Field testing and numerical investigation of streetscape vehicular anti-ram barriers under vehicular impact using FEM-only and coupled FEM-SPH simulations

Abstract

This article presents two field-scale crash tests of Streetscape Vehicle Anti-Ram barrier systems and LS-DYNA simulations to predict the global response of each system under vehicular impact. Tests 1 and 2 consisted of a five-post welded bus stop and a welded bollard, respectively; both were in a steel and concrete composite foundation embedded in compacted American Association of State Highway and Transportation Officials aggregate. Test 1 resulted in a P1 rating, where minimal foundation uplift and rotation were observed. Test 2 failed to result in a P1 rating, where significant foundation uplift, rotation, concrete cracking, and large deformation of surrounding soil were observed. For each test, two LS-DYNA models, namely, a finite element method–only model and a hybrid finite element method–smoothed particle hydrodynamics model, were created to predict the global response of the system. In the finite element method–only model, traditional finite element method approach was used for the entire soil region; in the hybrid finite element method–smoothed particle hydrodynamics model, the near-field soil region was modeled using the smoothed particle hydrodynamics approach, whereas the far-field soil region was modeled using the finite element method approach. For Test 1, both the finite element method–only model and the hybrid finite element method–smoothed particle hydrodynamics model were able to match the recorded global response of the system. For Test 2, however, the finite element method–only approach was not able to accurately predict the global response of the system; on the other hand, the hybrid finite element method–smoothed particle hydrodynamics approach was able to capture the global response including the bollard pullout, soil upheaval, and vehicle override. This research suggests that the hybrid finite element method–smoothed particle hydrodynamics approach is more appropriate in simulating the field performance of embedded structures under impact loading when large deformation of the surrounding soil is expected.

Keywords

Anti-ram system barrier bollard crash test large deformation numerical model smoothed particle hydrodynamics method soil-structure interaction

Introduction

Vehicle anti-ram systems have been widely used for protecting sensitive buildings and facilities against vehicular impacts. These systems generally include Streetscape Vehicle Anti-Ram (SVAR) systems and Landscape Vehicle Anti-Ram (LVAR) systems. The SVAR system (e.g. anti-ram bollards) is generally used in urban areas, which typically comprised man-made materials including steel and concrete. The LVAR system is more often used in suburban areas and typically made of natural materials such as boulders. It is important to examine the crashworthiness of anti-ram systems, and field-scale testing and numerical modeling are two common methods. An integrated computational and experimental approach is particularly attractive. In this approach, implicit/explicit dynamic solvers are first utilized to run crash simulations and arrive at an initial design of the system, and full-scale crash tests are subsequently utilized to validate the initial design and provide the needed data for calibrating simulation parameters.

Numerous researchers have investigated typical SVAR systems under vehicular impact using the LS-DYNA research/commercial code (Hallquist, 2006) and field-scale crash tests (Ferdous et al., 2011; Hu et al., 2011; Krishna-Prasad, 2006; Liu et al., 2008; O’Hare et al., 2012; Omar et al., 2007; Uzzolino et al., 2012). O’Hare et al. (2012) developed various SVAR systems with shallow foundations, including street benches, bus stops, and street signs, which can be selected based on site restrictions, availability and cost of materials, and varying architectural aesthetics. Designs of these SVAR systems were optimized using LS-DYNA and then validated through field-scale crash testing (O’Hare et al., 2012).

LS-DYNA is known to be a reliable program for modeling vehicular impact and is based on the finite element method (FEM). The FEM is efficient for large-scale explicit dynamic problems. One shortcoming associated with the method, however, is the difficulty in dealing with large deformations, which may lead to severe distortion of meshes, inaccurate results, and failure of convergence. Advanced techniques such as adaptive remeshing (Khoei and Lewis, 1999) and Arbitrary Lagrangian–Eulerian method (Hughes et al., 1981) have been used to remediate this problem. However, these remeshing techniques become problematic when complex constitutive models are employed (Bui et al., 2008). Overall, continuum-scale numerical methods that do not require a mesh (i.e. mesh free) are considered more desirable for the simulation of problems involving both large-scale and large deformations. In recent years, several mesh-free methods tracking materials by a set of particles instead of grids have been developed. A detailed discussion of various mesh-free methods is presented by Liu and Liu (2003). Among these mesh-free continuum-scale methods, the Smoothed Particle Hydrodynamics (SPH) method is a relatively mature one. Originally developed for astrophysical applications by Lucy (1977) and Gingold and Monaghan (1977), SPH method has been widely used to simulate free surface flows and multiphase flows (Monaghan, 1994; Monaghan et al., 2003; Monaghan and Kocharyan, 1995) and flow through porous media (Zhu et al., 1999). More recently, SPH method has been used to simulate the elastic response of solids (Gray et al., 2001; Libersky et al., 1993) and elasto-plastic behavior of geomaterials (Bui et al., 2008; Chen and Qiu, 2012, 2014). Additionally, coupled SPH and FEM formulations have been developed to utilize the benefits of both methods (Beal et al., 2013; Bojanowski, 2014) so that coupling of the two domains, one consisting of particles and the other consisting of meshes, is improved and the computation time is optimized.

Published comparisons between traditional FEM and coupled FEM-SPH simulations for soil-structure interaction involving large soil deformation are remarkably sparse in literature, particularly when the comparison is validated using instrumented, field-scale tests (Reese et al., 2012, 2014; Zhou et al., 2016). This article presents the numerical simulations and field-scale crash tests of two SVAR systems: a five-post welded bus stop and a welded bollard, both embedded in soil. For the former, little deformation of soil was observed from the crash test, whereas large soil deformation was observed for the latter. For each crash test, two LS-DYNA models, namely, an FEM-only model and a hybrid FEM-SPH model, were created to predict the global response of the system. In the following sections, the field-scale crash tests are first discussed, followed by descriptions of the FEM-only and coupled FEM-SPH models. The simulations and crash test results are compared. Finally, conclusions are reached regarding the predictive capabilities and limitations of the FEM-only and coupled FEM-SPH formulations in LS-DYNA simulations of SVAR barriers.

Field-scale testing

Vehicular impact tests were completed according to American Society for Testing and Materials (ASTM) F2656-07:2007 (2007)—Standard Test Method for Vehicle Crash Testing of Perimeter Barriers, which establishes penetration ratings for perimeter barriers subjected to vehicular impact, at the Larson Transportation Institute affiliated with the Pennsylvania State University. For M50 impact (i.e. vehicular speed of 80.5 km/h or 50 miles/h), a penetration distance of equal to or less than 1 m is required to achieve a P1 rating. Figure 1 shows a description of the P1 rating according to ASTM F2656-07. The penetration distance is measured from the inside face or non-impact surface of the test article (blue dotted line in Figure 1) to the front of the cargo bed (red circle in Figure 1) when the test vehicle has reached its final position. In Figure 1, the red circle should not exceed the red dotted line for P1 rating. The test facility uses a rigid rail to provide vehicle guidance, a reverse towing system to accelerate the test vehicle to the required speed, and a release mechanism that disconnects the tow cable and steering guidance prior to impact. For a detailed description of the system, please refer to Reese et al. (2012, 2014). The test vehicles used in this study were 1999 International 4700 single-unit flatbed medium-duty diesel trucks. Barrels filled with ballast were secured on the bed of the truck making the test inertia weight of approximately 6750 kg. The height of the lower and upper edges of the front bumper was 0.48 and 0.75 m, respectively.

Figure 1.

Description of P1 rating according to ASTM F2656-07.

High-speed cameras were implemented during testing to record pertinent information such as barrier translational and rotational displacements and global response of the system which includes truck deformation. Figure 2 shows where the high-speed cameras were placed. Camera 1 was positioned at a 90° angle to the center of the test article to measure dynamic penetration. Camera 2 was positioned at a 90° angle above the center of the test article to capture enough surface area prior to and after impact to determine impact speed, impact angle, exit angle, and debris field. Camera 3 was positioned behind the test article centered along the guide rail to record the approach of the test vehicle to track its alignment with the center of the test article during impact.

Figure 2.

Location of high-speed video cameras during field-scale test (not to scale).

SVAR barriers

Two full-scale crash tests of SVAR barriers for M50 impact were conducted for this research. Test 1 consisted of a five-post welded bus stop in a steel and concrete composite foundation. Figure 3 shows the dimensions of the device. The foundation has a dimension of 3556 mm × 1219.2 mm × 457.2 mm (140 in × 48 in × 18 in). The device utilized a fully welded design and E70XX (½ inch) welds were used at all connections. The five vertical posts consisted of 152.4 mm × 101.6 mm × 12.7 mm (6 in × 4 in × ½ in) A500 Grade B steel tubes protruding above grade to a height of 2641.6 mm (104 in), with a clear spacing of 711.2 mm (28 in). To enable above-grade load sharing between the vertical tubes, a 254 mm × 101.6 mm × 12.7 mm (10 in × 4 in × ½ in) A500 Grade B steel horizontal girt tube spanned between the vertical tube members. Vertical members were also connected below grade to horizontal 304.8 mm × 304.8 mm × 15.9 mm (12 in × 12 in × 5/8 in) A500 Grade B steel tubes through member penetration. The vertical members passed completely through the horizontal members and protruded 25.4 mm (1 in) below these members, forming an “L” shape in elevation (see Figure 3). To strengthen and interconnect each vertical and horizontal tube system, a pair of stacked transverse 76.2 mm × 76.2 mm × 9.5 mm (3 in × 3 in × 3/8 in) A500 Grade B steel tubes penetrated both the horizontal and vertical members orthogonally to ensure the transfer of bending, shear, and torsion and to prevent vertical member pullout. The transverse tubes had a vertical center-to-center spacing of 152.4 mm (6 in). Normal-strength concrete was then poured into the foundation and filled the horizontal and vertical steel tubes. Concrete on the day of testing was recorded having a compressive strength of 29.6 MPa (4296 psi). There were no aesthetic features attached to this device. Figure 4 shows photographs of the test article installation.

Figure 3.

Dimensions of five-post welded bus stop: (a) plan view and (b) side view.

Figure 4.

Photographs showing installation of five-post welded bus stop.

Test 2 consisted of a steel tube in a steel and concrete composite foundation. Figure 5 shows the dimensions of the device. The foundation has a dimension of 1400 mm × 1220 mm × 480 mm (55 in × 48 in × 18 in). The device utilized a fully welded design and the impacted member consisted of a vertical 254 mm × 254 mm × 15.9 mm (10 in × 10 in × 5/8 in) A500 Grade B steel tube protruding above grade to a height of 1000 mm (39 in). This vertical tube was internally stiffened with a W8 × 48 (203.2 mm × 1219.2 mm) A992 stiffener member. Vertical members were connected below grade to a horizontal 304.8 mm × 304.8 mm × 15.9 mm (12 in × 12 in × 5/8 in) A500 Grade B steel tube through member penetration. The vertical members passed completely through the horizontal members and protruded 25.4 mm (1 in) below, forming an “L” shape in elevation (see Figure 5). To strengthen and interconnect the vertical and horizontal tube system, a pair of stacked transverse 50.8 mm × 50.8 mm × 6.4 mm (2 in × 2 in × ¼ in) A500 Grade B steel tubes penetrated both the horizontal and vertical members orthogonally to ensure the transfer of bending, shear, and torsion and to prevent vertical member pullout. The transverse tubes had a vertical center-to-center spacing of 152.4 mm (6 in). There were no aesthetic features added to this device. Figure 6 shows photographs of the test article installation.

Figure 5.

Dimensions of welded bollard: (a) plan view and (b) side view.

Figure 6.

Photographs showing installation of welded bollard.

The vehicle used in Test 1 was a 1997 NAVSTAR 4700 and that used in Test 2 was a 1995 Chevrolet Kodiak. These vehicles conform to the ASTM F2656 requirements for the medium-duty diesel truck. The test vehicles were structurally sound, having no major rust or weaknesses noted. No structural modifications or additions were observed that might enhance or otherwise affect test performance. Five 55-gallon drums with removable lids were filled with ballast consisting of quarry waste/gravel and placed in two rows at each truck’s front end of the bed. The drums were secured with ratchet straps to each truck’s front bed bulkhead. The weight of the vehicle in Test 1 was 6812 kg (15,020 lbs) and in Test 2 was 6831 kg (15,060 lbs), which is within the test weight range of 6660–6940 kg (14,691–15,309 lbs) as specified by ASTM F2656.

Test results

Figure 7 shows the final positions of the truck and device for both tests. For Test 1, the impact was centered on the device’s centerline. Large deformations of the vertical posts were observed. The vertical posts showed similar deflections averaging at approximately 1120 mm (44.1 in) and good above-grade load-sharing capability. The impacted vertical post showed double-curvature deflection, whereas the remaining four posts showed single-curvature deflection. Minimal foundation uplift and rotation was observed (less than 12.7 mm of vertical foundation uplift on the attack side). As seen in Figure 7(a), the front of the truck bed stopped at 1320 mm (52 in) before the back face of the impacted post. Therefore, Test 1 resulted in a P1 penetration rating.

Figure 7.

Final positions of barrier and truck after impact: (a) side and top views of Test 1 (five-post welded bus stop) and (b) side and top views of Test 2 (welded bollard).

Test 2, however, did not result in a P1 penetration rating. As shown in Figure 7(b), final penetration of the front corner of the cargo bed was 9100 mm (358 in) beyond the pre-test inside edge of the barrier. The vertical post, stiffener, horizontal tube, rebar, and concrete primarily remained intact as one unit but was pulled out of the ground. Significant foundation uplift, rotation, and concrete cracking were observed; the steel and concrete barrier translated 8100 mm (319 in). Concrete spalling was observed over a majority of the top surface.

LS-DYNA model

The LS-DYNA research/commercial code (Hallquist, 2006) was utilized to simulate the two crash tests. In this section, the numerical model is first described, including material properties and descriptions of the FEM-SPH contact algorithms used within LS-DYNA. The general numerical model consists of three major parts which are the medium-duty truck, the SVAR barrier device, and the surrounding soil and concrete slab. Figure 8 shows the numerical models for the two tests.

Figure 8.

Numerical models: (a) Test 1 and (b) Test 2.

Truck model

The truck model used for the simulations was modified from a model readily available in the National Crash Analysis Center (NCAC, 2008) database. The NCAC truck model was developed to ensure that the load transfer between the truck and hardware, the deformation of the truck, and the overall behavior of the truck during impact simulations could be as accurate as feasible given the model computational requirements. Based on requirements from ASTM F2656-07:2007 (2007), the modified truck model consisted of 1606 eight-node constant stress solid elements, 20,333 four-node Belytschko-Tsay shell elements, and 377 Hughes-Liu beam elements with cross section integration. The truck model was validated by Reese et al. (2014) using checks of equilibrium, conservation of energy principles, and the amount of energy absorption that occurred through plastic deformation of truck components. The numerical simulation by Reese et al. (2014) indicated that the truck absorbed approximately 69% of the impact energy and the barrier and soil absorbed the rest of the impact energy when hitting the barrier, which is consistent with the field-scale test conducted by Omar et al. (2007).

Material models and properties

The LS-DYNA Material Type 173, “Mohr-Coulomb (M-C)” (Hallquist, 2013), was utilized to model the soil beneath the concrete slab (see Figure 8). The soil is AASHTO (American Association of State Highway and Transportation Officials) uniformly graded coarse aggregate and was compacted to 90% relative compaction as evaluated by ASTM D698-12:2012 (2012). The M-C model was used due to its simplicity and found adequate in modeling the behavior of AASHTO aggregate when an embedded boulder was subject to vehicular impact by Reese et al. (2014). The M-C model characterizes failure of a material based on its cohesion, normal stress on an element, and friction angle as follows (Hallquist, 2006, 2013):

τ_{\max} = c + σ_{n} \tan (φ)

(1)

where τ_max is the shear strength on any plane, σ_n is the normal stress on that plane, c is the cohesion, and φ is the friction angle. Based on the gradation and angularity of the AASHTO coarse aggregate, the friction angle is estimated to be 45° and the dilation angle is estimated to be 15° based on an empirical relation between friction angle and dilation angle from Bolton (1986). Model parameters for the soil are summarized in Table 1, which were calibrated and validated by Reese et al. (2014).

Table 1.

Model parameters for soil.

	Density (kg/m³)	Elastic shear modulus (MPa)	Poisson’s ratio	Cohesion (kPa)	Friction angle (degrees)	Dilation angle (degrees)
Soil	2100	20	0.25	4.8	45	15

The LS-DYNA Material Type 159, “Smooth or Continuous Surface Cap Model,” was utilized to model the concrete, in which the essential material properties include density, elastic modulus, Poisson’s ratio, uniaxial compressive strength, tensile strength, and tensile fracture energy. Instead of fitting a set of material model parameters to experimental data, typical material properties were used in this study. Specifically, with a given uniaxial compressive strength of 21 MPa and a maximum aggregate size of 38 mm, the other material properties such as elastic modulus and tensile fracture energy were calculated based on empirical equations available in the literature (Murray, 2007). The material parameters for the concrete are summarized in Table 2.

Table 2.

Model parameters for concrete.

	Density (kg/m³)	Elastic modulus (GPa)	Poisson’s ratio	Uniaxial compressive strength (MPa)	Tensile strength (MPa)	Tensile fracture energy (N/m)
Concrete	2320	23	0.15	21	2	54

The LS-DYNA Material Type 24, “Elasto-Plastic Material” (Hallquist, 2013), was utilized to model the rebar, stiffeners, studs, and tubes, and the material parameters for each part are summarized in Table 3. In addition, the horizontal and transverse tubes, as shown in Figure 9, were modeled using reduced yield strength and plastic strain to failure (as compared to the properties of vertical tube) to account for the welding between them.

Table 3.

Model parameters for rebar, stiffeners, studs, and tubes.

	Density (kg/m³)	Elastic modulus (GPa)	Poisson’s ratio	Yield strength (MPa)	Tangent modulus (GPa)	Plastic strain to failure
Rebar	7830	200	0.3	476	2.1	0.12
Stiffeners	7830	200	0.3	344	2.1	0.25
Studs	7830	200	0.3	400	2.1	0.12
Vertical tube	7830	200	0.3	315	2.1	0.25
Horizontal and transverse tubes	7830	200	0.3	283	2.1	0.20

Figure 9.

Horizontal and transverse tubes.

Soil domain size

The size of soil domain surrounding the SVAR device plays an important role in the LS-DYNA simulations and was determined through a parametric study by gradually increasing the soil domain size until convergence in simulation results was obtained. Figure 10 presents the soil domain in the field and in an initial LS-DYNA model. A small domain size was utilized in the initial simulation for computational efficiency, although the domain is much larger in the field.

Figure 10.

Soil domain in the field and in an initial LS-DYNA model.

For the parametric study, the size of the soil domain varied from two times to eight times of the initial model in horizontal directions, as shown in Figure 11, to examine the effects of reflected compression waves that may interfere with the impact response. The fixed boundary conditions for all of directions were utilized for the four side boundaries and bottom boundary. In addition, the non-reflecting boundary conditions, which are important for limiting the spatial extent of the finite element mesh and thus the number of solid elements for geo-mechanical problems, were used to reduce the effect of reflected compression waves from the four side boundaries and bottom boundary. Based on the parametric study, a soil domain that is five times the initial domain size was used to simulate the crash tests.

Figure 11.

LS-DYNA model with different soil domain sizes.

SPH and FEM-SPH coupling

Traditional FEM formulations have been discussed extensively in the literature and hence are not presented herein. The SPH formulation used in this study is briefly discussed in this section. In SPH, the computational domain is discretized into a finite number of particles, each representing a certain volume and mass of the material (fluid or solid) and carrying simulation parameters such as velocity, acceleration, density, and pressure/stress. The particles interact according to a set of rules. Figure 12 shows a description of particle approximation based on a kernel function W for particles within an influence domain Ω defined by a radius kh, where h is the initial particle spacing and k is a constant (1.2 was used in this study). The widely used cubic spline kernel function (Monaghan and Lattanzio, 1985) was used in this study. There has been an issue of FEM mesh truncating the influence domain of SPH particles in the vicinity of a FEM-SPH boundary. To address this issue, Sakakibara et al. (2008) conducted analyses of the effects of changing formulation type while keeping the smoothing length constant. In this study, to account for the issue, a renormalization technique readily available in LS-DYNA was used for all SPH analyses.

Figure 12.

Particle approximation based on kernel function W in influence domain Ω with radius kh.

Both SPH and FEM formulations in LS-DYNA are based on the Lagrangian approach. Therefore, it is possible to link both methods at an interface. The interface should ensure continuous bonding of the two methods. At the interface, the SPH particles are constrained and move with the FEM elements. The influence domain of the particles at/near the interface zone covers both FEM elements and SPH particles, and hence, certain considerations are required in the computation. For strain and strain rate calculations of each particle, only those from the SPH particles within the influence domain are considered, whereas the contributions from both SPH particles and FEM elements inside the influence domain are included to calculate forces (Johnson, 1994).

LS-DYNA allows FEM and SPH to exist and interact in one simulation, allowing users to take advantage of both procedures. The interaction or coupling between FEM and SPH can be defined using traditional tied- or penalty-based contact definitions (Beal et al., 2013). Since there is no mesh connectivity for the SPH particles, it is imperative that only “nodes_to_surface” contact definitions are utilized in which SPH particles are always defined to be the slave nodes and finite elements are defined to be the master surface.

Tied-based contact consists of “tying” SPH slave nodes to FEM surfaces to connect the two domains. LS-DYNA ties translational degrees of freedom of nodes to a specified surface. The constraints are only imposed on the slave nodes, so the more coarsely meshed side of the interface should be the master surface (i.e. FEM; Hallquist, 2006). Ideally, each master node should coincide with a slave node to ensure complete displacement compatibility along the interface, but this is difficult, if not impossible, to achieve.

Consequently, the standard penalty-based contact formulation was utilized for this study. In this formulation, a contact consists of placing normal interface springs with stiffness factor of k_i between all penetrating nodes and the contact surface. The interface stiffness is chosen to be approximately the same order of magnitude as the stiffness of the interface element normal to the interface particle. In applying the penalty method, each slave node is checked for penetration through the master surface. If the slave node does not penetrate, nothing is done. If it does penetrate, interface force is applied between the slave node and its contact point. The magnitude of this force is proportional to the amount of penetration (Hallquist, 2006).

The stiffness factor, k_i, is determined in LS-DYNA by several ways, including minimum of the master segment and slave node stiffness, the master segment stiffness, the slave node stiffness, or the area-/mass-weighted slave node value. Since the same material is across the boundary between the SPH particles and the solid FEM segments, the stiffness will be identical and therefore the default of using the minimum of the master segment and slave node stiffness was used.

FEM and hybrid FEM-SPH models

Two numerical models were created for each test to compare their performance at capturing global response of the SVAR system when varying magnitudes of soil deformation occurred. The first model consisted solely of finite elements for the SVAR barrier and soil domain, whereas the second model used a hybrid FEM-SPH approach for modeling soil. In the hybrid approach, SPH formulations were used in the near-field soil region to take advantage of SPH’s capabilities in modeling large deformations, whereas finite elements were used in the far-field soil region to take advantage of FEM’s computational efficiency. The same constitutive material models and parameters were used in both models. Figures 13 and 14 show the two LS-DYNA models for the five-post welded bus stop and welded bollard, respectively.

Figure 13.

LS-DYNA models for five-post welded bus stop: (a) FEM model and (b) hybrid FEM-SPH model.

Figure 14.

LS-DYNA models for welded bollard: (a) FEM model and (b) hybrid FEM-SPH model.

In the FEM-only model, eight-node constant stress solid elements were used for the surrounding soil. The soil element size was approximately 100 mm based on a parametric study conducted by Reese et al. (2014). A single layer of fully integrated solid elements was used to model the thin concrete slab as shown in Figure 15. The fully integrated solid elements are capable of modeling bending and torsional mode of deformation (Hallquist, 2006, 2013).

Figure 15.

Modeling concrete slab using a single layer of fully integrated solid elements.

Results and discussion

Figure 16 shows comparisons of recordings from Camera 1 (see Figure 1) against simulation results from the FEM and hybrid FEM-SPH models at various times for the five-post welded bus stop. Figure 16 illustrates that both models were able to satisfactorily capture the global response of the device. Both models predicted P1 rating of the crash test. Figure 17 shows a more detailed view of the simulated mode of deformation of the bus stop from the two models. Figure 17 illustrates a double-curvature deformation mode for the impacted center post. The maximum deflection of the vertical posts in both of the FEM and hybrid FEM-SPH models was approximately 830 mm, whereas the vertical posts in the crash test showed similar deflections averaging at approximately 1120 mm. Although there was a minor difference, the simulation results were generally consistent with post-test field observations.

Figure 16.

Comparison of crash test and simulations from FEM and hybrid FEM-SPH models at various times for five-post welded bus stop.

Figure 17.

Simulated mode of deformation of five-post welded bus stop: (a) FEM model and (b) hybrid FEM-SPH model.

Figure 18 shows comparisons of recordings from Camera 1 (see Figure 1) against simulation results from the FEM and hybrid FEM-SPH models at various times for the welded bollard. Figure 18 shows that the FEM model drastically underpredicted the global deformation of the welded bollard and truck, whereas the hybrid FEM-SPH model was able to capture the pullout of the welded bollard and subsequent truck overrun. The FEM model predicted a P1 rating of the crash test; however, the crash test failed to meet the P1 rating, which was predicted by the FEM-SPH model. Figure 19 shows a more detailed view of the simulated deformation of the welded bollard from the two models. Figure 19 illustrates that the FEM model was able to capture the initial uplift of the welded bollard; however, the bollard did not flip out of the ground, likely due to the lack of large deformation in the surrounding soil. The hybrid FEM-SPH model was able to capture the large deformation of the surrounding soil and, hence, pullout of the welded bollard.

Figure 18.

Comparison of crash test and simulations from FEM and hybrid FEM-SPH models at various times for welded bollard.

Figure 19.

Simulated deformation of welded bollard at t = 0.5 s: (a) FEM model and (b) hybrid FEM-SPH model.

A motion analysis software, Photron, was used to calculate displacement of the front corner of the cargo bed in Test 2 in order to compare with simulation results of FEM and hybrid FEM-SPH models. Figure 20 shows a screen shot of the point tracking in Photron analysis. Figure 21 shows a quantitative comparison of truck displacement versus time from crash test and model simulations. Figure 21 shows that the crash test resulted in a gradual increase in the front corner’s displacement to over 4500 mm at t = 0.4 s. The penetration of the front corner of the cargo bed exceeded the limitation of P1 penetration rating at about t = 0.33 s. The FEM model simulation yielded a maximum displacement of approximately 2600 mm that was reached at about 0.35 s and remained constant afterward. The hybrid FEM-SPH model was able to capture the gradual increase of truck displacement, although the magnitude of displacement was about 4100 mm at t = 0.4 s and was smaller than that observed in the crash test. From the hybrid FEM-SPH simulation, the penetration of the front corner of the cargo bed exceeded the limitation of P1 penetration rating at about t = 0.37 s, which was late by 0.04 s as compared to the crash test. Nevertheless, the hybrid FEM-SPH model did a much better job in matching the crash test than the FEM model did.

Figure 20.

Point tracking in Photron FASTCAM software.

Figure 21.

Comparison of displacements of front corner of cargo bed.

Conclusion

This article presents two field-scale crash tests of SVAR barrier systems and LS-DYNA simulations to predict the global response of each system under vehicular impact. Tests 1 and 2 consisted of a five-post welded bus stop and a welded bollard, respectively; both were in a steel and concrete composite foundation embedded in compacted AASHTO aggregate. For each test, two LS-DYNA models, namely, an FEM-only model and a hybrid FEM-SPH model, were created to predict the global response of the system under vehicular impact. In the FEM-only model, traditional FEM approach was used for the entire soil region. In the hybrid FEM-SPH model, the near-field soil region was modeled using the SPH approach, whereas the far-field soil region was modeled using the FEM approach. Based on the results of this study, the following conclusions can be made:

Test 1 resulted in a P1 rating of the device, where minimal foundation uplift and rotation were observed. The vertical posts showed similar deflections averaging at approximately 1120 mm (44.1 in) and good above-grade load-sharing capability. The front of the truck bed stopped at 1320 mm (52 in) before the back face of the impacted post.

For Test 1, both the FEM-only model and the hybrid FEM-SPH model were able to match the recorded global response of the system. The crash test and both models showed a double-curvature deformation mode for the impacted center post. Although there was a minor difference, the simulation results were generally consistent with post-test field observations in terms of maximum deflection of the vertical posts and displacement of the front of the truck bed.

Test 2 failed to result in a P1 rating for the device, where significant foundation uplift, rotation, concrete cracking, and large deformation of surrounding soil were observed. Final penetration of the front corner of the cargo bed was 9100 mm (358 in) beyond the pre-test inside edge of the barrier. The steel and concrete barrier translated 8100 mm (319 in).

For Test 2, however, the FEM-only approach was not able to accurately predict the global response of the system. The FEM-only model simulation resulted in a maximum displacement of approximately 2600 mm that was reached at about 0.35 s and remained constant afterwards, whereas the crash test resulted in a gradual increase in the front corner’s displacement to over 4500 mm at 0.4 s. On the other hand, the hybrid FEM-SPH model was able to capture the gradual increase of truck displacement, although the magnitude of displacement was about 4100 mm at 0.4 s and was smaller than that observed in the crash test. The hybrid FEM-SPH model did a much better job in matching the crash test than the FEM model. This research suggests that the hybrid FEM-SPH approach is more appropriate in simulating the field performance of embedded structures under impact loading when large deformation of the surrounding soil is expected.

Footnotes

Acknowledgements

The authors would like to thank the United States Department of State and the Larson Transportation Institute at Pennsylvania State University for their continuing support of this research.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

This study was funded in part by a grant from the United States Department of State. The opinions, findings and conclusions stated herein are those of the authors and do not necessarily reflect those of the United States Department of State.

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