In municipal road management, the degradation of manhole covers and adjacent pavement areas poses significant safety risks and maintenance challenges. Traditional covers often lead to issues such as cracking, settlement, and upheaval, necessitating frequent repairs that disrupt traffic and incur high costs. To address these problems, a new type of flange spheroidal graphite cast iron manhole cover has been widely adopted. This design, made from durable spheroidal graphite cast iron, features a spring-locking mechanism and a flanged interface that distributes loads more evenly to the pavement structure, thereby reducing impact from vehicular traffic and extending service life. However, despite these improvements, field observations indicate that settlement and pavement deterioration like loosening and potholing still occur around these covers due to factors such as construction quality and environmental conditions. Currently, there is no mature evaluation system specifically for assessing the service state of such covers and their surrounding pavement. This study aims to develop a comprehensive assessment model using field measurements and fuzzy analytic hierarchy process (FAHP) to evaluate and predict the service life of flange spheroidal graphite cast iron manhole covers, providing a foundation for intelligent urban infrastructure management.
As a researcher in transportation engineering, I conducted a field investigation to analyze the service state of these covers. The study focused on 18 flange spheroidal graphite cast iron manhole covers on a road in an urban area, with data collected at five intervals over eight months. The objective was to quantify the evolution of key performance indicators and establish a predictive model. The use of spheroidal graphite cast iron in these covers enhances their durability and load-bearing capacity, but understanding their long-term behavior requires systematic monitoring.
This image illustrates the typical structure of spheroidal graphite cast iron components, highlighting the material’s robustness essential for manhole covers.
Field Investigation and Data Collection
To assess the service state, I measured two primary aspects: the cover itself and the surrounding pavement. For the flange spheroidal graphite cast iron cover, the key indicators were inclination angle and settlement, which reflect its alignment with the road surface. For the pavement, the indicators were loosening rate and pothole rate, representing surface deterioration. A laser rangefinder with 0.1 mm accuracy, a tripod, and a protractor were used for measurements. The cover was assumed as a rigid circular body, and points on its perimeter and adjacent pavement were targeted to compute spatial coordinates. Inclination angle was derived from the tilt between the cover and pavement, while settlement was the maximum vertical difference. For pavement, digital photos were taken from a fixed height, and image processing software (like Photoshop) was employed to isolate the annular area around the cover (inner diameter 0.9 m, outer diameter 1.48 m). Pixels corresponding to loosened and potholed areas were counted to calculate rates as percentages of the total annular area. Table 1 summarizes the measurement methods and calculations for these indicators.
| Indicator | Measurement Method | Calculation |
|---|---|---|
| Inclination Angle | Laser rangefinder targeting points on cover edge | Angle from computed spatial coordinates |
| Settlement | Vertical distance difference between cover and pavement | Maximum height difference in mm |
| Loosening Rate | Image analysis of pavement surface | Percentage of loosened pixels in annular area |
| Pothole Rate | Image analysis of pavement surface | Percentage of potholed pixels in annular area |
The data collected over time revealed trends in these indicators. For instance, the average inclination angle increased linearly at approximately 0.2° per month, while settlement rose by 0.12 mm per month on average. The loosening rate showed initial growth but later declined slightly as loosened areas transformed into potholes, and the pothole rate increased at an accelerating rate, averaging 1.4% per month. These findings suggest that even with the advanced design of flange spheroidal graphite cast iron covers, pavement deterioration persists, often due to construction issues like poor compaction during backfilling.
Standardization of Indicators
To enable combined analysis, the four indicators—with different units and scales—were standardized into relative values ranging from 0 to 100, where higher values indicate better service state. Based on field surveys and standards, I defined limit values for each indicator. For inclination angle, a value of 15° or above was considered critical, corresponding to a standard score of 0, while 0° gave a score of 100. For settlement, limits were set at ≤5 mm (score 100) and ≥30 mm (score 0). For loosening rate, 0% gave a score of 100 and 30% gave 0; for pothole rate, 0% gave 100 and 40% gave 0. Linear interpolation was used for intermediate values. The standardization formulas are as follows:
For inclination angle \( X_1 \) (in degrees):
$$ S_1 = 100 – \frac{100}{15} \times X_1 \quad \text{for } 0 \leq X_1 \leq 15 $$
For settlement \( X_2 \) (in mm):
$$ S_2 = 100 – \frac{100}{25} \times (X_2 – 5) \quad \text{for } 5 \leq X_2 \leq 30 $$
with \( S_2 = 100 \) for \( X_2 \leq 5 \) and \( S_2 = 0 \) for \( X_2 \geq 30 \).
For loosening rate \( X_3 \) (in %):
$$ S_3 = 100 – \frac{100}{30} \times X_3 \quad \text{for } 0 \leq X_3 \leq 30 $$
For pothole rate \( X_4 \) (in %):
$$ S_4 = 100 – \frac{100}{40} \times X_4 \quad \text{for } 0 \leq X_4 \leq 40 $$
This standardization allows the indicators to be integrated into a single evaluation model. The choice of limits is based on practical thresholds for safety and comfort, ensuring that the scores reflect real-world performance of spheroidal graphite cast iron covers.
Comprehensive Evaluation Model Using Fuzzy Analytic Hierarchy Process
To assess the overall service state, I employed a fuzzy analytic hierarchy process (FAHP), which combines the analytic hierarchy process (AHP) for weight determination and fuzzy mathematics for handling uncertainties. First, I constructed a hierarchical structure with the goal of evaluating service state, criteria of cover state and pavement state, and indicators as inclination angle, settlement, loosening rate, and pothole rate. Experts were invited to compare the relative importance of these indicators using a nine-point scale, resulting in pairwise comparison matrices. For example, one expert’s matrix might be:
$$ B = \begin{bmatrix} 1 & 1/2 & 1 & 1/2 \\ 2 & 1 & 4 & 2 \\ 1 & 1/4 & 1 & 1/2 \\ 2 & 1/2 & 2 & 1 \end{bmatrix} $$
Consistency was checked using the consistency ratio \( CR \), calculated as \( CR = \frac{CI}{RI} \), where \( CI = \frac{\lambda_{\text{max}} – n}{n-1} \) and \( RI \) is the random index (0.89 for n=4). Matrices with \( CR \leq 0.1 \) were accepted. Weights \( Q_i \) for each indicator were derived from the normalized eigenvectors of the matrices. Aggregating inputs from multiple experts, the average weights were determined as: inclination angle (0.13), settlement (0.43), loosening rate (0.13), and pothole rate (0.31). This highlights settlement as the most influential factor, followed by pothole rate, emphasizing the critical role of spheroidal graphite cast iron cover alignment in service performance.
Next, I defined a fuzzy evaluation set with four grades: Excellent, Good, Qualified, and Unqualified. The standardized scores were mapped to these grades using membership functions to avoid sharp boundaries. For each indicator, trapezoidal or semi-trapezoidal functions described the degree of membership to each grade. For example, if a standardized score \( S_i \) is 85, the membership vector might be [0.5, 1, 0.5, 0] for Excellent, Good, Qualified, and Unqualified, respectively. The fuzzy relation matrix \( R \) for a cover is constructed as:
$$ R = \begin{bmatrix} r_{11} & r_{12} & r_{13} & r_{14} \\ r_{21} & r_{22} & r_{23} & r_{24} \\ r_{31} & r_{32} & r_{33} & r_{34} \\ r_{41} & r_{42} & r_{43} & r_{44} \end{bmatrix} $$
where \( r_{ij} \) is the membership of indicator \( i \) to grade \( j \). The comprehensive evaluation vector \( C \) is obtained by multiplying the weight vector \( Q \) with \( R \):
$$ C = Q \cdot R = [c_1, c_2, c_3, c_4] $$
Here, \( c_j \) represents the overall membership to grade \( j \). A final score \( Y \) is computed using the weighted average method:
$$ Y = \frac{\sum_{j=1}^{4} V_j \cdot c_j^K}{\sum_{j=1}^{4} c_j^K} $$
where \( V_j \) are the median values for grades (Excellent: 95, Good: 85, Qualified: 70, Unqualified: 30) and \( K=1 \). This model was applied to the 18 covers over five surveys, yielding scores that decreased over time, as shown in Table 2 for a subset of covers.
| Cover ID | March Score | May Score | July Score | September Score | November Score |
|---|---|---|---|---|---|
| 1 | 85.2 | 78.5 | 65.3 | 70.1* | 62.4 |
| 2 | 90.1 | 88.7 | 85.4 | 82.9 | 80.5 |
| 3 | 88.3 | 86.2 | 83.1 | 79.8 | 76.2 |
*Score increased due to pavement repair, but then declined again.
The scores effectively captured the service state degradation, with covers in high-traffic areas like intersections showing faster declines. This validates the model’s ability to reflect real conditions for spheroidal graphite cast iron covers.
Service Life Prediction Based on Score Trends
To predict the remaining service life, I analyzed the relationship between the comprehensive score \( Y \) and its rate of change \( \frac{dY}{dt} \). Plotting these for the 17 covers (excluding one that underwent repair), I observed that lower scores corresponded to faster degradation rates, indicating accelerated deterioration as the cover and pavement approach failure. This is likely due to increased dynamic loads from vehicles on already compromised surfaces. The data were fitted with S-curve functions to define upper and lower bounds for the rate of change. The derived equations are:
Upper bound:
$$ \frac{dY}{dt} = \frac{3.49}{1 + e^{-0.22(Y – 72.4)}} – 3.48 $$
Lower bound:
$$ \frac{dY}{dt} = \frac{4.26}{1 + e^{-0.15(Y – 88.15)}} – 3.64 $$
Integrating these differential equations gives the time \( t \) as a function of score \( Y \), allowing prediction of when the score will drop below 60, a threshold for unqualified state. For example, the upper bound integration yields:
$$ t = 83.75 + 1.31 \ln\left|0.01 + 3.48e^{-0.22Y + 15.93}\right| – 454.55 \ln\left|0.01e^{-0.22Y + 15.93} + 3.48\right| $$
And the lower bound:
$$ t = 44.9 + 1.83 \ln\left|0.62 + 3.64e^{-0.15Y + 13.22}\right| – 10.75 \ln\left|0.62e^{-0.15Y + 13.22} + 3.64\right| $$
Using these, I estimated the time for scores to fall below 60. As summarized in Table 3, the shortest predicted times ranged from 5 to 10 months, while the longest ranged from 15 to 44 months, depending on initial conditions and environmental factors.
| Cover Condition | Shortest Time (months) | Longest Time (months) |
|---|---|---|
| High traffic, poor initial state | 5-10 | 15-25 |
| Moderate traffic, good initial state | 10-15 | 30-44 |
These predictions highlight the variability in service life and underscore the importance of proactive maintenance for spheroidal graphite cast iron covers.
Conclusions and Future Perspectives
This study developed a comprehensive framework for assessing the service state of flange spheroidal graphite cast iron manhole covers and surrounding pavement. Through field measurements, I quantified key indicators—inclination angle, settlement, loosening rate, and pothole rate—and standardized them for integration. The fuzzy analytic hierarchy process model effectively synthesized these indicators into a single score, reflecting real-world degradation patterns. The results confirm that while spheroidal graphite cast iron covers improve durability, they are not immune to issues like settlement and pavement deterioration, particularly in high-traffic areas. The service life prediction model, based on score trends, provides a practical tool for forecasting maintenance needs, with predicted lifetimes varying from months to years depending on conditions.
Looking ahead, this research can be extended by incorporating larger datasets from diverse urban environments to refine the model parameters. Advanced technologies such as computer vision for automated image analysis and IoT sensors for real-time monitoring could enhance data collection and accuracy. Moreover, integrating this evaluation system into smart city platforms would enable predictive maintenance, optimizing resource allocation and improving road safety. The use of spheroidal graphite cast iron in manhole covers represents a significant advancement, and with intelligent management, its full potential can be realized for sustainable urban infrastructure. Future work should also explore the impact of material variations in spheroidal graphite cast iron on long-term performance, as well as the effects of climate and load spectra on degradation rates.