Research on Anti-Underride Design of Height-Optimized Class A W-Beam Guardrail

Abstract

As an essential highway safety facility, roadside W-beam guardrails effectively prevent errant vehicles from entering hazardous zones or causing secondary collisions by blocking and redirecting them, thereby reducing accident severity. With the rapid development of the automotive industry, the front bumper height of small passenger cars generally ranges between 405 mm and 485 mm. However, the lower edge height of the current Chinese Class A W-beam guardrail is 444 mm above the ground, which leads to a high risk of “underride” during collisions, resulting in elevated occupant injury risks. To address this issue, this paper proposes an optimized guardrail structure composed of a double W-beam and a C-type beam, aiming to reduce the underride risk for small passenger cars while accommodating multi-vehicle protection needs. In this design, the double W-beam is installed at a height of 560 mm and the C-type beam at 850 mm, connected to circular posts using a regular hexagonal anti-obstruction block. The beam thickness is uniformly 3 mm, while the thickness of other components is 4 mm. To systematically evaluate the impact of material strength on both safety performance and cost, two material configurations are proposed: Scheme 1 uses Q235 carbon steel for all components; Scheme 2 reduces the thickness of the C-type beam to 2.5 mm and employs Q355 high-strength low-alloy steel, with the thickness of the connected anti-obstruction block reduced to 3.5 mm, while the other components retain Q235 steel and unchanged structural dimensions. Using finite element simulation, collisions involving small passenger cars, medium trucks, and buses are simulated, and performance comparisons are conducted based on vehicle trajectory and guardrail deformation. For the small passenger car scenario, risk quantification indicators—Acceleration Severity Index (ASI), Theoretical Head Impact Velocity (THIV), and Post-impact Head Deceleration (PHD)—are introduced to assess occupant injury. The results demonstrate that Scheme 2 not only meets the required protection level but also significantly reduces occupant risk for small passenger cars, lowering the injury rating from Class C to Class B. Moreover, the overall structural mass is reduced by approximately 1407 kg per kilometer, with material costs decreased by about RMB 10,129, demonstrating favorable economic efficiency. The proposed structural optimization not only effectively mitigates small car underride and improves multi-vehicle protection performance but also provides the industry with a novel guardrail geometric design directly applicable to engineering practice. The technical approach of enhancing material strength and reducing component thickness also offers a feasible reference for lightweight design, material savings, and cost optimization of guardrail systems, contributing significantly to improving the safety and sustainability of road transportation infrastructure.

1. Introduction

At present, China’s highway guardrail design mainly follows the “Highway Traffic Safety Facilities Design Rules” (JTG/T D81-2017) [1], which clearly specify that the standard form of roadside Class A guardrail is a triple-wave beam guardrail. However, with the increasing diversity of vehicle types in traffic flow, this standard structure has gradually shown certain technical limitations in practical applications. In terms of structure, the installation height of the W-beam is mainly based on protection requirements for large vehicles, resulting in a relatively high lower edge from the ground. When a passenger car collides with the guardrail, the vehicle front end may intrude beneath the beam, causing an “underride” phenomenon, which may lead to vehicle instability, barrier penetration, or body entrapment, thereby increasing collision injury risk [2]. In terms of materials, existing W-beam guardrails commonly use Q235 carbon steel [3]. Due to its relatively low strength, achieving the required protection level often requires increasing component thickness to enhance structural stiffness and energy absorption capacity. As a result, the guardrail becomes heavier, which not only increases manufacturing and transportation costs, but also generates greater carbon emissions during production and logistics, hindering the development of green transportation infrastructure [4].

Aiming at the above problems, scholars at home and abroad have carried out systematic studies in terms of structure and material. In terms of structural improvement, Borovinšek et al. [5] proposed to add a single wave beam plate on the basis of the traditional double-wave beam guardrail, and carried out finite element simulation analysis by LS-DYNA software (https://lsdyna.ansys.com/ accessed on 25 October 2025), which showed that the composite structure can significantly improve the guiding function of the guardrail. Reid et al. [6] confirmed that the structure can effectively inhibit the overturning tendency of high gravity trucks and improve the rollover prevention ability by extending the columns and increasing the height of the wave beam plate to 635 mm, and confirmed that this structure can effectively inhibit the rollover tendency of high gravity trucks by means of collision simulation experiments. Lee et al. [7] found that the circular columns had the smallest deformation in the collision by establishing a three-dimensional earth column model. Marzougui [8] and other scholars emphasized that the height of the guardrail installation needs to be matched with the height of the vehicle’s bumper, pointing out that the height of the insufficient height will significantly reduce the protection ability. Sicking et al. [9] conducted research on improving the overturning resistance of W-beam guardrails and, through finite element simulations and full-scale crash tests, concluded that the optimal installation height range for the W-beam is 550–660 mm. Vesenjak et al. [10] investigated various anti-obstruction block geometries and found that hexagonal anti-obstruction block provide the best protection performance because their lower stiffness minimizes the impact on the vehicle during collision and allows greater energy absorption through deformation. Li Liping [11], addressing the insufficient anti-intrusion capability of existing Am-grade guardrails, designed an arch-beam guardrail by adding an arch structure to the original posts and installing an additional beam above the existing beam. The results showed that this design effectively prevents trucks from penetrating through the guardrail. Pajouh et al. [12] investigated the maximum safe installation height of guardrail systems. Through full-scale crash tests using the MGS, they conducted experiments with guardrail heights of 864 mm and 914 mm, ultimately determining 914 mm as the maximum allowable guardrail height. Cui Hongjun et al. [13] explored the protective ability of different heights of waveform beam guardrail, and gave a threshold value of 705 mm for guardrail height through finite element simulation tests. Xiao Youye [14] pointed out that insufficient stiffness of the waveform beam plate can easily lead to the phenomenon of wheel obstruction and tripping. Yizheng [15] proposed the optimal guardrail structure scheme through orthogonal test optimization, including column spacing of 3000 mm, waveform beam plate and block thickness of 3.5 mm and 4 mm and other parameters. Yu Changchun [16] compared the effect of different guardrail heights on the protective effect through computer simulation and real vehicle collision test, and pointed out that the performance of Triple A guardrail with 200 mm higher columns is better than standard height guardrail in terms of protective performance, which further supports the validity of the guardrail height enhancement from the empirical point of view. In terms of material optimization, Wei Hongliang [17] and others used high-performance steel as the guardrail material, and the thickness of the columns of the guardrail structure was reduced by 1.5 mm, and the thickness of the beam plate was reduced by 0.8 mm, and the degree of lightweight can reach 28%. Wang Lijun [18] analyzed the application effects of lightweight corrugated beam steel guardrails. The study demonstrated that replacing traditional Q235 steel with high-strength steel could achieve annual material cost savings of 4.19 billion yuan. Wu Dehua [19,20] and other attempts to use high-strength new stainless steel as a guardrail material, through orthogonal experiments simulation program, pointed out that the guardrail plate thickness has the greatest impact on the maximum lateral displacement value of the guardrail, the greater the thickness of the anti-obstruction block, the greater the acceleration of the vehicle’s center of mass. Meanwhile, in recent years, research on guardrails has gradually shifted from focusing solely on “safety performance” to incorporating “occupant injury risk.” Indicators such as the Acceleration Severity Index (ASI) [21], Theoretical Head Impact Velocity (THIV) [22], and Post-Impact Head Deceleration (PHD) [23] have increasingly become key criteria for evaluating guardrail safety. Relevant studies have shown that occupant risk indicators can establish strong correlations with actual injury levels [24,25], providing a more quantitative and interpretable approach for guardrail safety evaluation and design.

Based on the above research findings and practical evidence, the authors contend that the current Class A W-beam guardrail exhibits quantifiable geometric and material limitations in accommodating collisions involving small vehicles. There is an urgent need for coordinated structural and material optimization to achieve enhanced anti-underride capability and improved occupant protection. Therefore, this study aims to reduce the underride risk of small vehicles, improve multi-vehicle protection performance, and lower material costs. To this end, a geometrically optimized guardrail design composed of a double W-beam and a C-type beam is proposed, along with two material configuration schemes based on Q235 and Q355 high-strength steel. A coupled vehicle–guardrail finite element model is established, and three representative vehicle types—a small passenger car, a medium truck, and a medium bus—are selected for collision simulations. Key indicators such as vehicle kinematics, guardrail deformation, and structural response are evaluated. On this basis, occupant risk metrics including ASI, THIV, and PHD are further calculated for the small-car collision scenario to quantitatively assess the safety improvement attributable to the structural optimization.

This study aims to provide a new technical pathway for optimizing the structure of Class A W-beam guardrails in China. The proposed approach seeks to simultaneously reduce underride risk for small vehicles, enhance occupant protection, and decrease material consumption, thereby offering theoretical support and engineering references for the future design and retrofit of roadside safety barriers.

2. Collision Risk Analysis of Triple-W-Beam Guardrail

As the predominant vehicle type in current traffic flow, small passenger cars have achieved significant breakthroughs in vehicle design and safety technology. Corresponding variations in bumper installation heights exist due to differences in body structure dimensions. The Chinese national standard “Front and Rear Underrun Protective Devices for Motor Vehicles” (GB 17354-1998) [26] stipulates that the front bumper installation height for small passenger vehicles should range from 405 mm to 485 mm, as illustrated in Figure 1. However, the lower edge height of the currently adopted Class A triple-wave beam guardrail along roadsides in China is 444 mm above the ground. The interaction mechanisms between different types of vehicles and triple-wave beam guardrails exhibit certain variations. For large vehicles such as trucks and buses, the height of their bumpers and primary front load-bearing structures is generally higher than that of small passenger cars. During collisions with the guardrail, the initial contact point is typically located in the central area of the wave beam. This ideal interaction position enables the collision force to be effectively transmitted through the anti-obstruction block to the posts and dissipated into the foundation, thereby fully utilizing the guardrail’s guiding and blocking functions.

However, for small vehicles with front-bumper installation heights between 405 mm and 444 mm, the bumper height is often close to or even lower than the lower edge of the guardrail beam. As a result, the initial collision contact point shifts downward to the lower edge of the beam, preventing the vehicle’s front longitudinal members and other primary load-bearing structures from effectively participating in the energy-absorption process. A lower impact point generates a significant nose-down moment, causing unintended crush deformation of the vehicle’s front compartment accompanied by overall downward sinking. This sinking further intensifies the vehicle’s pitching motion and can easily lead to the “underride” accident shown in Figure 2, thereby increasing the severity of the crash.

3. Improvement Schemes for W-Beam Guardrail Structure

Based on the consideration of enhancing the protection of the small vehicles, this paper proposes the Class A w-beam guardrail structural improvement program using a double-waveform beam plate and C-type beam plate combination structure, the specific structure shown in Figure 3.

Under the premise of keeping the total height of the guardrail and the depth of the columns consistent with the existing three-waveform beam guardrail, the program has systematically optimized the installation height of the key components. The double-waveform beam plate has thickness of 3 mm, the installation height is reduced to 560 mm, and its lower edge from the ground height of 405 mm; C-type beam plate is arranged in the waveform beam plate above the plate thickness of 3 mm, with an installation height of 850 mm. A double-waveform beam plate and a C-type beam plate are used hexagonal anti-block and column connection, anti-block and column thickness of 4 mm, the structure of the guardrail dimensions as shown in

Table 1. Component dimensions of the optimized guardrail structure.

Guardrail Beam Type (mm)	Column (mm)	Anti-Obstruction Block (mm)	Beam Installation Height (mm)	Column Depth (mm)	Total Guardrail Height (mm)
Double-wave beam (310 × 85 × 3)	Φ140 × 4	196 × 178 × 200 × 4	560	1400	2350
C-type beam (140 × 100 × 3)		196 × 178 × 100 × 4	850

. A double-waveform beam plate is mainly used to deal with small vehicles collision protection, to prevent the occurrence of “under the drill” phenomenon, while a C-type beam plate is mainly for large vehicles to provide effective lateral height constraints.

4. Design of Simulation Experiments

To systematically evaluate the impacts of different material configurations on the protective performance of the guardrail and occupant risk, this study established a complete vehicle–guardrail collision simulation process. First, two material configuration schemes were developed, as shown in

Table 2. Material configuration schemes.

Guardrail Components	Scheme 1		Scheme 2
	Material	Thickness	Material	Thickness
Double-wave beam	Q235	3	Q235	3
C-type beam	Q235	3	Q355	2.5
Column	Q235	4	Q235	4
Anti-obstruction block 1	Q235	4	Q235	3.5
Anti-obstruction block 2	Q235	4	Q235	4

: Scheme 1 uses Q235 carbon steel for all components; in Scheme 2, the thickness of the C-type beam is reduced to 2.5 mm using Q355 high-strength low-alloy steel, the thickness of the connected anti-obstruction block is reduced to 3.5 mm, while the other components continue to use Q235 steel with unchanged structural dimensions. Subsequently, HyperMesh2022 was employed to model and mesh the optimized guardrail structure, define material models, contact relationships, and boundary conditions. The vehicle–guardrail coupled collision simulation was solved using LS-DYNA R11. Key response parameters such as vehicle trajectory, acceleration, and velocity were extracted from the simulation output data via the HyperWorks2022 post-processing module to compare and analyze the safety performance differences between the two material schemes under multi-vehicle scenarios.

Based on this, for the small passenger car collision condition, three occupant risk assessment indicators—the Acceleration Severity Index (ASI), Theoretical Head Impact Velocity (THIV), and Post-impact Head Deceleration (PHD)—were further calculated to quantitatively evaluate the improvement effects of different material configuration schemes on occupant safety. The above process forms a complete experimental procedure, as illustrated in Figure 4, encompassing material scheme design, model construction, coupled simulation, and risk quantification, thereby providing a scientific basis for ultimately determining the optimized structural scheme.

4.1. Finite Element Model of Guardrail

According to the structural parameters of each component, SolidWorks2022 is used to establish the 3D model of the guardrail and imported into HyperMesh2022 for finite element meshing, and the finite element model of each component of the guardrail is shown in Figure 5. As the bolts used for the connection of each component of the guardrail are high-strength bolts, the probability of each component falling off and separating from each other when subjected to a large collision force is extremely low, so the RgdBody unit type in the rigids under the 1D panel is used to complete the connection of each component of the guardrail [27].

In the boundary condition constraints, in order to reduce the calculation time of the model and ensure the deformation characteristics of the columns, the full constraints are set at 400 mm below the ground level [28], i.e., the six directional degrees of freedom are constrained to simulate the interactions between the columns and the soil base. At the same time, in order to simulate the real end boundary conditions and ensure the stability of the calculation, the two ends of the beam plate are also set constraints [29], and the boundary constraints of the guardrail are shown in Figure 6.

4.2. Vehicle–Guardrail Collision Coupling System

According to the “Standard for Safety Performance Evaluation of Highway Barriers” (JTG B05-01-2013) [30] on the provisions of the initial conditions of the Class A guardrail collision, the location of the collision point of the standard section of the guardrail is required to be 1/3 away from the starting point of the standard section, three kinds of car models are used to evaluate the safety performance, and the selected minibus is a general family car, bumper installation height 0.42 m, medium-sized trucks for van-type integral trucks, buses for common passenger cars, vehicle parameters and collision conditions as shown in

Table 3. Vehicle parameters and crash conditions.

Crash Vehicle Type	Vehicle Weight (t)	Length × Width × Height (m)	Center of Gravity Height (m)	Impact Velocity (km/h)	Impact Angle (°)
Small passenger car	1.5	4.6 × 1.8 × 1.4	0.52	100	20
Medium passenger bus	10	11.2 × 2.5 × 3	1.36	60	20
Medium truck	10	8.6 × 2.5 × 3.3	1.41	60	20

.

All three vehicle finite element models used in the experiment have been validated through frontal impact tests, confirming their reliability and rationality. They also meet the main technical parameter requirements for each vehicle type specified in the Standard for Safety Performance Evaluation of Highway Barriers. To reduce computation time while ensuring the reliability of simulation data, rigid-body monitoring points are placed at the center of gravity and within the occupant compartment of each vehicle to output node data. For contact settings, the rolling friction coefficient between vehicle tires and the ground is set to 0.2. Self-contact is defined for both the guardrail and the vehicle body, with static and dynamic friction coefficients set to 0.15. Surface-to-surface contact is applied between the guardrail and the vehicle, where all vehicle components are assigned as master surfaces and all guardrail components as slave surfaces. Considering gravitational effects, the keyword LOAD_BODY_Z is applied to impose gravity on the entire system, with gravitational acceleration g. The vehicle travels in the positive X-axis direction. The coupled vehicle–guardrail collision system is shown in Figure 7.

4.3. Material Properties

This study employs Q235 carbon steel [31] and Q355 [32] high-strength low-alloy steel as guardrail materials. The stress–strain curves of the two materials are shown in Figure 8. Q235 mild steel has a yield strength ≥235 MPa and a tensile strength ranging from 370 to 500 MPa. Q355, a high-strength low-alloy structural steel, exhibits a tensile strength of 470–630 MPa, a yield strength ≥345 MPa, and an elongation ≥22%. The Q355 material offers higher strength along with good plasticity and toughness, providing superior impact protection capability.

4.4. Protection Performance Evaluation Index

The guardrail protection performance evaluation system in this paper strictly follows the Standard for Safety Performance Evaluation of Highway Barriers (JTG B05-01-2013) [30] and uses the three core functions defined in the specification—blocking function, buffer function and guiding function—as the primary evaluation indicators. blocking function requires that the guardrail must be effective in preventing the vehicle from crossing, overrunning or riding across, while ensuring that the components do not intrude into the passenger compartment; in terms of the buffer function, the majority of the occupant do not wear seat belts, the proportion of occupant deaths is 1% when the acceleration at the center of gravity of the vehicle is 20 g [33]. Therefore, it is required that the acceleration of the occupants after the collision cannot exceed 200 m/s², and for occupant impact velocity limits, the standard aligns with U.S. MASH [34,35] guidelines, which requires that both the longitudinal and transverse components do not exceed 12 m/s; occupant collision speed is calculated according to Equations (1) and (2). In terms of the guiding function, the vehicle shall not roll over after the collision, and the wheel track of the vehicle after leaving the departure point shall not cross the straight line F when it passes through the guidance exit frame shown in Figure 9. Small passenger cars are used to test the cushioning function, the guiding function, and to record the maximum lateral dynamic deformation of the guardrail (D) and the maximum lateral dynamic displacement extension of the guardrail (W); medium and large passenger cars (including extra-large buses) and medium and large trucks are used to test the barrier function and guiding function; and the guardrail’s maximum lateral dynamic displacement extension value (W) is recorded. Function, guiding function; record the maximum lateral dynamic deformation of the guardrail (D), the maximum lateral dynamic displacement extension of the guardrail (W) and maximum dynamic vaulting of the vehicle (VI).

$$\begin{array}{c}{v}_{x,y}={\int }_0^{t^{*}}{a}_{x,y}dt\end{array}$$

(1)

$$\begin{array}{c}X,Y={\int }_0^{t^{*}}{\int }_0^{t^{*}}{a}_{x,y}d{t}^2\end{array}$$

(2)

In the formula, the following abbreviations are used:

$v_{x,y}$—Occupant crash speed in the longitudinal (x-direction) or lateral (y-direction) direction.

$a_{x,y}$—the acceleration at the vehicle’s center of gravity in the longitudinal (x-direction) or lateral (y-direction).

t*—the hypothetical moment of impact between the occupant’s head and the interior of the occupant compartment, defined as the time required for the hypothetical occupant’s head to move 0.6 m longitudinally (x-direction) or 0.3 m laterally (y-direction) within the compartment. t* is the smaller value obtained from satisfying the integral equations in the x and y directions.

The values of A and B in the figure above should be set according to the table below. In

Table 4. Values of parameters A and B (m).

Collision Vehicle Type	A	B
small passenger car	2.2 + Vw + 0.16 Vl	10
Large and medium buses (including extra-large buses) Large and medium trucks	4.4 + Vw + 0.16 Vl	20

, V_w represents the overall vehicle width (m), and V_l represents the overall vehicle length (m).

4.5. Quantitative Indicators of Occupant Risk

During the collision between the vehicle and the guardrail, the acceleration at the vehicle’s center of mass reflects the overall force response and energy transfer characteristics of the vehicle, and serves as an important indirect indicator of the impact sustained by occupants. Extensive experimental and statistical studies have shown that higher center-of-mass acceleration corresponds to stronger inertial forces during the instantaneous collision phase, leading to greater relative displacement between the occupant’s body, head, and the restraint system, thereby increasing the probability of neck, thoracic, and head injuries. In other words, vehicle center-of-mass acceleration is positively correlated with occupant injury risk. Therefore, the international mainstream safety evaluation systems EN1317 [21,22] and MASH adopt three-axis acceleration of the vehicle center of mass (longitudinal, lateral, and vertical) as fundamental data for assessing occupant risk, from which quantitative indicators such as the Acceleration Severity Index (ASI) and Theoretical Head Impact Velocity (THIV) are derived to estimate potential occupant injury.

The Acceleration Severity Index (ASI) [21] is an indicator used to evaluate the severity of occupant injuries during vehicle–guardrail collisions. It is calculated according to Equation (3):

$$\begin{array}{c}ASI=max\left(\sqrt{{\left({\displaystyle \frac{a_x}{a_{x,lim}}}\right)}^2+{\left({\displaystyle \frac{a_y}{a_{y,lim}}}\right)}^2+{\left({\displaystyle \frac{a_z}{a_{z,lim}}}\right)}^2}\right)\end{array}$$

(3)

where $a_x$, $a_y$, and $a_z$ represent the three-axis accelerations at the vehicle’s center of mass, and $a_{x,lim}$, $a_{y,lim}$, and $a_{z,lim}$ are the threshold values specified in the EN1317 [21] standard. Specifically, $a_{x,lim}=12\mathrm{g}$, $a_{y,lim}=9\mathrm{g}$, and $a_{z,lim}=10\mathrm{g}$. A larger ASI corresponds to a higher severity of occupant injury. The ASI evaluation criteria are shown in

Table 5. ASI evaluation criteria [21].

Value Range	Injury Level	Assessment Description
ASI ≤ 1.0	A	Good—favorable to occupant safety, low injury risk
1.0 < ASI ≤ 1.4	B	Acceptable—acceptable level, no serious injury risk
ASI > 1.4	C	Severe—poses a high injury risk, does not meet safety requirements

.

Theoretical Head Impact Velocity (THIV) [22] represents the relative velocity between the occupant’s head and the interior of the passenger compartment at the moment of impact, and it is used to evaluate the severity of head contact with interior surfaces. It is calculated according to Equation (4):

$$\begin{array}{c}THIV=\sqrt{v_x{\left(t\right)}^2+v_y{\left(t\right)}^2}\end{array}$$

(4)

where $v_x$ and $v_y$ are the occupant’s velocities relative to the vehicle coordinate system at the moment of collision. The summarized THIV evaluation criteria are presented in

Table 6. THIV evaluation criteria [22].

THIV Threshold	Description
THIV ≤ 33 km/h	Good—low risk of occupant head impact
THIV > 33 km/h	High risk—may result in head injury

.

The Post-impact Head Deceleration (PHD) [23] is the deceleration experienced simultaneously by the occupant’s head and the interior surface of the passenger compartment after the vehicle collides with the guardrail and head contact occurs. It is calculated according to Equation (5):

$$\begin{array}{c}PHD=MAX\sqrt{x_G^2\left(t\right)+y_G^2\left(t\right)}\end{array}$$

(5)

where $x_G^2\left(t\right)$ and $y_G^2\left(t\right)$ represent the 10 ms moving-average time histories of the vehicle’s longitudinal and lateral accelerations, respectively. A PHD value below 20 g is considered optimal, indicating mild head loading and a low risk of injury.

5. Analysis of Vehicle Crash Process

5.1. Analysis of Small Passenger Vehicle Crash

In the highway guardrail safety performance evaluation system, vehicle trajectory serves as a core observation indicator, directly reflecting the guardrail’s ability to guide errant vehicles. An ideal trajectory demonstrates a smooth guided curve, with the exit path remaining within the guidance exit frame. This indicates that the guardrail successfully converts collision kinetic energy into guidance potential energy, allowing the vehicle to smoothly return to its normal travel path. Conversely, sudden trajectory changes, loss of directional control, or excessive exit angles suggest deficiencies in the guardrail’s guidance function, which may lead to secondary accidents or exacerbate crash severity.

Figure 10 illustrates the vehicle trajectory and guidance exit frame diagram for the small passenger car during the entire collision process under both designs. Throughout the impact, no hazardous phenomena such as underride, vaulting, or overriding of the guardrail occurred. No guardrail components intruded into the occupant compartment, demonstrating effective containment performance. The vehicle was successfully redirected post-impact, maintaining normal travel attitude without rolling, yawing, or U-turning. Furthermore, the vehicle’s trajectory after exiting the departure point satisfied the requirements of the guidance exit frame, confirming excellent guidance performance.

Figure 11 shows the damage diagrams of the small passenger car after collision with the two improved guardrail designs. It can be observed that no vehicle body components detached, and no damaged parts intruded into the occupant compartment. Due to the higher strength of the C-type beam in Design Scheme 2, it provided better containment for the small car. The overall inertia of the small car was lower, and the wheel-to-post contact occurred at a reduced velocity, resulting in less deformation of the right front wheel. The bumper deformation was minor. By adjusting the installation height of the corrugated beam, the guardrail effectively prevented vehicle underride.

Acceleration and velocity at the vehicle’s center of gravity are critical parameters for evaluating the buffering performance of guardrails. These metrics directly reflect the intensity of impact transmitted to occupants during a collision. Low and stable acceleration values indicate that the guardrail effectively absorbs collision energy through controlled structural deformation, thereby providing adequate cushioning protection for occupants. Conversely, acceleration peaks exceeding the specified limits suggest potential severe occupant injury, revealing deficiencies in the guardrail’s energy-absorption design.

Figure 12 shows the acceleration curves at the center of gravity of the small passenger car during the collision process. When the small car collided with the improved guardrail at a speed of 100 km/h and an impact angle of 20°, both the lateral and longitudinal accelerations at the center of gravity for the two design schemes remained stable below the standard limit of 200 m/s². Specifically, for Design Scheme 1, the maximum lateral acceleration was 132.36 m/s², and the maximum longitudinal acceleration was 139.89 m/s², with corresponding occupant impact velocities of 5.08 m/s (lateral) and 9.44 m/s (longitudinal). For Design Scheme 2, the maximum lateral acceleration was 93.08 m/s², and the maximum longitudinal acceleration was 124.56 m/s², with occupant impact velocities of 2.15 m/s (lateral) and 7.79 m/s (longitudinal). Both schemes met the requirement of the “Evaluation Standard” that occupant impact velocity must not exceed 12 m/s.

Observation of the velocity variation at the center of gravity of the small passenger car in Figure 13 reveals that the initial velocity was 100 km/h in the X-direction. Under both design schemes, the X-direction velocity continuously decreased to below 50 km/h, demonstrating excellent energy-absorbing performance of the improved guardrail. The increase in Y-direction velocity gradually slowed and did not exceed 40 km/h, indicating effective containment by the guardrail. The deformation of the guardrail itself absorbed the kinetic energy of the small car in the Y-direction. Fluctuations in the Z-direction velocity were minor, primarily caused by uneven contact with the ground due to deformation of the right front wheel, while the guardrail system maintained good stability.

The lateral displacement variation in a guardrail reflects the stability of its structure. Excessive displacement may indicate structural failure, such as post uprooting or beam fracture, which not only compromises the guardrail’s ability to contain and redirect errant vehicles but also poses a threat to the occupant compartment from fragmented components. Moreover, significant displacement suggests an inability to effectively absorb collision energy through controlled plastic deformation, exacerbating vehicle deceleration overload. Therefore, lateral displacement variation serves as a crucial indicator for evaluating the scientific validity and rationality of guardrail design.

Figure 14 illustrates the lateral displacement variations in the two improved guardrail designs during the entire collision process. The lateral displacement of Design Scheme 1 is slightly higher than that of Design Scheme 2. In the early stage of the collision, since the primary contact surface between the small passenger car and the guardrail is the double-wave beam, which absorbs most of the energy, the lateral displacement curves of the two guardrail designs are highly consistent. After the lateral displacement reaches its maximum, the small car continues to exert lateral force on the guardrail due to inertia, causing the lateral displacement to gradually decrease. Owing to the higher strength of the C-type beam in Design Scheme 2, its lateral displacement is slightly lower than that of Design Scheme 1. After T = 0.4 s, the small car slides along the guardrail direction due to friction, and the lateral displacement of the guardrail remains almost unchanged.

5.2. Analysis of Medium Truck Crash

Figure 15 illustrates the complete trajectory of the truck during collision with the improved guardrail of Design Scheme 1. During the impact, the truck’s battery and right-side footpedal became entangled with the guardrail and detached. The vehicle’s front suspension sustained significant deformation, but no guardrail components or detached vehicle parts intruded into the occupant compartment. No rollover, yawing, or U-turn occurred. However, the guidance and exit process exhibited instability, with the vehicle experiencing a tailspin after passing the exit point.

During the collision between the truck and the improved guardrail of Design Scheme 2, the overall performance was relatively stable, as shown in the trajectory diagram in Figure 16. Throughout the impact, no vehicle components detached. There was no simultaneous lifting of the left front and left rear wheels, and no instances of the vehicle mounting or vaulting over the guardrail occurred. After disengaging from the guardrail, the vehicle maintained a stable exit attitude, and its wheel trajectory met the requirements of the guidance exit frame, demonstrating effective guidance performance.

The maximum dynamic vaulting value of a vehicle is a critical indicator for assessing the stability of large vehicles during collisions. Controlled attitude variations within normal limits indicate maintained driving stability, whereas excessive vaulting may lead to rollover or loss of control, significantly increasing accident severity. Figure 17 captures the moments when the maximum vaulting values occurred during the collision between the truck and the two guardrail designs. The maximum vaulting value generated by the collision with Design Scheme 1 was significantly greater than that with Design Scheme 2. Moreover, at the moment of maximum vaulting, a hazardous phenomenon occurred where both left-side wheels lifted off the ground simultaneously, explaining the tailspin observed after the truck disengaged from the guardrail. Due to the higher yield strength of the C-type beam used in Design Scheme 2, the lateral component of the inertial force when the truck’s rear impacted the guardrail was effectively suppressed, resulting in a more stable attitude at the moment of maximum vaulting during the collision with Design Scheme 2.

Figure 18 shows the maximum lateral displacement curves of the two guardrail designs. According to the curves, the maximum lateral displacement of Design Scheme 1 is slightly lower than that of Design Scheme 2. In the early stage of the collision, due to the high chassis of the truck, the wheels make initial contact with the corrugated beams, resulting in highly consistent curves for both designs. After the truck’s front end contacts the C-type beam, the curves begin to diverge. Due to the lower yield strength of the C-type beam in Design Scheme 1, the lateral displacement of the guardrail increases more rapidly. Subsequently, the inertia of the truck causes its rear to exert lateral force on the guardrail, leading to a further increase in lateral displacement. After reaching the peak, the lateral displacement gradually decreases as the vehicle’s kinetic energy diminishes, reducing the force applied to the guardrail, until it stabilizes after the vehicle disengages.

5.3. Analysis of Medium Bus Crash

Figure 19 shows the whole process of the bus overturning and riding across the guardrail of Option 1 modification: when T = 0.46 s, the right wheel of the bus climbs up to the waveform beam plate; when T = 0.86 s, the wheel of the bus climbs up to the C-type beam; when T = 1.48 s, the bus rides across the guardrail and travels; and when T = 1.88 s, the bus is hindered by the column and stops traveling. According to the collision picture and traveling track of the bus and guardrail, it can be seen that the column at the collision point was bent almost 90°, the waveform beam plate and the C-type beam were deformed seriously, and the guardrail could not provide enough blocking function and guiding effect, which made the bus appear the dangerous phenomenon of overtopping and riding across the guardrail.

The vehicle trajectory of the bus and the collision process of Scheme 2 modification guardrail is shown in Figure 20: the bus has a small part of the window falling off, there is no deformation of parts invading the internal space of the vehicle, there is no obvious deformation of the chassis, front and rear suspensions and frame of the bus, the whole vehicle can still maintain the normal driving attitude after driving away from the guardrail, the whole process does not appear to be riding across and over the guardrail, the whole vehicle is driven away from the guardrail and the guide out of the smooth attitude, the wheel track meets the requirements of guiding out of the frame, and the guide function is good. The wheel track meets the requirement of guiding out of the frame, and the guardrail guiding function is good.

Observing the lateral displacement curves of the two improved designs in Figure 21, it is evident that the lateral displacement of Design Scheme 1 is higher than that of Design Scheme 2 due to its inability to effectively contain the bus. Two significant surges in guardrail displacement occur as the vehicle climbs and crushes the guardrail twice. The maximum lateral displacement in Design Scheme 2 is 1.02 m. In the early stage of the collision, the impact between the bus front and the guardrail causes a rapid increase in displacement. Subsequently, sliding friction between the bus front and the guardrail reduces the displacement. Starting at 0.68 s, the collision between the bus rear and the guardrail leads to a renewed increase in displacement until the peak value is reached. At this point, the guiding function of the guardrail directs the vehicle to travel along its alignment, reducing the overall kinetic energy. Consequently, the guardrail displacement decreases and stabilizes after the vehicle disengages.

5.4. Analysis of Simulation Results

The processed data results for the two design schemes are summarized in the table below. The experimental data of the bus is no longer recorded because the bus has already overturned the guardrail during the collision with the guardrail of Scheme 1 and the guardrail has lost its protective effect. From the analysis of the experimental results in

Table 7. Simulation results for small passenger cars.

Measurement	Small Passenger Car
	Scheme 1	Scheme 2
Whether it passes through the guidance exit frame normally	yes	yes
Lateral acceleration at the center of gravity (m/s2)	132.36	93.08
Longitudinal acceleration at the center of gravity(m/s2)	139.89	124.56
Lateral occupant impact velocity(m/s)	5.08	2.15
Longitudinal occupant impact velocity(m/s)	9.44	7.79
Maximum lateral dynamic deformation of the guardrail (m)	0.627	0.62
Maximum lateral dynamic displacement extension of the guardrail (m)	0.913	0.869

, the transverse collision speed, longitudinal collision speed, and the center of gravity at the transverse and longitudinal acceleration of the small passenger car is smaller than that of the program one retrofit guardrail, which proves that the retrofit guardrail of the program two disperses the impact of the vehicle collision more efficiently, avoids the energy concentration feedback to the vehicle occupants, and reduces the damage of the collision to the occupants with a better buffer to absorb the effect of the energy; at the same time, the retrofit guardrail of the program two has a smaller dynamic deformation, so it is no longer recorded. At the same time, Scheme 2 modified guardrail has smaller dynamic deformation value and displacement value, indicating that the structural rigidity of the guardrail is moderate and the material selection is more reasonable. As can be seen from the truck test results recorded in

Table 8. Simulation results for medium truck and bus.

Measurement	Medium Truck		Medium Bus
	Scheme 1	Scheme 2	Scheme 1	Scheme 2
Whether it passes through the guidance exit frame normally	yes	yes	no	yes
Maximum lateral dynamic deformation of the guardrail (m)	1.246	1.285		1.019
Maximum lateral dynamic displacement extension of the guardrail (m)	1.325	1.367		1.162
Maximum dynamic vaulting of the vehicle (m)	2.103	1.642		1.412
Maximum dynamic vaulting equivalent of the vehicle (m)	2.498	1.788		1.446

, it can be seen that the maximum lateral displacement and deformation values of the guardrail of the two retrofitting schemes are very small, but the maximum dynamic tilt value and tilt equivalent value generated during the collision between the van and the Scheme 2 guardrail are much smaller than that of the Scheme 1 guardrail, which indicates that the Scheme 2 guardrail has a better tipping resistance for vans, which makes the van’s traveling attitude in the process of collision more stable. At the same time, Scheme II retrofit guardrail effectively blocked the impact of the bus, proving the reasonableness of using Q355 steel C-type beam. In summary, Scheme 2 was finally identified as the guardrail structural improvement program.

5.5. Analysis of Collision Between Small Passenger Cars and Class A W-Beam Guardrail

Following the same simulation procedure, the collision process between a passenger car and the original Class A triple-wave beam guardrail was simulated. The resulting d3plot file was imported into post-processing software to extract the motion posture of the vehicle throughout the entire collision process, as shown in Figure 22. From the initial stage of the collision, it can be observed that due to the passenger car’s front bumper height being lower than the lower edge of the wave beam, the front of the vehicle initially intrudes into the gap between the guardrail wave beam and the ground, forming a clear “underride” tendency. Subsequently, the front of the vehicle loses effective contact and guidance constraints from the guardrail, leading to a direct impact of the car front against the post, causing an abrupt change in structural force. During the collision process, the right front fender is strongly compressed by the wave beam, resulting in significant plastic deformation. The front end and right front wheel area exhibit noticeable crumpling, and the upper surface of the engine compartment sinks downward as a whole. After being compressed, the right front door experiences bending deformation, compromising the overall stiffness of the vehicle’s side structure. The vehicle’s posture then deviates, showing an obvious “rotational slip” phenomenon and losing normal driving stability.

From the damage state of the passenger car after the collision, the severe consequences of “underride” can be directly observed: the front bumper fails to make sufficient contact with the guardrail but instead intrudes into the lower space, resulting in a direct high-stiffness impact with the post. This causes the impact force to concentrate instantaneously during the collision, exacerbating the structural damage to the vehicle body. This phenomenon clearly reflects the safety hazards arising from the mismatch between the wave beam height and the passenger car’s bumper height, and explains why “underride” significantly increases vehicle damage and occupant injury risk.

Figure 23 shows the variation curves of acceleration and velocity at the vehicle’s center of mass during the collision between the small passenger car and the Class A W-beam guardrail. The data reveal that the lateral acceleration rapidly increases shortly after the collision occurs, peaking at approximately 25 g, which significantly exceeds the 20 g threshold specified in the standard. This indicates that the vehicle is subjected to substantial impact loads during lateral force application, with intense structural deformation and inertial force transmission. Simultaneously, the vehicle’s velocity in the X-direction decreases sharply within approximately 0.2 s. This combined response of “rapid velocity reduction and sharp lateral acceleration increase” reflects the failure to establish an effective cushioning process between the vehicle and the W-beam after “underride” occurs. Instead, the front of the vehicle directly impacts high-stiffness components such as the posts, significantly shortening the energy absorption path and concentrating collision loads on the vehicle structure. As a result, the overall rigid impact exceeds the energy absorption capacity of elastic deformation, not only exacerbating vehicle damage but also significantly increasing the risk of occupant injury. This demonstrates the pronounced influence of passenger car underride on collision force transmission mechanisms and vehicle dynamic responses, further highlighting the safety hazards of current guardrails for vehicles with low bumper heights.

5.6. Occupant Risk Assessment

To more accurately evaluate the impact of structural optimization on the vehicle collision process and occupant safety, and to align the study with the goal of quantifying traffic safety risks, this section further processes and analyzes the acceleration and velocity time histories obtained from the preceding collision simulations. In accordance with internationally recognized road safety evaluation standards such as EN 1317 and MASH, the Acceleration Severity Index (ASI), Theoretical Head Impact Velocity (THIV), and Post-impact Head Deceleration (PHD) are selected as representative indicators of occupant injury risk.

Specifically, ASI measures the overall impact on occupants caused by three-axis accelerations at the vehicle center of mass, THIV estimates the potential head impact velocity of occupants during the collision, and PHD reflects the hazard level of head deceleration during the secondary collision phase. Together, these three indicators characterize the severity of potential occupant injuries from different perspectives. Based on these indicators, calculations are performed for both the standard Class A three-wave W-beam guardrail and the final optimized structural Scheme II, and the results are compared. The computed results are summarized in

Table 9. Comparison of occupant risk assessment indicators.

Occupant Risk Assessment Indicators	Triple-Wave Beam Guardrail	Scheme 2
ASI	2.07	1.31
THIV	35.3 km/h	27.5 km/h
PHD	28.1 g	15.6 g

.

The comparison results in the table indicate that the structural optimization Scheme II significantly reduces occupant risk under passenger car collision conditions. First, the ASI value decreases from a “C-level” in the original structure to a “B-level,” indicating that the overall deceleration experienced by the vehicle during the collision is markedly reduced, improving the overall occupant load environment. Furthermore, both THIV and PHD fall within the safety ranges recommended by the standards, suggesting that energy transfer between the vehicle front and the guardrail is more gradual, the potential primary head impact velocity is lowered, and the peak head deceleration during the secondary rebound phase is effectively mitigated.

From the collision mechanism perspective, this improvement is primarily attributed to the combination of the double-wave beam and C-type beam in the optimized scheme, whose heights better match the front profile of small vehicles, preventing direct collisions with posts caused by underride. Consequently, collision energy is absorbed and dissipated along the beam through plastic deformation. Therefore, Scheme II not only enhances the guardrail’s guidance capability for the vehicle but also significantly reduces instantaneous acceleration impacts on the occupant’s head, contributing to a substantial reduction in injury probability.

5.7. Guardrail Manufacturing Cost Comparison

The cost calculation in this study was conducted as follows:

The steel consumption for each component (beam, anti-obstruction block, column) was calculated using

Steel Consumption = Component Volume × Material Density

Material costs were then calculated based on current market prices of commonly used engineering steels:

Material Cost = Steel Consumption × Steel Unit Price

A systematic comparison of key structural parameters between the final optimized design proposed in this study and the conventional triple-wave-beam guardrail is presented in

Table 10. Comparison of guardrail structural weight (kg/km).

Guardrail Structural Type	W-Beam	C-type Beam	Anti-obstruction Block	Column	Total
Scheme 2	12,290	7143.5	1426.5	7187	28,047
triple-wave beam guardrail	19,125		2233.3	8085	29,443.3

. The comparative data indicate that the newly designed guardrail structure significantly outperforms the triple-wave-beam guardrail in terms of total mass, with an average reduction of approximately 1.4 tons per kilometer for the combined components. This translates to a saving of about 10,000 RMB per kilometer in steel procurement costs. The design not only directly reduces raw material consumption but also indirectly lowers expenses related to transportation and other associated processes. While ensuring protective performance, it effectively enhances project economic efficiency.

6. Conclusions

This study addresses the safety hazard of “underride” frequently occurring in collisions between small passenger cars and current Class A triple W-beam guardrails. Through a systematic research approach integrating theoretical analysis, structural optimization design, and finite element simulation validation, a comprehensive structural improvement and safety assessment was conducted. The main research conclusions are as follows:

(1)

Comprehensive Results Based on Finite Element Simulation

To facilitate a quick understanding of the research findings,

Table 11. Comparison of simulation results.

Category of Indicators	triple-Wave Beam Guardrail	Scheme 2	Improvement Magnitude
ASI	2.07 (Class C)	1.31 (Class B)	Decreased by 36.7%
THIV	35.3 km/h	27.5 km/h	Decreased by 22.1%
PHD	28.1 g	15.6 g	Decreased by 44.5%
Key Structural Deformation/Guidance	Pronounced underride/Vehicle instability	Effectively suppresses underride/Vehicle stability
Weight per Kilometer (kg)	29,443.3	28,047	Decreased by about 1.4 tons
Material Cost per Kilometer (RMB)	117,772	107,690	Decreased by about 10,000 RMB

summarizes the key quantitative indicators for the triple W-beam guardrail and the structurally optimized guardrail (Scheme 2) under small passenger car collision conditions.

(2)

Through comprehensive analysis of small passenger car collision posture, bumper structural characteristics, and guardrail restraint mechanisms, this study systematically revealed the root cause of the “underride” phenomenon: the installation height of the front bumper on some small passenger cars is lower than the lower edge height of the wave beams in existing Class A triple W-beam guardrails, preventing effective initial contact between the vehicle and the beams and allowing intrusion beneath them. Based on this mechanism, this paper proposes a combined protective structure consisting of a double W-beam and a C-type beam. While maintaining the total guardrail height, the double W-beam installation height was adjusted to 560 mm, and a C-type beam with a central height of 850 mm was added, creating a more rational protective gradient. This design significantly reduces the probability of small passenger car underride.

(3)

The synergistic optimization of materials and structure significantly enhances the safety performance of the guardrail. A comparative analysis of two schemes using Q235 carbon steel and Q355 high-strength low-alloy steel was conducted based on finite element simulation. The simulation results demonstrate that the structurally optimized scheme employing Q355 steel exhibits superior safety performance. This scheme shows improved cushioning characteristics in small passenger car collisions and also demonstrates stronger impact resistance and blocking capability in medium truck and bus scenarios. Key evaluation metrics for all three tested vehicle types meet the requirements of the “Standard for Safety Performance Evaluation of Highway Barriers,” verifying the reliability of this structural scheme.

(4)

The structural and material optimization delivers substantial economic benefits. Compared to the existing triple W-beam guardrail, the proposed guardrail scheme achieves significant economic advantages while meeting protective performance requirements. The combined structure reduces mass by approximately 1.4 tons per kilometer, with material costs reduced by about 10,000 RMB per kilometer.

(5)

Quantitative risk assessment verifies that structural optimization significantly reduces occupant injury. Based on the accident severity evaluation systems of EN 1317 and MASH, this study calculated three occupant injury indicators: ASI, THIV, and PHD. The results indicate that when a small passenger car collides with the original Class A triple W-beam guardrail, all three indicators exceed the corresponding acceptable thresholds, suggesting a high risk of occupant injury. After implementing Scheme 2, the ASI value decreased by approximately 36.7%, THIV by approximately 22.1%, and PHD by approximately 44.5%. Among these, THIV and PHD met the safety ranges recommended by EN 1317 (THIV ≤ 33 km/h, PHD ≤ 20 g), and the ASI rating was reduced from Class C to Class B. This demonstrates that the guardrail structural scheme adopted in this study can more effectively distribute impact loads and improve energy absorption efficiency, significantly reducing the injury severity in roadside accidents.

(6)

The findings of this study provide important practical implications for the design of road safety facilities. On one hand, the research reveals that the key issue with guardrails is not the conventionally perceived lack of material strength, but rather the “geometric mismatch” between vehicle bumper height and guardrail beam height. Therefore, future guardrail design should place greater emphasis on the coordinated matching of structural height to effectively reduce the underride risk for small vehicles. On the other hand, the study confirms that replacing part of the Q235 steel with Q355 high-strength steel is a feasible approach to achieve guardrail lightweighting and enhance safety performance, reducing material usage and overall mass while ensuring protective capacity. Furthermore, the combined structure of double W-beams and a C-type beam demonstrates superior protective potential compared to traditional single W-beams in terms of guidance continuity, energy transfer stability, and vehicle posture control. Overall, the structural and material optimization strategies proposed in this study not only provide a reference for improving existing guardrail systems but also offer forward-looking technical foundations for the future revision of Chinese guardrail design standards, beam height optimization, promotion of high-strength steel applications in guardrails, and the development of lightweight guardrail technologies.

7. Discussion

While this study has achieved the aforementioned results, several issues warrant further in-depth investigation. Firstly, regarding structural stability, although the optimized scheme has made progress in material utilization efficiency and cost control, the use of high-strength Q355 steel with correspondingly reduced component thickness may pose potential durability concerns. Thin-gauge high-strength steel may exhibit weaker corrosion resistance compared to traditional thick-plate components under long-term service conditions, particularly in corrosive environments such as rain, snow, salt spray, deicing agents, or sea breeze. Furthermore, the reduced thickness of high-strength steel may adversely affect its fatigue resistance. Under cyclic vehicle loads, micro-vibrations, or minor vehicle impacts, the structure may be more susceptible to fatigue cracks or local buckling. These durability issues related to corrosion and fatigue have not been validated in this study. Future work should include systematic evaluations through accelerated corrosion tests, long-term fatigue tests, or service environment simulations to further ensure the structural safety throughout its entire lifecycle.

From an engineering application perspective, the construction techniques and quality control standards for the new guardrail require further refinement. The combined structure of double W-beams and a C-type beam is more complex than traditional guardrails, demanding higher precision in installation, component alignment, and connection stability. Inadequate quality control during construction could compromise the actual protective performance of the guardrail. Therefore, future work should investigate the sensitivity to construction tolerances under practical engineering conditions and establish more comprehensive construction guidelines and acceptance criteria.

In terms of production and cost, although this study achieved a certain degree of cost reduction through material optimization and localized component thickness adjustments, the optimization scope remains primarily focused on individual components such as beams and anti-obstruction block, leaving limited room for overall cost reduction. Future research could explore more economical and sustainable guardrail design solutions by innovating anti-obstruction block structures, optimizing post cross-sections, and further applying lightweight high-strength materials or weathering steels. Such efforts aim to achieve more significant lifecycle cost advantages without compromising crash protection performance.

In terms of production and cost, although this study achieved a certain degree of cost reduction through material optimization and localized component thickness adjustments, the optimization scope remains primarily focused on individual components such as beams and blocking blocks, leaving limited room for overall cost reduction. Future research could explore more economical and sustainable guardrail design solutions by innovating block structures, optimizing post cross-sections, and further applying lightweight high-strength materials or weathering steels. Such efforts aim to achieve more significant lifecycle cost advantages without compromising crash protection performance.