Fig. 1. Types and sub-types of on-road hazard categories in the context of anomaly and defect detection using computer vision [12]

Paper [14] discusses the peculiarities of road structures in the area of bridge and bridge approach junction, as well as the main types of defects in the pavement of bridges and bridge approaches. The author considers the following defects in the pavement of bridges and bridge approaches: approach soil settlement, asphalt concrete pavement cracks, soil erosion, water leakage. These types of defects reduce the reliability and durability of asphalt pavement at bridge crossings and can cause the emergence of the “key effect” hazard.

Article [15] discusses the issue of designing the pavement structure considering the specifics of oversized and heavy transportation. A special aspect in addressing this issue is to consider the strength and bearing capacity of bridges and road structures and the selection of appropriate specialized rolling stock. The paper considers the following types of pavement defects: grid cracks, potholes, longitudinal cracks, transverse cracks, block cracks, cement concrete slab breaks, peeling, chipping, sinking, crumbling, and others.

In [3], the authors determine the cost of 1 m2 of each type of bridge repair, which can be used in the financial and economic module of the Analytical Expert Bridge Management System. The study proposes an expert distribution of defects depending on their impact on the technical condition of structures or the structure as a whole:

1. Unacceptable.

2. Limitedly permissible.

3. Acceptable.

Note that this expert distribution of defects applies to all seven groups of bridge elements.

In their scientific work [3], the authors consider the adequacy of the existing methodology for assessing the levelness of roads at bridge crossings and note that defects in artificial highway structures significantly affect the comfort and safety of traffic. In their conclusions, they note that the existing methodology for assessing the smoothness of roads does not provide for the allocation of areas where artificial structures are located, since the assessment of the smoothness of the pavement is performed on a kilometer-by-kilometer basis, so bridge crossings are left unattended.

The Road Disease Manual developed with the support of USAID [22] considers the following factors that cause the most common deformations and destruction of road structures: operational, climatic, construction and design factors, as well as the impact of the vehicle on the formation of the most common deformations and destruction of road structures. It is noted that the most significant impact of these factors is the vertical impact of the vehicle, untimely repairs, and shortcomings in the design and construction of the road structure. The paper identifies the following types of deformation and destruction of road pavements: formation of potholes, loss of strength, subsidence, crack network, peeling, crumbling, edge destruction, individual cracks, rutting, potholes. Bridge crossings are not considered separately in the manual.

The main part. Road surface defects are characterized by the shape of the profile (harmonic, parabolic, rectangular, etc.), its dimensions (length, height), and its location. From the point of view of the theory of vehicle movement, road surface irregularities are usually classified depending on their impact on the vehicle. There are macro-profile bumps (wavelength – 100 m and more), micro-profile bumps (wavelength – 10 cm to 100 m) and pavement roughness (wavelength – less than 10 cm) [2]. It is noted that the former and the latter have almost no effect on the process of vehicle oscillation (macro-profile irregularities significantly affect only the operation of the engine and transmission (Fig. 2a), and roughness is absorbed by the tires (Fig. 2b) [2]) [17].

(a)                                                           (b)

Fig. 2.  Characteristics of the car’s overcoming the macro-profile bump (a)

and absorption of the bump by its pneumatic tire (b) [21]

Professor A.P. Soltus emphasizes [20], that the microprofile of the bearing surface is one of the most significant factors that leads to the emergence of dynamic reactions in the contact of the wheel with the bearing surface. In addition, the microprofile directly affects the process of oscillation of the vehicle [21]. Thus, Figure 2 shows the nature of the change in the position of the center of the wheel (unsprung mass) of the vehicle and its characteristic point on the body (sprung mass). The positions of these points before the beginning of overcoming the pavement defect of the bridge crossing expansion joint are shown in Fig. 3а. The change in the position of these points during the overcoming of the negative (Fig. 3b) and positive (Fig. 3c) angles of attack [17] of the pavement defect is also shown.

Fig. 3c shows a significant decrease in the distance between the suspended and unsprung masses of the vehicle, as well as an increase in the deformation of its tire. This indicates an increase in the dynamic forces acting both in its suspension and in the contact patch between the car wheel and the road surface of the bridge crossing. Taking into account that these phenomena most significantly affect the nature of vehicle movement, which leads to dynamic loads on the bridge crossing, we further consider the irregularities of the microprofile.

The microprofile consists of bumps (bump spacing ranges from 0.1 m to 100 m [2]). In this case, irregularities up to 1 cm in height with a length not exceeding the length of the tire’s footprint are usually called roughness. The minimum length of a micro-profile bump is taken from 0.2 m to 0.4 m. Y. M. Pevzner notes that the most intense fluctuations of the unsprung masses of the vehicle and fluctuations in the dynamic reactions between the wheel and the road are observed on bumps with a wavelength of 1 m to 2 m when driving at average operating speeds. With an increase in vehicle weight and bump height, the normal reactions of the uneven bearing surface increase [17]. At the same time, an increase in the angle of attack of a road bump leads to a decrease in the coefficient of stability of the vehicle against skidding [20].

Fig. 3.  Influence of micro-profile irregularities on the vehicle’s movement pattern

In view of the above, it can be concluded that the main influence on the nature of vehicle traffic, which leads to additional dynamic loads on the bridge, is exerted by road surface defects, which, by their geometric parameters, belong to the microprofile, i.e., the length of the roadway defects is larger than the tire imprint.

It is worth noting that [8] analyzes the disturbing effect of road irregularities on a vehicle. The author emphasizes that wave-like sections of asphalt roads have an intense disturbing effect. Measurements and static processing of such sections showed that the most common wavelengths are from 1.5 m to 4.5 m.

At the same time, harmonic irregularities can be single, both with a negative height (potholes whose sharp edges are smoothed out by the wheels of vehicles) and with a positive height (for example, protrusions in the area of manholes (Fig. 4a) [13]) [17]. The harmonic bump profile is often chosen (in accordance with the standardized methodology for calculating the smoothness of a car’s ride) when studying the interaction of a car wheel with an uneven road surface [1, 2, 5, 6, 9, 11, 13, 17, 18, 23].

The profile characteristic of a harmonic bump (Fig. 4a) allows the tire contact patch to be considered as a plane that changes its height and inclination relative to the horizon (bump attack angle). This greatly simplifies the mathematical modeling of the processes that occur when an elastic tire interacts with an uneven road surface (Fig. 4b) [17].

It should be noted that from the point of view of the micro profile and its impact on the nature of vehicle movement (Fig. 3), a characteristic defect of the pavement of bridge crossings occurs in the area of expansion joints (Fig. 3, Fig. 5).

Fig. 4. Photo of a road surface defect with a harmonic profile (а) [13]

and visualization of mathematical modeling of its overcoming by a car (b) [17]

Fig. 5. Characteristic defects of bridge pavement in the area of expansion joints

From the analysis of Figures 3 and 4, it can be seen that from the point of view of mathematical modeling of the interaction of a car wheel with a bearing surface, defects in the pavement of bridge crossings in the area of expansion joints, as well as potholes, the sharp edges of which are smoothed out by the wheels of vehicles on the one hand and absorbed by the pneumatic tire on the other (Fig. 1b), can be considered as bumps of a harmonic profile with a negative height.

Conclusions. 1. A literature review has shown that most studies [7, 12, 22, 24] are aimed at fixing and detecting defects in the bearing elements of reinforced concrete road bridges using modern monitoring technologies, such as high-resolution cameras, neural networks, and artificial intelligence. Scientific works that consider defects and damage to roadway elements of road bridges [3, 14, 15, 19] are aimed at solving the problem of road and pedestrian safety, as well as planning the time and cost of repairs.

2.  From the point of view of the theory of car movement, the unevenness of the bearing surface is classified depending on their impact on the car. There are macro-profile, micro-profile and pavement roughness irregularities. The microprofile directly affects the process of oscillation of the vehicle and leads to the appearance of dynamic loads acting in the contact of the car wheel with the road surface.

3.  The main influence on the nature of vehicle movement, which leads to dynamic loads on the bridge crossing, is exerted by road surface defects, which by their geometric parameters belong to the microprofile (wavelength – from 10 cm to 100 m). The most intense fluctuations in the unsprung mass of the vehicle and fluctuations in the dynamic reactions between the wheel and the road are observed on bumps with a wavelength of 1 m to 2 m when driving at average operating speeds. The harmonic bump profile is often chosen (in accordance with the standardized methodology for calculating the smoothness of a vehicle) when studying the interaction of a vehicle wheel with an uneven road surface. The profile characteristic of a harmonic bump makes it possible to treat the bearing surface of the bump as a plane that changes its height and inclination relative to the horizon in the area of the tire contact patch. This greatly simplifies the mathematical modeling of the processes that occur when an elastic tire interacts with an uneven road surface. From the point of view of the micro-profile and its impact on the nature of vehicle movement, a characteristic defect of the bridge pavement occurs in the area of expansion joints, which, from the point of view of mathematical modeling of the interaction of a car wheel with the bearing surface, as well as potholes, the sharp edges of which are smoothed out under the action of vehicle wheels on the one hand and absorbed by the pneumatic tire on the other, can be considered as bumps of a harmonic profile with a negative height.

Acknowledgement Research reported in this publication was supported by the National Research Foundation of Ukraine under award number 2022.01/0142 “Development of a load model based on the actual parameters of heavy rolling stock to determine the carrying capacity of road bridges during their restoration and operation in the war and post-war periods”.

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