It is very important for pavement engineers to know which factors are the main reasons for the damage of the paving around manholes. Based on the investigation on the damage of paving around manholes, a vibration model with multidegree of freedom for the vehicle-manhole cover was established and analyzed. After that, the Matlab software was used to obtain the variation law of impact load over time, and the 95% fourth power of the aggregate force was used as the index to evaluate the pavement damage. Finally, many influencing factors on pavement damage were analyzed by the method of grey correlation entropy. The results indicated that the impact load reached the maximum for the first time when the vehicle reached the top of the manhole cover, which was 1.29 times that of the static load, and the pavement damage coefficient was 2.12 times that of the static load. The influencing factors had different degrees of influence on the pavement damage; from large to small, they were change of road longitudinal slope > driving speed > damping of tire > stiffness of tire > height difference from the pavement damage > height difference from the manhole settlement > stiffness of the manhole cover.

Manholes play an important role in the installation, inspection, and maintenance of urban facilities. Many manholes are located on urban roads, and they are weak parts. Under repeated vehicle load, the paving around manholes easily sustain serious damage, such as settlement, cracks, and pits [

Damage to manholes and paving around manholes.

When the paving around manhole sustains damage, it not only affects the beauty of the pavement but also worsens pavement roughness. When a vehicle passes over uneven pavement, a significant “bump” occurs. At the same time, as a rigid plate with limited thickness, the manhole cover undergoes obvious deformation and vibration under the vehicle load, which would lead to increased vibration of the vehicle, resulting in greater vehicle impact load, accelerating the destruction of the pavement, which would in turn increase the vibration of the vehicle, forming a vicious circle. In the maintenance of urban roads, the cost of repairing the paving around manholes is very high each year, but there remains the problem of further destruction very soon [

At present, research on manholes and the paving around manholes mostly focuses on manhole settlement mechanisms [

In the above studies, the dynamic load of a vehicle was a key factor. There were three main ways to obtain the dynamic load of a vehicle: software analysis, mathematical modeling, and the field test. Liu et al. [

When the vehicle passed over the paving around the manhole, the vibration characteristics of the vehicle were significantly different from those when passing over the general pavement. This was because the vehicle and the pavement were a weakly coupled system [

Therefore, based on the investigation on the damage of paving around manholes, this paper studies the dynamic characteristics of a vehicle when it passes over a manhole and lays the foundation for research on the failure mechanism of the paving around manholes. In the research, the deformation and vibration of the manhole cover is considered, a vibration model with multidegree of freedom for the vehicle-manhole cover is established, and the 95% fourth power of the aggregate force is used to evaluate the pavement damage. At the same time, the variation law of impact load over time is studied, and many influencing factors on pavement damage are analyzed with the method of grey correlation entropy, the key factors are identified, and provide reference for maintenance and design of paving around manholes.

From March 10 to 25, 2019, investigations including on damage type to the paving around manholes and settlement of manholes were carried out on four roads—Jingshidong (300 manholes), Xinluo (100 manholes), Tianchen (100 manholes), and Xueshan (100 manholes)—in Jinan, Shandong Province, China. During the investigations, the damage was divided into four categories: manhole settlement, pavement cracks, pavement damage, and pavement deformation. Pavement damage included pit slot, looseness, and repaired areas. The deformation included settlement, rutting, and waves.

During the investigations, it was found that the settlement in the “Up” point was often less than that in the “Down” point (Figure

“Up” point and “Down” point of manhole.

Investigation data of pavement damage and manhole settlement.

Road names | Time of road construction | Damage region (m) | Damage number | ||||
---|---|---|---|---|---|---|---|

Radius of damaged region (m) | Mean radius (m) | Manhole settlement | Pavement cracks | Pavement damage | Pavement deformation | ||

Xinluo | 2016.7 | 0.5–0.7 | 0.66 | 92 | 40 | 32 | 2 |

Tianchen | 2016.7 | 0.4–0.8 | 0.64 | 91 | 33 | 51 | 2 |

Xueshan | 2014.5 | 0.4–0.8 | 0.61 | 44 | 98 | 56 | 3 |

Jingshidong | 2004.9 | 0.7–1.2 | 0.84 | 50 | 140 | 300 | 0 |

Settlement of manholes and changes of road longitudinal slope.

Investigation item | Damage number | ||||
---|---|---|---|---|---|

Tianchen | Jingshidong | ||||

Up point | Down point | Up point | Down point | ||

Settlement | 0–5 mm | 62 | 59 | 54 | 49 |

5–10 mm | 11 | 13 | 11 | 15 | |

10–15 mm | 2 | 3 | 1 | 4 | |

15–20 mm | 5 | 2 | 7 | 8 | |

>20 mm | 0 | 3 | 7 | 4 | |

−3%–−1% | 0 | 7 | |||

−1%–0% | 77 | 32 | |||

0%–1% | 3 | 31 | |||

1%–2% | 0 | 10 | |||

>2% | 0 | 0 |

As shown in Table

It can be seen from Table

As shown in Table

As a complex system of multimass vibration, a vehicle is generally considered to have 18 degrees of freedom (DOF). It is very complicated to build a model according to the actual situation; so, it needed to be simplified. The current simplified models are the 1/2 vehicle vibration model with 5 DOF [

Vehicle-manhole cover vibration model.

As shown in Figure _{1}, _{2}, _{3}, and _{4} are the weights of the vehicle seat, frame, wheel, and manhole cover; _{1}, _{2}, _{3,} and _{4} are the displacements; _{1}, _{2}, _{3}, and _{4} are the stiffness coefficients; _{1}, _{2}, _{3}, and _{4} are the damp coefficients;

It was assumed that the pavement roughness was good except for the manhole settlement and any damage to the paving around the manhole. Considering the damage as an unevenness incentive in the calculation process, the 3-DOF vibration model was established:

The 4 DOF vibration model was established:

When the vehicle was driving on the manhole cover, the impact load factor (

Referring to the literature [

Parameters for the vehicle and manhole cover.

Parameters | Value |
---|---|

_{1} (kg) | 70 |

_{2} (kg) | 4500 |

_{3} (kg) | 430 |

_{4} (kg) | 56 |

_{1} ( | 1800 |

_{2} ( | 7000 |

_{1} ( | 2100 |

_{2} ( | |

_{3} ( | |

_{4} ( | |

_{3} ( | 5000 |

_{4} ( | 0 |

We assumed that the maximum height difference caused by the damage to paving around the manhole was _{1} = 1 cm, and the position was 0.6 m from the edge of the manhole cover; the diameter of the manhole cover was 0.7 m, and its settlement was _{2} = 1 cm; if _{1} = 0.01, _{2} = 0.01, and _{3} = 0.01. In stage (2), the initial conditions of equation (_{1} = _{1} (_{1}) + 0.01, _{2} = _{2} (_{1}) + 0.01, _{3} = _{3} (_{1}) + 0.01, _{4} = 0 (_{1} was the duration of the vehicle driving on the paving around the manhole), and so on for the remaining stages. The transfer matrix method [

Impact factor of load variations over time.

It can be seen from Figure

At present, there are three main indexes for the evaluation of pavement damage: dynamic load coefficient (^{4} is the fourth power of the aggregate force, ^{4}, and ^{4}.

Since the vibration caused by the vehicle passing over the manhole was transient vibration, referring to the literature [

There are many factors affecting the dynamic load and pavement damage [_{1}), the manhole settlement (_{2}), the changes of road longitudinal slope (_{4}), the tire stiffness coefficient (_{3}), and the tire damping coefficient (_{3}), were analyzed. For each factor, _{1} was determined by the pavement damage, _{2} was determined by the manhole settlement, _{4} was determined by the material type of the manhole cover, and _{3} and _{3} were determined by the tire model and material. By equations (

As can be seen from Figure

As can be seen from Figures _{1} and _{2}, the maximum _{1} increased from 0.5 cm to 8 cm, _{2} increased from 0.5 cm to 8 cm, _{1} and _{2} were the same as the unevenness of the pavement, their influences on _{1} was greater than the influence of _{2}. At this time, the presence of the manhole cover with elastic characteristics buffered the vehicle vibration and reduced

As can be seen from Figure _{4} increased, the maximum _{4} increased from 10^{2} N/m to 10^{9} N/m, _{4} had little influence on

As can be seen from Figure

As can be seen from Figures _{3}, the maximum _{3} increased from 10^{3} to 10^{4}, _{3} increased, the maximum _{3} was about 8 × 10^{5}, _{3} and _{3} had a certain degree of influence on the pavement damage, but in fact, _{3} and _{3} were mainly affected by the tire pressure, and as the tire pressure was basically stable, _{3} and _{3} varied little; therefore,

Time history curves for impact load coefficients (_{1}. (c) Factor of _{2}. (d) Factor of _{4}. (e) Factor of _{3}. (g) Factor of _{3}.

Pavement damage coefficients (

Influencing factors | ||
---|---|---|

10 | 1.73 | |

20 | 1.87 | |

30 | 2.03 | |

40 | 2.18 | |

50 | 2.32 | |

60 | 2.44 | |

70 | 2.55 | |

80 | 2.64 | |

1 | 1.72 | |

2 | 1.84 | |

3 | 1.98 | |

4 | 2.12 | |

5 | 2.25 | |

6 | 2.37 | |

7 | 2.47 | |

8 | 2.57 | |

_{3} (10^{5} N/m) | 1 | 1.64 |

2 | 1.92 | |

4 | 2.02 | |

5 | 2.15 | |

_{1} (cm) | 0.5 | 2.07 |

1 | 2.12 | |

2 | 2.27 | |

3 | 2.44 | |

4 | 2.60 | |

5 | 2.74 | |

6 | 2.87 | |

8 | 3.07 | |

_{2} (cm) | 0.5 | 2.08 |

1 | 2.12 | |

2 | 2.22 | |

3 | 2.34 | |

4 | 2.45 | |

6 | 2.67 | |

8 | 2.84 | |

10 | 2.97 | |

_{3} (10^{5} N/m) | 6 | 2.24 |

8 | 2.31 | |

10 | 2.26 | |

15 | 2.22 | |

_{4} (N/m) | 10^{2} | 2.49 |

10^{3} | 2.48 | |

10^{4} | 2.47 | |

10^{5} | 2.39 | |

10^{6} | 2.19 | |

10^{7} | 2.12 | |

10^{8} | 2.11 | |

10^{9} | 2.11 | |

_{3} (10^{3} N·s/m) | 1 | 2.27 |

2 | 2.23 | |

4 | 2.16 | |

5 | 2.12 | |

6 | 2.09 | |

7 | 2.06 | |

8 | 2.02 | |

10 | 1.97 |

Through the above analysis, it is clear that all the above factors had a certain degree of influence on

Grey correlation refers to the uncertain relationship between different things. It is a systematic analysis method to measure the degree of correlation between factors and systems and to compare the influence degree between each factor. 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 _{i} and the reference set _{0}, which was

The process of grey correlation entropy analysis is summarized into the following 5 steps:

Step 1. The grey correlation coefficient of _{i}–_{0} was obtained from the following equation:

where

Step 2. The distribution density of grey correlation entropy was obtained according to equation (

Let

where

Step 3. The grey correlation entropy was obtained from equations (

Let _{1}, _{2}, …, _{n}), _{i} ≥ 0, and

where _{i} is attribute information.

The grey correlation entropy of _{i} is

Step 4. The grey entropy correlation degree of _{i} was obtained from the following equation:

where

Step 5. According to the magnitude of the grey entropy correlation degree, which factor was more important was determined. The larger the value, the more important the factor.

Grey correlation entropy analysis for the 7 factors shown in Table

Computed results and ordered correlation values of grey entropy.

Factors | Grey correlation entropy | Grey entropy correlation degree | Ordered |
---|---|---|---|

3.95118 | 0.999984 | 2 | |

_{1} | 3.95047 | 0.999805 | 5 |

3.95120 | 0.999988 | 1 | |

_{3} | 3.95117 | 0.999980 | 3 |

_{3} | 3.95109 | 0.999961 | 4 |

_{2} | 3.95015 | 0.999723 | 6 |

_{4} | 3.94565 | 0.998584 | 7 |

As can be seen from Table _{3} > _{3} > _{1} > _{2} > _{4}. Among them, _{3} and _{3} were mainly determined by the tire pressure, but tire pressure was basically stable; so, the range of _{3} and _{3} was small and had little influence on _{1}, and _{2} were the 4 major factors that needed consideration.

Considering the deformation and vibration of the manhole cover, the coupled vibration model of the vehicle-manhole cover was established, and the road damage was evaluated by

When there was a new unevenness excitation, the vehicle dynamic load changed obviously. With the basic parameters,

When there was damage in the paving around the manhole and the manhole cover, which made the pavement roughness worse, the impact load of the vehicle was greatly increased, and the damage to the pavement was accelerated, and the repair of this pavement should be timely. Although the two factors of _{1} and _{2} were the same as the unevenness of the pavement, their influences on _{1} was greater than the influence of _{2}. At this time, the presence of the manhole cover with elastic characteristics buffered the vehicle vibration and reduced

According to the analysis of grey correlation entropy, the order of degree of influence of each factor on _{3} > _{3} > _{1} > _{2} > _{4}. Among them, _{3} and _{3} were mainly determined by the tire pressure, but tire pressure was basically stable, so the range of _{3} and _{3} was small and had little influence on _{1}, and _{2} were the 4 major factors that had significant influence on the

However, during the analysis of pavement damage, the influence of load time was not considered, which affected the accuracy of the analysis results. It is suggested that in subsequent research, the influence of load magnitude and time on pavement damage should be considered, and the pavement damage problem should be studied in depth.

The test data used to support the findings of this study are included within the article.

The authors declare that they have no conflicts of interest.

This research was supported by the project ZR2018BEE039 supported by Shandong Provincial Natural Science Foundation and project 2019GSF109067 supported by the Key Research and Development Program of Shandong Province. The authors gratefully acknowledge the financial support.