Driving Comfort Analysis Method of Highway Bridge Based on Human-Vehicle-Bridge Interaction

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Introduction
In recent years, there are many long-serving highway bridges subjected to adverse external factors such as weather conditions and vehicle overloading.Tese factors have resulted in a growing issue of road surface roughness, which signifcantly impairs the comfort of drivers.Terefore, assessing an individual's capacity to withstand vehicle vibrations and extending this evaluation to quantify the comfort of driving on bridges present a challenging task.Te study of bridge driving comfort is closely linked to the development of VBI theory and technology.British and French scholars conducted experiments on the Britannia Bridge model in the mid-19th century to study the load-bearing capacity and dynamic performance of bridges under moving loads.In the case of highway bridges, the excitation mechanisms for VBI are more intricate.With the rapid advancement of computers and numerical simulation technology, theoretical research related to VBI has made signifcant strides.Tis includes the study of bridge dynamic impact factors, bridge fatigue issues, and bridge structural damage identifcation.It also involves research into vibration control on highway bridges, driving comfort on bridges, and dynamic load identifcation of vehicles on bridges.
To accurately evaluate the driving comfort of highway bridges, it is crucial to consider factors such as road surface roughness, bridge and vehicle dynamics, and human sensory perception.
Scholars globally have conducted comprehensive experimental and theoretical studies on driving comfort, specifcally addressing the coupled vibration of the vehicle-bridge system.Tis approach provides a more thorough understanding of driving comfort issues.
In prior studies, bridge driving comfort has often relied on assessing the driver's tolerance to vehicle vibrations [1,2].Some scholars have streamlined the analysis by directly using the vehicle's vibration response.Tis method has a high computational efciency but a large error [3].Te processing of the vehicle's vibration acceleration results based on geometric relationships allows retroactive calculation of the driver position's vibration acceleration response.Tis method yields a higher calculation precision in assessing driving comfort [4].Moreover, scholars have extensively studied the factors afecting driving comfort, with a focus on two main aspects: the impact of external adverse loads and changes in the vehicle or driving parameters on driving comfort.Research literature shows that road surface roughness and wind loads are key external factors afecting the bridge's driving comfort [5].Furthermore, changes in parameters such as vehicle speed, weight, type, and trafc characteristics also signifcantly impact the bridge's driving comfort.With advancing research, there is a growing interest in investigating the intricate interactions between wind, trafc, and bridges concerning driving comfort [6].Nguyen et al. explored safety and comfort in slender arch bridges subjected to turbulence and vehicles [7].Research also delves into passenger comfort when vehicles traverse sea-crossing bridges in cold marine conditions with ice loads [8].Furthermore, alterations in bridge pier height infuence driving comfort to some extent [9].
Extensive research reveals the human body as a highly intricate and dynamic elastic system with vibrational characteristics infuenced by environmental factors, posture, and psychological elements, displaying notable individual variations [10].Furthermore, variations in vibrations exist between the driver and the vehicle body, a facet not adequately addressed by current driving comfort assessment standards [11].In recent years, scholars have delved into comprehensive research on interaction analysis models for passenger-vehicle-railway bridge systems [12,13].For example, Wang et al. simplifed passengers as a fve-degree-of-freedom spring-damping model, conducting a comparative analysis of passenger and train dynamic responses [14].Tey evaluated passenger comfort based on the ISO 2631 standard [15].Similarly, Yu et al. treated passengers as a single-degree-of-freedom system attached to the bottom of the train carriages, employing the Newmark-β method to analyze the time-domain numerical solution of the passenger-train-path vertical interaction model [16].In another study, Liu et al. developed an 8-degree-of-freedom human dynamic model and a 31-degree-of-freedom vehicle model.Tey explored the impact of vehicle speed, passenger count, and passenger positioning on human comfort levels [17].Tese studies indicate that future research focusing on the driver's human dynamic response in the context of bridge driving comfort is meaningful.
Te current research in the feld of highway bridgedriving comfort primarily relies on vehicle's vibration responses.However, it often overlooks the distinctions between human and vehicle responses, which could potentially afect the evaluation of driving comfort on these bridges.Tis paper introduces an enhanced analysis model for the interaction within the human-vehicle-bridge system, specifcally tailored to highway bridges.It also simulates road surface roughness, considering the diference in vehicle wheel paths.In addition, an evaluation method of highwaybridge driving comfort considering the vibration response of 3D space human-vehicle system and the diference in wheel path roughness is proposed.To validate this method, a threespan continuous SCCBB serves as the background.Tis study utilizes the proposed method for a comprehensive assessment of driving comfort for two-axle trucks and compares the results with traditional methods for evaluating driving comfort.In addition, the meanings of all abbreviations in the paper are shown in Table 1.

Theoretical Framework of the New Driving Comfort Evaluation Method
Te new method for analyzing driving comfort on highway bridges in this paper comprises three key components.First, it introduces an interaction analysis method for the human-vehicle-bridge system.Tis involves creating 3D fnite element models for the bridge, a spatial whole-vehicle model, and an elastic human body model to analyze the interaction relationships.Second, it considers the diference in road surface roughness between the left and right wheel paths of the vehicle during motion.Te paper proposes a method to simulate this roughness in wheel paths.Lastly, it presents a comprehensive method for evaluating the driving comfort by taking into account both the human and vehicle vibration responses.In summary, this new method uses HVBSI analysis to evaluate driving comfort on highway bridges, incorporates diferences in wheel path roughness, and considers both human and vehicle vibrations.

Human-Vehicle-Bridge Spatial Interaction Analysis
Method.Early bridge-vehicle interaction analyses often relied on 2D planar beam models due to their computational efciency and readily obtainable analytical solutions [18].However, real-world bridges and vehicles exist in a 3D space, resulting in complex interaction relationships between the 3D bridge, spatial vehicles, and the human body subsystems.Tis complexity often leads to convergence issues in fnite element analysis.To address this challenge, this section introduces an HVBSI analysis method based on ANSYS.Te method involves two computation domains: (1) for the bridge structure, solid and shell elements follow conventional meshing and (2) for the human-vehicle system, two parallel lines above the bridge deck depict its motion trajectory.Tis separation of the human-vehicle system mesh from the bridge structure reduces computational workload.Furthermore, updating the trajectory mesh during calculations does not require modifying the bridge structure's grid division, thus enhancing modeling efciency.

Shock and Vibration
In addition, this method requires defning two coordinate systems: (1) reference coordinate system (R) for the initial positions of human-vehicle system trajectory nodes and (2) moving coordinate system (M) for positions at the bridge contact points during movement.Figure 1 illustrates the human-vehicle-bridge interaction method with a two-axle vehicle traveling at a constant speed on the bridge roadway.To establish the reference coordinate system at the initial analysis moment, two infnitely stif plates are placed at both bridge ends, representing the pre-bridge and post-bridge ground.Teir length is L G , having no impact on results but accommodating the vehicle in the initial and fnal analysis stages.
Vectors X R and X M denote the positions of the humanvehicle system and bridge coupling nodes in the reference and moving coordinate systems.Te following equation illustrates the use of node grid displacement functions to determine the vehicle's position on the bridge during travel: where X is the vehicle's distance from the initial moment, X 1 R and X 2 R are the initial positions of the vehicle's front and rear wheels in the reference coordinate system, and X 1 M and X 2

M
represent the positions of the front and rear wheels in the moving coordinate system during travel.We defne the moment when the vehicle's front wheels are about to ascend the bridge as the initial moment (t � 0) as where L w is the distance between the front and rear wheels.Assuming that the vehicle travels at a constant speed v, then the position X t M of the vehicle in the moving coordinate system at time t is Te distance X t of the vehicle from the initial moment at any time can be determined by equations ( 1)- (3).Tis represents the constraint displacement along the vehicle's travel direction in each time step of the human-vehiclebridge method, as shown in the following equation: In ANSYS, the HVBSI method involves the following steps: (1) Establishing a 3D bridge model: the bridge model is established based on ANSYS, and the specifc modeling steps can be referred from reference [18] where Cons represents the constant term within the constraint equation, Conef (i) denotes the coefcient for the i-th node, U (i) signifes the i-th degree of freedom, and N stands for the total number of terms in the equation.(4) Achieving the HVBSI analysis.To achieve the HVBSI analysis, we applied diferent horizontal constraint displacements (Ux) of magnitude X t � X t M − X 0 R to the four vehicle-bridge coupling nodes in each load step (implemented via the D command based on known velocities).At the end of each load step, the constraints were reapplied to the human-vehicle system nodes as outlined in step (3).We coupled the four-axle nodes with the nodes moved to the bridge surface using vertical displacement (Uz) as per equation (5).We considered bridge surface roughness with samples defned by the Cons parameter in equation (5).Ten, we used a * do loop Human-vehicle-bridge interaction analysis method.

Vehicle-bridge coupling nodes
Ce command is used to establish the coupling constraint equation in ANSYS.

Human-vehicle coupling nodes
Vehicle-bridge coupling nodes Displacement coupling method   Shock and Vibration command to iterate through all load steps until X t � [L + L w , L], indicating the completion of calculations as the vehicle leaves the bridge.

A Simulation Method considering the Roughness Diference of Wheel Paths.
Road surface roughness plays a crucial role in afecting vehicle vibration response.While past studies extensively explored simulating roughness along the longitudinal axis of the bridge, coupling a spatial vehicle model with bridge analysis reveals noticeable diferences in roughness along the transverse wheel paths.
In Figure 3, roughness difers between paths I and II, afecting the fve wheels on path I simultaneously.In addition, at a specifc moment, wheel 3's roughness consistently matches those experienced by wheel 2 T w seconds earlier, with time gaps between roughness for each adjacent pair of wheels.Using 2D rod or beam elements in the bridge model overlooks these roughness diferences, potentially impacting coupled vehicle-bridge dynamic response results.Introducing an elastic human model in the vehicle for a human-vehicle-bridge interaction analysis may further amplify this impact, often neglected in prior research.
Te road surface roughness is treated as a zero-mean Gaussian random process, and the power spectral density of the road surface roughness can be expressed as follows: where G d (n 0 ) represents the bridge surface roughness coefcient, determined based on the bridge surface roughness levels defned in the "Vehicle vibration-Describing method for road surface roughness" GB/T7031-2005 [19].Diferent road surface roughness levels (R0, R1, and R2) are defned by using the parameter G d (n 0 ).Te parameter n 0 signifes the reference spatial frequency, typically set to 0.1 m −1 .Te frequency exponent, denoted as w, is commonly assigned a value of 2, and n represents the spatial frequency (m −1 ).Te samples of bridge surface roughness values are generated by using the triangular series method, as shown in the following equation: where r(x) represents the bridge surface roughness value at a specifc node along the bridge surface, with x denoting the distance from the starting point of the bridge, N represents the number of sampling points, L c is the length of the bridge surface considered for roughness, and θ k represents a set of independent random variables following a uniform distribution in the range of [0, 2π].Te meanings of other parameters are consistent with those in equation (6).
Te method for simulating road surface roughness while considering diferences in wheel paths is implemented based on the HVBSI method and involves the following steps: (1) Using the power spectral density of road surface roughness and the trigonometric series method stochastically, we generated two sets of roughness samples.Te length of these samples should match the number of fnite element nodes along the bridge surface corresponding to the vehicle's path.(2) Ten, the roughness sample values were stored as TXT fles in the ANSYS working directory.(3) Te time required for an element length (T n ) was determined by the ratio of the longitudinal distance between every two bridge nodes (L n ) to the vehicle speed (v), as shown in equations ( 8) and ( 9).Tis, in turn, established the wheelbase time gap (T w ) based on the distance between adjacent vehicle axles.
where i denotes the axle number.For example, for a two-axle vehicle, i equals 2, and so forth.(4) We then used the * Create and * Vread commands to access the two sets of roughness data, as shown in equation (10).At the end of each time step, the roughness sample values were determined for each wheel at the next moment T based on the wheelbase time gap.Finally, these roughness values were substituted into the coupling constraint equations at points where the vehicle's wheels connected with the bridge surface (refer to step 4 in the previous section).where R L and R R are the roughness samples for the left and right sides of the vehicle's paths.T represents a specifc moment during the vehicle's travel.R i L(R) is the index of roughness samples for each wheel at time T, where L and R indicate the left and right sides of the vehicle, and i is the axle number.r i L (T) represents the roughness value for the i-th wheel on the left side of the vehicle at time T.
(5) Finally, HVBSI analysis was performed till all time steps were completed.Ten, we moved to the POST26 postprocessing module to extract dynamic response results, considering the diferences in path roughness.

New Method for Evaluating Driving Comfort.
In this section, a method for assessing the driving comfort of vehicle drivers is proposed, considering the dynamic response of the backrest, seat, vehicle foor, and the driver body's center of mass.Tis method difers from traditional driving comfort evaluations by considering both the driver and vehicle vibrations and accounting for the roughness diference of wheel paths.Te traditional method only focuses on vehicle vibration and does not address the roughness diference of wheel paths.Te ISO 2631 standard specifes that 12 vibration components sufciently represent the vibration exposure for a seated driver, as illustrated in Figure 4. Previous studies have indicated that the impact of vibration in the vehicle's longitudinal, lateral, and yawn directions on human comfort can generally be neglected [20][21][22].Terefore, when transferred to the driver, only fve directions of vibrations are typically considered: vertical vibration of the vehicle foor (z f ), vertical vibration of the backrest (z b ), vertical vibration (z s ), pitch vibration (r y ), and roll vibration (r x ) for the seat.Tese fve types of vibration are fundamentally derived from vehicle vibration accelerations (see equations (13a)-(13c)).
To account for the diferences between human and vehicle vibration responses, this method considers vertical vibration at the driver body's center of mass (z h ) in addition to the fve vibrations associated with the vehicle.Te vertical vibration response of the human body can be extracted directly by using the HVBSI method.
where a ij is the acceleration time histories in various directions for the driver, where i and j have the meanings as explained in the frst paragraph of this section.Furthermore, a z , r y , and r x denote the vertical, pitch, and roll vibration accelerations of the vehicle's center of mass.d s , y s , and h s , respectively, denote the longitudinal, lateral, and vertical distances between the vehicle's center of mass and the seat.
Considering the variations in a driver's sensitivity to vibration direction and frequency, the ISO 2631 standard introduces frequency weighting functions for diferent vibration directions.Tese weighting functions adjust the vibration acceleration for various directions to simulate the impact of vibrations at diferent frequencies on driver comfort (see Figure 4).Given that, a driver primarily experiences vertical vibrations through direct contact with the seat support surface during vehicle operation.Tis method assumes that the frequency weighting function for vertical vibration at the driver body's center of mass (z h ) is calculated based on W k .
Te frequency-weighted acceleration in all directions is calculated by using the fast Fourier transform (FFT) method.Initially, there is a time-varying acceleration time-history signal, denoted as a(t).It undergoes discrete Fourier transform (DFT) to convert the time-domain acceleration time-history signal a(t) into the frequency domain (consisting of N discrete values, a(t) � a(i), where i � 1, 2, 3, . .., N).Tis transformation reveals the distribution of the original acceleration time-history signal a(t) at various frequencies, as shown in the following equation: After DFT transformation, A(r) becomes a set of complex conjugate numbers.Frequency weighting is applied to N/2 data points in A(r) containing relevant information.Tis involves multiplying A(r) by the frequency weighting function W(r) for both real and imaginary parts, thus resulting in the frequency-weighted acceleration frequency domain data A ′ (r), as shown in equation (15).Finally, DFT converts A ′ (r) back into the time-domain acceleration signal a ′ (t), as shown in the following equation: Te calculation of comfort levels relies on the method of HVBSI analysis, which involves the following fve main steps: (1) Te HVBSI method is employed to compute the vibration acceleration in diferent directions at the vehicle's center of mass, as well as the VVA of the driver's body.In this process, the infuence of the roughness diference of the wheel path is considered.Following this, the vibration accelerations of the vehicle's seats, backrest, and foor are derived by using equation ( 13).( 2 where T is the total duration of the vibration acceleration time path a′ ij (t).(4) Te ISO 2631 standard specifes axis weighting factors for vibrations in various directions, as shown in Table 2.By applying axis weighting factors, the RMS ij values of various types of vibration accelerations are weighted and summed to obtain the OVTV, as shown in equation (18).We then calculate the L eq based on the OVTV, as shown in the following equation: where the meaning of the subscript i and j is the same as that of the equation (13).K ij denotes the axis weighting factors and a 0 is the RMS value of the reference acceleration, that is, a 0 � 10 −6 m/s 2 .Noteworthily, ISO 2631 does not provide clear guidelines for axis weighting factors in vertical vibrations at the driver's body's center of mass.Consequently, the author approaches the determination of these factors from two perspectives: (1) assuming that both the seat and the driver's body's vertical vibration responses consistently contribute to the overall human-vehicle system dynamics in theory and (2) in the human-vehicle system, the driver's body's vertical vibration response is caused by the vehicle seat's vertical vibration.Tere is a transmission relationship between them.Based on the analysis, the paper aligns the axis weighting factors for vertical vibrations at the driver's body's center of mass with those of the seat, as shown in Table 2. (5) ISO 2631 standard classifes comfort levels based on the relationship between human subjective feelings and the OVTV.It also considers the L eq .Tese classifcations are detailed in Table 3, and the relevant parameters are derived from experiments on human vibration comfort [23].
Te technical route of the new driving comfort analysis method is shown in Figure 5.

Case Analysis
3.1.Bridge Profle.Tis study focuses on a three-span continuous SCCBB.Te bridge has a span of 3 × 40 meters and a width of 12.75 meters.It is designed for highway class I loading, with a single lane in each direction and a design speed of 100 km/h.Structural parameters can be found in [24].Te fnite element model is built using ANSYS APDL commands, with reference to the element types illustrated in Figure 6.Te bridge model includes a total of 90,920 nodes and 66,610 elements.

Human-Vehicle System.
Studies show that vehicle weight signifcantly infuences driving comfort, with lighter vehicles leading to higher RMS values of weighted vibration acceleration and increased discomfort.To account for the most unfavorable impact while managing the complexity

Shock and Vibration
introduced by incorporating a human model into the system, a lightweight two-axle truck is chosen for the study (see Table 4 for vehicle and human parameter values).Te fnite element model of the human-vehicle system has been detailed in the frst section of the paper.It will not be reiterated here.

Scenario Setting.
Te study in this paper focuses on the following key areas: (1) assessing the efectiveness of the HVBSI analysis method, (2) highlighting the necessity of simulating road surface roughness considering wheel path diferences, and (3) comparing the newly proposed method for evaluating driving comfort in this paper with the traditional comfort evaluation methods.Te specifc scenarios are as follows: (1) For the frst key area, two scenarios are considered: single-vehicle crossing and human-vehicle system crossing (without considering the wheel path roughness diferences).Each scenario is tested at four diferent speeds: 40 km/h, 60 km/h, 80 km/h, and 100 km/h.
(2) For the second key area, two scenarios are considered: human-vehicle system crossing with wheel path roughness diferences and human-vehicle system crossing without wheel path roughness diferences.Each scenario is tested at four diferent speeds: 40 km/h, 60 km/h, 80 km/h, and 100 km/h.Tree levels of road surface roughness are also taken into account: no roughness (R0), low-level roughness (R1), and high-level roughness (R2).R1′ and R2′  (3) For the third key area, two analysis methods are considered: the newly proposed method for evaluating driving comfort and the traditional driving comfort evaluation methods.Both methods are applied to human-vehicle system crossing scenarios considering wheel path roughness diferences.Each method is tested at four diferent speeds and three levels of road surface roughness, which is consistent with the scenarios in the second key area.
Te technical route is depicted in Figure 7. Previous research has shown that vehicle weight is one of the signifcant factors afecting vehicle comfort.Smaller vehicle weight leads to higher RMS values of weighted vibration acceleration and greater discomfort [3].To consider the most adverse efects, this study focuses on a lightweight two-axle truck as the research subject.Specifc details and parameters of this vehicle can be found in reference [4].Prior studies show that BVVD time curves at the midpoint of midspan often display a U-shaped pattern in traditional VBI analysis.Practically, if vehicle type, speed, and road roughness remain consistent, the vibration response in the midpoint of the bridge's span should be almost the same for both a single-vehicle model and a humanvehicle model crossing it.Based on the abovementioned analysis, the following section conducts a study using the scenarios set in the frst key area (refer to the previous section).
By observing Figure 8, it becomes clear that the trends in the BVVD time-history curves obtained through HVBSI and VBI methods closely align and demonstrate good agreement.However, the BVVA values obtained using the HVBSI method are marginally higher than those obtained from the VBI method, and this variance can be attributed to the transmission characteristics of the elastic human body model.Nevertheless, when viewed from a broader perspective, the trends in the midpoint BVVA time-history curves from both methods consistently agree.
To avoid relying solely on a single speed calculation result, additional analysis was carried out for scenarios involving speeds of 60 km/h, 80 km/h, and 100 km/h.Figures 9(a       Shock and Vibration methods across various speed scenarios.Figure 9 clearly shows that, when the speed is consistent, the peak BVVD values obtained using both methods are almost identical.In addition, the diferences in the RMS of BVVA are minimal.Furthermore, Table 5 provides the relative errors in peak BVVD and RMS of BVVA obtained through the HVBSI and VBI methods.For each speed scenario, the relative error in peak BVVD calculated by both methods is under 4%, while the relative error in the RMS of BVVA is less than 9%.Tus, by integrating an elastic human body model into the VBI method, the HVBSI calculation program performs efectively.Furthermore, the vertical vibration response results of the bridge, obtained through both HVBSI and VBI methods, demonstrate a high degree of agreement.Tis confrms the viability of the HVBSI method presented in this paper and supports its suitability for future analyses.

Infuence Analysis of Wheel Path Roughness Diference.
At 40 km/h, Figure 10 illustrates vehicle vibration acceleration time histories, comparing scenarios with and without wheel path roughness diferences.In Figure 10(a), VVA and PVA time-history curves show similar trends and close acceleration amplitudes under R1 roughness, regardless of these diferences.However, considering wheel path roughness diferences results in a notable change in the RVA time history, displaying a signifcant increase in amplitude compared to the scenario without these diferences.Similar observations apply to R2 roughness, as depicted in Figure 10(b).
In Figure 11, the VVA peaks and PVA peaks of the vehicle show no signifcant variation under diferent speeds, regardless of wheel path roughness diferences.However, when considering these diferences, RVA peaks experience a substantial increase.In addition, the consideration of wheel path roughness diferences results in a maximum percentage change of 23.2% in VVA peaks and 20.6% in PVA peaks, as indicated in Table 5.
From Table 6 and Figure 11(c), it is evident that with constant road roughness and vehicle speed, the increase in RVA, when considering path roughness diference, far surpasses PVA and VVA.Tis efect is more pronounced with road roughness R2 compared to R1. Poorer road conditions amplify the impact of considering path roughness diferences on RVA.At a speed of 100 km/h and road roughness R2, RVA exhibits the maximum increase at 12583.0%, while corresponding increases for VVA and PVA are only 2.8% and 11.4%, respectively.Tis phenomenon highlights the substantial impact of wheel path roughness diferences on the vehicle's roll vibration.
Figure 12 illustrates that considering wheel track unevenness diferences leads to increased RMS values for VVA, PVA, and RVA.Notably, VVA and PVA experience modest maximum increases of 17.24% and 21.96%, respectively.Conversely, RVA is signifcantly impacted by wheel track unevenness diferences, with a staggering maximum increase of 22,839.22%.Upon further calculation of OVTV and L eq values, it becomes evident that, with constant road roughness class and speed, OVTV values considering wheel track unevenness diferences surpass those without such considerations.Similarly, L eq values exhibit a comparable pattern, as shown in Figure 13.
Tus, considering wheel path roughness diferences results in slightly increased vertical and pitch vibration responses of the vehicle, but the impact is relatively small.However, it signifcantly afects roll vibration response.Shock and Vibration judge a driver's comfort, as outlined in reference [22].Te previous section of the paper demonstrates the signifcant impact of considering wheel path roughness diferences on vehicle RVA.To account for this infuence, all subsequent driving comfort analyses consider wheel path roughness diferences.

Comparative Analysis of Driving Comfort Evaluation Methods. Traditional methods for assessing driving comfort primarily rely on evaluating vehicle's vibration responses to
We compared and analyzed OVTV and L eq values obtained from both the traditional and new methods, as shown in Figures 14 and 15.OVTV′ and L ′ eq represent the results obtained by using the new method.From Figure 14, it is evident that, regardless of the road surface roughness level, both the traditional and new methods yield   12 Shock and Vibration

Shock and Vibration 13
increasing OVTV values with higher vehicle speeds.Notably, OVTV′ values obtained using the new method consistently exceed those obtained using the traditional method.A similar pattern is observed in the results of L eq values.For Table 7, it is observed that for a road surface roughness level of R0, the new method yields OVTV′ values (L ′ eq values) with a maximum increase of 109.04% (6.74%) compared to the OVTV values (L eq values) obtained through the traditional method.For a road surface roughness level of R1, the maximum increases are 104.32% and 5.97%, respectively.Under R2 surface roughness conditions, these maximum increases are 91.04% and 4.87%, respectively.Te maximum values of these increases are shown in bold in Table 7.
Figure 15 shows that at a constant vehicle speed, both methods produce higher OVTV and L eq values as the road surface roughness level increases.Similarly, with constant vehicle speed and road surface roughness level, the OVTV′ and L ′ eq values obtained using the new method consistently surpass the results obtained through the traditional method (OVTV and L eq ).Te impact of road surface roughness on comfort indices is outlined in Table 8.Table 8 demonstrates that at a speed of 40 km/h, under the infuence of three diferent road surface roughness levels, the maximum increase in OVTV′ values relative to OVTV values is 108.40%.Likewise, the maximum increase for L ′ eq values relative to L eq values is 6.74%.When the vehicle speeds are 60 km/h, 80 km/h, and 100 km/h, the maximum increases for OVTV′ values relative to OVTV values are 108.79%,108.84%, and 109.04%,respectively.In addition, for L ′ eq values relative to L eq values, the maximum increases are 6.54%, 6.40%, and 6.31%, respectively.Te maximum values of these increases are shown in bold in Table 8.
Based on both the traditional method (Med1) and the new method (Med2), further analysis was conducted to determine the driving comfort grades under three road surface roughness levels and four vehicle speeds, as shown in Figure 16. Figure 16 reveals that, when not considering road surface roughness (R0), both the traditional and new methods yield a driving comfort level of grade I (not uncomfortable).However, for road surface roughness level R1, at vehicle speeds of 40 km/h and 60 km/h, both methods produce identical grade I (not uncomfortable) driving comfort levels.As the vehicle speed increases to 80 km/h and 100 km/h, the new method results in grade II (slightly uncomfortable), while the traditional method maintains grade I (not uncomfortable) driving comfort levels.
Te modifed content is as follows: When the road surface roughness level is R2 and is calculated using the traditional method, the resulting driving comfort levels for four diferent vehicle speeds are grade III, grade III, grade III, and grade IV, respectively.Conversely, the new method calculates higher driving comfort levels, specifcally grade IV, grade IV, grade V, and grade V for the respective vehicle speeds.In particular, a higher grade indicates a lower level of comfort.
Tus, when analyzing driving comfort using the newly proposed method (which includes the driver's body's vibration response), OVTV and L eq show an increase compared to the traditional methods that solely consider vehicle vibration response.When speed and road surface roughness levels remain constant, the driving comfort levels obtained using the new method are consistently equal to or greater than those obtained through the traditional method.Tis suggests that the traditional method tends to be conservative in assessing driving comfort.Taking the driver's body's vibration response into account results in a deterioration of driving comfort.Tis illustrates the necessity of considering both the driver's vibration response and the vehicle's vibration response when evaluating ride comfort comprehensively.

Conclusions
Te paper introduces a new method for analyzing the driving comfort of highway bridges.Tis method comprehensively considers both the driver and vehicle vibrations and accounts for the roughness diference of wheel paths.By using a three-span continuous SCCBB as a case, the efectiveness and necessity of this method are compared and verifed.Te key fndings are as follows: (

4
At the same time, each wheel experienced different values of roughness.Path I Path II There are differences in the roughness of the two sides of the wheel track.

Figure 4 :
Figure 4: Frequency weighting function and the driver seated coordinate system.

3. 4 .
Verifcation of the HVBSI Analytical Method.VBI analysis with fnite element methods is well-established.However, when incorporating an elastic human body model into a spatial vehicle model, it is crucial to confrm the functionality of the HVBSI analysis program.Tis involves verifying result convergence and alignment with typical expectations.
) and 9(b) illustrate the peak of BVVD and the RMS of BVVA, calculated using both the HVBSI and VBI

Figure 8 :
Figure 8: Comparison of vertical vibration response in the midpoint of side (mid) span.(a) Vertical vibration displacement.(b) Vertical vibration acceleration.

Figure 9 :
Figure 9: Comparison of vertical vibration response in the midpoint of side (mid) span of HVBSI and VBI.(a) Te peak of vertical vibration displacement.(b) Te RMS of vertical vibration acceleration.

Figure 11 :
Figure 11: Te peak value of vehicle's vibration acceleration without the wheel path roughness diference.(a) Te peak value of VVA.(b) Te peak value of PVA.(c) Te peak value of RVA.

Figure 12 :
Figure 12: Te RMS value of the vehicle body's vibration acceleration changes.(a) Te RMS value of vehicle VVA.(b) Te RMS value of vehicle PVA.(c) Te RMS value of vehicle RVA.

Figure 16 :
Figure 16: Comparison of driving comfort levels.

Table 1 :
Te meaning of abbreviations used in the paper.

Table 2 :
Axis weighting factors of vibration component.

Table 3 :
Comfort evaluation criteria based on OVTV and L eq .

Table 4 :
Mechanical parameters of the human-vehicle system.

Table 5 :
Comparison of bridge vibration response relative error.

Table 6 :
Te percentage change of peak acceleration of vehicle's vibration without the wheel path roughness diference.

Table 7 :
Comfort index increase under the infuence of vehicle speed.Te maximum values of these increases are shown in bold.

Table 8 :
Comfort index increase under the infuence of bridge surface roughness.
Te maximum values of these increases are shown in bold.
1) Te HVBSI method directly captures the driver's vertical dynamic response, showing good agreement with the VBI method.Te relative errors for peak values of VVD obtained through both methods consistently remain below 4%.Furthermore, the relative errors for the RMS values of VVA in the midpoint of the span are consistently below 9%.Tis afrms the reliability of employing the HVBSI Diferences in wheel path roughness have minimal impact on vertical and pitch vibrations but signifcantly afect roll acceleration.Considering these roughness diferences, RVA experiences a substantial increase of 12583.0%,with a signifcant rise in RMS value by 22839.22%.In contrast, the maximum increases in VVA and PVA are below 24%.Comfort indicators such as OVTV and L eq show a noticeable increase, emphasizing the nonnegligible impact of wheel path roughness diferences on driving comfort.(3)Considering the driver's vertical vibration response, the driving comfort deteriorates compared to only considering the vehicle's dynamic response.Comfort indicators such as OVTV and L eq show increased results compared to traditional methods, with maximum increments of 109.04% and 6.74%, respectively.Tis suggests that the traditional methods for bridge driving comfort evaluation may be somewhat conservative and highlight the necessity of comprehensively considering both the driver's body' dynamic response and the vehicle's dynamic response in driving comfort analysis.(4) Te mass-spring-damper-based elastic human body model lacks the ability to capture multidirectional vibrations directly.Current methods for simulating road surface roughness may underestimate the vehicle's roll vibration response.Further research is needed to develop comprehensive numerical simulation methods considering both the depth and width of road surface roughness, contributing to enhancing the highway bridge-driving comfort evaluation framework.