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The contact between a vehicle tire and the road surface has been usually assumed as a single-point contact in the numerical simulation of vehicle–bridge interacted vibrations. In reality, the tire contacts the road surface through a patch instead of a single point. According to some recent studies, the single-point tire model may overestimate the dynamic amplification of bridge responses due to vehicle loadings. A new tire model, namely, the multi-point tire model, is therefore proposed in this paper with the purpose of improving the accuracy of numerical simulation results over the single-point model, while maintaining a certain level of simplicity for applications. A series of numerical simulations are carried out to compare the effect of the proposed tire model with those of the existing single-point model and disk model on the bridge dynamic responses. The proposed tire model is also verified against the field test results. The results show that the proposed multi-point tire model can predict the bridge dynamic responses with better accuracy than the single-point model, especially under distressed bridge deck conditions, and is computationally more efficient and simpler for application than the disk model.

In most related studies on road surface roughness, the vehicle’s wheel is often using a contact point model rather than a disk model. This results in neglecting the wheel’s size and interaction with the road. Consequently, the vehicle’s response may not be genuinely reflected, especially for the massive topic of noise, vibration, and harshness (NVH). Unlike the existing approach targeting the power spectrum, this paper proposes a new convolution method to tackle the disk effect and operates directly on the spatial domain, i.e. road surface roughness. By using a designed periphery function, it can simulate the wheel geometry passing through road surface roughness. The periphery function acts as a filter to the road surface roughness that can filter out smaller oscillations. Some examples involving roughness from ISO 8608 standards were tested. It is shown herein that the proposed method can match the theoretical result (using the geometry method (GM)) not only in the spatial domain but also in the power spectral density (PSD). Since the convolution is performed under the spatial domain, the proposed method can directly apply the disk model to any existing road surface roughness with different spectral compositions in practice. Understanding the disk effect reduces the higher frequency of the vehicle’s response depending on roughness severity, which may significantly impact the vehicle design for ride comfort, road surface roughness extraction, bridge health monitoring using the drive-by method, etc.

Vehicle’s wheels were mostly modeled as a point, which can touch the valleys of pavement roughness, creating unrealistic high-frequency oscillation. This can be avoided by using the disk model for the wheels, which however adds significant complexity to the vehicle–bridge interaction (VBI) analysis. In this paper, a refined roughness formula is generated to account for the wheel size effect such that it can be used by point model. Still, the low-frequency part of the roughness presents some masking effect on the bridge scanning by the test vehicle. To this end, two countermeasures are suggested, i.e. residual response and traffic flows. This study has demonstrated that: (1) the roughness generated by the refined formula can reflect the trace of the disk model; (2) the refined formula facilitates the VBI analysis by using the point model; and (3) the two countermeasures for roughness are effective for improving the scanning of bridge frequencies.