The pervasive and persistent distress around traditional municipal road manholes—manifesting as cracking, cover rocking, and localized settlement or upheaval—poses significant safety risks and incurs substantial maintenance costs, often disrupting traffic flow. In recent years, the flange-type nodular cast iron manhole cover has emerged as a widely adopted solution. Engineered with a spring-locking mechanism and a socket connection between the frame and the shaft, its defining feature is a large, flanged bearing plate designed to distribute approximately 80% of the live load directly onto the surrounding pavement layers. This design aims to mitigate dynamic impact and extend the service life of both the cover and the adjacent asphalt.
However, field observations indicate that despite the advantages of the nodular cast iron construction and the flanged design, problems such as settlement and pavement disintegration are not entirely eliminated. Factors including construction quality and the challenging road environment contribute to these issues. Currently, a mature, quantitative system for evaluating the comprehensive service state of these newer manhole assemblies is lacking. Existing standards focus primarily on the cover’s physical condition (e.g., loss, breakage) but offer limited guidance on quantifying the interactive performance between the cover and the pavement, which is critical for road safety and maintenance planning. This study aims to address this gap by developing a data-driven assessment model and a predictive framework for the service life of flange-type nodular cast iron manhole systems.
1. Field Investigation and Data Acquisition
A longitudinal field investigation was conducted on 18 in-service flange-type nodular cast iron manhole covers located on an urban road. The condition was monitored over five distinct time points spanning eight months. The service state was characterized through two primary aspects: the condition of the manhole cover itself and the condition of the surrounding annular pavement area.
1.1 Manhole Cover Condition Metrics
The cover’s performance is primarily governed by its planarity relative to the road surface. Two quantitative indices were defined and measured: cover tilt angle and maximum differential settlement.
Measurement Protocol: A laser distance meter, mounted on a tripod, was used. By taking distance and angle measurements from the instrument to specific points on the cover’s perimeter and the adjacent pavement, the three-dimensional coordinates of these points were calculated. Assuming the cover is a rigid circular body, the tilt angle (the angle between the cover plane and the road surface plane) and the maximum vertical displacement difference between the cover edge and the nearby pavement were derived.
The statistical analysis of the collected data revealed clear trends. The average cover tilt increased approximately linearly over the monitoring period. The differential settlement showed a more rapid initial increase before the rate slowed down in subsequent months.
1.2 Surrounding Pavement Condition Metrics
The pavement within a defined annulus (inner radius 0.45m, outer radius 0.74m) around the cover was analyzed for distress. The primary failure modes observed were:
- Raveling: Loss of binder leading to aggregate looseness (areas > 0.01 m²).
- Potholing: Localized disintegration forming depressions deeper than 20mm (areas > 0.01 m²).
Standardized digital photographs were taken from a fixed height. The area of raveled and potholed regions was initially measured on-site and then digitally delineated and quantified using image processing software (e.g., pixel counting). The distress severity was expressed as:
Raveling Ratio (Rr) = (Area of Raveling / Total Annulus Area) × 100%
Potholing Ratio (Rp) = (Area of Potholing / Total Annulus Area) × 100%
Analysis of 17 covers (one was excluded due to interim repair) showed that while the raveling ratio initially increased and then slightly decreased—partly due to the conversion of raveled areas into potholes—the potholing ratio exhibited a consistent and accelerating increasing trend over time.
2. Normalization of Evaluation Indicators
The four core indicators—Tilt Angle (α), Settlement (S), Raveling Ratio (Rr), and Potholing Ratio (Rp)—have different units and scales. To enable comprehensive analysis, they must be normalized to a common, dimensionless scale. A score of 100 represents an ideal state, and 0 represents a defined failure threshold. The normalization functions are piecewise linear interpolations between these points.
| Indicator | Ideal/Threshold Value (Score=100) | Failure Threshold (Score=0) | Normalization Function (for intermediate values) |
|---|---|---|---|
| Tilt Angle, α | α = 0° | α ≥ 15° | $$ X_1 = 100 – \frac{100}{15} \cdot \alpha $$ |
| Settlement, S | |S| ≤ 5 mm | |S| ≥ 30 mm | $$ X_2 = 100 – \frac{100}{25} \cdot (|S| – 5) $$ |
| Raveling Ratio, Rr | Rr = 0% | Rr ≥ 30% | $$ X_3 = 100 – \frac{100}{30} \cdot R_r $$ |
| Potholing Ratio, Rp | Rp = 0% | Rp ≥ 40% | $$ X_4 = 100 – \frac{100}{40} \cdot R_p $$ |
Here, \(X_i\) (i=1,2,3,4) represents the normalized score for each indicator, ranging from 0 to 100.
3. Comprehensive Evaluation Model Using Fuzzy Analytic Hierarchy Process (FAHP)
The Fuzzy Analytic Hierarchy Process integrates the systematic weighting of AHP with the fuzzy set theory’s ability to handle vague boundaries between evaluation grades, reducing subjectivity.
3.1 Determining Indicator Weights via AHP
The hierarchical structure consists of:
- Goal: Comprehensive Service State (A).
- Criteria: Cover State (B1) and Pavement State (B2).
- Indicators: Tilt (C1), Settlement (C2), Raveling (C3), Potholing (C4).
Pairwise comparison matrices were constructed based on expert judgment using the Saaty 1-9 scale. The weight vector for the four indicators relative to the overall goal was calculated. Consistency checks (Consistency Ratio, CR < 0.1) were performed for all matrices to ensure logical judgment. The aggregated weight vector from multiple experts was found to be:
$$ \mathbf{W} = [w_{\alpha}, w_{S}, w_{R_r}, w_{R_p}] = [0.13, 0.43, 0.13, 0.31] $$
This result underscores that Settlement (\(w_S = 0.43\)) is the most dominant factor influencing the overall service state, followed by Potholing Ratio (\(w_{R_p} = 0.31\)), for these flange-type nodular cast iron covers.
| Expert | Weight for Tilt (α) | Weight for Settlement (S) | Weight for Raveling (Rr) | Weight for Potholing (Rp) | CR |
|---|---|---|---|---|---|
| #1 | 0.16 | 0.44 | 0.13 | 0.27 | 0.011 |
| #2 | 0.12 | 0.40 | 0.14 | 0.34 | 0.013 |
| #3 | 0.14 | 0.43 | 0.10 | 0.33 | 0.054 |
| #4 | 0.11 | 0.44 | 0.14 | 0.31 | 0.045 |
| Aggregate (W) | 0.13 | 0.43 | 0.13 | 0.31 | – |
3.2 Fuzzy Comprehensive Evaluation
An evaluation set of four service states is defined: \(V = \{\text{Excellent (E)}, \text{Good (G)}, \text{Fair (F)}, \text{Poor (P)}\}\). The standardized scores \(X_i\) are mapped to these states using membership functions to avoid sharp, unrealistic boundaries between categories. Trapezoidal and semi-trapezoidal membership functions were employed.
| State Grade | Membership Function \( \mu_{Grade}(X_i) \) | Typical Score Range |
|---|---|---|
| Excellent (E) | $$ \mu_E(X_i) = \begin{cases} 1, & X_i \geq 90 \\ \frac{X_i – 80}{10}, & 80 \leq X_i < 90 \\ 0, & X_i < 80 \end{cases} $$ | 90-100 |
| Good (G) | $$ \mu_G(X_i) = \begin{cases} \frac{90 – X_i}{10}, & 80 \leq X_i < 90 \\ 1, & 70 \leq X_i < 80 \\ \frac{X_i – 60}{10}, & 60 \leq X_i < 70 \\ 0, & \text{otherwise} \end{cases} $$ | 80-89 |
| Fair (F) | $$ \mu_F(X_i) = \begin{cases} \frac{80 – X_i}{10}, & 70 \leq X_i < 80 \\ 1, & 60 \leq X_i < 70 \\ \frac{X_i – 0}{60}, & 0 \leq X_i < 60 \\ 0, & X_i \geq 80 \end{cases} $$ | 60-79 |
| Poor (P) | $$ \mu_P(X_i) = \begin{cases} 1, & X_i < 60 \\ \frac{70 – X_i}{10}, & 60 \leq X_i < 70 \\ 0, & X_i \geq 70 \end{cases} $$ | 0-59 |
For a specific manhole cover with a normalized indicator vector \(\mathbf{X} = [X_1, X_2, X_3, X_4]\), the membership degree for each indicator to each grade forms the fuzzy evaluation matrix \(\mathbf{R}\):
$$ \mathbf{R} = \begin{bmatrix} \mu_E(X_1) & \mu_G(X_1) & \mu_F(X_1) & \mu_P(X_1) \\ \mu_E(X_2) & \mu_G(X_2) & \mu_F(X_2) & \mu_P(X_2) \\ \mu_E(X_3) & \mu_G(X_3) & \mu_F(X_3) & \mu_P(X_3) \\ \mu_E(X_4) & \mu_G(X_4) & \mu_F(X_4) & \mu_P(X_4) \end{bmatrix} $$
The comprehensive fuzzy evaluation vector \(\mathbf{B}\) is obtained by synthesizing the weight vector \(\mathbf{W}\) and the matrix \(\mathbf{R}\):
$$ \mathbf{B} = \mathbf{W} \circ \mathbf{R} = [b_E, b_G, b_F, b_P] $$
where \(b_j\) represents the overall membership degree of the cover system to grade \(j\). The final composite score \(Y\) is calculated using the weighted average method, assigning representative values \(V_E=95, V_G=85, V_F=70, V_P=30\) to each grade:
$$ Y = \frac{\sum_{j \in \{E,G,F,P\}} (b_j)^k \cdot V_j}{\sum_{j \in \{E,G,F,P\}} (b_j)^k} $$
with \(k=1\).
Applying this FAHP model to the 18 monitored covers over five periods yielded composite scores that effectively captured their degradation trajectories. Covers in high-traffic areas (e.g., intersections) showed significantly faster deterioration rates, validating the model’s sensitivity to operational conditions.
4. Service Life Prediction Modeling
Analyzing the temporal evolution of the composite score \(Y\) reveals a crucial pattern: the rate of deterioration accelerates as the condition worsens. This is logical, as initial distress (e.g., minor settlement or cracking) amplifies dynamic vehicle loads, leading to progressively faster degradation. This relationship between the score \(Y\) and its rate of change \(dY/dt\) can be modeled.
By plotting the average score against its discrete time derivative for the measurement intervals, an inverse correlation is evident. The data envelope can be fitted with S-curve (sigmoid-type) functions, representing the upper and lower bounds of deterioration rates observed in the field.
The bounded relationships are expressed as:
$$ \text{Upper Bound (Fast Deterioration): } \frac{dY}{dt} = \frac{-3.49}{1 + e^{-0.22(Y – 72.4)}} + 3.48 $$
$$ \text{Lower Bound (Slow Deterioration): } \frac{dY}{dt} = \frac{-4.26}{1 + e^{-0.15(Y – 88.15)}} + 3.64 $$
These differential equations describe the deterioration speed as a function of the current service score \(Y\). By solving these equations, we can project the time \(t\) required for a cover’s score \(Y\) to decline from its initial value to a critical threshold, such as \(Y_c = 60\) (the “Poor” state boundary). The solution provides a predictive lifespan range.
For a cover system starting in “Good” condition (\(Y_0 \approx 85\)), the model predicts that under the fastest observed deterioration rate, the system could enter the “Poor” state within approximately 5 to 10 months. Under the slowest observed rate, the service life could extend to between 15 and 44 months. This range highlights the significant variability based on location-specific factors like traffic load and construction quality, even for the improved flange-type nodular cast iron design.
5. Conclusions and Future Perspectives
This study presents a quantitative framework for assessing and predicting the service state of flange-type nodular cast iron manhole covers and their surrounding pavement. The key findings are:
- While the flange-type nodular cast iron cover demonstrably improves performance, field data confirms it is not immune to distress. Settlement and pavement disintegration remain primary concerns, exacerbated by high-traffic environments.
- A robust, four-indicator evaluation system (Cover Tilt, Cover Settlement, Pavement Raveling Ratio, Pavement Potholing Ratio) was established, with metrics normalized for integrated analysis.
- The Fuzzy AHP model successfully integrates these indicators, with weights highlighting Settlement (43%) and Potholing Ratio (31%) as the most critical factors. The model outputs a composite score that accurately reflects observed field conditions and degradation trends.
- The relationship between the composite score and its rate of change enables predictive modeling. The developed sigmoid-based differential equations provide upper and lower bound estimates for service life, offering a practical tool for proactive maintenance planning.
The methodology, though developed with a specific set of nodular cast iron covers, is broadly applicable. Future work will focus on scaling this approach through automated data collection technologies. Integrating computer vision for distress detection and embedded sensors for real-time settlement or tilt monitoring can feed continuous data streams into the FAHP model and life prediction algorithms. This evolution towards a data-centric, predictive maintenance framework is essential for developing intelligent urban infrastructure management systems, ultimately contributing to the vision of safer, more efficient smart cities. The inherent durability of nodular cast iron provides a strong material foundation upon which such intelligent management systems can maximize infrastructure lifespan and performance.