Keywords

1 Introduction

In recent years, numerous scholars have conducted extensive research on driving comfort and pedestrian comfort. + quantified the concept of comfort through a calculation formula, proposed a comfort evaluation index J, and determined the standard value of comfort limits. At the same time, he also conducted research on the frequency of vibration and found that different frequencies of vibration have different factors affecting comfort. In terms of railways, German scholar Sperling first began research on train comfort, while British scholar Loach developed and improved it, proposing the Sperling comfort index. This indicator takes into account the varying sensitivity of the human body to vibrations of different frequencies. Currently, many European countries adopt this standard [2]. This article uses the allowable limit value of vertical acceleration in Yu Zhisheng [3]'s book “Automobile Theory” to determine driving comfort.

Huang Xin [4] proposed suggestions for optimizing pedestrian comfort of pedestrian bridges based on parameters that affect pedestrian comfort and proposed four measures to improve pedestrian comfort based on engineering examples of pedestrian cable-stayed bridges. The advantages and disadvantages of these four measures were comprehensively analyzed from three aspects: economy, science, and efficiency. Domestic and foreign scholars have proposed many evaluation indicators for pedestrian comfort, but there is also no unified standard. Zou R et al. [5] summarized and compared pedestrian comfort standards in various countries, and the results showed that the International Organization for Standardization ISO10137 standard is the strictest; Liu Cong et  al.  [6] analyzed the vertical and horizontal comfort of the North Canal Bridge in Beijing based on the design specifications for pedestrian bridges in various countries; This article uses the vertical acceleration limit value proposed by the German EN03 specification [7] to determine pedestrian comfort.

2 Establishment and Verification of the Finite Element Model

2.1 Modeling

The cable arch bridge model is based on the Nannan'ao Sea Crossing Bridge, which is located in Yilan County, Taiwan, China Province, China, and was completed in 1999. As one of the iconic landmarks in the local area, it has a span length of 140 m, a bridge width of 15 m, two lanes, and a total of 13 steel cables.

The finite element model of a cable arch bridge is mainly divided into three parts: the bridge deck and arch as a whole, and the bridge piers and steel cables. The bridge deck, arch, and pier use C3D4 solid units. A total of 131851 units. The bridge deck and piers are connected as a whole using ABAQUS's built-in Tie technology. The steel cable adopts B31 beam elements, with a total of 156 elements and a circular cross-section. The impact body is defined as a rigid element attribute using the * Rigid Body command. In the performance analysis of the cable arch bridge structure under accidental lateral load, the impact body has an infinite mass and does not deform or break. The contact between the steel cable and the impact body of the cable arch bridge is analyzed using the * General contact technology provided by ABAQUS. The finite element model is shown in Fig. 1 [8]

Fig. 1.
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Finite element model.

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2.2 Material Model and Boundary Conditions

The bridge deck, arch, and pier in this article are all made of C40 concrete. According to the standard GB/T50081–2019 “Test Methods for Physical and Mechanical Properties of Concrete” [9], their mechanical properties are shown in Table 1.

Table 1. Mechanical Properties of Concrete
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The data on concrete damage parameters are shown in Table 2 [10].

Table 2. Concrete damage parameters 9
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The material parameters of the steel cable are shown in Table 3 [8].

Table 3. Material parameters of steel cables
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The impactor is a drone, with a mass generally greater than 7 kg and less than 116 kg. Its speed is less than 100 km/h, or 27.8 m/s, in full horsepower level flight [11]. In finite element simulation, the mass of the impact body is 10 kg, and the impact lifting speed is 10 m/s.

Apply a fully fixed constraint on the four bases of the bridge pier to fix the entire cable arch bridge model on the ground. The impactor adopts sliding constraints and only moves along the Z-axis direction.

3 Specification for Driving and Pedestrian Comfort

In the book “Automobile Theory”, Yu Zhisheng [3] specified the allowable limit values of vertical acceleration based on the degree of human perception, as shown in Table 4.

Table 4. Relationship between vertical acceleration and driving comfort ( based on automobile theory) [3]
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The German EN 03 specification [7] proposes a four-level comfort level based on acceleration as a pedestrian comfort index, as detailed in Table 5.

Table 5. Comfort level defined in German EN 03 [6]
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The schematic of the output acceleration position is shown in Fig. 2, and the acceleration history curve at position 5 is shown in Fig. 3.

According to Yu Zhisheng's [3] limit on vertical acceleration, the driving comfort here is slightly uncomfortable. According to German EN 03 standards, pedestrian comfort is the best.

Fig. 2.
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Illustration of measuring the location of vertical acceleration in the bridge deck.

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Fig. 3.
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Time history of vertical acceleration at No.5 positions of the bridge deck.

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4 Analysis of Influencing Factors

4.1 Quality

The light unmanned aerial vehicle is used as the impactor, with a speed of 10 m/s and a mass of 10 kg, 20 kg, 30 kg, and 40 kg, as shown in Table 6.

Table 6. Impact Mass Conditions
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Table 7. Evaluation of driving and pedestrian comfort (Impact with different mass)
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Table 8. Impact Velocity Conditions
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Table 9. Evaluation of driving and pedestrian comfort (Impact with different velocities)
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The vertical acceleration history curves of different masses are shown in Fig. 4.

Fig. 4.
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Time history of vertical acceleration at No.5 positions of the bridge deck.

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The evaluation of driving comfort and pedestrian comfort at different masses is shown in Table 7.

As the mass increases, the vertical acceleration value increases, making driving and pedestrians feel increasingly uncomfortable. This is because the vertical acceleration is related to the initial kinetic energy input, which is directly proportional to the mass. As the mass increases, the initial kinetic energy increases and the vertical acceleration value increases, making driving and pedestrians increasingly uncomfortable.

4.2 Velocity

The mass of the impactor is 10 kg, and the velocity of the impactor is taken as 4 m/s, 10 m/s, 16 m/s, and 20 m/s, as shown in Table 8.

The vertical acceleration history curves of different Velocities are shown in Fig. 5.

Fig. 5.
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Time history of vertical acceleration when a bridge is under lateral impact with different Velocity (a: Operating mode 5; b: Operating mode 6; c: Operating mode 7; d: Operating mode 8)

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The evaluation of driving comfort and pedestrian comfort at different Velocities is shown in Table 9.

As the Velocity increases, the vertical acceleration value increases, making driving and pedestrians more uncomfortable. This is because the vertical acceleration is related to the initial kinetic energy input, which is proportional to the square of the velocity. As the speed increases, the initial kinetic energy increases and the vertical acceleration value increases, making driving and pedestrians increasingly uncomfortable.

5 Conclusion

After accidental load impact, the driving comfort at position 5 on the cable arch bridge showed slight discomfort, with pedestrian comfort being the best.

Quantitative study on the impact of impactor mass and speed on driving and pedestrian comfort. When the mass is less than 20kg, driving comfort is slightly uncomfortable, while pedestrian comfort is moderate. When the mass exceeds 20 kg, the driving comfort is quite uncomfortable, and the pedestrian comfort is moderate. This is because the mass is proportional to the initial kinetic energy. As the quality increases, the discomfort of driving and pedestrians increases; When the speed is less than 10m/s, pedestrian comfort is the best. As the speed increases, pedestrians become more uncomfortable, while driving comfort becomes more uncomfortable as the speed increases. This is because the initial kinetic energy is proportional to the square of the speed, and as the speed increases, driving and pedestrians become increasingly uncomfortable.