Field test and numerical modeling of vehicle impact on a boulder with impact-induced fractures

Abstract

Landscape Vehicle Anti-Ram systems, typically comprising natural materials such as boulders, are effective in protecting sensitive structures against threats. However, fracturing of these materials under vehicular impact can be detrimental to the performance of Landscape Vehicle Anti-Ram systems. This study presents a field-scale crash test and LS-DYNA modeling of a Landscape Vehicle Anti-Ram system subjected to vehicular impact. The Landscape Vehicle Anti-Ram system consisted of three boulders connected through a reinforced concrete foundation embedded in compacted American Association of State Highway and Transportation Officials soil. The central boulder fractured upon vehicular impact. An advanced material model was adopted to model the rock fracture and crushing. The global response of the truck, including cab deformation and dynamic penetration, from the simulation showed good agreement with the field observations. The failure patterns of the boulder, including the fracture plane and minor crushing, also agreed well with the field observations. Through a parametric study, the dynamic penetration of the truck is found to be influenced by the elastic modulus and fracture energy of the boulder, and the Landscape Vehicle Anti-Ram system is more effective with a stiffer and tougher boulder.

Keywords

Anti-ram system boulder crash test fracture numerical modeling

Introduction

Vehicle anti-ram systems have been found effective in protecting critical buildings and facilities against vehicular impacts. These systems generally include Streetscape Vehicle Anti-Ram (SVAR) systems and Landscape Vehicle Anti-Ram (LVAR) systems, among others. The SVAR system is generally used in urban areas, with anti-ram bollards and foundations, which typically comprise man-made materials such as steel and concrete. The LVAR system is more often used in suburban areas and is 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. So far, most work has been focused on SVAR (Chen et al., 2015; Hu et al., 2011, 2014; Krishna-Prasad, 2006; O’Hare et al., 2012) with very limited work available for LVAR (Reese et al., 2012, 2014), especially when an embedded boulder is fractured upon vehicular impact. For example, Reese et al. (2014) conducted a field-scale crash test and modeled the vehicular impact on a boulder embedded in compacted fill for an LVAR system when no fracture of the boulder was observed.

For field-scale crash tests, several standards have been established to examine the crashworthiness of anti-ram barriers, including the Specification for Vehicle Crash Test of Perimeter Barriers and Gates (SD-STD-02.01), and the Test Method for Vehicle Crash Testing of Perimeter Barriers and Gates (SD-STD-02.01 Revision A) established by the US Department of State (DOS) in 1985 and 2003, respectively (US Department of State, 1985, 2003). Recently, a new standard—Standard Test Method for Vehicle Crash Testing of Perimeter Barriers (F2656-07) was established by the American Society for Testing and Materials (ASTM) in 2007 (ASTM, 2007). The purpose of an anti-ram barrier is to stop a vehicle effectively at all costs so as to minimize the dynamic penetration, which is measured from the pre-test inside of the barrier to the leading edge of the cargo bed when the vehicle has reached its final position (ASTM, 2007).

Numerical modeling of anti-ram barrier systems has been generally conducted using LS-DYNA (Hallquist, 2009), which is known to be a reliable program for modeling vehicular impact and contains a library of constitutive models developed for high-strain-rate loads for a number of materials. LS-DYNA also has several different contact formulations that are effective in high-strain-rate impacts including single-surface, one- and two-way contacts (Hallquist, 2009; Reese et al., 2014). These common contact formulations accurately maintain compatibility between parts within the model. In the study of Reese et al. (2014), no significant crushing or fracture of the boulder was observed in the field-scale test and, hence, the boulder was modeled using the simple Mohr-Coulomb failure criterion. However, crushing or fracture is not uncommon for quasi-brittle materials such as concrete and rock. Modeling the rock failure subjected to vehicular impact is a challenging task, and the challenges arise from several aspects including: (1) the rock failure mode, crushing or fracture, is not known a priori; and (2) the location where fracture initiates and propagates is also unknown.

In this study, the performance of an LVAR system involving an embedded boulder fractured upon vehicular impact is investigated through field-scale testing and numerical modeling. In the following sections, the field-scale crash test is first described, followed by descriptions of the LS-DYNA model. In particular, an advanced material model capable of modeling rock crushing and fracture is discussed. The developed LS-DYNA model is subsequently calibrated and validated by comparing the numerical results with observations from the field-scale crash test. A parametric study is conducted to investigate the effect of stiffness and fracture energy of the embedded boulder on energy absorption and dynamic penetration of the truck.

Field-scale crash test

A vehicular crash test was conducted according to ASTM F2656-07 (ASTM, 2007), which establishes a penetration rating for perimeter barriers. The impact condition designation for the test was M30 and the desired penetration level was P1. In other words, the dynamic penetration was designed to be smaller than 1 m when the truck impacted the test article at a speed of 48.3 km/h (30 mph).

LVAR barrier

The test article was three American Black boulders each with a mass of 3675 kg and dimensions of 0.74 m wide (W) × 0.64 m length (L) × 2.54 m height (H). The three boulders were spaced 1.2 m apart and embedded 1.5 m in compacted American Association of State Highway and Transportation Officials (AASHTO) soil with a concrete foundation 0.50 m above the base of the boulders. The dimension of the concrete foundation was 5.85 m wide (W) × 2.60 m length (L) × 0.30 m height (H), and it was reinforced by two layers of #16 rebar. Figure 1 shows the design details and concrete footing of the LVAR system in the field. The uniaxial compressive strength and Brazilian tensile strength of the boulders were 168 MPa and 14 MPa, respectively, based on small-scale laboratory tests conducted. The uniaxial compressive strength of the concrete in the footing was 21 MPa.

Figure 1.

LVAR barrier details: (a) side and impact views detailing dimensions; and (b) reinforcement in concrete foundation.

Truck

A 2003 GMC C 6500 medium-duty diesel truck was used in the test, which is shown in Figure 2(a). Barrels with ballast were secured on the truck bed making the total test weight 6845 kg, which is within the test weight range of 6660–6940 kg as specified by the ASTM F2656-07 (ASTM, 2007). The test vehicle was structurally sound, having no major rust or weaknesses noted. 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. The towing system used to bring the test vehicle up to the desired impact speed consists of a tow vehicle, a tow cable, two re-directional pulleys anchored to the ground, a speed multiplier pulley attached to the tow vehicle, a quick-release mechanism, and a ground anchor. For a detailed description of the system, please refer to Reese et al. (2012, 2014).

Figure 2.

Truck in field test: (a) prior to impact; and (b) post impact.

Test results

In the field test, the truck impacted the tested article at the center line of the central boulder. The field test was instrumented with high-speed cameras to record the motions of the truck and boulder immediately prior to and after the impact. For a detailed description of the cameras and their locations, please refer to Reese et al. (2014). Severe damages were observed on the truck, such as the fracture and large deformation of the cab, as shown in Figure 2(b), and the dynamic penetration was measured to be 2.11 m. The central boulder fractured upon impact, and the fractured piece rotated under the truck and came to rest under the carriage of the truck. Post-test investigation showed that the boulder fractured along a plane near the top of the concrete foundation, as illustrated in Figure 3(a). Besides this primary failure pattern of fracture, minor crushing was also observed on the edge of the boulder on the impacted face, as shown in Figure 3(b). No significant crushing or fracture was observed in the concrete foundation, and it did not appear to have absorbed significant energy from the vehicular impact.

Figure 3.

Damage of rock: (a) fracture along a plane near top of concrete foundation; and (b) crushing of rock.

LS-DYNA model

The LS-DYNA code was utilized to perform finite element method (FEM) simulations to model the crash test. In this section, the FEM model is first discussed, including the mesh and element type for different components, followed by descriptions of the material constitutive models with an emphasis on the rock and concrete materials. The material parameters and contact algorithms are also discussed.

FEM model

The FEM model consisted of two parts, the truck and the LVAR device. The truck model is shown in Figure 4(a). It was modified from a model readily available in the National Crash Analysis Center (NCAC) database (Mohan et al., 2007; National Crash Analysis Center (NCAC), 2008) to satisfy the truck requirement for ASTM F2656-07. 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. Field-scale frontal impact tests have indicated that a truck typically absorbs approximately 70% of the impact energy for a M30-rated test against anti-ram barriers with small deformations (Omar et al., 2007). The truck model was calibrated and has the capability to absorb approximately 69% of the impact energy through plastic deformation and fracture (Reese et al., 2014) and is, hence, considered adequate for the purpose of modeling the overall performance of the LVAR device subjected to vehicular impact. For detailed descriptions of the calibration and validation of the track model, please refer to Reese et al. (2014).

Figure 4.

FEM model: (a) truck and LVAR device; and (b) detailed configuration of boulders, concrete foundation, and rebars.

The LVAR device comprised three boulders, a reinforced concrete foundation, and surrounding soil, as shown in Figure 4(a). Detailed configuration of the concrete foundation and rebars buried underground is shown in Figure 4(b). Eight-node constant stress cubic solid elements were used for the boulder, concrete foundation and soil, and Hughes-Liu beam elements with cross-section integration were used for the rebar. The solid element size was 25 mm for the central boulder and 100 mm for the other two, and 50 mm for the concrete. The soil domain, representing the AASHTO uniformly graded coarse aggregate, had dimensions of 6.9 m wide (W) × 11.1 m length (L) × 2.0 m height (H). The size of the soil domain was selected so that the reflected compression waves did not interfere with the impact response (i.e. short duration) as discussed in Reese et al. (2014). The element size varied from 50 mm near the boulders to 167 mm at the exterior of the soil domain as seen in Figure 4(a). Normal translation of the exterior and bottom boundaries of the soil domain was constrained. A total number of 10,368 beam elements and 273,444 solid elements were used for the LVAR device.

Constitutive models

The LVAR device consisted of several materials, including rock, concrete, soil, and rebar, which required different constitutive models. The soil was modeled using the Mohr-Coulomb failure criteria (*MAT_173), and the rebar was modeled as an elasto-plastic material with bilinear stress–strain curve (*MAT_24). Different from a previous study by Reese et al. (2014), in which no fracture of the boulder was observed, the central rock in the current LVAR system fractured upon impact. Therefore, the simple Mohr-Coulomb failure criteria used by Reese et al. (2014) to model the rock was not appropriate and an advanced material model capable of capturing the post-failure strain softening and fracture was necessary. Thus, a continuous surface cap model (*MAT_159) was adopted in this study for the quasi-brittle materials, including the rock and concrete. This material model was previously used for the crushing failure of concrete in roadside safety simulations (Murray, 2007), and it was found to be also effective in modeling the fracture of rocks (Lin et al., 2011; Zhou and Lin, 2013, 2014).

Main features of the model include a plastic yield surface with a smooth cap, a damage-based softening (e.g. modulus and strength reduction) with erosion, and rate effects for modulus and strength increase in high-strain-rate applications (Murray, 2007). The theoretical background and numerical implementation of this material model are well documented in the literature (Jiang and Zhao, 2015; Murray, 2007; Schwer and Murray, 1994). Key features closely related to this study are discussed next, including the yield surface and strain softening.

The yield surface of the model comprises a shear surface, a cap surface, and a continuous and smooth intersection between the two, as shown in Figure 5(a). The strength is modeled by a shear surface in tensile and low-confining pressure regimes, and by a cap surface in low-to-high confining pressure regimes (Murray, 2007). The cap is used to model the plastic volume change related to pore collapse. As the stress state is primarily in the tensile and low-confining pressure regimes in this study, emphasis is placed on the shear surface. The shear failure function F_f on the compression meridian is defined as

F_{f} = \sqrt{J_{2}} = α - λ e^{- β I_{1}} + θ I_{1}

(1)

where I₁ and J₂ are the first invariant of stress tensor and the second invariant of deviatoric stress tensor, respectively. The values of parameters α, β, λ, and θ can be obtained by fitting the shear surface of the model with experiment data from triaxial compression tests.

Figure 5.

Key features of continuous surface cap model: (a) yield surface on compression meridian; and (b) strain softening in uniaxial tension (Murray, 2007).

One of the most important features of this model is its capability of modeling the strain softening under tension, shear, compression, and other complex-loading conditions (Murray, 2007; Zhou and Lin, 2013). This is achieved by defining three fracture energies: the fracture energy due to tension, or mode I, G_ft, the fracture energy due to shear, or mode II, G_fs, and the fracture energy due to compression, G_fc. The failure initiates with strain softening when the stress reaches the yield surface. As the strain softening continues, failure eventually takes place when the cumulative energy release, or the stress times the displacement, equals the material fracture energy. Specifically for tension, the strain softening is illustrated in Figure 5(b). When the stress reaches the tensile strength σ_t with peak strain ε_p, a damages index D initiates from 0 and approaches 1 at final failure with strain ε_f. The tensile fracture energy is defined as

G_{f t} = \int_{x_{p}}^{x_{f}} σ (1 - D) d x

(2)

where x_p and x_f are the displacements at yielding and fracture, respectively. The two other fracture energies are defined similarly, by integrating the stress–displacement curve in the softening part. For an arbitrary stress state, the fracture energy is then calculated as a function of the stress state characterized by the first invariant of stress tensor and the second invariant of deviatoric stress tensor (Murray, 2007).

For a material with strain softening, mesh size sensitivity has been observed with the straightforward use of stress–strain relationship, as fracture will accumulate in smaller elements with smaller fracture energies (Bažant, 1976). With the fracture energy as part of the material property, the mesh sensitivity is addressed by adjusting the softening part of the stress–strain curve according to element size so that constant fracture energy is maintained (Bažant and Oh, 1983; He et al., 2008; Hillerborg et al., 1976). This feature is well implemented in *MAT_159 and numerical simulations have been conducted to check the implementation (Murray, 2007; Zhou and Lin, 2014).

Material properties

The model material parameters for the rock, concrete, soil, and rebar are discussed as follows. Both the concrete and rock were modeled with the continuous surface cap model, in which the essential material properties included density, elastic modulus, Poisson’s ratio, uniaxial compressive strength, tensile strength, and tensile fracture energy. Due to the lack of data from triaxial compression tests, the shear surface of rock in the compression meridian was approximated based on available Brazilian tensile strength and uniaxial compressive strength. A parametric study showed that the simulation results, especially the dynamic penetration, were sensitive to the elastic modulus E and tensile fracture energy G_ft of the boulder. The dynamic penetration was in good agreement with the field-scale test using E = 120 GPa and G_ft = 146 N/m, and thus they were used for the baseline case. The shear fracture energy was set equal to the tensile fracture energy, and the compressive fracture energy was selected to be 100 × G_ft in this study (Murray, 2007).

Instead of fitting a set of material model parameters to experimental data, standardized material properties have been implemented to make the model easy to use. Specifically, with given uniaxial compressive strength and aggregate size, other material properties such as elastic modulus and tensile fracture energy are automatically calculated based on empirical equations (CEB-FIP Model Code 1990, 1993). For concrete, a uniaxial compressive strength of 21 MPa and a typical aggregate size of 19 mm were used. The material parameters for both the rock and concrete used in the simulations are summarized in Table 1.

Table 1.

Summary of material parameters for boulder and concrete used in simulations.

	Density (kg/m³)	Elastic modulus (GPa)	Poisson’s ratio	Uniaxial compressive strength (MPa)	Tensile strength (MPa)	Tensile fracture energy (N/m)
Boulder	3055	120	0.30	168	14	146
Concrete	2320	23	0.15	21	2	54

For the soil modeled using the Mohr-Coulomb failure criterion, the density, elastic shear modulus, Poisson’s ratio, cohesion, friction angle, and dilation angle were 2100 kg/m³, 20 MPa, 0.25, 0.0048 MPa, 45°, and 15°, respectively (Reese et al., 2014). Typical material properties were adopted for the elasto-plastic rebar, and the density, elastic modulus, Poisson’s ratio, yield strength, and secant modulus were 7830 kg/m³, 200 GPa, 0.3, 476 MPa, and 2.1 GPa, respectively.

Contact algorithms

Besides internal energy of the truck and LVAR barrier, kinetic energy was also dissipated through frictional contacts. The frictional energy dissipation took place between two contact objects, such as the truck and LVAR system, the truck and ground surface, the boulders and concrete, and the boulders and soil. LS-DYNA offers reliable contact algorithms for these contacts, including one- or two-way contact, standard penalty-based contact, or soft constraint penalty contact for stability considerations, among others. Most of the contact algorithms in this study were chosen to be similar with previous settings (Reese et al., 2014). The coefficient of friction was an important parameter for the energy dissipation within frictional contact, and typical coefficients of friction ranging from 0.4 to 0.8 were used, as limited information was available for all of these complex contacts. Although velocity-dependent coefficients have been found to produce more accurate simulation results (Consolazio et al., 2003), a constant value also represents a viable approximation (Atahan, 2006; Reese et al., 2014; Thilakarathna et al., 2010). The difference between dynamic and static coefficients of friction was not investigated in this study.

Concrete is usually reinforced with rebar. Instead of creating a mesh with merged nodes between the rebar and concrete, the reinforcement was coupled to the surrounding concrete continuum with a special constraint feature readily available in LS-DYNA. With this methodology, the rebar could be conveniently placed anywhere inside the concrete continuum without any special mesh accommodation (Murray, 2007).

Comparison of crash test and numerical simulations

The crash test and numerical simulations were compared qualitatively and quantitatively. Figure 6 provides a visual comparison of crash test versus simulation results, with the initial collision, ramping, dropping, and final position of the truck. The sequential side views show that there were similar behaviors of the vehicle for each of the stages shown. In particular, the dynamic penetration of the truck was 2.23 m in the numerical simulations, which compared well with the crash test measurement of 2.11 m. For the failure pattern of the rock, as shown in Figure 7, the simulation results also agreed well with the field observations as shown in Figure 3. The rock fracture initiated on the impact face close to the top of the concrete foundation, where high tensile stresses were concentrated, and propagated along the horizontal plane (see Figure 3(a)). It is worth noting that the fracture propagated very fast. No crack was observed during the simulation time of 0.06 s, and then the crack length along the length direction of the boulder was around 0.5 m at 0.08 s, and the boulder fractured into two pieces at 0.10 s. In addition, the simulation results show minor damages on the two edges of boulder on the impact face, where the damage index was close to 1 as shown in fringe levels (damage index) of Figure 7, and this failure pattern generally agreed with the field observations in Figure 3(b).

Figure 6.

Sequential side views of crash test versus simulation results.

Figure 7.

Failure pattern of rock from numerical simulations.

From the qualitative comparison in Figure 6, minor differences were also observed between the simulation results and crash test. For example, the truck hood did not detach and the barrels did not eject in the simulations. In addition, the fragmented rock piece traveled a longer distance in the simulations and the front part of the truck rested on the rock. Despite these minor differences, the LS-DYNA model generally captured the overall impact behavior and global response of the LVAR device.

For the simulations, energy balance was checked to ensure there was no significant spurious energy, such as hourglass energy. Figure 8 shows that the total energy was approximately constant, and the hourglass energy was very small. Significant amount of energy was dissipated by the internal energy, and the truck absorbed around 59% of the total energy through plastic deformation and fracturing.

Figure 8.

Energy balance diagram.

As the central boulder fractured into two pieces, it was of interest to estimate the amount of energy dissipated through fracture. Assuming the fracture was predominantly caused by tension, the energy dissipation could be estimated by multiplying the tensile fracture energy and the cross-section area of the boulder. It was estimated that the energy dissipation through fracture was less than 1% of the total energy. Thus, the fracture of boulder was very detrimental to the LVAR device, as the system integrity was broken without dissipating much energy.

Parametric study

An anti-ram barrier could be rigid or non-rigid depending on the materials used. A non-rigid anti-ram barrier, typically made of metals and energy-absorbing materials, absorbs a significant amount of energy through large plastic deformation; while a rigid anti-ram barrier, typically made of concrete or boulders with low deformation capacity, transfers more energy to the truck (Itoh et al., 2007). A parametric study was conducted herein to investigate the effect of elastic modulus and fracture energy of the boulder on the energy absorption and dynamic penetration of the truck.

For the parametric study, three E values were used, namely 40, 80, and 120 GPa (i.e. baseline case) and five G_ft values were used, namely 50, 100, 146 (i.e. baseline case), 200, and 250 N/m. The values of E and G_ft were chosen based on the properties of typical rocks, including limestone, sandstone, granite, and quartz, as shown in Table 2 (Atkinson and Meredith, 1987; Durham University, n.d.). For each G_ft value, the shear fracture energy was equal to the tensile fracture energy, and the compressive fracture energy was 100 times that of the tensile fracture energy. All other material properties, such as tensile strength and uniaxial compressive strength, were fixed as the baseline case.

Table 2.

Elastic modulus and tensile fracture energy of typical rocks (Atkinson and Meredith, 1987; Durham University, n.d.).

	Elastic modulus (GPa)	Tensile fracture energy (N/m)
Limestone	3~70	15~84
Sandstone	10~120	19~273
Granite	2~50	19~520
Quartz	28~80	154~210

Table 3 shows the effect of boulder elastic modulus and tensile fracture energy on the ratio of energy absorbed by the truck (i.e. energy absorbed divided by total kinetic energy). Table 3 indicates that the ratio of energy absorbed by the truck was not very sensitive to the fracture energy. Despite minor fluctuation, the ratio generally slightly increased with the fracture energy. For example, the ratio increased from approximately 52 to 63% when the fracture energy increased from 50 to 250 N/m for E = 120 GPa. The ratio of energy absorbed by the truck generally increased with the elastic modulus of the boulder. For example, the ratio increased from approximately 38 to 59% when the elastic modulus of the boulder increased from 40 to 120 GPa for G_ft = 146 N/m.

Table 3.

Effect of boulder properties on ratio of energy absorbed by truck.

	Energy ratio
E (GPa)	Gft = 50 (N/m)	Gft = 100 (N/m)	Gft = 146 (N/m)	Gft = 200 (N/m)	Gft = 250 (N/m)
40	0.40	0.40	0.38	0.42	0.44
80	0.44	0.47	0.46	0.46	0.51
120	0.52	0.56	0.59	0.62	0.63

Table 4 shows the effect of boulder properties on dynamic penetration of the truck. The results are shown for all of the cases when the truck stopped within the simulation time of 2 s. For the case of G_ft = 50 N/m, the truck did not stop for all the three E values used. For the cases of G_ft = 100 and 146 N/m, the truck only stopped when E = 120 Gpa was used (i.e. the truck did not stop when a smaller elastic modulus was used). Table 4 indicates that the dynamic penetration was very sensitive to the fracture energy and was significantly reduced using a boulder with larger capacity to resist fracture. For example, the dynamic penetration decreased from around 4.37 to 0.17 m when the elastic modulus increased from 80 to 120 GPa for G_ft = 250 N/m, and the corresponding final positions of the truck are shown in Figure 9.

Table 4.

Effect of boulder properties on dynamic penetration of truck.

	Dynamic penetration (m)
E (GPa)	Gft = 50 (N/m)	Gft = 100 (N/m)	Gft = 146 (N/m)	Gft = 200 (N/m)	Gft = 250 (N/m)
40	N/A	N/A	N/A	N/A	N/A
80	N/A	N/A	N/A	5.10	4.37
120	N/A	4.36	2.23	0.85	0.17

Figure 9.

Final positions of truck with different elastic modulus of boulder: (a) E = 80 GPa, G_ft = 250 N/m; and (b) E = 120 GPa, G_ft = 250 N/m.

The parametric study shows that the performance of the LVAR system could, in general, be improved using a stiffer and tougher boulder. As relatively high stiffness and tensile fracture energy values were used in this study, alternative ways are necessary to further improve the LVAR performance, which include incorporating high energy-absorbing materials into the system or utilizing a larger size boulder.

Conclusion

A field-scale crash test and numerical modeling with LS-DYNA were conducted for an LVAR system subjected to vehicular impact. The LVAR system consisted of three boulders connected through a reinforced concrete foundation embedded in compacted AASHTO soil. The central boulder fractured upon vehicular impact. As the traditional Mohr-Coulomb failure criterion is inadequate to capture the strain softening and fracture behavior of quasi-brittle materials, such as concrete and rock, an advanced material model was adopted in the numerical simulations. The global response of the truck in the crash test was well-reproduced by the numerical simulations, including the initial collision, ramping, dropping, and final position of the truck. In addition, the failure patterns of the central rock were also well reproduced, including the fracture plane near the top of the concrete foundation and minor crushing on the edge of the boulder on the impact face. The fracture of the boulder was found to be very detrimental to the LVAR system, as the system integrity was broken without dissipating much energy. It was desirable to decrease the dynamic penetration of the truck to improve the performance of the LVAR system, and a parametric study showed that this could be achieved using a stiffer and tougher boulder.

Footnotes

Acknowledgements

The authors would like to thank the United State Department of State and the Larson Transportation Institute at The 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

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This paper 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.

References

American Society for Testing and Materials (ASTM) F2656-07 (2007) Standard test method for vehicle crash testing of perimeter barriers. West Conshohocken, PA: ASTM International.

Atahan

(2006) Finite-element crash test simulation of New York portable concrete barrier with I-shaped connector. Journal of Structural Engineering 132: 430–440.

Atkinson

Meredith

(1987) Fracture mechanics of rock. In: Atkinson

(ed.) Experimental Fracture Mechanics Data for Rocks and Minerals. London: Academic Press, pp. 477–525.

Bažant

(1976) Instability, ductility, and size effect in strain-softening concrete. Journal of the Engineering Mechanics Division 102: 331–344.

Bažant

(1983) Crack band theory for fracture of concrete. Materials and Structures 16: 155–177.

CEB-FIP Model Code 1990 (1993) Comité Euro-International du Béton. London: Thomas Telford House.

Chen

Xiao

. (2015) Test and numerical simulation of truck collision with anti-ram bollards. International Journal of Impact Engineering 75: 30–39.

Consolazio

Chung

Gurley

(2003) Impact simulation and full scale crash testing of a low profile concrete work zone barrier. Computers & Structures 81: 1359–1374.

Durham University (n.d.) Foundations—modulus of elasticity. Available at: http://community.dur.ac.uk/~des0www4/cal/dams/geol/mod.htm (accessed 18 July 2015).

10.

Hallquist

(2009) LS-DYNA Keyword User’s Manual. Livermore, CA: Livermore Software Technology Corporation.

11.

Liew

(2008) A fracture energy based constitutive model for the analysis of reinforced concrete structures under cyclic loading. Computer Methods in Applied Mechanics and Engineering 197: 4745–4762.

12.

Hillerborg

Modeer

Petersson

(1976) Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement and Concrete Research 6: 773–781.

13.

Sun

(2014) Numerical investigation of K4-rating shallow footing fixed anti-ram bollard system subjected to vehicle impact. International Journal of Impact Engineering 63: 72–87.

14.

Chen

. (2011) State-of-the-art review on anti-ram bollards. Applied Mechanics and Materials 90: 3206–3213.

15.

Itoh

Liu

Kusama

(2007) Modeling and simulation of collisions of heavy trucks with concrete barriers. Journal of Transportation Engineering 133: 462–468.

16.

Jiang

Zhao

(2015) Calibration of the continuous surface cap model for concrete. Finite Elements in Analysis and Design 97: 1–19.

17.

Krishna-Prasad

(2006) Protective Bollard Design for High Speed Impact Energy Absorption. Wichita, KS: Wichita State University.

18.

Lin

J-S

Mendoza

Jaime

. (2011) Numerical modeling of rock cutting. In: 12th ISRM congress, Beijing, China, 18–21 October.

19.

Mohan

Marzougui

Kan

(2007) Validation of a single unit truck model for roadside hardware impact. International Journal of Vehicle Systems Modelling and Testing 2: 1–15.

20.

Murray

(2007) User Manual for LS-DYNA Concrete Material Model 159. Mclean, VA: U.S. Department of transportation, Federal Highway Administration.

21.

National Crash Analysis Center (NCAC) (2008) Finite element model archive: Ford single unit truck, reduced model. Available at: http://www.ncac.gwu.edu/vml/models.html (accessed 3 September 2013).

22.

O’Hare

Linzell

Brennan

. (2012) Development of shallow foundation streetscape vehicular anti-ram (SVAR) systems through modeling and testing. In: Proceedings of 83rd shock and vibration, New Orleans, LA, 4–8 November 2012.

23.

Omar

Bedewi

Hylton

(2007) Cost-effective structural anti-ram security barriers: new design, computer modeling and test validation. In: ASME 2007 international mechanical engineering congress and exposition, Seattle, WA, 11–15 November 2007, pp. 341–350. New York: ASME.

24.

Reese

Qiu

Linzell

. (2012) Development of landscape vehicular anti-ram systems through computational and experimental methods. In: Proceedings of 83rd shock and vibration, New Orleans, LA, 4–8 November 2012.

25.

Reese

Qiu

Linzell

. (2014) Field tests and numerical modeling of vehicle impacts on a boulder embedded in compacted fill. International Journal of Protective Structures 5: 435–452.

26.

Schwer

Murray

(1994) A three-invariant smooth cap model with mixed hardening. International Journal for Numerical and Analytical Methods in Geomechanics 18: 657–688.

27.

Thilakarathna

HMI

Thambiratnam

Dhanasekar

. (2010) Numerical simulation of axially loaded concrete columns under transverse impact and vulnerability assessment. International Journal of Impact Engineering 37: 1100–1112.

28.

US Department of State (1985) SD-STD-02.01. Specification for vehicle crash test of perimeter barriers and gates.

29.

US Department of State (2003) SD-STD-02.01 Revision A. Test method for vehicle crash testing of perimeter barriers and gates.

30.

Zhou

Lin

J-S

(2013) On the critical failure mode transition depth for rock cutting. International Journal of Rock Mechanics and Mining Sciences 62: 131–137.

31.

Zhou

Lin

J-S

(2014) Modeling the ductile-brittle failure mode transition in rock cutting. Engineering Fracture Mechanics 127: 135–147.