Effects of wind barrier on the safety of vehicles driven on bridges

J. Wind Eng. Ind. Aerodyn. 143 (2015) 113–127

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Journal of Wind Engineering and Industrial Aerodynamics journal homepage: www.elsevier.com/locate/jweia

Effects of wind barrier on the safety of vehicles driven on bridges Ning Chen, Yongle Li n, Bin Wang, Yang Su, Huoyue Xiang Department of Bridge Engineering, Southwest Jiaotong University, 610031 Chengdu, Sichuan, PR China

art ic l e i nf o

a b s t r a c t

Article history: Received 5 October 2014 Received in revised form 26 April 2015 Accepted 26 April 2015 Available online 11 June 2015

The evaluation of the sheltering efficiency of wind barriers is directly related to the safety of vehicles under crosswind. A series of work has been carried out in order to optimize the wind barrier scheme. Firstly, based on a large scale section model of bridge in the wind tunnel, the aerodynamic coefficients of two types of high-sided road vehicles, located on bridge deck, are obtained as different wind barriers installed on the bridge. Then the expressions of the aerodynamic forces on road vehicles are deduced based on the quasi-steady theory after considering the effects of turbulent wind on the yaw angle. Taking the natural wind, vehicle and bridge as an interaction system, a three-dimensional analytic model for the wind–vehicle–bridge coupling vibration system is presented. And the judging criterias for the vehicle safety are proposed according to the dynamic response of the vehicles. Based on the analytical model and the safety criteria, the sheltering efficiency of the wind barriers affecting the safety of vehicles driven on bridge has been finally investigated. The results show that the wind barriers have dramatically improved the driving stability of vehicles. Therefore, it can be recommended to adopt wind barriers according to their sheltering efficiency. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Wind barrier Wind tunnel Crosswind Aerodynamic coefficient Wind–vehicle–bridge system

1. Introduction The effects of crosswind on the ground vehicle have received increasing concerns in terms of traffic safety. And high-sided road vehicles are prone to suffer from wind-induced accidents at exposed locations (e.g. coastal and oversea bridge, viaduct and open road) according to a post-disaster investigation of windinduced traffic accidents (Baker and Reynolds, 1992). On August 11, 2004, seven high-sided road vehicles were overturned by high wind when they were driven on the Humen suspension bridge in China just before a strong typhoon (Zhu et al., 2012). To ensure the vehicle safety, it is necessary to assess the risk of vehicle accidents due to strong crosswind, which is a complex and multidisciplinary task involving the stochastic characteristic of wind process, aerodynamic actions of crosswind and the dynamic model of vehicle. Baker (1987) established the analytic model of vehicle under crosswind and investigated the critical wind speed for vehicle safety based on wind tunnel tests. Snæbjornsson et al. (2007) introduced a response hyper-surface in the space of basic variables into the limit state function of vehicle performance and quantified the risk of safety by safety index. Chen and Chen (2011) n

Corresponding author. Tel.: þ 86 28 87601119. E-mail addresses: [email protected] (N. Chen), [email protected] (Y. Li), [email protected] (B. Wang), [email protected] (Y. Su), [email protected] (H. Xiang). http://dx.doi.org/10.1016/j.jweia.2015.04.021 0167-6105/& 2015 Elsevier Ltd. All rights reserved.

adopted the response surface method to provide an efficient estimation of accident risks. Chen and Chen (2010) developed a single-vehicle accident assessment model and introduced new critical variables in assessing the accident risks under comprehensive hazardous driving conditions. The above research only focused on the accidents risks of vehicles without considering the effects of wind barriers. Without the aid of wind barrier, it has to frequently close the traffic or bridge in strong wind or typhoon days, which brought out great inconvenience due to the inefficient traffic. It has been recognized that wind barriers, including trees, shrubs and perforated plates, have been widely used in environmental protection (Cornelis and Gabriels, 2005), to protect people and their property from the effects of harsh climate. Recently, wind barriers have been introduced into bridge engineering to reduce the effects of crosswind on the trains (Imai et al., 2002) or road vehicles (Coleman and Baker, 1992). Kwon et al., (2011) investigated the design criteria required for wind barriers to protect vehicles driven on an expressway under a high crosswind. Considering the sudden change of the aerodynamic forces on road vehicles, Charuvisit et al. (2004) analyzed the aerodynamic coefficients of vehicles in the wind tunnel test under the conditions of considering or neglecting the wind barriers as vehicles approach the bridge towers. Kozmar et al. (2012) paid great attention to the mean velocity field and turbulence structure behind the wind barrier on the bridge and concluded that wind barrier greatly reduced the mean velocity of the incoming wind. Further,

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N. Chen et al. / J. Wind Eng. Ind. Aerodyn. 143 (2015) 113–127

Chu et al. (2013) analyzed the influence of wind barriers on the aerodynamic coefficients of vehicles. The sheltering efficiency of wind barriers is affected by many factors, such as height, ventilation rate and barrier types. The wind barriers in actual bridges should be adopted according to the safety of vehicle crossing the bridge. The evaluation of the sheltering efficiency of wind barriers, depending on the aerodynamic coefficients of vehicles (Argentini et al., 2011; Charuvisit et al., 2004; Chu et al., 2013) and the flow field above bridge deck (Kozmar et al., 2012), is still far from perfect. In the present study, the aerodynamic coefficients of high-sided vehicles (commercial van and articulated lorry) are firstly obtained by a large scale section model in the wind tunnel. The wind tunnel test is devoted to investigate the influence of bridge scenario with different wind barriers on the aerodynamic coefficients of high-sided road vehicle. Moreover, new expressions of aerodynamic forces acting on road vehicles have been deduced considering the influence of turbulent wind on the yaw angle. Then the aerodynamic force on vehicle is available based on the wind tunnel results and the expressions of the aerodynamic force. Taking the natural wind, road vehicle and bridge as an interaction system, the framework of the wind–vehicle–bridge interaction system is established. Finally, the effects of wind barrier parameters on the dynamic behavior of vehicles are especially investigated.

2. Wind tunnel experiments The purpose of the wind tunnel test is to provide analytical parameters for the coupling analysis of the wind–vehicle–bridge

system. Due to the lack of the aerodynamic coefficients of specific road vehicles, approximate aerodynamic coefficients have been adopted in the previous studies (Cai and Chen, 2004; Guo and Xu, 2006). Considering the effects of wind barriers with various ventilation ratios on the aerodynamic coefficients, it is necessary to investigate the aerodynamic coefficients of vehicles by means of wind tunnel test. The experiments are carried out in the wind tunnel (XNJD-3) at Southwest Jiaotong University. It is a closed circuit facility and comprises of a boundary test section that is 36 m long, 22.5 m wide and 4.5 m high. The wind speed can be adjusted from 0.5 to 16.5 m/s. 2.1. Models of vehicle, bridge and wind barrier High-sided vehicles are vulnerable to crosswind because of their relatively large side areas. Two types of chinese high-sided vehicle models are examined: a commercial van and an articulated lorry. The geometric scales of the two vehicles are set as 1:20. The details and dimensions of the vehicles are given in Fig. 1. The bridge deck is composed of two parallel concrete flat box girders and carries a dual three-lane carriageway, as shown in Fig. 2. The dimension of the cross section of the deck is 35.5 m in width and 3.0 m in height. The six lanes are identified as Lane 1–6 (from the windward side to the leeward side). The same scale (1:20) is adopted for the bridge deck model. Besides, a pair of pipes and hand rail, and two sets of safety fence are installed on the deck model to reflect the real environment of the deck because of their significant influence on the aerodynamic forces of vehicles. According to the principle of the equivalent ventilation rate, the

Fig. 1. Vehicle geometrical sizes in full scale (a) commercial van (b) articulated lorry (unit: m).

Fig. 2. Cross section of bridge deck (unit: mm).

N. Chen et al. / J. Wind Eng. Ind. Aerodyn. 143 (2015) 113–127

real hand rail is simplified as a rectangular structure while other parts are modeled in the light of geometrical similarity. Three types of wind barrier are investigated in the wind tunnel tests (see Fig. 3). One is made of a perforated aluminum alloy plate with 3 mm thickness and approximately 25% ventilation ratio. The other two, shaped like bars, are made of high stiffness plastic with 2 mm thickness and approximately 41% and 50% ventilation ratios. Wind barriers are installed above the safety fences. The wind barriers are solidly fixed on the rods spaced with intervals along the bridge deck as shown in Fig. 4, to prevent the deformation and vibration of the wind barriers. The wind barriers and the safety fences are combined as a whole to prevent the vehicles from the crosswind. The height of the wind barriers above the fence is 100 mm and the height of the fence is given as 72 mm, then the total height of the combined structure is 172 mm. 2.2. Measurement settings The deck model was installed on a steel support located in the center of the wind tunnel at 1.2 m above the tunnel floor. The steel support provided enough stiffness in the horizontal and vertical directions to ensure the measurement accuracy of the aerodynamic forces on the vehicle models. To reduce the effects of the boundary on the wind velocity, two sets of side fairing are adopted for the steel support, mounted in the front and the back of the steel support respectively. The vehicle models are mounted on the

115

perceiving end of a six-component force balance by using a Z-shape link, which is made of steel bar. The other end of the balance is fixed on the centerline of one lane on the bridge deck (see Fig. 4). 1–2 mm gap is left between the vehicle wheels and the upper surface of the deck to prevent the vehicle wheels from contacting the deck surface. Considering the unfavorable status of traffic flow (Zhang et al., 2001), three identical vehicles with a spacing of 0.5 m (10 m in full scale) (Xu and Guo, 2004) are arranged in a single traffic lane. The test vehicle is positioned in the middle of the bridge. The free-stream wind speed Vw is 10 m/s. In order to obtain the mean aerodynamic coefficients of road vehicles, the sampling time and the sampling frequency are set as 120 s and 142 Hz respectively. Besides, the sampling frequency is high enough to record the fluctuating signal of the aerodynamic forces acting on the vehicles located on bridge. The full-scale Reynolds number, with respect to the vehicle height for the commercial van and articulated lorry, varies from 2.3  106 to 6.5  106 in the normal operation under crosswind varying from 10 m/s to 25 m/s. In the wind tunnel test, the Reynolds numbers of the scaled road vehicle are 1.15  105 and 1.29  105 for the commercial van and articulated lorry, respectively. Although Reynolds number has certain influence on the aerodynamic coefficients of vehicles, especially at large yaw angles, the wind tunnel test is inevitably constrained by the experimental conditions (Dorigatti et al., 2012). In the previous wind tunnel tests, Reynolds numbers (Baker, 1991; Zhu et al., 2012) with lower values of 0.88  105 and

Fig. 3. Configurations and dimensions of wind barriers and protection rail models (unit: mm).

Fig. 4. Vehicle models in the wind tunnel.

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¯ i is the mean value of the force component in the i direction; M moment about the ith axis (Fig. 1) evaluated with respect to the center of gravity; Af represents the front projection area of the vehicle (YZ plane, Fig. 1); hv represents the height of the vehicle gravity center from the bridge deck; ρ is the air density. The tested aerodynamic coefficients of the commercial van located in different lanes are depicted in Fig. 5 as different wind barriers mounted on the deck. It can be seen that the side force coefficient (CFY) is mainly affected by the ventilation ratio of the wind barrier and the location of vehicle. There are obvious differences in the side force coefficients with and without wind barriers. In the absence of wind barrier, the side force coefficient of vehicle on Lane 1 gains the maximum approximately equal to 3.2, and the larger the ventilation ratio, the greater the side force coefficient. It seems that the lift force coefficient (CFZ) changes sharply from Lane 1 to Lane 2. The reason is probably that Lane 1 is close to the safety fence, negative pressures on the top side of vehicle are formed due to the influence of the wake of safety fence.

0.45  105 were adopted. Reynolds number is high enough considering the constraint of the experimental conditions. In addition, the main goal of this paper is to compare the effects of several different wind barriers. Reynolds number has the same effect for different cases. So we believe that Reynolds number has limited influence on the results of the comparison in the current study. 2.3. Test results The aerodynamic coefficients of the vehicles can be defined as

CFi = CMi =

F¯i 1/2ρV w2 A f

(i = Y , Z )

¯i M 1/2ρV w2 A f hv

(i = X , Y , Z ) (1)

where CFi and CMi are the aerodynamic force and moment coefficients, respectively; F¯i is the mean value of the aerodynamic

3.5

0.8

25% 41% 50% No windbreak

3.0 2.5

0.6 0.4

CZ

CY

2.0 1.5 1.0

0.2 0.0

0.5

-0.2

0.0

-0.4 L1

L2

L3

L4

L5

L1

L6

L3

L4

L5

L6

0.5

0.25

0.4

0.20

0.3

CMZ

0.15

CMX

L2

Location of vehicle on the bridge

Location of vehicle on the bridge

0.10

0.2

0.05

0.1

0.00

0.0 -0.1

-0.05 L1

L2

L3

L4

L5

L1

L6

L2

L3

L4

L5

L6

Location of vehicle on the bridge

Location of vehicle on the bridge 0.05 0.00 -0.05

CMY

-0.10 -0.15 -0.20 -0.25 -0.30 -0.35 -0.40 L1

L2

L3

L4

L5

L6

Location of vehicle on the bridge Fig. 5. Mean aerodynamic coefficients of commercial van: (a) side force coefficients; (b) lift force coefficients; (c) rolling moment coefficients; (d) yaw moment coefficients; (e) pitching moment coefficients. L1 is lane no. 1 of the six lanes on the bridge. Lane 1 is at the windward side where as Lane 6 is at the leeward side.

N. Chen et al. / J. Wind Eng. Ind. Aerodyn. 143 (2015) 113–127

Meanwhile, the velocity of the bleed flow is reduced after it passes through the gaps of the safety fence (Dong et al., 2007). With the aid of wind barriers, the lift coefficients seem to be varying smoothly from windward lanes to leeward lanes. The rolling (CMX), yaw (CMZ) and pitching (CMY) moment coefficients show the same trends as the force coefficients in the same condition, but the change of moment coefficients is more complex under the circumstances of different wind barriers and lanes. Fig. 6 shows the aerodynamic coefficients of the articulated lorry. Both the locations and the ventilation ratios have significant influence on the side force coefficients (CY) and the rolling moment coefficients (CMX). In the absence of wind barrier, the side force coefficient decreases from lane 1 to lane 4 with maximal value of 6.8 and rises up gradually in the leeward lanes. The rolling moment (CMX) coefficients appear in the same trend as the side force coefficients. Moreover, the side force and rolling moment coefficients increase almost with the increasing ventilation ratio. One of the major reasons is that the magnitude of the rolling moment largely depends on the magnitude of the side force. The

7

5

3. Wind loads The wind loads acting on bridges can be decomposed into three components: static wind forces due to mean wind speed, buffeting forces due to wind turbulence and self-excited forces due to the aero-elastic interaction between bridge motion and wind velocity. Considering the normal operation of road vehicles going through

1.5

4

1.0

CZ

CY

lift coefficient of the lorry on Lane 1 is negative while that on other traffic lanes are positive in the absence of the wind barriers. With the aid of wind barriers, it seems that the lift coefficient of the lorry is not significantly affected by the ventilation ratio of the wind barriers and the vehicle locations. The yaw moment (CZ) coefficient and pitching moment coefficient (CY) show great changes from windward lanes to leeward lanes as there is no wind barrier on the bridge deck. The change trends of the yaw and pitching moment coefficients become smooth with the existence of wind barriers.

25% 41% 50% No windbreak

6

117

3

0.5

0.0

2 -0.5

1 0 L1

L2

L3

L4

L5

-1.0

L6

Location of vehicle on the bridge

L1

L2

L3

L4

L5

L6

Location of vehicle on the bridge 0.7

0.35

0.6

0.30

0.5 0.25

CMZ

CMX

0.4 0.20 0.15 0.10

0.3 0.2 0.1

0.05

0.0

0.00

-0.1

-0.05

-0.2 L1

L2

L3

L4

L5

L6

L1

L2

L3

L4

L5

L6

Location of vehicle on the bridge

Location of vehicle on the bridge 0.1 0.0

CMY

-0.1 -0.2 -0.3 -0.4 -0.5

L1

L2

L3

L4

L5

L6

Location of vehicle on the bridge Fig. 6. Mean aerodynamic coefficients of articulated lorry: (a) side force coefficients; (b) lift force coefficients; (c) rolling moment coefficients; (d) yaw moment coefficients; (e) pitching moment coefficients. L1 is lane no. 1 of the six lanes on the bridge. Lane 1 is at the windward side where as Lane 6 is at the leeward side.

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the bridge, the wind speed is very low. So the self-excited forces of the continuous concrete bridges can be omitted as the coupling effects between the bridges and the wind are very weak. Due to the sharp-edged blunt bodies of road vehicles, the three-dimensional effects of aerodynamic forces acting on road vehicles are very prominent. Based on the quasi-steady theory and considering the fluctuating wind velocity, the new expressions of the aerodynamic forces acting on road vehicles have been deduced from a theoretical derivation, which involves the derivatives of the aerodynamic coefficients on the attack angle and yaw angle (Baker, 2010). While the traditional formulas in buffeting forces (Cai and Chen, 2004; Xu and Guo, 2003) often ignore the effects of the derivations of aerodynamic coefficients. 3.1. Wind loads on bridge The steady-state wind loads on a bridge deck in unit span length are the lift force (Lst), drag force (Dst) and moment (Mst) in the vertical, lateral and torsion direction, respectively. They can be expressed as follows:

Lst = 0.5ρU 2CL B

(2a)

Dst = 0.5ρU 2CD B

(2b)

Mst = 0.5ρU 2CM B2

(2c)

where U is the mean wind speed; B is the deck width; CD, CL and CM are the drag, lift and moment coefficients, respectively. The aerodynamic coefficients can be obtained from wind tunnel through section model tests. Taking into account the aerodynamic admittance functions in the buffeting analysis in the time domain, the buffeting forces on a deck per span length suggested by Scanlan (1978, 1988, 1990) are given by the following expressions:

Lb (x, t ) =

u (x, t ) w (x, t ) ⎤ 1 2 ⎡ + (CL′ + CD ) χLw ρU B ⎢2CL χLu ⎥ ⎣ U U ⎦ 2

(3a)

Db (x, t ) =

1 2 ⎡ u (x, t ) w (x, t ) ⎤ + CD′ χDw ρU B ⎢2CD χDu ⎥ ⎣ 2 U U ⎦

(3b)

Mb (x, t ) =

u (x, t ) w (x, t ) ⎤ 1 2 2⎡ ′ χ + CM ρU B ⎢2CM χMu Mw ⎥ ⎣ U U ⎦ 2

(3c)

where Lb (x, t ), Db (x, t ) and Mb (x, t ) are the buffeting lift, drag ′ are the slope of the CL , CD and moment, respectively; CL′ , CD′ and CM and CM , respectively; u (x, t ) and w (x, t ) are the horizontal and vertical velocity components of fluctuating wind, respectively; and χ( ) is the aerodynamic admittance function. It is difficult to obtain the explicit expressions of the aerodynamic admittance functions in the time domain. For the sake of security and simplicity, aerodynamic admittance functions are usually set as 1.0 for bridge decks with blunt cross-sections. Primarily, the fluctuating wind velocities u (x, t ) and w (x, t ) in Eq. (3) should be simulated to get the buffeting forces. The fast spectral representation method proposed by Yang et al. (1997) is adopted here for the simulation of the stochastic wind velocities. The time history of wind component u (t ) at the jth point along the bridge span can be generated with j

uj (t ) =

2Δω

ωml = (l − 1)Δω + Δω·m /n, m ≤ j, j = 1, 2, ⋯ , n, l = 1, 2, ⋯ , N − 1; Su (ωml ) represents the horizontal spectrum of the turbulent wind; φml represents the random phase uniformly distributed between 0 and 2π; and

⎧ 0, when 1 ≤ j < m ≤ n ⎪ ⎪ G jm (ωml ) = ⎨ C j − m, when m = 1, m ≤ j ≤ n ⎪ ⎪ ⎩ C j − m 1 − C 2 , when 2 ≤ m ≤ j ≤ n

(5a)

⎛ −λωΔ ⎞ ⎟ C = exp ⎜ ⎝ 2π U ⎠

(5b)

where λ is the exponential decay coefficient and usually taken between 7 and 20; Δ represents the distance between adjacent points; and C j − m in Eq. (5a) represents the coherence function between points j and m, which was proposed by Davenport (1967).

3.2. Wind loads on road vehicles Assuming that the mean wind velocity U is perpendicular to the longitudinal axis of the bridge deck (the X-axis) in the buffeting analysis of the bridge. Furthermore, the vehicle drives over the bridge at a constant velocity of VT. Due to the vertical fluctuation w, an inclined angle α is formed between mean velocity U and resultant wind velocity UR, which is the combination of Uþu (in the horizontal plane B1B2B3B4) and w (in the vertical plane A1A2A3A4) as shown in Figs. 7 and 8. Then, we get

(U + u)2 + w 2 = (UR + uR )2

(6)

tan α = w /(U + u)

(7)

The moving direction of the vehicle is always perpendicular to the vertical plane A1A2A3A4. Due to the influence of the horizontal fluctuation component u on the yaw angle ψ , a transient yaw angle ψ′ is formed as shown in Fig. 9. The final resultant wind velocity VR + vR is available. Then, we get

(VR + vR )2 = (UR + uR )2 + V T2

(8)

V R2 = UR2 + V T2

(9)

tan ψ = UR /VT

(10)

N

∑∑ m= 1 l= 1

Su (ωml ) G jm (ωml ) cos (ωml t + φml )

(4)

where N is a sufficiently large number representing the total number of frequency intervals; Δω = ωup /N is the frequency increment; and ωup is the upper cutoff frequency;

Fig. 7. Relation of wind velocity, vehicle velocity and aerodynamic forces.

N. Chen et al. / J. Wind Eng. Ind. Aerodyn. 143 (2015) 113–127

A1

A2 FL

O4 FS

MR

A3

)

(15)

(16)

1 ρ (VR + vR )2CS (α, ψ + ψ ′) A f 2 ⎡ 2Uu dCS dCS ⎤ 1 1 = ρA f V¯ 2CS (ψ ) + ρA f V¯ 2 ⎢ ψ′ + α CS (ψ ) + ⎥ 2 2 dψ dα ⎦ ⎣ V¯ 2 ⎡ ⎤ 1 1 dCS = ρA f V¯ 2CS (ψ ) + ρA f CS (ψ ) Uu ⎢1 + cot ψ ⎥ 2 2Cs (ψ ) dψ ⎣ ⎦

A4

Fig. 8. Resultant wind velocity of UR in vertical plane.

O4

dCS w 1 ρA f V¯ 2 2 dα U ⎛ 2 dCS 1 w dCS ⎞ = ρA f ⎜V¯ CS (ψ ) + 2CS (ψ ) Uu + VT u + V¯ 2 ⎟ 2 U dα ⎠ dψ ⎝

B1

+

FS Oo uR UR

VR+vR

1 ρ (VR + vR )2CR (α, ψ + ψ ′) A f hv 2 ⎛ dCR w dCR ⎞ 1 = ρA f hv ⎜V¯ 2CR (ψ ) + 2CR (ψ ) Uu + VT u + V¯ 2 ⎟ U dα ⎠ 2 ⎝ dψ

MR =

VR

O3

B4

Fig. 9. Final resultant wind velocity of VR + vR .

tan (ψ + ψ ′) = (UR + uR )/VT

(11)

The higher-order items, such as u2 , u R2 , uw , can be neglected due to their small value with respect to the mean velocity U. The following relations can be obtained by combination of Eqs. (6)– (11) (Baker, 2010)

VR ψ ′ = uR cos ψ

(17)

Similarly, the rolling moment force of the vehicle can be expressed by Eq. (18). Furthermore, the other components of the aerodynamic force acting on road vehicles can be obtained in the same way.

O2

VT

(12)

Considering the moving property of the vehicle and the influence of turbulence, the aerodynamic coefficients of the road vehicle are not only function of the inclined angle α but also function of the transient yaw angle ψ + ψ ′. Then, the aerodynamic coefficients of the road vehicle can be expanded in the Taylor’s series form. get

dCi Ci (α, ψ + ψ ′) = Ci (0, ψ + ψ ′) + α dα dCi dCi = Ci (0, ψ ) + ψ′ + α dψ dα dCi dCi = Ci (ψ ) + ψ′ + α dψ dα

(

FS =

V

B3

⎛ dCi dCi ⎞ 1 ρA f U 2 + V T2 + 2Uu ⎜Cs (ψ ) + ψ′ + α ⎟ 2 dψ dα ⎠ ⎝

Inserting Eqs. (12) and (16) into Eq. (15), then

O3

O1

Inserting Eqs. (8) and (13) into Eq. (14), then

V¯ 2 = U 2 + V T2

UR+uR

B2

(14)

For simplification, the following relation is defined:

Oo

w

1 ρ (VR + vR )2Cs (α, ψ + ψ ′) A f 2

FS =

FS =

U+u

119

(13)

where i = S, L, R, Y , P represents the components of the aerodynamic coefficients, corresponding to the side, lift, rolling, yaw and pitching aerodynamic force, respectively. Based on the assumption of quasi-steady theory and taking the side force for instance, the side force acting on the road vehicle can be expressed as follows:

(18)

where V¯ represents the equivalent mean velocity; Af is the side projection area of the vehicle body; hv is the height of the center of gravity above the ground. The aerodynamic coefficients are affected by many factors, such as the geometry of the vehicle, landscapes (bridge, road, wind barrier, etc.) and crosswind environments (Reynolds number, turbulence intensity, turbulence length scale etc.). Baker (1987); Coleman and Baker (1990) investigated four types of road vehicle and simplified the expressions of the aerodynamic coefficients, which can be expressed by the following formulas as functions of the yaw angle:

CS (ψ ) = a1 (ψ )0.382

(19a)

CL (ψ ) = a2 (1 + sin 3ψ )

(19b)

CD (ψ ) = a 3 (1 + 2 sin 2ψ )

(19c)

CY (ψ ) = − a 4 (ψ )1.77

(19d)

CP (ψ ) = a5 (ψ )1.32

(19e)

CR (ψ ) = a6 (ψ )0.294

(19f)

The sign convention of the forces and moments were obtained with respect to the gravity center of the truck body and a set of orthogonal axis through the center as shown in Fig. 1, and a1, a2, ⋯ , a6 are the fitting parameters. In this paper, the aerodynamic coefficients of the commercial van and articulated lorry are obtained by wind tunnel test at a yaw angle of 90°. Assuming that the aerodynamic coefficients of the commercial van and articulated lorry varying with the yaw angles are similar to the

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results of Baker due to the similar geometry and bridge landscape, the fitting parameters a1, a2, a 4 , a5, a6 can be obtained. The lift coefficient, at a yaw angle of 90° as shown in Eq. (19b), is zero. Referring to Baker's work, the lift coefficient is expressed as follows:

CL, van (ψ ) = 0.4 (1 + sin 3ψ ) + b1

(20)

CL, lorry (ψ ) = 0.93 (1 + sin 3ψ ) + b2

(21)

where CL, van and CL, lorry represent the lift coefficients of commercial van and articulated lorry, respectively; the const 0.4 and 0.93 are obtained from the results of Baker; b1 and b2 represent the lift coefficients of the vehicles at a yaw angle of 90°. Then, the yaw angle derivative can be obtained by directly taking the derivative of the expressions of the aerodynamic coefficients.

4. Dynamic model of wind–vehicle–bridge system Natural wind will produce aerodynamic effects on both the vehicle and the bridge. Besides, the vehicle–bridge system has self-excited characteristic: the moving vehicles and the bridge are able to produce coupling vibration as vehicles travel on the bridge even in the absence of external loads. Considering the interaction among natural wind, road vehicle and bridge, the wind–vehicle– bridge system can be expressed as follows: i i i i Miv u¨ iv + Civ u̇ iv + K iv uiv = f vg + f bv + f stv + f buv

(22a)

n

Mb u¨ b + Cb ub + Kb ub = fbg +

∑ f bvi i=1

+ fstb + fbub

(22b)

where i (i ¼1, 2, …, n) represents the ith vehicle on the bridge; the subscripts b and v represent the bridge and vehicle, respectively; M, C, K represent the mass matrix, damping matrix and i i and f vb represent the interaction stiffness matrix respectively; f bv forces of the ith vehicle in the vehicle–bridge system; fbg and fvg represent the bridge's and vehicle's weight, respectively; fstb is the static wind forces acting on the bridge as expressed by Eq. (2), fstb ¼{Lst, Dst, Mst}; fbub is the buffeting forces acting on the bridge as expressed by Eq. (3), fbub ¼{Lb, Db, Mb}; fstv and fbuv are the static wind forces and the buffeting forces acting on the vehicle as expressed by Eqs. (17) and (18), respectively. In the existing vehicle models (referred to Eq. (22a)), a vehicle consists of several rigid bodies, suspension systems and tires, which are connected by a series of linear or nonlinear springs and damping devices. The elasticity of the suspension system and tires is modeled as springs. The energy dissipation capacities of the suspensions and tires are modeled as viscous damping. Fig. 10 shows a typical configuration of the dynamic model of a road

vehicle. According to the requirement of the coupling vibration analysis, the vehicle body is considered with 5 Degrees of Freedom (DOF), including the vertical DOF Zv, the lateral DOF Yv, the rolling DOF Φv, the yawing DOF φv, and the pitching DOF θv. Meanwhile, only the vertical DOF (Zs) and lateral DOF (Ys) of each tire are taken into account. Therefore, a two-axle vehicle has a total of 13 DOFs, which can be expressed as follows:

u v = {Zv Yv φv ϕv θv Zs1 Ys1 Zs2 Ys2 Zs3 Ys3 Zs4 Ys4 }

(23)

where the subscripts v and s represent vehicle body and tire, respectively. A four-axle vehicle has a total of 21 DOFs which can be expressed as follows:

uv = {Zv Yv φv ϕv θv Zs1 Ys1 Zs2 Ys2 Zs3 Ys3 Zs4 Ys4 Zs5 Ys5 Zs6 Ys6 Zs7 Ys7 Zs8 Ys8 }

(24)

For the bridge system described in Eq. (22b), ub is the displacement vector of bridge nodes represented in the Finite Element Method (FEM). The structural damping Cb is assumed to be Rayleigh damping and is expressed by

Cb = αKb + βMb

(25)

where the damping constants α and β are determined by two specific frequencies with the corresponding structural damping ratios. In the presented study, the fundamental frequency and the frequency of the1st lateral symmetric mode are chosen as the reference frequencies, and the corresponding damping ratio is set as 0.02 for concrete bridge. As far as the coupling interaction between vehicle and bridge is concerned, it involves two aspects: on one hand, the bridge deck and the tires of the vehicles are assumed to be point-contact without separation, and the deformation is satisfied via geometric compatibility, as shown in Fig. 11; on the other hand, the equilibrium is satisfied via horizontal forces and vertical contact forces that transfer the vehicle weights to the bridge. Assuming that rci(x) is the road roughness of the ith wheel at the location of x, equivalent road roughness is formed after considering the deformation of the bridge, it can be written as (Cai and Chen, 2004) Zv Y

ei

Z

vb

wb b

Yv

hi O

Fig. 11. Geometric relationship between the wheel and bridge deck.

Fig. 10. Dynamic model of vehicle.

N. Chen et al. / J. Wind Eng. Ind. Aerodyn. 143 (2015) 113–127

Zci = rci (x) + wb + ei θxb

(26)

where Zci represents equivalent road roughness; wb and θxb are the displacements of the bridge in vertical and rotating direction, respectively; ei is the horizontal distance from the wheel to the girder center. Similarly, the lateral excitation of wheel i can be written as follows:

Yci = vb + hi θxb

(27)

where Yci is the lateral excitation of the ith wheel; vb is the displacement of the bridge in lateral direction; hi is the vertical distance from the wheel to the girder center. The Hermitian cubic polynomials and liner functions are often employed in the finite element method to serve as interpolation functions, which transfer the node displacements of the bridge to the displacements of the contacting points between wheels and bridge deck (Azimi et al., 2013; Guo and Xu, 2001) as follows:

ue (x, t ) = N (x) δe

(28)

e

where u is the displacement vector of the contacting point between wheel and bridge deck, ue ¼{vb wb θxb}; N(x) is the interpolation function; δe is the node displacements of bridge. Assuming that the vehicle travels on the bridge at a constant velocity of VT, the velocity vector of the contacting point is also available, it gets

u̇ e (x, t ) =

∂ue ∂ue dx ∂N (x) e e + = N (x) δ̇ + δ VT ∂t ∂t dt ∂x

(29)

It is clear that the principal factors affecting the dynamic response of vehicles are the equivalent excitations from the contacting point between the wheel and bridge deck. According to the dynamic equilibrium equation of the wheel, the force vector fbv can be written as follows:

fbv = {fbvz1 , fbvy1 , ⋯, fbvzi , fbvyi }

(30)

where fbvzi and fbvyi are the vertical and lateral forces acting on the wheel i. They can be expressed by

fvbzi = Clzi Zci̇ + Klzi Zci

fvbyi = Clyi Yci̇ + Klyi Yci

(31a)

121

damping matrix and the load vector may vary with the motion of vehicle. Therefore, it has a considerable advantage to use the separation iterative method (Li et al., 2005) to independently solve Eq. (22(a) and (b)) at each integration step, and then achieve the solution through equilibrium iterations according to the coupling relationship of the two subsystems (Cai and Chen, 2004; Xu et al., 2004). The iteration between the vehicle and bridge is used to satisfy the balance of vertical and lateral contact forces. With the separation iterative method, the coefficient matrices in the motion equations for vehicle and bridge remain constant at each time step. 4.1. Road surface roughness Road surface roughness is one of the main excitations for vehicle vibration. It is usually assumed as a zero-mean stationary Gaussian random process and can be expressed through a Power Spectral Density (PSD). The relationship between the PSD S(n) and the spatial frequency n (cycles/m) can be described as (Guo and Xu, 2001)

⎧ − p1 n < n ⎪ G 0 (n / nd ) d S (n) = ⎨ ⎪ p 2 − n > nd ⎩ G 0 (n/nd )

(34)

where p1 and p2 are the exponents; G0 is the roughness coefficient (m3/cycle) related to the road condition; nd is the discontinuity frequency of 1/2π (cycle/m). It is worthy of considering the correlation of the road surface roughness between the left and right wheels on the same axle. From field test results, Ammon (1992) simplified the description of the correlation function and deduced a formula to reflect the correlation properties of the left and right wheels. In consideration of the correlation between the left wheel and right wheel and the specification of PSD, the road surface roughness in the time domain can be simulated by applying the inverse fast Fourier transformation on S(n) as follows (Zhu and Law, 2002): N

rxL =

∑γ

2S (nk )Δn cos (2πnk x + φkL )

k=1 N

rxR = γ (nk ) (31b)

∑

2S (nk )Δn cos (2πnk x + φkL )

k=1 N

where Clzi, Clyi are the vertical and lateral damping coefficients of the tire, respectively; Klzi, Klyi are the vertical and lateral spring stiffness of the tire, respectively. According to the equilibrium conditions of the wheel and taking into account the weight transferred to the bridge, the force vector fvb can be written as follows:

fvb = {fvbz1 , fvby1 , fvbRx1 , ⋯, fvbzi , fvbyi , fvbRxi }

(32)

where fvbzi and fvbyi are the vertical and lateral forces acting on the bridge deck, respectively; fvbRxi is the resultant moment from fvbzi and fvbyi. It can be expressed as follows:

fvbzi = Clzi (Zsi̇ − Zci̇ ) + Klzi (Zsi − Zci ) + FGi

(33a)

fvbyi = Clyi (Ysi̇ − Yci̇ ) + Klyi (Ysi − Yci )

(33b)

+

1 − γ 2 (nk )

∑

2S (nk )Δn cos (2πnk x + φkR )

k=1 −p ⎡ ⎛ n ⎛ s ⎞a⎞w ⎤ k γ (nk ) = ⎢1 + ⎜⎜ ⎜ ⎟ ⎟⎟ ⎥ ⎢ ⎝ np ⎝ m ⎠ ⎠ ⎥⎦ ⎣

(35)

(36)

where rxL and rxR represent the road roughness of the left wheel and the right wheel, respectively; γ (nk ) is Ammon’s correlation function; np , m , a, w, p are constants related to the road condition; s is the distance between the left and the right wheel of an axle; nu and nl are the lower and upper cutoff frequencies, respectively; ΦkL and ΦkR are the phase angle uniformly distributed between 0 and 2π; nk = nl + (k − 1/2)Δn; Δn= (nu − nl ) /N . 4.2. Safety criteria for road vehicles

fvbRxi = ei ·fvbzi + hi ·fvbyi

(33c)

where Zsi and Ysi are the vertical and lateral displacements of the ith wheel, respectively; FGi is the weight transferred to the bridge by the wheel. In the motion equations of the wind–vehicle–bridge system given in Eq. (22(a) and (b)), the mass matrix, stiffness matrix,

The displacements of the vehicle and bridge and the dynamic contact force of the wheels on the deck are obtained in time domain with the separation iterative method. The time history of the contact force can reflect the stability status of road vehicle perfectly. Two safety criteria are adopted here based on the contact force. The RSF (Roll Safety Factor) proposed by Liu (1999) is

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adopted as a criterion for the rolling safety accident, defined by the following formula. k

RSF =

∑i = 1 (Fvli − Fvri ) k

∑i = 1 (Fvli + Fvri )

≤1 (37)

where Fvli and Fvri represent the vertical contact forces of the left and right wheels for the ith axle, respectively. k represents the number of the axles of the road vehicle except the first axle. According to the engineer convention, if the quotient of the RSF proposed by Liu (1999) is reversed, the modified definition of the safety criteria can be expressed by k

RSC =

∑i = 1 (Fvli + Fvri ) k

∑i = 1 (Fvli − Fvri )

≥1 (38)

The time-history value of the RSC (Roll Safety Criteria) is located in the interval [1,þ1), and the vehicle safety varies with the increasing value of RSC. According to general engineering experience, taking account of the security reserve for the rolling accident is very meaningful. The reserve coefficient could be set as 0.2. In considering of the unfavorable status of the vehicle, the criteria of the rolling accident could be expressed by

⎛ k ∑i = 1 (Fvli + Fvri ) RSC = min ⎜ ⎜ ∑k (F − F ) vri ⎝ i = 1 vli

⎞ ⎟ ≥ 1.2 ⎟ ⎠

(39)

Based on the judging criteria of sideslip accident proposed by Li et al. (2012) and the same reserve coefficient adopted in the rolling accident, non-dimensional SSC (Sideslip Safety Criteria) is defined as follows:

F¯SR − 1.645σSR SSC = ≥1 0.2μs Ga

A computer program WVBRoad (Wind–Vehcile–Bridge System for Roadway) is used to perform a case study based on the formulas derived above (Cai and Chen, 2004; Guo and Xu, 2006). The Newmark-β method is adopted here to solve the differential equations of bridge and vehicle. 5.1. Analytical parameters The total length of the prototype bridge is 1270 m which is composed of seven continuous girder concrete bridges. The first and the second bridges have a span arrangement of 3  45 m2 and the others have the same span arrangement of 4  50 m2. The boundaries of each bridge are set as simply-supported boundary condition. In the current study, the fourth bridge is taken as the representative bridge. Its overall sketch and detailed cross-section dimensions of the piers are given in Fig. 12. The details of the main beam are referred to Fig. 2. Given that the bridge deck is composed of two parallel girders and the structure is symmetrical, the left girder in the windward side is adopted in the analysis. The four natural modes of the bridge, having significant influence on the dynamic responses of bridge, are listed in Table 1, which ignores the influence of the foundation stiffness. The bridge deck is 51.0 m above the sea level. The exponent of wind profile is set as 0.12 according to the exponential law of the mean wind velocity profile. Based on the simplified simulation method developed by Yang (1997), fluctuating wind velocity fields along the bridge deck in vertical and horizontal directions are generated. The horizontal and vertical wind spectrum proposed by Panofsky and McCormick (1960) and Simiu and Scanlan (1996) can be expressed, respectively as follows:

nSu (n) u*2

(41)

where Fvl and Fvr represent the vertical contact forces of the left and right wheels of an axle, respectively; Fhl and Fhr represent the lateral contact forces of the left and right wheels of an axle, respectively.

=

200f (1 + 50f )5/3

(42)

6f (1 + 4f )2

(43)

and

(40)

where F¯SR is the mean value of sideslip resistance FSR; sSR is the mean square root of sideslip resistance FSR; μs ¼ 0.7 or 0.5, is the friction coefficient of tire on dry or wet road surface. Ga is the gravity of the lightest axle. Then, 0.2μsGa is equal to 5.49 kN and 3.92 kN for van as μs ¼0.7 and 0.5 separately, similarly it equals to 4.43 kN and 3.17 kN for lorry as μs ¼0.7 and 0.5 separately. FSR is expressed as follows:

FSR = μs (Fvl + Fvr ) − (Fhl + Fhr )

5. Numerical examples

nSw (n) u*2

=

where f = nZ /U (Z ); n is the frequency in Hertz; u* = KU (Z )/ denotes the shearing wind velocity; Z denotes the height of points above the ground or sea level; U(Z) is the mean

(ln (Z − zd )/z0 )

Table 1 Structural natural frequencies and mode features. Order

Natural frequency (Hz)

Mode shape

1 2 3 4

0.868 1.092 2.182 2.574

1st 1st 1st 1st

Fig. 12. Configuration of bridge and cross-section of girders and piers.

lateral mode-symmetric lateral mode-asymmetric vertical mode-asymmetric vertical mode-symmetric

N. Chen et al. / J. Wind Eng. Ind. Aerodyn. 143 (2015) 113–127

u(t) (m/s)

w(t) (m/s)

3.0 1.5 0.0 -1.5 -3.0 5.0 2.5 0.0 -2.5 -5.0 0

20

40

60

80

100

120

140

160

180

200

Time (s)

Fig. 13. Example of the simulated wind velocities along the bridge deck.

Table 2 Aerodynamic coefficients of the bridge. Aerodynamic coefficients

CL (lift) CD (drag) CM (moment)

Ventilation ratio of wind barrier 25%

41%

50%

100%

 0.197 1.043 0.098

 0.197 1.043 0.098

 0.190 1.009 0.115

0.050 0.883 0.115

Note: no wind barrier is logically equivalent to a 100% ventilation ratio.

0.030

Road roughness (m)

wind velocity at the height of Z; K is the Von Karman constant and K ¼0.4; z0 is the ground roughness length; zd = H¯ − z0/K , H¯ is the average height of the buildings around. The wind velocity field is simulated for a total of 255 points, uniformly distributed along the bridge deck axis with an interval of 5.0 m. The main parameters in Eqs. (42) and (43) are set as Z¼ 51 m, z0 ¼0.01, H¯ ¼0.5 m. Typical time-histories of the wind velocity with the mean wind velocity U¼15 m/s are shown in Fig. 13. Due to the influence of the wind barriers on the aerodynamic characteristics of the bridge, it is notable that the bridge with various wind barriers has different aerodynamic coefficients. The effects of vehicles on the aerodynamic characteristics of bridges are limited (Han et al., 2014; Li and Ge, 2008), so the effects of vehicles on the aerodynamic coefficients for the bridge are ignored. The aerodynamic coefficients of the vehicle should fully consider the effects of the bridge deck, which are obtained by means of wind tunnel test presented in Chapter 2. Due to the scale of the bridge model being relatively great, the weight of the section model is more than 1500 N, which exceeds the full-scale value of the measuring device. It is impossible to obtain the aerodynamic coefficients of the bridge in wind tunnel. The aerodynamic coefficients of the bridge are obtained by means of CFD as listed in Table 2. For some reasons, the aerodynamic coefficients of the bridge equipped with 25% ventilation ratio wind barrier are not available, which are approximately substituted by the aerodynamic coefficients of the bridge equipped with 41% ventilation ratio wind barrier. This strategy is an approximate treatment on the aerodynamic coefficients of the bridge due to the lack of data. Taking account of the high stiffness of the bridge (Table 1), we believe that the aerodynamic coefficients of the bridge are not the controlling factor for the evaluation of the vehicle safety. The roughness coefficient G0 in Eq. (34) is taken as 20  10  6 m3/cycle according to ISO specification for a good road (ISO 8608, 1995). The power exponent p1 and p2 are both set as 2 in order to simplify the Eq. (34), which was suggested by Huang and Wang (1992). Considering the Ammon coherence function, the main parameters are set as w¼0.21, np ¼0.73, p ¼0.45, a¼ 0.60 and s ¼1.8, which describe the road conditions of the asphalt concrete pavement in the federal highway of Germany. The vertical road surface profile as shown in Fig. 14 is used in the case study. A two-axle vehicle and a four-axle lorry are represented by the commercial van and articulated lorry, respectively. Both of them

123

0.015 0.000 -0.015

Left Right

-0.030 0

8

16

24

32

40

48

56

64

72

80

Distance along the bridge deck (m) Fig. 14. Road surface profiles of the left and right wheel.

are prone to suffer from wind-induced traffic accidents. The main parameters of the commercial van and articulated lorry are listed in the Table 3. The spacing of the adjacent vehicles is chosen to be 10 m (full scale) in the wind tunnel tests. The length of the commercial van is 9.6 m (Fig. 1) and the total length of the fourth bridge is 200 m (Fig. 12). Assuming that all the vehicles are driven on the fourth bridge deck at a specific moment. So, on one traffic lane, the number of vehicle is set to be 10 for both of the van and the lorry. The distance between two vehicles is taken as 10 m in the analysis.

5.2. Dynamic response of vehicle and bridge under crosswind Primarily, the dynamic responses of the vehicle and bridge are investigated. With the absence of wind barrier, Figs. 15 and 16 depict the time histories of the lateral and vertical dynamic responses of the forth bridge (see Fig. 12) at the midpoint of the second span. The commercial van and articulated lorry are studied separately and the vehicle fleet runs on the bridge at a speed of V¼75 km/h. It is shown that the vertical vibration amplitude of the bridge produced by the articulated lorry is greater than that of the commercial van. Since the vertical stiffness of the bridge is relatively large (refer to Table 1), it seems that the crosswind only has slight effects on the vertical displacement response of the bridge. The vertical displacements of the bridge under and without the action of crosswind are almost identical. Besides, the articulated lorry has greater influence on the vertical dynamic responses of the bridge than the commercial van. It can be concluded that the strong coupling effect and the weight of vehicle contribute to the vertical vibration of the bridge. As far as the lateral vibration of the bridge is concerned, both of the commercial van and articulated lorry have limited influence on the lateral displacement of the bridge. Comparatively, the articulated lorry has larger impact on the lateral displacement of the bridge than that of the commercial van. The reason is probably that the weight of the articulated lorry is greater than that of the commercial van. The lateral interaction forces which transfer to the bridge via articulated lorry are greater than commercial van. Moreover, the lateral displacement of the bridge under crosswind is far larger than that of the case without crosswind. Crosswind obviously enhances the lateral vibration of the bridge. It can be concluded that the lateral vibration of the bridge is mainly excited by the crosswind. To illustrate the dynamic characteristics of vehicles, the dynamic time-histories of the fifth vehicle are adopted in the following discussion. Time histories of RSC and sideslip resistance are depicted in Figs. 17–19. It can be seen that the RSC is not sufficient to turn over the vehicle as U is less than 20 m/s. With respect to the road surface condition, the sideslip resistance of vehicle on dry road is much greater than that of vehicle on wet road. It can be deduced that wet road surface is the key controlling factor of the sideslip accidents of vehicle.

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Table 3 Major parameters for commercial van and articulated lorry. Lorry

Van

Unit

Mass of rigid body (Mv) Pitching moment (θv) inertia Jyv Rolling moment (φv) inertia Jxv Yawing moment (ψv) inertia Jzv Front axle mass (Ms1, Ms5) Middle axle mass (Ms2, Ms6) Rear axle Mass (Ms3, Ms4, Ms7, Ms8) Upper vertical spring stiffness for front axle (Kuz1, Kuz5) Upper vertical spring stiffness for middle axle (Kuz2, Kuz6) Upper vertical spring stiffness for rear axle (Kuz3, Kuz4, Kuz7, Kuz8) Lower vertical spring stiffness (Klz1, Klz2, Klz3, Klz4, Klz5, Klz6, Klz7, Klz8) Upper lateral spring stiffness (Kuy1, Kuy2, Kuy3, Kuy4, Kuy5, Kuy6, Kuy7, Kuy8) Lower lateral spring stiffness (Kly1, Kly2, Kly3, Kly4, Kly5, Kly6, Kly7, Kly8) Upper vertical damping for front axle (Cuz1,Cuz5) Upper vertical damping for middle axle (Cuz2, Cuz6) Upper vertical damping for rear axle (Cuz3, Cuz4, Cuz7, Cuz8) Lower vertical damping (Clz1, Clz2, Clz3, Clz4, Clz5, Clz6, Clz7, Clz8) Upper lateral damping for front axle (Cuy1, Cuy5) Upper lateral damping for middle axle (Cuy2, Cuy6) Upper lateral damping for rear axle (Cuy3, Cuy4, Cuy7, Cuy8) Lower lateral damping (Cly1, Cly2, Cly3, Cly4, Cly5, Cly6, Cly7, Cly8) Reference height (hv) L1 L2 L3 L4 b1 h1

13,300 28,000 7590 300,000 490 808 653 300 500 400 750 299 260 5 5 5 0.8 5 5 5 0.8 1.7 5.1 1.6 4.2 5.55 1.02 0.8

4480 5516 1349 10,000 800 – 710 399 – 399 351 299 121 23.21 – 5.18 0.8 23.21 – 5.18 0.8 1.5 2.6 3.0 – – 1.1 0.8

kg kg m2 kg m2 kg m2 kg kg kg kN/m kN/m kN/m kN/m kN/m kN/m kN s/m kN s/m kN s/m kN s/m kN s/m kN s/m kN s/m kN s/m m m m m m m m

0.6

van, U=0 m/s lorry,U=0 m/s

0.4

van, U=20 m/s lorry,U=20 m/s

Sideslip resistance (kN)

Vertical displacement (×10 m)

Parameter

0.2 0.0 -0.2 -0.4

35 30 25 20 15 10

U=0 m/s

5

-0.6 20

25

30

35

40

45

0

50

10

U=20 m/s

20

30

Dry road surface

40

50

60

70

80

Time (s)

Time (s)

Fig. 18. Sideslip resistance of commercial van on dry road surface.

Fig. 15. Vertical displacement response of bridge.

Sideslip resistance (kN)

Lateral displacement (×10 m)

25 6 5 4 3 van, U=0 m/s lorry,U=0 m/s

2

van, U=20 m/s lorry,U=20 m/s

10 5 U=0 m/s

0

0

10

U=20 m/s

20

30

Wet road surface

40

50

60

70

80

Time (s) 20

25

30

35

40

45

50

55

60

Fig. 19. Sideslip resistance of commercial van on wet road surface.

Time (s) Fig. 16. Lateral displacement response of bridge.

5.3. Influence of vehicle speed and traffic lane

24

60

20

50

16

40

12

30

8

20

4

U=0 m/s

0

8

16

10

U=20 m/s

24

32

40

48

56

64

72

Time (s)

Fig. 17. The time-history of RSC of the commercial van.

80

0

RSC of vehicle (U=0 m/s)

RSC of vehicle (U=20 m/s)

15

0

1

0

20

The RSC and the SSC of vehicle varying with vehicle speed are depicted in Fig. 20 as vehicles driven on the first traffic lane without wind barrier. Generally, the driving instability of vehicles under crosswind increases with the increasing vehicle speed. On the other hand, vehicle speed has different influence on different types of vehicles. The vehicle speed, especially high speed, has important influence on the rolling accident of the commercial van. When vehicle speed is up to 90 km/h, the RSC of the van approaches the limit value of 1.2 for rolling accident under the crosswind U¼ 20 m/s. By contrast, vehicle speed mainly affects the

N. Chen et al. / J. Wind Eng. Ind. Aerodyn. 143 (2015) 113–127

125

60 km/h 75 km/h 90 km/h

5 4 3 2 1

3 2

Sideslip safety criteria

Rolling safety criteria

6

1 0 -1

Threshold value

-2 -3

60 km/h 75 km/h 90 km/h

-4

Threshold value

-5

0

15

20

25

30

35

15

20

Wind speed (m/s)

Wet road surface

25

30

35

Wind speed (m/s)

Fig. 20. Safety indicators with vehicle speed (—— Van; —— Lorry; Lane 1).

3

Rolling safety criteria

5 4 3 2 1

2

Sideslip safety criteria

Lane1 Lane2 Lane3

6

1 0 -1

Threshold value

-2 -3

Lane1 Lane2 Lane3

-4

Threshold value

-5

0

15

20

25

30

35

15

20

Wind speed (m/s)

Wet road surface 25

30

35

Wind speed (m/s)

Fig. 21. Safety indicators with traffic lane (—— Van; —— Lorry; vehicle speed V ¼ 90 km/h).

3.0

25% 41% 50%

16

12

8

4

2.5

Sideslip safety criteria

Rolling safety criteria

20

2.0 1.5 1.0

Threshold value 25% 41% 50%

0.5

Threshold value 0

Wet road surface

0.0

15

20

25

30

35

Wind speed (m/s)

15

20

25

30

35

Wind speed (m/s)

Fig. 22. Safety indicators with the ventilation ratio of wind barrier (—— Van; —— Lorry; Lane 1; vehicle speed V ¼90 km/h).

sideslip accidents for the lorry on wet road surface. And lorry is more sensitive to the wind velocity than the vehicle speed. Under the condition that the crosswind U is 20 m/s, sideslip accident can occur for the lorry at any vehicle speed. Aerodynamic coefficients of vehicles vary with the location of traffic lanes and the eccentricity of the traffic lane also has effects on the vibration characteristics of the bridge. Fig. 21 shows the safety indicators of the vehicle driven on different traffic lanes at a speed of 90 km/h. It is seen from Fig. 21 that the first traffic lane in windward side is the most unfavorable for the vehicle safety. Under the crosswind of speed U¼30 m/s, the rolling accident has occurred for the van driven on the first traffic lane. Besides, SSC is below the threshold value of 1.0 for the lorry under the crosswind of speed U¼20 m/s for all of the traffic lanes in the windward side.

5.4. Influence of wind barriers Wind barrier is one of the important measures to guarantee the vehicle safety. Considering that wind barriers with various ventilation ratios (25%, 41%, and 50%) are mounted on the bridge, the RSC and SSC for both the van and the lorry are depicted in Fig. 22 as vehicles are driven on the first traffic lane at a speed of 90 km/h. It is notable that wind barriers obviously enhance the vehicle stability under crosswind. The RSC is far greater than the limiting value of 1.2 for both the van and the lorry. Moreover, the SSC of the van is much greater than the threshold value of 1.0 within the range of the crosswind U¼0–35 m/s. For the sideslip accident, the lorry could be safe on condition that the crosswind speed is lower than U¼ 30 m/s. Furthermore, Table 4 lists the critical wind speed

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Table 4 Critical wind speed of the vehicles driven on bridge. Bridge condition

Dry road surface

Vehicle velocity (km/h)

60.0

75.0

90.0

60.0

75.0

90.0

Z 35.0 Z 35.0 Z 35.0 Z 35.0 r30.0 Z 35.0 Z 35.0 Z 35.0

r 30.0a Z35.0 Z35.0 Z35.0 r 20.0 Z35.0 Z35.0 Z35.0

r20.0a Z 35.0 Z 35.0 Z 35.0 r 15.0 r30.0 Z 35.0 Z 35.0

Z 35.0 Z 35.0 Z 35.0 Z 35.0 r 15.0 Z 35.0 Z 35.0 Z 35.0

r 30.0 Z35.0 Z35.0 Z35.0 r15.0 r 30.0 Z35.0 Z35.0

r 20.0a Z 35.0 Z 35.0 Z 35.0 o 15.0 r 30.0 r 30.0 Z 35.0

Ventilation ratio of wind barrier

100% 50% 41% 25% 100% 50% 41% 25%

Commercial van

Articulated lorry

Wet road surface

Note: no wind barrier is logically equivalent to a 100% ventilation ratio. a

Indicates that the safety is mainly controlled by the roll-over accident.

of the vehicles driven on bridge. If there were no wind barrier on the bridge, the critical wind speed is less than 20 m/s for the commercial van on the wet road surface at a speed of V¼90 km/h. Meanwhile, it is less than 15 m/s for the articulated lorry on the same condition. Due to the sheltering effects of wind barriers (25%, 41% and 50%) on road vehicles, the critical wind speed of the van increases to 35 m/s regardless of the road surface condition and vehicle speed. The critical wind speed of the lorry could reach 35 m/s on the condition that wind barrier with ventilation ratio of 25% has been mounted on the bridge. The wind barrier with ventilation ratio of 50% could ensure the safety of the lorry under the crosswind speed of U ¼30 m/s, and the vehicle speed should not be more than 75 km/h. The sheltering efficiency of the wind barrier with 41% ventilation ratio falls between that of the wind barriers with 25% and 50% ventilation ratios. Although greater ventilation ratio is unfavorable for the vehicle safety, it has minimum influence on the wind-resistance behavior of the bridge. So it is better to adopt the wind barrier scheme depending on its sheltering efficiency for the vehicle safety.

of the bridge. The strong coupling and the weight of vehicle contribute to the vertical vibration of the bridges. It reveals that the wet road surface is the key controlling factor of the sideslip accident of vehicle, and the rolling accident is mainly influenced by the mean wind speed. (3) Both the vehicle speed and the location of the vehicle on the bridge (lane) have significant influence on the vehicle safety. The first traffic lane on windward side is unfavorable for the vehicle safety. The safety of commercial van is more vulnerable to the vehicle speed than that of the articulated lorry. (4) Wind barrier dramatically improves the dynamic behavior of vehicle in crosswind environments. The critical wind speeds for the van and the lorry increase from 15 m/s to greater than 35 m/s with the aid of wind barrier. Based on an overall consideration of various factors, it is recommended to adopt the wind barrier schemes according to their sheltering efficiency for the purpose of ensuring vehicle safety.

Acknowledgments 6. Conclusions The present work has investigated the aerodynamic coefficients of two types of vehicle (commercial van and articulated lorry) located in different lanes on a bridge deck by means of wind tunnel test. Based on the quasi-steady theory and considering the effects of the turbulent wind on the yaw angle, the expressions of aerodynamic force on road vehicle are deduced. The analysis framework of wind–vehicle–bridge is established taking the natural wind, vehicle and bridge as an interaction system. Criteria for the vehicle safety, including the RSC and SSC, are presented based on the dynamic response of the vehicle. Based on an engineering application, the influence factors of the vehicle safety and the sheltering efficiency of wind barrier are investigated. The following conclusions can be drawn: (1) Due to the difference of the geometric configuration, two types of high-sided vehicles exhibit different aerodynamic characteristics. The aerodynamic coefficients of the vehicle on bridge deck are mainly affected by the ventilation ratio of wind barrier and the location of the vehicle. Wind barrier has greatly decreased the aerodynamic coefficients of vehicles. Generally, aerodynamic coefficients of vehicles on the windward side of bridge are greater than that of vehicles on the leeward side. (2) The lateral vibration of bridges is mainly affected by the crosswind. The lateral coupling between the bridge and the vehicle also plays an indispensable role in the lateral vibration

The writers are grateful for the financial supports from the Applied Basic Research Project of Ministry of Transport of the People's Republic of China (2014319J13100), the Construction Technology Project of Ministry of Transport of the People's Republic of China (2014318800240), the Sichuan Province Youth Science and Technology Innovation Team(2015TD0004) and the 2013 Doctoral Innovation Funds of Southwest Jiaotong University (Grant number A0920502051214).

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