A Study on Factors Influencing Ground Subsidence and a Risk Analysis Method Using the Attributes of Sewer Pipes

Abstract

In recent years, we have witnessed an increase in road subsidence accidents in urban areas, threatening the safety of citizens. Various road facilities, such as water and sewage pipes, and telecommunication facilities are buried under roads, and the aging of these facilities is one of the factors causing road subsidence. In particular, old sewer pipes are a primary cause of road subsidence. However, most maintenance work on such facilities is carried out based on how long ago they were buried underground, without considering the risk of road subsidence caused by them. Therefore, this study aims to present a reliable method to assess road subsidence risk that considers various sewer pipe specifications and the environment surrounding them. To derive the factors influencing subsidence, sewer pipes near the target region, where road subsidence occurs the most, were extracted to analyze the correlation between road subsidence, pipe integrity, and the surrounding environment. An effective analysis method was selected by comparing logistic regression analysis and AHP (Analytic Hierarchy Process) analysis, and a weighted road subsidence risk assessment method was proposed by evaluating the importance of factors affecting ground subsidence. Its applicability was examined by comparing actual road subsidence data and analyzing risk in a pilot study area to validate the reliability of the proposed methodology. The results showed that it was possible to make reliable predictions of road subsidence risk areas.

1. Introduction

As more and more road collapse accidents are occurring in densely populated urban areas, national interest in managing underground facilities and buried pipes is increasing. As more people live in urban areas, transportation facilities, such as subways and underpasses, and utility pipes (water, sewage, telecommunications, and electricity) have been constructed without systematic planning, increasing the risk of road subsidence. In particular, the risk and frequency of road cave-ins have increased in recent years due to the accelerated aging of such facilities [1].

A recent study on road subsidence in Seoul, Korea, found that about 4700 road cave-ins occurred from 2010 to 2016, and this trend increased year by year [2]. In Seoul, more than 80% of road cave-ins were caused by damage to sewer pipes. In Japan, 30~50% of road subsidence accidents from 1999 to 2009 were caused by damage to sewer pipes, and the risk of subsidence increased rapidly when the age or service life of sewer pipes exceeded 30 years [3].

In 2015, the Korean government conducted a detailed inspection of old pipes in response to frequent road subsidence accidents. Accounting for 30% of all sewage pipes nationwide, approximately 40,000 km of old pipes aged over 20 years were inspected. The Ministry of Environment published a Sewer Pipeline Standard Inspection Manual (2015) specifying how to diagnose the inside of old pipes [4]. However, this direct inspection of underground pipelines had limitations in predicting the risk of road cave-ins nationwide due to budget and time constraints. Accordingly, Korea has promulgated the (Special Act on the Safety Management of Underground Facilities). The Act calls for preventing urban disasters caused by subsidence and managing underground facilities and is planned for implementation. The government is also preparing an integrated underground space map and underground space safety management system as part of establishing an underground safety information system. In addition, many studies have been conducted to investigate the mechanism of road subsidence and analyze the risk to prevent such accidents. Studies have been pursued to identify the mechanism of road subsidence by simulating ground cavities and relaxation zones using the finite element method [5]. This has also included investigating the mechanism of ground cavities by simulating sewer pipe cracks using model tests in sandy soil and visualizing the occurrence of ground cavities using X-ray and CT [6]. In addition, studies using decision tree analysis (a machine learning algorithm) were conducted to derive the factors affecting ground subsidence, calculate their weight [7], and predict the risk of ground subsidence using the attributes of underground utilities [8]. As such, many studies have been conducted to prevent road cave-ins. Therefore, this study evaluated the risk of road subsidence caused by sewer pipes, one of the primary causes of such accidents, based on the integrated facility information managed by the Ministry of Land, Infrastructure and Transport in Korea. The influencing factors for risk assessment were derived by analyzing the correlation between road subsidence and various aspects of information. These include pipe ID (Identifier), installation year, pipe type, pipe diameter, length, burial depth, exploration results, drainage method, and management agency based on GIS data from the integrated map of underground space. In addition, a methodology to assess the risk of road subsidence was presented by selecting the optimal analysis technique and evaluation method based on logistic regression and AHP (Analytic Hierarchy Process) analyses of the influencing factors.

To verify the reliability of the proposed method for assessing road subsidence risk, this study compared and analyzed the actual incidence of road subsidence and the risk assessment results using sewer pipe information in a pilot study area.

2. Factors Influencing the Risk of Road Subsidence around Sewer Pipes

In Korea, management authorities inspect sewer pipes in urban areas every year by performing internal inspections using security cameras in specific sections. Due to concerns over road subsidence, the Korean government recently conducted a detailed investigation of pipes that were over 20 years old. Subsequently, repairs were carried out according to the survey results. However, this approach has limitations in identifying the risk of road subsidence nationwide due to budget and time constraints. As integrated management of sewer data can only use a portion of the information gathered through actual sewer inspections, there are limits to using various data points to determine the health and integrity of sewer pipes.

Therefore, this study aimed to derive a methodology to predict the risk of road subsidence using limited information on sewer pipes collected. The purpose was to establish an integrated underground space map. This methodology may be less reliable than assessments or road subsidence predictions based on more facility information. However, this approach is more realistic because it uses available information and allows us to make wide-range predictions of areas where sewer pipes are buried.

Table 1. Sewer Layer of Underground Space Integrated Map.

	List	Item
1	Sewer Management Information	Topography mark, management number, area code, map number, management agency code, construction number, start and end point, manhole management number
2	Sewer Data	Installation data, sewer expense, texture, scale, conformation, pipe size, extension
3	Sewer Burying Information	Start and end point, sewer invert elevation mean slope, lane passage number
4	Sewer Discharge Information	Storm and sewage drainage area, velocity of flow

shows the sewer pipe data used to predict the incidence of road subsidence (pipe management, sewer data, installation, and discharge information). Comparative analyses were performed between the incidence of actual subsidence and the target information to check the association of each data point and road subsidence.

The data on the nearest sewer pipeline to 3266 road cave-ins that occurred in urban areas were used for analysis. The impact of road subsidence was evaluated by comparing each sewage pipe item related to ground subsidence with the current status of road subsidence.

2.1. Data

Table 1 shows the sewer pipe data used to predict the incidence of road subsidence (pipe management, sewer data, installation, and discharge information). The target area correlates to the sewer network data of the metropolitan area in Korea where we obtained 380,141 data points. The collected data were sourced from municipal authorities in the Republic of Korea and pertained to sewage pipeline infrastructure. In addition to leveraging the collected data, essential information for analysis was extracted using ArcGIS Pro 2.2.

Sewer pipes were classified based on the standard pipe unit between the joints.

Table 2. Data attributes.

Attribute	Data	Remarks
Pipeline	Numerical	2017—Year of installation + 1
Pipe type	String	HP, RC, GPR, DCIP, THP
Pipe diameter	Numerical	-
Buried depth	Numerical	-
Removal method	String	Combined, storm, sewer

shows the attributes of the sewer pipe data. Pipeline age refers to the year of installation, which is calculated using the difference between the installation year and 2017 when the final data were collected. Pipe diameter and buried depth were analyzed using raw numerical data. The sewer removal method (system) was classified into combined pipes (combined box pipe, open ditch, side gutter, combined sewer, interception pipe, inlet pipe connection line, interception box pipe), sewer pipes (sewage pipe, sewage box pipe), and storm pipes (stormwater pipe, stormwater box pipe). The pipe type was analyzed using raw string data.

Comparative analyses were performed between the incidence of actual subsidence and the target information to check the association of each data point and road subsidence.

2.2. Pearson Correlation Analysis

The Pearson correlation analysis was conducted to examine the correlation between pipeline age and diameter within the collected sewer pipe data and the incidence of road subsidence.

This is the most common method of measuring a linear relationship between an independent variable (incidence of road subsidence) and dependent variables (pipeline age and diameter). The coefficient of determination (R²) represents the degree of correlation, with a value between −1 and 1. The closer the value is to −1 or 1, the higher the correlation between the two variables. The coefficient of determination between variables is calculated by Equations (1) and (2) [9,10].

$$\mathrm{C}\mathrm{o}\mathrm{r}\mathrm{r}(\mathrm{X},\mathrm{Y})=\rho (\mathrm{X},\mathrm{Y})=\frac{\mathrm{C}\mathrm{o}\mathrm{v}(\mathrm{X},\mathrm{Y})}{{\mathsf{\sigma }}_{\mathrm{x}}{\mathsf{\sigma }}_{\mathrm{y}}}$$

(1)

$$\mathrm{r}=\frac{{\mathrm{s}}_{\mathrm{x}\mathrm{y}}}{{\mathrm{s}}_{\mathrm{x}}{\mathrm{s}}_{\mathrm{y}}}=\frac{\sum _{\mathrm{i}=1}^{\mathrm{n}}({\mathrm{X}}_{\mathrm{i}}-\overline{\mathrm{X}}\left)\right({\mathrm{Y}}_{\mathrm{i}}-\overline{\mathrm{Y}})}{\sqrt{\sum _{\mathrm{i}=1}^{\mathrm{n}}({\mathrm{X}}_{\mathrm{i}}-\overline{\mathrm{X}}{)}^2\sum _{\mathrm{i}=1}^{\mathrm{n}}({\mathrm{Y}}_{\mathrm{i}}-\overline{\mathrm{Y}}{)}^2}}$$

(2)

${\mathrm{s}}_{\mathrm{x}\mathrm{y} }:$ covariance of X and Y variables, ${\mathrm{s}}_{\mathrm{x}}:$ standard deviation of variable $\mathrm{X}, {\mathrm{s}}_{\mathrm{y}}:$ and standard deviation of variable Y.

2.3. Analysis of Pipeline Age (Installation Year) and Road Subsidence

Pipeline age or the year of installation is the most significant factor in determining the priority of inspections and repairs using security cameras. In Japan, sewer pipes older than 30 years are inspected annually and prioritized for reinforcement or replacement [10]. It has also been reported that the installation year (pipeline age) is highly correlated with ground subsidence [11].

Figure 1 shows the results of analyzing the pipeline age and the road subsidence rates for all sewer pipes managed in urban areas in Korea. Pipes older than 40 years were excluded from the analysis. The data showed that road subsidence occurred most frequently in pipes older than 40 years. However, 30% of the data errors were marked older than 100 years in cases where the exact installation year was uncertain. Therefore, the data on sewer pipes older than 40 years were excluded from the analysis. As shown in Figure 1, the rate of ground subsidence increases as the pipeline age increases.

2.4. Analysis of Sewer Pipe Diameter and Road Subsidence Probability

Based on the collected sewer pipe data, 450 mm was the most common pipe diameter (about 38%). This was followed by 600 mm (30%) and 300 mm (12%). In relation to the 21 types of sewer pipes found near road cave-ins, the predominant pipe diameters were 600 mm (42%), followed by 450 mm (26%), and 800 mm (7%) (Figure 2).

Figure 3 shows the ratio of the length of sewer pipes to the diameter across the collected data and the ratio of the length of sewer pipes to the diameter in the sections where road subsidence occurred. As a result of examining the frequency of road subsidence accidents according to the sewer pipe diameter, it was observed that the section experiencing road subsidence had a higher occurrence of sewer pipes with larger diameters. In addition, the Pearson correlation coefficient between pipe diameter and road subsidence was about 0.7, indicating a high correlation between the pipe diameter and ground subsidence. The results demonstrate that the larger the pipe diameter, the higher the risk of subsidence.

2.5. Analysis of Road Subsidence Probability by Sewer Pipe Type

Four main types of pipes are buried in the target area. Hume pipes (HP) account for 88%, followed by RC-BOX at 8%, THP at 2%, and PVC pipes at 1%.

Table 3. The ratio of main sewer types in the target region and road subsidence accidents.

Sewer Type	Number of Sewers	Ratio (%)	Number of Sewers Closest to Subsidence	Ratio (%)
HP	299,164	88.2	2658	92.1
PVC	2921	0.9	7	0.2
RC-Box	28,913	8.5	148	5.1
GRP	1474	0.4	11	0.4
DCIP	139	0.0	1	0
THP	6627	2.0	60	2.0
Total	339,238	100	2885	100

shows the number and ratio of sewer pipes by type. In the case of HP with the most road subsidence, the ratio of road subsidence (92.1%) is higher than that of the buried HP (88.2%), indicating that HP pipes are at high risk of ground subsidence. This is likely because HPs account for the majority of sewer pipes, they are less durable than other pipes, and a significant portion of them are aged.

2.6. Correlation Analysis between Sewer Pipe Burial Depth and Road Subsidence

As shown in

Table 4. Sewer pipes’ buried depth in the target region.

Buried Depth	Number of Sewers	Ratio (%)	Number of Sewers Closest to Subsidence	Ratio (%)
5 m or more	1554	0.4	18	0.5
3~5 m	6261	1.6	40	1.2
2~3 m	16,386	4.3	108	3.3
1~2 m	105,108	27.7	1115	34.2
1 m or less	250,743	66.0	1984	60.8
Total	380,052	100	3265	100

, most sewer pipes were buried at depths between 0~2 m. In terms of the burial depth of sewer pipes closest to road subsidence, less than 1 m was the most common (about 60%). This was followed by depths ranging from 1~2 m (34%), 2~3 m (3%), 3~5 m (1%), and 5 m (0.5%). According to the results, there is a positive correlation between burial depth and the likelihood of road subsidence—that is, the shallower the burial depth, the higher the probability of road subsidence. In particular, the findings show the need for measures against road subsidence around sewer pipes buried at depths less than 1 m.

2.7. Relationship between Sewer Pipe Removal Method and Road Subsidence

Sewer pipes in the target area consist of combined, stormwater, and sanitary pipes.

Table 5. Sewer removal system in the target region.

Removal System	Number	Ratio (%)	Number of Sewers Closest to Subsidence	Ratio (%)
Combined Pipe	318,083	92.7	2992	92.8
Storm Pipe	8274	2.4	80	2.5
Sewer Pipe	16,748	4.9	153	4.7
Sum	343,105	100	3225	100

shows the number and ratio of sewer pipes in the target area according to the sewer pipe removal method in the target area and the sewer pipe removal method closest to the locations where road subsidence occurred. In terms of the sewer pipes closest to the locations of road subsidence, approximately 92.8% were combined pipes, followed by sanitary pipes (4.74%), and stormwater pipes (2.48%). Accordingly, due to the predominant presence of combined sewer pipes, a substantial number of sewer pipes were found near road cave-ins.

3. Research Method

3.1. Logistic Regression Analysis

Regression analysis is the most widely used method to analyze the correlation between one dependent variable and several independent variables [12,13]. Typical regression analysis assumes a linear relationship between the independent variables and the dependent variable. This is not suitable for dealing with binary events, such as ground subsidence, where the dependent variable is represented by the incidence of subsidence [14]. Meanwhile, logistic regression is a model that estimates the logistic regression coefficient by assuming that the relationship between the dependent and independent variables is nonlinear. This is suitable for analyzing the relationship between the dependent and independent variables that have only two values [15].

Therefore, logistic regression was chosen as the first method for analyzing ground subsidence in urban areas in Korea. The relationship between the dependent and independent variables was assessed. The dependent variable was whether or not ground subsidence occurred. The independent variables consisted of factors influencing ground subsidence. These factors included pipe diameter, pipe type, pipeline age or year of installation, removal system, buried depth, and surrounding roads. This analysis was conducted using the collected sewer pipe attributes and ground subsidence history data. As for the dichotomous dependent variable, such as ground depression, $E_{\left(yx\right)}$ refers to the probability of ground subsidence occurring given the independent variable x. If the range of x is from −∞ to +∞, the value is a probability, so the p-value ranges from 0 to 1. P′ has a model of a curve close to an S-shape, and this characteristic has the advantage of converting the incidence of ground subsidence into a probability. Therefore, it can be expressed as Equation (3).

$$E_{\left(yx\right)}=\frac{\mathrm{e}\mathrm{x}\mathrm{p}(B_0+B_{1}x)}{1+\mathrm{e}\mathrm{x}\mathrm{p}(B_0+B_{1}x)}$$

(3)

The logistic function above is nonlinear for B₀ and B₁x; however, assuming E(yx) = P, it is possible to linearize the equation as follows.

$$P^{’}=\ln \left(\frac{p}{1-p}\right)=\mathrm{l}\mathrm{n}\left(\frac{E_{\left(yx\right)}}{1-E_{\left(yx\right)}}\right)$$

(4)

By substituting Equation (3) into Equation (4), it is possible to linearize the equation as follows.

$$P^{’}=B_0+B_{lx}$$

(5)

Such a transformation is called logistic transformation, and P′ is called Logit [16].

3.2. AHP Analysis

Based on the sewer pipe data near road cave-ins in downtown Korea, a correlation analysis was conducted to analyze the relationship with road subsidence. The results showed that pipe type, pipe diameter, pipeline age (year of installation), and drainage type demonstrated high correlations with road subsidence. The buried depth was excluded from the evaluation because approximately 95% of the pipes were buried within a depth of 2 m, and the Pearson correlation coefficient between depth and road subsidence was low (0.2). In addition, the state and maintenance of the surrounding roads were added as items that can indirectly affect pipeline integrity. This inclusion of data considered the opinions of experts (25 university professors and geotechnical researchers). With regard to the detailed evaluation, each item was divided into three levels based on the sewer pipe data near the road subsidence locations analyzed above. Then, the risk was calculated by assigning weights to each item through AHP analysis.

Based on the above process, the study proposes a method to evaluate the risk of road subsidence using six factors that are highly correlated with road subsidence. As shown in Equation (6), the evaluation method calculates the impact factor that each influencing factor contributes to road subsidence. The sum of the influencing factor multiplied by the impact factor represents the risk.

$${Factor}_1\times {IF}_1+{Factor}_2\times {IF}_2+{Factor}_3\times {IF}_3+\dots ={SRI}_s$$

(6)

where ${Factor}_x$: factor influencing road subsidence; ${IF}_x$: impact factor; ${SRI}_s$: road subsidence risk around the sewer pipe.

It is necessary to quantify the impact of each influence factor on the road subsidence evaluation score around the sewer pipe to evaluate the risk of road subsidence using sewer pipe information. To establish the impact factor, the Analytic Hierarchy Process (AHP), a multi-criteria decision-making (MCDM) technique, was used. The AHP was employed to stratify the decision-making problem and measure the relative importance of the alternatives in terms of each evaluation criterion, as well as the relative importance of the evaluation criteria by pairwise comparison [17]. The AHP is a method that can systematize the group decision-making of experts and is useful for determining the relative magnitude of decision items. It is suitable for predicting the risk of road subsidence because it can collect and analyze the opinions of experts through a structured questionnaire and calculate the aggregated weights.

The AHP technique has been widely applied in research on management techniques and their application in MCDM [18]. The AHP is a logical and convenient decision-making method that has both objective and subjective evaluation factors. Therefore, it is widely used in decision-making in various fields of research [19,20,21]. The AHP has also been used in civil engineering research to determine the age of water pipes [22] and prioritize river water quality improvement [23]. It has also been used in disaster prediction to analyze landslide risk areas [24].

3.2.1. Creating a Pairwise Comparison Matrix of Decision-Making Factors

Using the AHP, the road subsidence caused by sewer pipes can be represented in the structure shown in Figure 4 [16]. The influence factors derived from the road subsidence impact analysis are located in the Sub-criteria, and the evaluation section is found in Alternatives.

As a step to evaluate the decision maker’s preference for the importance of the influencing factors, a pairwise comparison matrix was created by comparing the evaluation factors within each measurement.

Table 6. Comparing the criteria for importance with respect to the goal.

Semantic Scale	Value
A, B equally important	3
A slightly more important than B	2
A strongly more important than B	1
A very strongly more important than B	1/2
A absolutely more important than B	1/3

shows the pairwise comparison scale for judging the importance of each factor [25].

Conducting pairwise comparisons according to the scale of importance results in a matrix (Equation (7)), known as an inverse matrix. In this matrix, the elements in the main diagonal are all equal to one, where w_i and w_j are the weights of the i-th and j-th attributes, and $i,j=1,2,3,\dots ,n$.

$$A_{ij}=w_i/w_j$$

(7)

3.2.2. Calculating Weights

Weight calculation methods include the arithmetic mean, geometric mean, least squares, and the eigenvector method. Of these, the eigenvector method can measure the consistency of the pairwise comparison matrix by using the eigenvector corresponding to the maximum among the eigenvalues of the pairwise comparison matrix as the importance of each element. The eigenvector W derived by matrix A represents the relative importance of the components. If the perfect consistency is maintained, the relative importance can be obtained from a single row among rows comprising matrix A, as shown in Equation (8) below [26].

$$\left[\begin{array}{c}{w}_1/w_2{w}_2/w_2\dots w_1/w_n\\ w_2/w_2{w}_2/w_2\dots w_2/w_n\\ \dots \\ w_n/w_2{w}_n/w_2\dots w_n/w_n\end{array}\right]\left[\begin{array}{c}{w}_1\\ w_2\\ \dots \\ w_n\end{array}\right]=\mathrm{n}\left[\begin{array}{c}{w}_1\\ w_2\\ \dots \\ w_n\end{array}\right]$$

(8)

The eigenvector W = ($w_1,w_2,\dots ,w_n$)T is the hypothetical actual relative weight, and the eigenvalue n is the number of components. However, in practice, the exact eigenvector W is unknown, making it impossible to obtain the exact matrix A. As matrix A is inconsistent, the importance can be calculated by Equation (9), which is an estimate of Equation (8) [27].

$$AW={\mathsf{\lambda }}_{max}W$$

(9)

where A is the pairwise comparison matrix obtained by the survey, and ${\lambda }_{max}$ is the maximum eigenvalue of A. In addition, the eigenvector W is calculated by the power method. As shown in Equation (10), W is calculated by multiplying matrix A by a sufficiently large integer, K, and then performing standardization as shown in Equation (11). This standardization involves dividing each matrix element by the sum of the columns corresponding to the elements, followed by taking the average value of each row [27].

$${\left(A\right)}^K$$

(10)

$$w_i=\frac{1}{n}{\sum }_{j=1}^n\frac{a_{ij}}{\sum _{i=1}^n{a}_{ij}}$$

(11)

3.2.3. Consistency Test

After making the comparisons, consistency can be verified by obtaining the consistency index (CI) and consistency ratio (CR). The CI is calculated using λ_max as shown in Equation (12).

$$CI=\frac{{\lambda }_{max}-n}{n-1}$$

(12)

Using the obtained CI here, CR is calculated as shown in Equation (13) [26].

$$CR=\frac{CI}{RI}$$

(13)

where RI is the random consistency index, which means that integers from 1 to 9 are randomly selected to form an inverse matrix. The consistency index is subsequently obtained from this process.

Table 7. General random consistency index.

n	1	2	3	4	5	6	7	8	9	10
RI	0	0	0.58	0.90	1.12	1.24	1.32	1.41	1.45	1.49

shows the average of the random consistency indices from 500 samples. The random consistency index RI values according to the number of factors (n) to calculate the relative importance through pairwise comparison can be obtained from Table 6, and the CR value can be obtained from it also. If the CR is less than 0.1, the matrix is consistent. If it is between 0.10~0.20, it indicates a reasonable level of consistency. However, if it exceeds 0.20, the matrix is considered inconsistent. In such cases, it should be recalculated or, in the case of a group survey, excluded from calculating the importance [25,26,27,28].

4. Research Results

4.1. Results of Applying Logistic Regression Analysis

This study performed logistic regression analysis after selecting areas with and without road cave-ins in Korea. The analysis was based on sewage pipe data in urban areas, and the aim was to estimate the most optimal regression model. After estimating the most optimal regression model, it was necessary to verify the accuracy of the results to see how well the prediction regression model classified the results. Among the statistical processing data,

Table 8. Classification accuracy.

Classification		Predicted Value		Classification Accuracy (%)
		Road Subsidence -Not Occurring	Road Subsidence -Occurring
Actual measurement	Road subsidence -not occurring	108	90	54.5
	Road subsidence -occurring	68	131	65.8
Average				60.2

shows how well the regression model predicted 198 areas with no ground subsidence and 199 areas where ground subsidence occurred. The classification accuracy in this model averaged 60%. As for the p-value, pipeline age (or installation year) was the most significant (0.041). Equation (14) calculates the probability of ground subsidence based on the logistic analysis.

$$\mathrm{P}\mathrm{r}\mathrm{o}\mathrm{b}\mathrm{a}\mathrm{b}\mathrm{i}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y}\mathrm{o}\mathrm{f}\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{n}\mathrm{d}\mathrm{s}\mathrm{u}\mathrm{b}\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e}=\frac{EXP\left(Logit\right)}{1+\left(EXP\left(Logit\right)\right)}$$

(14)

$$\begin{array}{c}\mathrm{L}\mathrm{o}\mathrm{g}\mathrm{i}\mathrm{t}={0.544}_x\mathrm{T}\mathrm{p}\mathrm{y}\mathrm{e}-{0.132}_{x}Drainagemethod-{0.772}_{x}Age-\\ {0.364}_{x}Diameter-{1.251}_{x}Roadaroundtheburied-{3.419}_{x}Maintenance+\\ 2.724\end{array}$$

(15)

4.2. Results of Applying AHP

Analysis Procedure

First, the items for the AHP analysis were established. The analysis items were those related to road subsidence among the data obtained from the sewer GIS data. They consisted of six influencing factors related to road subsidence based on the sewer pipe specifications analyzed above. The six factors are as follows:

-

Factor 1: Type of pipe

-

Factor 2: Pipe diameter

-

Factor 3: Pipeline age (installation year)

-

Factor 4: Drainage method

-

Factor 5: Status of roads around the buried pipe

-

Factor 6: Maintenance history

A pairwise comparison scale was created using the items above and distributed to 25 experts (university professors and geotechnical researchers). The scale consisted of judging the relative importance of the selected indexes in a format that requires a pairwise comparison of the evaluation items. The relative importance (weight) and consistency index (CI) of each evaluation item were reviewed to analyze the survey. The RI in this study was 1.24 (n = 6).

The AHP analysis showed two cases where the CI was inadequate, as shown in

Table 9. Results of CI and CR (Analytic Hierarchy Process).

No.	Consistency Index	Consistency Ratio	Suitability
1	0.0302	0.0243	Suitability
2	0.0375	0.0302	Suitability
3	0.0563	0.0454	Suitability
4	0.0960	0.0774	Suitability
5	0.0691	0.0558	Suitability
6	0.0843	0.0680	Suitability
7	0.1160	0.0935	Unsuitability
8	0.0383	0.0309	Suitability
9	0.0226	0.0182	Suitability
10	0.0514	0.0414	Suitability
11	0.0378	0.0305	Suitability
12	0.0544	0.0439	Suitability
13	0.0217	0.0175	Suitability
14	0.0326	0.0263	Suitability
15	0.0250	0.0202	Suitability
16	0.0479	0.0386	Suitability
17	0.0000	0.0000	Suitability
18	0.1649	0.1330	Unsuitability
19	0.0216	0.0174	Suitability
20	0.0443	0.0357	Suitability
21	0.0270	0.0218	Suitability
22	0.0215	0.0173	Suitability
23	0.0136	0.0110	Suitability
24	0.0605	0.0488	Suitability
25	0.0753	0.0607	Suitability

, These two cases were excluded from further analysis to minimize the margin of error in the results. The results of 23 expert surveys were analyzed after excluding two surveys with a CI of 0.1 or higher.

The order of importance of the factors affecting road subsidence used in this study was pipeline age (installation year) → type of pipe → maintenance history → surrounding roads → drainage method → pipe diameter.

Table 10. Weight factors from AHP analysis.

	F1	F2	F3	F4	F5	F6
	Type of Pipe	Diameter of a pipe	Buried Year	Removal System	Lane Passage Number	Maintenance Control
Weight	0.1639	0.1270	0.2670	0.1352	0.1458	0.1653
Ranking	2	6	1	5	4	3

and Figure 5 show the weights for each item.

To verify the weights calculated through the AHP analysis and the analysis method, the study examined the condition of sewer pipes and the actual incidence of road subsidence in urban areas in Korea. The total length of sewer pipes in the target area was 441,171 m. The results of assessing road subsidence risk conditions using the proposed Equation (6) are shown in

Table 11. Result of sewer condition evaluation in the pilot plant.

	A	B	C	D	E	F
Length (m)	5853	16,448	36,518	75,121	71,124	236,107
Ratio (%)	1.33	3.73	8.28	17.03	16.12	53.52

.

To check the applicability of the assessment results, sewer pipes near the section where road subsidence occurred in the pilot area were extracted for risk assessment.

Figure 6 shows the results. Compared with the road subsidence risk assessment results of the entire sewer line, over 80% were categorized as E and F grades, indicating a high risk of road collapse. These results show that the proposed risk assessment method is effective in predicting road subsidence.

5. Conclusions

This study proposed a risk assessment method using data from an integrated underground space map. It involved analyzing the causes of road subsidence, pipeline integrity, and the correlation between the surrounding environment and road subsidence to assess the risk of road subsidence caused by sewer pipes. The main findings are summarized as follows.

(1)

The specifications of sewer pipes were analyzed using a sewer network map to calculate the risk of road subsidence around sewer pipes. Except for buried depth, items such as pipeline age (installation year), pipe diameter, type of pipe, burial depth, and removal method were related to road subsidence. In addition, the current status of surrounding roads and maintenance history were added for the analysis.

(2)

As a result of logistic regression analysis, the following equation was obtained: Logit = 0.544 × pipe type − 0.132 × drainage method − 0.772 × installation year − 0.364 × pipe diameter − 1.251 × surrounding road − 3.419 × maintenance + 2.724. As a result of the AHP analysis, the weights were in the following order: installation year → pipe type → maintenance history → surrounding ground → drainage method → pipe diameter.

(3)

Logistic regression and AHP analysis were conducted to calculate the weights for each item. The probability technique for predicting ground subsidence had an accuracy rate of 60%. As a result of assessing the conditions of sewer pipes in the pilot area using the AHP analysis, most of them were found to have the lowest grade (F). The results of evaluating the conditions where actual road subsidence occurred showed that over 80% were classified as E and F grades, indicating danger. This finding suggests that the equations and weights proposed in the AHP analysis were valid.

This study analyzed the factors influencing road subsidence and their risk according to the sewer pipe attribute data using logistic regression and AHP analysis. Ground subsidence is usually caused by a combination of factors (damage to water pipes, excavation work, etc.). However, it is practically impossible to collect data on every individual factor. Therefore, this study conducted the AHP analysis to intuitively derive factors that influence road subsidence focusing on sewer pipelines. Additionally, logistic regression analysis was performed considering the characteristics of the data obtained. Analyzing the factors affecting road subsidence and the aging of sewer pipes will improve the accuracy of calculating sewer pipe maintenance priorities and road cave-in risks. However, the AHP analysis used in this study has a problem that may include many subjective opinions of experts. Hence, it can be inferred that measurable variables have the potential to yield outcomes of substantial reliability when the factors influencing them are assessed through mathematical methodologies, such as statistical analysis and machine learning. Furthermore, this study focused on acquiring sewage pipeline data from a specific urban area in the Republic of Korea. In the future, it is also expected that highly reliable results will be obtained by analyzing the factors and risks of road subsidence using water pipelines, excavation frequency, and subway data.