In order to study the driving comfort and influencing factors when vehicles pass over manholes and pavement around manholes on an urban road, the deformation and vibration of the manhole cover were considered, a multidegree of freedom vibration model of the humanvehiclemanhole cover was established, and the variation characteristics of driving acceleration was analyzed. The root mean square of weighted acceleration was taken as the basic index, and driving comfort was evaluated based on ISO 263111997 standard. After that, 9 influencing factors were analyzed, such as driving speed, subsidence of manhole, manhole cover stiffness, and longitudinal slope. Then, grey correlation entropy analysis was used to evaluate the influencing factors, and the main factors were determined. The results showed that the maximum acceleration was 3.6 m/s^{2} when a vehicle was passing over a manhole cover under the basic parameters. At the same time, the root mean square of weighted acceleration was 0.975 m/s^{2} and driving comfort degree was “uncomfortable.” Driving direction and vibration of the manhole cover had little influence on driving comfort, while the remaining influencing factors had significant influence on that. The ranking of key influence factors on driving comfort was longitudinal slope, driving speed, height difference caused by pavement damage, height difference caused by manhole cover subsidence, tire stiffness, manhole stiffness, and tire damping. Therefore, in order to ensure driving comfort and safety, damage to pavement around manholes and manhole cover subsidence should be repaired in a timely manner.
Urban pipeline networks are an important part of municipal facilities, known as the “arteries of the city,” and manholes are indispensable components of urban pipeline networks, playing an important role in installation, inspection, and maintenance processes. Due to the difference of stiffness and structure, these areas are weak points in the pavement. Investigations have found that more than 90% of manholes in China have damage, which can be divided into subsidence in manhole, cracking in pavement around the manhole, cover fracture, and subsidence in pavement around the manhole [
Existing research on manholes and pavement around manholes (referring to the pavement in a certain range around manholes) mainly focuses on the settlement mechanism of manholes, design of new manhole structures, development mechanism of damage in pavement around manholes, and the repair materials for damage in pavement around manholes. A longitudinal vibration equation of manholes under traffic loads was constructed [
However, there is currently little research on the comfort and safety of vehicles passing over manholes. When damage to manholes and pavement around manholes occurs, driving comfort can be seriously affected, and serious traffic accidents can occur. A vehicle vibration model and roughness model were constructed to analyze the dynamic load characteristics of vehicles by different simplifying vehicle models [
At present, there are many studies on driving comfort. Based on MATLAB/Simulink simulation analysis, a 1/4 vehicle vibration model and a comprehensive evaluation method of airport and highway pavement roughness were proposed [
When the vehicle passed over a manhole, the vehicle vibration characteristics and driving comfort were obviously different from those when passing over a normal section of road. While the vehicle passed over the pavement around a manhole and a normal section of pavement, deformation (order of magnitude of 0.1 mm) and vibration of the pavement were small enough to be ignored. However, when the vehicle passed over the manhole cover, obvious deformation and vibration of the manhole cover occurred, which greatly aggravated the vibration of the vehicle and seriously affected driving comfort. In order to evaluate the driving comfort and find the key influence factors on the driving comfort while vehicle passing through the manhole, a coupled vibration model of a humanvehiclemanhole cover was established considering the deformation and vibration of the manhole cover, and weighted root mean square acceleration was used as the evaluation index of driving comfort. The driving comfort of a vehicle passing over a manhole was evaluated according to ISO 263111997 standard. Grey correlation entropy analysis was used to analyze the influence of vehicle speed, manhole cover stiffness, longitudinal slope, subsidence of manhole, etc., on driving comfort and to figure out the key influencing factors in order to lay a foundation for the maintenance of the pavement around manholes.
As a complex system of multiparticle vibration which is generally considered to have 18 degrees of freedom, it is difficult to build a model according to the actual situation. Therefore, it is necessary to simplify the model. At present, the 1/2 vehicle vibration model of 5 DOFs [
Humanvehiclemanhole cover vibration model.
In Figure
It was assumed that the pavement roughness was good except for the degradation of manhole settlement and the pit slot in the pavement around the manhole. Considering the damage as an unevenness incentive in the calculation process, the 3DOF vibration model was established as follows:
Obvious deformation and vibration of the manhole cover occurred due to the vehicle passing over it, and the humanvehiclemanhole cover 4DOF vibration model was established, as shown in the following equation:
The basic parameters of the vehicle and manhole cover model were obtained by accessing relevant references and are shown in Table
Parameters for the vehicle and manhole cover.
Parameters  Value 


70 

4500 

430 

56 

1800 

7000 

2100 







5000 

0 
The displacement and velocity parameters were obtained by using the transfer matrix [
When the vehicle passes over the pavement around the manhole from a normal section of pavement, it is assumed that the damage is located at the junction of the two areas. The height difference of the two sections caused by the damage was recorded as
When
When
When
When
When the vehicle was stationary on the manhole cover, the compressions of
When
When
When
When Δ
When the vehicle leaves the manhole cover area or the pavement around the manhole area, the initial conditions could be discussed according to those of the vehicle passing over the manhole cover.
In ISO 263111997, weighted root mean square (RMS) of acceleration is used as the basic evaluation index for driving comfort [
Relationships between driving comfort and RMS of weighted acceleration.
RMS of weighted acceleration (m/s^{2})  Driver’s comfort 

<0.315  Comfortable 
0.315∼0.630  Slightly uncomfortable 
0.500∼1.000  A little uncomfortable 
0.800∼1.600  Uncomfortable 
1.250∼2.500  Quite uncomfortable 
>2.000  Extremely uncomfortable 
Parts of the upper and lower limits for RMS of weighted acceleration overlap with other parts in Table
We assume the height differences caused by the pavement damage and the manhole cover were
Development law of driver acceleration with time.
There were three mutation points of driver acceleration due to the obvious change in road roughness and the new “excitation” of vehicle vibration.
The corresponding time of mutation point 1 was 0.06 s, when the vehicle entered the manhole cover area from the damaged pavement around the manhole area. And the acceleration increased from 1.5 m/s^{2} to 3.3 m/s^{2} instantaneously. The corresponding time of mutation point 2 was 0.13 s, when the vehicle left the manhole cover and entered the damaged pavement around the manhole area on the other side. And the acceleration decreased from 3.6 m/s^{2} to 1.1 m/s^{2} instantaneously. The corresponding time of mutation point 3 was 0.19 s. The vehicle drove into the normal section from the damaged pavement around the manhole section. At this time, the acceleration increased from 0.3 m/s^{2} to 2.9 m/s^{2} suddenly.
Driver’s acceleration reached the maximum value of 3.6 m/s^{2} at 0.12 s when the vehicle was driving over the manhole cover. According to equations (
There are many factors that affect a driver’s comfort when driving on the road, including driver’s driving intelligence, vehicle vibration characteristics, and road condition (comprising road roughness, road alignment, and cultural landscape) [
Driver acceleration changes with time under the influence of different factors. (a) Vibration of the manhole cover. (b) Stiffness of the manhole cover. (c) Subsidence of manhole. (d) Driving speed. (e) Height difference. (f) Longitudinal slope value. (g) Driving direction. (h) Tire stiffness coefficient. (i) Tire damping coefficient.
Influencing factors and evaluation of driving comfort.
Influencing factors 

Driving comfort degree  

Driving speed (km/h)  10  0.533  A little uncomfortable 
20  0.663  A little uncomfortable  
30  0.849  Uncomfortable  
40  1.063  Uncomfortable  
50  1.291  Quite uncomfortable  
60  1.526  Quite uncomfortable  
70  1.766  Quite uncomfortable  
80  2.009  Extremely uncomfortable  


Longitudinal slope value (%)  1  0.525  A little uncomfortable 
2  0.631  A little uncomfortable  
3  0.790  A little uncomfortable  
4  0.975  Uncomfortable  
5  1.176  Uncomfortable  
6  1.384  Quite uncomfortable  
7  1.598  Quite uncomfortable  
8  1.814  Quite uncomfortable  


Tire damping coefficient (10^{4} N·s/m)  0.1  1.106  Uncomfortable 
0.5  0.975  Uncomfortable  
1  0.851  Uncomfortable  
2  0.692  A little uncomfortable  
8  0.545  A little uncomfortable  
20  0.638  A little uncomfortable  
40  0.754  A little uncomfortable  
100  0.911  Uncomfortable  


Manhole cover stiffness coefficient (N/m)  10^{2}  1.423  Quite uncomfortable 
10^{3}  1.420  Quite uncomfortable  
10^{4}  1.395  Quite uncomfortable  
10^{5}  1.220  Uncomfortable  
10^{6}  0.977  Uncomfortable  
10^{7}  0.975  Uncomfortable  
10^{8}  0.979  Uncomfortable  
10^{9}  0.979  Uncomfortable  


Height difference caused by damage to pavement around manhole (cm)  0.5  0.901  Uncomfortable 
1  0.975  Uncomfortable  
2  1.184  Uncomfortable  
3  1.443  Quite uncomfortable  
4  1.730  Quite uncomfortable  
5  2.033  Extremely uncomfortable  
6  2.346  Extremely uncomfortable  
8  2.989  Extremely uncomfortable  


Subsidence of manhole (cm)  0.5  0.968  Uncomfortable 
1  0.975  Uncomfortable  
2  1.019  Uncomfortable  
3  1.095  Uncomfortable  
4  1.198  Uncomfortable  
6  1.461  Quite uncomfortable  
8  1.769  Quite uncomfortable  
10  2.104  Extremely uncomfortable  


Tire stiffness coefficient (10^{5} N/m)  1  0.405  Slightly uncomfortable 
2  0.623  A little uncomfortable  
4  0.871  Uncomfortable  
8  1.227  Uncomfortable  
16  1.650  Quite uncomfortable  
32  1.780  Quite uncomfortable  
64  1.706  Quite uncomfortable  
128  1.622  Quite uncomfortable  


Considering Vibration of manhole cover or not  Yes  0.975  Uncomfortable 
No  0.830  Uncomfortable  


Diving direction  Uphill  1.099  Uncomfortable 
Downhill  0.975  Uncomfortable 
The following conclusions can be drawn by analyzing Figure
Figure
As shown in Figure
As the subsidence of the manhole increased from 1 cm to 3 cm and 6 cm, the maximum acceleration of the driver changed to 4.7 m/s^{2} and 6.6 m/s^{2}, an increase of 30.6% and 91.7%, respectively, as shown in Figure
Figure
Figure
As the longitudinal slope value changed from 4% to 2% and 6%, the maximum acceleration became 2.2 m/s^{2} and 5.1 m/s^{2}, a decrease of 38.9% and an increase of 52.8%, respectively, as shown in Figure
Figure
With the increase of tire stiffness, vehicle vibration periods decreased, and frequency increased gradually, which was detrimental to driving safety and comfort, as shown in Figure
Figure
Computed results and ordered correlation values of grey entropy.
Factors  Grey correlation entropy  Grey entropy correlation degree  Ordered 

Driving speed  3.9511324  0.9999718  2 
Height difference  3.9507091  0.9998647  3 
Longitudinal slope  3.9511341  0.9999723  1 
Tire damping coefficient  3.9449697  0.9984121  7 
Tire stiffness coefficient  3.9483077  0.9992570  5 
Subsidence of manhole  3.9501511  0.9997235  4 
Manhole cover stiffness coefficient  3.9453712  0.9985138  6 
It was found that driving speed, height difference caused by damage of the pavement around the manhole, longitudinal slope, subsidence of the manhole cover, tire damping and stiffness, and manhole cover stiffness all had a significant effect on driving comfort. However, the driving direction could be ignored for it had little effect on driving comfort.
While many factors had great influence on driving comfort, a further study needed to be done to identify which ones play the most significant role. The grey correlation entropy method was used to point out the main control factors of driving comfort.
Grey correlation refers to the uncertain relationship between different things. It is a systematic analysis method used to measure the degree of correlation between factors and systems to compare the influence degree between factors. However, this method can easily generate the problem that the local point correlation value controls the overall point correlation value, causing loss. To solve this problem, the grey correlation entropy method was proposed [
For grey correlation entropy analysis, let
The process of grey correlation entropy analysis is summarized into the following 5 steps:
The grey correlation coefficient of
The distribution density of grey correlation entropy was obtained according to equation (
Let
The grey correlation entropy was obtained from equations (
Let
The grey correlation entropy of
The grey entropy correlation degree of
Significance of influencing factors was determined by the grey entropy correlation degree.
Grey correlation entropy analysis for the 7 factors shown in Table
From Table
Under the same basic parameters, when the vehicle passed over the manhole cover, the driver’s acceleration reached the maximum of 3.6 m/s^{2}, the RMS weighted acceleration was 0.975 m/s^{2}, and the driving comfort degree was evaluated as “uncomfortable.” The existence of the manhole cover and damage to the pavement around the manhole greatly reduced the driving comfort.
Driving speed, height difference, longitudinal slope, subsidence of the manhole cover, tire damping and stiffness, and manhole cover stiffness all had significant influence on the driving comfort, and all of them should be paid more attention. Meanwhile, driving direction had little effect on driving comfort, which could be ignored.
Grey correlation entropy analysis showed that the order of significant influencing factors on driving comfort was longitudinal slope, driving speed, height difference, subsidence of inspection wells, tire stiffness, cover stiffness, and tire damping. Driving speed, height difference caused by damage to the pavement around the manhole, longitudinal slope, and subsidence of the manhole cover were the four most important factors which affected driving comfort.
The effect of height difference on driving comfort was greater than that of manhole cover subsidence. Thus, the existence of a manhole cover with elastic characteristics could reduce driving discomfort in poor roughness conditions.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare no conflicts of interest.
This research was supported by the Shandong Provincial Natural Science Foundation (project ZR2018BEE039), Key Research and Development Program of Shandong Province (project 2019GSF109067), and funds from Doctoral Research Foundation of Shandong Jianzhu University (no. XNBS1844). The author gratefully acknowledges the financial support.