Example: repainting of the barrier. Modifications concern at least one components of the barrier where their effects on the performance of the safety system can be determined by static or dynamic analysis or other appropriate means. Example: for a cable barrier - reduction of the section length between anchorages. Modifications excess the range of the categories A and B. Example: steel barrier where type or grade of metal is changed.

2.3. Certification of modified barrier based on simulations The barrier to be installed as road safety equipment on Polish and European roads must pass test and conditions specified in EN 1317 standard. Computer simulations, in accordance with EN 1317 part 5 [20], may be in some cases the origin for the certification of safety barrier system that bases on previously product allowed to use, but have undergone some modification. This opportunity significantly raises the importance of numerical simulations in the device certification process. Part 5 of the EN 1317 standard introduces three categories of modifications of existing safety barriers systems, which are summarized in Table 1. Modification within category A requires only a description of the proposed changes. To obtain the certification of a product modified in category C, a new full-scale crash test must be carried out. To obtain the certification of a product meeting the requirements of modification within category B, written report setting out the evidence, used methods, calculations and results compared to original values has to be supplied. Within this category, numerical simulations can be used. Firstly, a numerical model of the original restraint system that has been certified based on full-scale crash tests has to be created. This model must correctly pass the validation process in accordance with standard PD CEN/TR 16303:2012 „Road restraint systems – Guidelines for computational mechanics of crash testing against vehicle restraint system” [45–48]. Afterwards, to such numerical model the modifications of the category B needs to be applied and then the calculation has to be performed. On the basis of the results from the simulation, the modified product may obtain the certification. The advantage of this approach is the reduction of the number of expensive crash tests. The standard [20] indicates that all calculations, where computer models were used, need independent third party confirmation. The scheme of the certification process of modified products based on numerical simulations is shown in Fig. 4. 3. LS-DYNA software overview In this work, numerical simulations were employed to evaluate the performance of cable barrier. The calculations were conducted by using finite element code of LS-DYNA (MPP double precision R8.1.0) on supercomputer Tryton managed by Academic Computer Centre (CI TASK) in Gdańsk, Poland. The LS-DYNA system is the basic and world-known tool for performing the simulations of the crash tests. This system uses special form of explicit central difference method to integrate the equations of motion [50–52]. Nonlinear equation of motion discretized by FEM at time n reads:

M x¨ n = r n − f n − hn ,

(2)

where M is the diagonal global mass matrix, x¨ denotes the global nodal acceleration vector, r n accounts for the vector of external loads, f n is the vector of internal loads and damping and hn is the vector of forces resulting from hourglass control. To advance vectors ẋ and x to time tn+1 the following formulae are used (the superposed dot represents time derivative):

x¨ n = M−1 (r n − f n − hn ), 1

(3)

1

ẋ n + 2 = ẋ n − 2 + Δtn x¨ n,

(4)

Fig. 4. Device certification process based on the numerical calculation (based on [49]). 232

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xn + 1 = xn + Δtn + 1 ẋ n + 2 ,

(5)

1 (Δtn + Δtn + 1). 2

(6)

2

Δtn + 1 = 2

In the above formulae ẋ is the global nodal velocity vector and x is the global nodal displacement vector. As a result of the implementation of above formulation of the method, the results are much less sensitive to round-off errors than in case of classical formulation [50]. To ensure the stability of the solution, the time step is evaluated from the following relation: (7)

Δt = α Δtcrt

where α is the Courant number (default value is 0.90 [50]) and Δtcrt is the critical time step which depends on characteristic spatial dimension of the finite elements (the algorithm considers the 1D, 2D and 3D elements) and material properties. The minimum value from time steps calculated for N number of finite elements is assumed as the time step for next time instance, that is

Δt n + 1 = α min{Δt1 , Δt2 , Δt3,…, ΔtN }.

(8)

Since LS-DYNA is used as computational tool, all specific terms used in following sections, are described in details in codes theory documentation [50,53]. In order to perform numerical simulations, a transient explicit analysis was carried out. 4. Real scale test and numerical model 4.1. Vehicle description According to best authors' knowledge, entities conducting crash tests are likely to use BMW e34 (5 series) vehicles whenever 1500 kg car is needed. Another choice, for purpose of those tests, could be Dodge Neon (which needs additional weighting from initial mass of about 1200 kg to desired 1500 kg). Unlike the Dodge Neon, which represents the U.S. vehicle market, the BMW vehicle represents the European vehicle market, which means that its geometry and dimensions are more similar and corresponding to vehicles that can be found on Polish and European roads than Dodge Neon. This enables to achieve the most accurate results. In this study, it was decided to use BMW e34 in full-scale crash test, as well as in the corresponding numerical simulation. An example of another work where the BMW vehicle was used is given in [54], in which the steel barrier was considered. Numerical model of BMW car consists of 22,428 nodes and 21,558 finite elements (20,562 shells, 970 solids, 8 beams, 18 discrete elements). The vehicle is equipped with a special finite element working as an accelerometer, placed near to the centre of gravity. This finite element record accelerations and angular velocities in local vehicle coordinate system. Based on this data, severity indices ASI, THIV and PHD can be determined [55]. The model was developed by Transpolis (formerly LIER), the French crash-test house and digital simulation office for road safety equipment.

Fig. 5. The numerical model of the BMW (on the left) and BMW used in crash test (on the right). 233

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Table 2 Comparison of parameters between numerical vehicle, the BMW from crash test and EN 1317 requirements. Vehicle specifications

Simulation

Full-scale crash test

EN 1317 [12]

Requirement fulfilment

Vehicle name Vehicle mass, kg Ballast mass, kg Total vehicle mass, kg Dimensions: Vehicle length, m Vehicle width, m Front wheel track, m Rear wheel track, m Front wheel radius, m Rear wheel radius, m Wheel base, m Location of the centre of gravity: Longitudinal distance from front axle (CGX) Lateral distance from vehicle centre line (CGY) Height above ground (CGZ) ATD (type, mass)

BMW e34 1499.74 1499.74

BMW e34 520 1398.6 126.2 (45.5 + 81) 1524.8

≤180 1500 ± 75

FULLFILLED FULLFILLED

4.714 1.774 1.492 1.492 0.295 0.295 2.761

4.715 1.760 1.445 1.480 0.300 0.310 2.760

1.500 ± 0.225 1.500 ± 0.225 Not applicable Not applicable Not applicable

FULLFILLED FULLFILLED

CGX: 1240.29 mm CGY: 0.82 mm CGZ: 557.31 mm No

CGX: 1282 ± 8 mm CGY: 7 ± 5 mm CGZ: 546 ± 8 mm Yes (Hybrid III, 81 kg)

CGX: 1240 ± 124 mm CGY: ± 80 mm CGZ: 530 ± 53 mm Not required

FULLFILLED FULLFILLED FULLFILLED

Full scale BMW view with a comparison to the corresponding numerical model is displayed in Fig. 5. Detailed comparison of vehicles specification is listed in the Table 2. Last column consist of information whether standard's requirement is fulfilled (if requirement is included in standard). It can be concluded that the vehicle's numerical model corresponds very well to the full scale car. 4.2. Cable barrier The numerical model of the barrier was prepared in LS-DYNA environment, corresponding in details to the system tested in the full-scale impact test. The overall view of the system and test site is shown in Fig. 6 and Fig. 7. The N2/W4/A class barrier was tested, so this means that this device successfully undergoes standard TB11 and TB32 crash test (see Fig. 2). Cable barrier system consists of three pre-stretched wire ropes which are mounted to the steel posts with hooks. On the top of each post the post cap is mounted. The height of the system is 0.75 m. The length of the single post is 1.7 m and it is embedded 0.95 m in the soil. The post spacing is equal to 2.0 m. Two extreme posts at the both ends of the barrier are equipped with additional steel elements, which stabilize the post in the soil. They are made in the form of a horizontal rectangular and a vertical triangular plates, which are welded to the post. General view of the first three posts and soils is presented in Fig. 7b. Total length of tested system was 68.2 m (52.0 m straight and horizontal section and two 8.1 m terminals). In created numerical model length of safety system was changed slightly, namely 52.0 m straight and horizontal section, two 6.062 m terminals at the both barrier's ends. In full-scale test the ends of cable are mounted to buried concrete anchorages. The motion of concrete anchorages was not observed during crash. Consequently, it was decided to fix the ends of the wire ropes in the numerical model at the ground level, keeping cables' course in terminals, but neglecting possible motion of cables' ends. Numerical model of the barrier consists of 182,333 nodes and 206,064 finite elements. 4.2.1. Wire rope In considered safety system, the guardrail consists of three parallel 19 mm diameter 3 × 7 wire ropes (see Fig. 8) attached to the posts. Wire rope is modelled using Belytschko-Schwer beam elements (ELFORM = 2) and the *MAT_MOMENT_CURVATURE_BEAM (*MAT_166) material model. The parameter EPFLG is 1.0 (multi-linear plastic analysis). The length of a single beam element is 25 mm. The material properties of the wire rope were determined based on the report [39]. This report describes in detail the material data for the cable model. The authors carried out experiments to determine material properties (e.g. quasi-static and dynamic tensile testing), they performed a numerical simulation of boogie impact and compared the results with experiment.

Fig. 6. Comparison of the overall view from rear side of a) numerical model, b) full-scale object. 234

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Fig. 7. The views of a) test site, b) discretization (on the left) and view (on the right) of the first three posts of the cable barrier, c) numerical model of the cable barrier.

Fig. 8. The wire rope: a) cross sections, b) a photo of the fragment of the rope, c) the numerical model.

Afterwards, this wire rope model was used in crash test consistent with NCHRP Report No. 350 TL-3 using Chevrolet C2500 pickup model. Results of the crash test and the numerical simulation were compared. Authors of this report determined the wire rope response to be accurate. The real wire rope density is 7948 kg/m3, the Young's modulus is equal to 116 GPa (determined from the stress-strain curve, which was obtained from the force-strain curve – Fig. 9). The cross-sectional area is 154.5 mm2 (the diameter of single wire is 3.058 mm). In the prepared model cable was simplified as beam elements with a solid, circular cross section. Diameter of 19 mm (area 283.5 mm2) is assumed to enable proper contact with other parts of the model (as Fig. 8a shows). Therefore, the density was reduced by ratio of cross-sectional area of the rope to the area of the circle of diameter of cable numerical model and was set to 4308.5 kg/m3. The Young modulus was reduced in the same manner, assuming the final value of 62.8824 GPa. In the material wire rope model three curves were implemented: force-strain, bending moment-bending curvature and torque-rate of twist (Fig. 9). Those properties are taken from the report [39]. In numerical simulation the wire ropes are pretensioned to force F0=22.6 kN [56] in the manner that imitates in full-scale crash test. In full-scale crash test the tension was introduced by special-purpose hydraulic device, installed temporary and locally on the rope during system installation. Device is located between the posts no. 4 and no. 5. To perform pretension in similar manner in

Fig. 9. Curves [39]: force-strain, bending moment-bending curvature, torque-rate of twist. 235

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numerical model, the beam elements (ELFORM = 6) with *MAT_CABLE_DISCRETE_BEAM (*MAT_071) material model were used to mimic mentioned device. The force F is given by following formula:

F = max ⎛F0 + ⎝

E ⋅A ⋅ΔL⎞ L ⎠

(9)

where E denotes Young's modulus, A is cross-sectional area, L stands for initial length and ΔL is the difference between current length and initial length [53]. In the cable model *DAMPING_PART_STIFFNESS with the Rayleigh damping coefficient of 0.02 is used. The *DAMPING_FREQUENCY_RANGE with a coefficient of 0.12 was introduced [39] as well. 4.2.2. Post Cables are supported with steel posts C100. In numerical model the posts are discretized using the shell elements of Belytschko–Tsay formulation (ELFORM = 2). The characteristic shell element dimensions is ~13–15 mm. Material of the posts is assumed elasto-plastic *MAT_PIECEWISE_LINEAR_PLASTICITY (*MAT_024). The post's material density is 7850 kg/m3, the Young's modulus is equal to 205 GPa, the Poisson's ratio is equal to 0.3. The stress-strain curve was obtained from tensile testing performed on probes cut from similar barrier. In the model the strain rate effects are included. Strain rate is accounted using Cowper and Symonds model which scales the yield stress with the factor [53]. 1

ε̇ P 1+⎛ ⎞ ⎝C ⎠

(10)

where ε ̇ is the strain rate, C=8000 and P=8 [33], respectively. The *DAMPING_PART_STIFFNESS option is used, the damping coefficient is set to 0.01. View of upper part of post's model is shown in Fig. 10. The posts are equipped with the steel hooks, that keep the wire ropes at the correct height. They are discretized as a beam elements of Hughes-Liu formulation (ELFORM = 1). The *MAT_PIECEWISE_LINEAR_PLASTICITY (*MAT_024) was used as material model. The strain rate effects are taken into account in the same manner as for the posts. To define the contact between the hooks and other parts of the model, the artificial shell around the beams elements of the hooks is defined and is represented by *MAT_NULL (*MAT_009) material model (similar solution can be found in file containing cable barrier model in NCAC library [33]). The last beam element is assigned *MAT_SPOTWELD (MAT_100) with value of effective plastic strain at failure (EFAIL) set to 0.2. This is to enable the rope to be released from the hook. To prevent the wire ropes from penetrating through the posts, an additional null shell (*MAT_NULL material model, Belytschko–Tsay formulation, ELFORM = 2) was added to the posts in order to define the contact between ropes and posts. The cap was put on the top of each post. These post caps do not have a structural function, and as a result of impact, they often fall off the post on the ground. Therefore, it was decided to approximate its model and use very cost efficient material *MAT_RIGID (*MAT_020) [53]. 4.2.3. Soil On the test site, soil was consolidated according to obligatory performance rules. In the simulation, soil was modelled as individual cylinders in which the posts are embedded (diameter 80 cm, height 133 cm – straight section of barrier, 125 cm – two outermost cylinders at the both ends of the barrier). Similar solution can be found in [35,36,54] and also in files, which were available on NCAC public library [33]. Soil was discretized using solid elements of hexahedron and pentahedron shape. For posts at the ends of the barrier, which have an additional stabilizing plates, due to the complicated geometry, the soil was discretized using elements of tetrahedron shape. The view of the first three posts and soils and their discretization is presented in figure Fig. 7b. The first post of barrier terminals is embedded deeper than the others. The soil is represented using *MAT_SOIL_AND_FOAM (*MAT_005) card. The material properties was taken from [33]. The material density is 2200 kg/m3, the bulk modulus 75.428 GPa, the shear modulus 2.7834 GPa. Yield function constant for plastic yield function are as follow: A0 = 0.025013, A1 = A2 = 0, the pressure cutoff for tensile fracture is −0.3087. For the soil model the *CONTACT_INTERIOR card was used, which has to prevent solid elements to invert leading to negative volumes. All the nodes on the outside curved surface and circular base of the cylinder are fixed. On the remaining surfaces of cylinder the null shell is applied, which enables describe the contact interaction with the barrier's posts. This null shell is assigned *MAT_NULL material model. The *DAMPING_PART_STIFFNESS card with a coefficient of 0.1 was used

Fig. 10. Detail of numerical model of post's upper part. 236

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[36]. 4.2.4. Other model data Ground surface, on which the vehicle moves, is defined using *RIGIDWALL_PLANAR card. The friction coefficient between the tires and the ground was set to 0.3 [57]. Contact between the barrier and the vehicle was simulated by using the *CONTACT_AUTOMATIC_GENERAL and *CONTACT_AUTOMATIC_SINGLE_SURFACE cards. In this contacts one global Coulomb friction coefficient was used. In LS-DYNA [50] the actual friction coefficient is calculated by the formula:

μ = μd + (μs − μd ) e−c | ν |

(11)

where μd stands for the dynamic coefficient of friction, μs for static friction coefficient, c denotes a decay constant and ν = Δe/Δt, where Δe is the incremental movement of the slave node and Δt is the time step. In the model μs = 0.42; μd = 0.10 and c= 7·10−5. The contact between barrier posts and outside shell surface of the soil (ground) was simulated using *CONTACT_AUTOMATIC_SURFACE_TO_SURFACE card. The static coefficient of friction is 0.4, the dynamic coefficient of friction is 0.2, decay constant is 0.001 [33]. To eliminate zero-energy modes (hourglassing) the stiffness form of type 2 (Flanagan-Belytschko) in LS-DYNA is used. The value of the hourglass coefficient (QH) is set to 0.03. In the first phase of the vehicle motion, prior to impacting the barrier, the *DAMPING_GLOBAL was used in the model to damp the initial vibrations of the vehicle. During the impact and after leaving and continuing free motion by the vehicle, global damping is not active. 4.3. Crash test scenario The full-scale crash test was conducted in IBOS (Research Institute for Protective Systems, www.ibos.com.pl) in Inowrocław (Poland) by IBDiM (Road and Bridge Research Institute, www.ibdim.edu.pl) on 27th October 2016. Test was carried out as a part of the research project “The impact of time and operating conditions on the durability and functionality of traffic safety protection elements”. Overall view of test site is shown in Fig. 7 and Fig. 11. As mentioned before, nonstandard tests of cable barriers are not addressed in papers nor in reports, then impact angle is set to 7°, while rest of the parameters meets TB32 requirements [13]. During test, the vehicle (BMW e34) impacted the barrier between posts no. 9 and 10 (26 cm from the post no. 9) with the speed of 114 km/h (difference from nominal velocity is 4 km/h) and impact angle 7.28° (difference from nominal angle is 0.28°) (see Fig. 12). 5. Results of numerical simulation and comparison with full-scale crash test 5.1. Results In this section, description of crash test course is based mainly on real-scale test. Performance of barrier in numerical simulation was very similar, the only differences are emphasized in the following text. The car was in contact with the wire ropes at a length of 20 m (between the post 8 and 18). In numerical simulation, contact was initiated in between posts 9–10 and space between posts 8 and 9 is free of vehicle-barrier interaction. The vehicle was riding along the barrier, pushing against it and bending posts from no. 9 to 16 to the ground, whereas the posts no. 17 and 18 were slightly tilted from the vertical position. In simulation, post no. 9 remained almost vertical and post no. 17 was utterly deformed. The vehicle after leaving the barrier, from post no. 18 moved alongside the barrier without contact with it. Afterwards from the posts no. 22 and 23, the vehicle made a slight turn to the left, and then was again in the contact with the barrier to the post no. 27 (contact's length 7 m). The posts no. 23 and 24 were slightly tilted from the vertical position. In simulation, the vehicle after leaving the barrier did not touch the ending parts of the barrier again, free slide on the rigid surface is observed (see Fig. 13). The comparison of the trajectory of the vehicle between numerical simulation and full-scale rash test can be found in Fig. 14. A detailed comparison of the results of the numerical simulation with the results obtained from the crash test is presented in the Table 3, Table 4, Table 5. In these tables, the values describing barrier's deformation, vehicle behaviour and indices referring to

Fig. 11. Barrier installed on the test site, a) overall view, b) the end terminal of the barrier. 237

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Fig. 12. The conditions of vehicle impact and the location of the impact in a) simulation, b) full-scale crash test.

Fig. 13. Trajectory of the vehicle - numerical simulation.

Fig. 14. Comparison of the trajectory of the vehicle, a) top view, b) front view.

effects of impact on vehicle occupants were subject to evaluation, in accordance with the requirements of the standard [48]. The severity indices (ASI and THIV, Fig. 15) from simulation, as well as the working width, dynamic deflection and the length of contact, remain in good agreement with the results from crash test. On the graphs the time 0 s corresponds to the moment of vehicle impact from the full-scale crash test. 238

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Table 3 Assessment of the barrier deformation. Comparison between numerical simulation and full-scale results. Indicator

Numerical simulation

Full-scale crash test

Working width WM Normalised working width WN Class of normalised working width Working width criterion [48]

0.65 m 0.7 m (Wnormalized = 0.61 m, Wrounded = 0.7 m) W2 0.65 m–0.55 m ≤ ± (0.05 m + 0.1 × 0.55 m) 0.1 m ≤ 0.105 m FULLFILLED 0.50 m 0.5 m 0.52 m–0.50 m ≤ ± (0.05 m + 0.1 × 0.5 m) 0.02 m ≤ 0.10 m FULLFILLED 0.55 m 19.5 m

0.55 m 0.6 m W1

Dynamic deflection DM Normalised dynamic deflection DN Dynamic deflection criterion [48] Maximum permanent deflection Length of contact

0.52 m 0.5 m

0.70 m 20 + 7 = 27 m

Table 4 Assessment of the vehicle behaviour. Comparison between numerical simulation and full-scale results. Indicator

Numerical simulation

Full-scale crash test

Vehicle Vehicle Vehicle Vehicle

LS0000000 Yes No No

LS0000000 Yes No No

cockpit deformation index VCDI within „exit box” rolls over goes through the barrier

Table 5 Assessment of the impact severity. Comparison between numerical simulation and full-scale results. Indicator

Numerical simulation

Full-scale crash test

ASI value (rounded) ASI criterion [48]

0.38 (0.4) 0.38–0.35 ≤ ± 0.1 0.03 ≤ 0.1 FULLFILLED 0.195 s 0.195 s – 0.12 s ≤ ± 0.05 s 0.075 s > 0.05 s UNFULFILLEDa 15 km/h (9.2 km/h; −11.7 km/h) 16 km/h - 15 km/h ≤ ± 3 km/h 1 km/h ≤ 3 km/h FULLFILLED 0.24 s 0.240 s – 0.21 s ≤ ± 0.05 s 0.03 s ≤ 0.05 s FULLFILLED 10.7 g A

0.35 (0.4)

Time max ASI Time max ASI criterion [48] THIV (THIV-X; THIV-Y) THIV criterion [48] Time of flight of the theoretical head Time of flight of the theoretical head criterion [48] PHD (not required) Impact severity levels a

0.12 s

16 km/h (8.4 km/h; −13.0 km/h)

0.21 s

8.3 g A

The standard [48] allows, in justified cases, acceptance of a simulation that did not satisfy all requirements, more in Section 6.

Fig. 15. Graphs of ASI versus time (left) and THIV versus time (right).

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Fig. 16. Validation of virtual crash test with RSVVP programme, a) ASI, b) THIV.

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Fig. 17. Final configuration of cable barrier, a) experimental results, b) simulation.

Additionally, quantitative evaluation metric of curves comparison were obtained by Roadside Safety Verification and Validation Program [58]. The results for ASI are shown in Fig. 16a, for the THIV in Fig. 16b. All RSVVP criteria were met. 5.2. Damage assessment 5.2.1. The damage of the cable barrier system Overall views of damage of the system can be seen in Fig. 17. As a result of the impact in full-scale crash test, 10 posts (form no. 9 to 18) were damaged in the impact area and two posts at the end of the barrier (no. 23 and 24), due to vehicle rotation and its slight contact with these posts in the final phase of the event. This was described in the Section 5.1. In the numerical simulation the impact resulted in damage to 9 posts (from no. 10 to no. 18), so the difference is in the post no. 9 (the first post before the impact point), what can be clearly seen in Fig. 17 and Fig. 18. The posts no. 23 and 24 in the simulation were not damaged as in the crash test, because the vehicle did not push against the barrier again. The post with permanent deformation are considered as destroyed. A detailed comparison of the deformations of the individual posts in the impact area is presented in Fig. 18. The number of damaged post and their deformation (mostly bent to the surface of ground) from the simulation corresponds to the results from the experimental test. The deformation of the post no. 9 is different, because in the in-situ test after the impact, the rear of the car due to vehicle rotation, slightly struck this post and bent it. After the post no. 16, the vehicle began leaving the barrier, so the post no. 17 and 18 were slightly tilted from the vertical position (Fig. 18). The values and a graph showing the comparison of the residual displacements of the barrier (named “static working width” in Fig. 19) between the virtual and the real test are presented in Fig. 19. Here, the residual displacement of the barrier indicates the maximum lateral distance between the vertical surface passing through the undeformed barrier's face from the traffic side and the most outer part of the barrier after impact. It can be seen that the deformations obtained from the simulation are similar to those obtained from the crash test. 5.2.2. The damage of the vehicle As a result of the impact in full-scale crash test, the front bumper, the front left fender and wheel and the left doors were damaged. In numerical simulation the damage of the front parts of vehicle were similar. It should be recalled, that the tire or wheel breakage during collision event is common phenomena [59]. Comparison of vehicle's damage between the full-scale crash test and simulation is presented in Fig. 20. 5.3. Verification and evaluation of the numerical model One of the criteria for assessing the correctness of the simulation is to analyse the energy balance during simulation, which is shown in Fig. 21. Total energy during the simulation is constant. Since the model includes friction in contact definitions, the sum of slave side and master side contact energy (sliding energy) is positive. As seen from the energy balance in Fig. 21, the hourglass energy 241

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Fig. 18. Detailed comparison of deformation of the posts, crash test on the left, simulation on the right, the number of the post is given next to the photos.

(zero-energy modes of deformation that give as a result no strain and stress) is kept at low level in relation to the other components of energy. The verification of the numerical simulation according to the requirements from [48] can be seen in Table 6.

6. Discussion Both the experimental crash test and the conducted numerical simulation indicate that the analysed 3-cable guardrail barrier system is has sufficient strength to contain the errant 1500 kg car, preventing it from leaving the road, and successfully redirect the vehicle back onto the travel lane. Indicators describing the deformation of the barrier (Table 3) and the general assessment of the vehicle's behaviour (Table 4) from numerical simulation are similar to those obtained from the crash test. Although, different class of working width was obtained in the simulation than in the full-scale crash test, the difference in values is small and the criterion of the standard [48] is met. The obtained working width is insignificant due to the small angle of impact. The length of contact of the vehicle with the barrier in simulation and reality are similar (about 20 m). However, in full-scale crash test, once the vehicle left the barrier, the car slightly hit the end of the barrier and became in contact with the barrier again at the length of 7 m (Section 3 and Fig. 19). This phenomenon was not observed in the virtual test. This indicates that the behaviour of the vehicle after leaving the barrier may be uncontrolled and may depend on many different factors, for example technical condition of the vehicle. Therefore, there is small chance of getting the same results by carrying out the same test again, especially when it comes to the behaviour of the vehicle after leaving the barrier. The general behaviour of the virtual vehicle during the impact corresponds to the one from full-scale crash test (as can be observed on the view snapshots in Fig. 14). The results show very good compatibility of the ASI and THIV indices (Table 5, Fig. 15). This was also confirmed by an independent RSVVP program code [58] (Fig. 16). The graph's trend from the simulation corresponds to that from the crash test. 242

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Fig. 19. Comparison of the static working width between the virtual and the real test - values and graph.

Fig. 20. Comparison of the damage of the BMW car.

Analysing the ASI graph (left side on Fig. 15), the next peaks of the graph occur when the car hit the next posts. The peaks from numerical simulation and their time of occurrence are similar to those obtained from the experiment. It should be noted that the ASI values obtained in this test, because of the low impact angle, are not large. All analysed passenger safety assessment criteria (Table 5) were met, except one - the criterion regarding the time of occurrence of ASI. In experimental test, the highest value of ASI (ASI = 0.35) occurred when the vehicle collided with the second post (no. 11), while in the simulation the strike into the third post (no. 12) was the decisive factor for the ASI value (ASI = 0.38). Nonetheless, Sections 4.1 and 5 in the standard [48] concerning the validation procedures state that in the case of not meeting one of the criteria, the author can explain his motivation. In this case, it seems justified to consider this numerical result as correct and fully reflecting the nature of the course of the real impact. In addition, 243

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Fig. 21. Energy in the numerical simulation of the crash test.

Table 6 Verification and evaluation criteria. Verification and evaluation criteria [48] Is the result of simulation physically acceptable? Is the variation of total Energy < 10%? Is the hourglass energy < 10% of internal energy Is the mass added < 5% of total mass for every component? Are there any “shooting nodes”? Are there any Solid elements with negative volume? Is the sum of slave and master contact energy zero? Is the influence of strain rate considered?

Yes Yes Yes Yes No No No Yes

the compatibility of these graphs has been checked and confirmed with the aforementioned RSVVP code. The trend of the ASI function from the simulation reflects the result from the crash test and the local extremes have similar values. The present Authors based on their experience that for larger impact angles it is easier to obtain the proper time history of ASI in the simulation. This is because ASI value is usually higher (ASI 0.6–0.8) and the vehicle can faster leave the barrier (the length of contact can be shorter in standard TB32 test), which reduces the number of ASI peaks caused by the vehicle's strikes into the posts. The number of damaged posts (Section 5.2.1) is mainly due to the fact that the front left wheel was damaged and bent (Section 5.2.2). The barrier deformation obtained in the virtual test is similar to that obtained from the real impact test (Fig. 19). The damage of the posts is consistent with the description that can be found in the publications [8,15], i.e. the posts are generally weak and are bent to the ground during accident, and the main longitudinal structural elements containing the vehicle are pretensioned wire ropes. The numerical model can be considered as correct because the validation requirements based on [48] have been met. In addition, barrier damage have been accurately shown and compared. Energy balance is met in numerical simulation. It should be emphasized, that the crash test has the characteristic of incidental technical test and, because of the lack of possibility to limit random factors, its repeatability with a high level of detail is never possible in practice [29]. Though, as demonstrated in [10,60], their repeatability is quite good. Hence, in numerical simulations one should assume a certain acceptable level of conformity of the computational model with reality, and constructing solutions that raise this level is possible but there is no need and justification [29]. 7. Conclusion This paper presents the results of numerical modelling of the 1500 kg vehicle impact on the cable barrier under different conditions that EN 1317 standard concerning crash test assumes. The analysis of non-standard cases of vehicle impacts in cable barriers is important, as nowadays they are increasingly installed on roads. In order to investigate the crashworthiness of the cable barrier system, full-scale crash test and numerical simulation were conducted. Various indicators were analysed in detail, namely the severity indices, the trajectory and the behaviour of the vehicle, the barrier's damage, the energy balance. The experimental crash test as well as the numerical simulation show that the considered cable barrier is fully capable to contain and redirect the passenger vehicle back onto the road. Based on the simulation results, finite element method and LS-DYNA dynamic explicit code was demonstrated to be a useful and reliable tool in crash barrier development. Presented methodology of creating the numerical model of cable barrier crash test is accurate and the made model could be used in future investigations of various situations that may potentially occur on the roads. Acknowledgements This work was supported by the National Centre for Research and Development (NCBiR), Poland and General Director for National Roads and Motorways (GDDKiA), Poland under the research projects “Road Safety Equipment” (contract number DZP/RIDI-67/13/NCBR/2016) and "The impact of time and operating conditions on the durability and functionality of traffic safety protection 244

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