Quantifying Land Subsidence Probability and Intensity Using Weighted Bayesian Modeling in Shanghai, China

Abstract

Land subsidence, a slow-onset geohazard, poses a severe threat to cities worldwide. However, the lack of quantification in terms of intensity, probability, and hazard zoning complicates the assessment and understanding of the land subsidence risk. In this study, we employ a weighted Bayesian model to explicitly present the spatial distribution of land subsidence probability and map hazard zoning in Shanghai. Two scenarios based on distinct aquifers are analyzed. Our findings reveal the following: (1) The cumulative land subsidence probability density functions in Shanghai follow a skewed distribution, primarily ranging between 0 and 50 mm, with a peak probability at 25 mm for the period 2017–2021. The proportions of cumulative subsidence above 100 mm and between 50 and 100 mm are significantly lower for 2017–2021 compared to those for 2012–2016, indicating a continuous slowdown in land subsidence in Shanghai. (2) Using the cumulative subsidence from 2017–2021 as a measure of posterior probability, the probability distribution of land subsidence under the first scenario ranges from 0.02 to 0.97. The very high probability areas are mainly located in the eastern peripheral regions of Shanghai and the peripheral areas of Chongming District. Under the second scenario, the probability ranges from 0.04 to 0.98, with high probability areas concentrated in the eastern coastal area of Pudong District and regions with intensive construction activity. (3) The Fit statistics for Scenario I and Scenario II are 67% and 70%, respectively, indicating a better fit for Scenario II. (4) High-, medium-, low-, and very low-hazard zones in Shanghai account for 14.2%, 48.7%, 23.6%, and 13.5% of the city, respectively. This work develops a method based on the weighted Bayesian model for assessing and zoning land subsidence hazards, providing a basis for land subsidence risk assessment in Shanghai.

1. Introduction

Land subsidence is a slow-onset geohazard caused by the consolidation and compaction of loose strata [1,2,3]. It is a serious and long-lasting hazard, causing the irreversible loss of ground elevation and posing a significant threat to human environments and infrastructure safety [4,5]. Land subsidence has become a global challenge, affecting multiple cities across different countries [1]. More than 150 cities and regions worldwide have experienced land subsidence, including Madrid [6], Florence [7], Beijing [8], Xi’an [9], and others. This issue is especially critical in densely populated delta regions [10], such as California in the United States [11] and Shanghai in China [3]. According to the UNESCO Land Subsidence International Initiative (UNESCO LaSII), by 2040, 1596 cities globally will be at risk of land subsidence, potentially affecting 635 million people in flood-prone areas [10,12,13].

Numerous scholars at home and abroad have conducted relevant research on land subsidence. In terms of land subsidence monitoring, it mainly relies on leveling and synthetic aperture radar interferometry (InSAR) techniques [14]. Land subsidence drivers can be categorized into two main groups: (1) anthropogenic factors, including the extraction of subsurface fluids (e.g., water, oil, and natural gas) [11,15,16], land use change (construction activities), and underground facilities construction [17,18,19,20,21]; and (2) natural factors, including tectonic movement, and the consolidation or compaction of sediments [22,23]. Some studies indicate that natural and anthropogenic factors contribute 23.08% and 76.92% to land subsidence, respectively [1]. Anthropogenic factors have the potential to greatly accelerate the process of land subsidence. Since land subsidence is a slow-changing hazard, it is difficult to quantitatively assess the risk using the current methods for sudden-onset disasters. Thus, there is an urgent need to develop methods for assessing the hazard and risk of land subsidence to manage these risks effectively.

The quantitative analysis of land subsidence hazard includes both the intensity and probability of land subsidence. Previous researchers have studied land subsidence hazards in three main ways. (1) Many studies have adopted satellite Interferometric Synthetic Aperture Radar (InSAR) and the Global Navigation Satellite System (GNSS) to measure vertical land motions of subsidence quantitatively [15,18,24,25,26]. (2) Other studies have semi-quantitatively assessed subsidence susceptibility using multi-criteria evaluation methods [27,28]. For example, Wang [3] developed a hazard evaluation index by analyzing subsidence susceptibility in Shanghai using long-term monitoring data. (3) Some researchers have studied subsidence hazards based on physical processes. Sundell et al. [29] estimated local land subsidence hazards by coupling two probabilistic models, the soil stratification model and the subsidence model, based on geophysical processes. Oh et al. [30] employed probabilistic-based sensitivity analysis to assess the influence of input factors in generating a land subsidence hazard map. Some studies have assessed regional subsidence hazards and identified high-risk areas using spatial modeling methods using GIS [31,32,33], multi-objective decision making [34], and the fuzzy set theory [35]. However, many of the produced risk maps remain qualitative. Mohebbi Tafreshi et al. [35] adopted fuzzy functions to standardize the parameters with different dimensions, though this approach did not fully address the fuzziness of parameter importance.

The previous studies have primarily employed qualitative or semi-quantitative techniques, such as index systems or physical models, which do not provide a quantitative estimation of the likelihood of subsidence [5,36]. Although some studies have attempted to use geo-statistic-based physical models for probabilistic studies [29], land subsidence is a complex process involving multiple factors, such as geology, hydrogeology, and engineering activities, making it challenging for physical models to comprehensively account all the relevant factors and their interactions. Additionally, the application of physical models relies on extensive input data, such as geologic structures, groundwater levels, and soil properties [37]. Limited access to data can constrain the application and validity of these models.

The probability of land subsidence represents the likelihood of ground subsidence occurring in a specific area within a given time period due to natural factors (e.g., crustal movement and soil compression) or human factors (e.g., groundwater over-extraction and large-scale engineering construction). It provides a quantitative assessment of the potential for land subsidence, with values ranging between 0 and 1. Therefore, in this study, a weighted Bayesian network model was chosen to calculate the probability of land subsidence occurrence. Bayesian networks [38], consisting of directed acyclic graphs and conditional probability tables, can graphically and probabilistically describe the causal relationships between variables [39]. Bayesian modeling has been widely used in the study of natural disasters, including landslides [40,41,42], wildfires [43], and floods [44], as well as probabilistic studies related to ecosystems and chemistry [37,45]. For land subsidence, some researchers have used Bayesian models to estimate probability distributions by analyzing groundwater extraction scenarios over different periods [33]. However, there is limited research that comprehensively integrates multiple influencing factors to calculate the probability of land subsidence using Bayesian models.

This study utilizes a weighted Bayesian model to quantitatively investigate the occurrence probability of land subsidence in Shanghai. Cumulative land subsidence is represented as posterior probability to reduce ambiguity. The influencing factors, including soft soil layer thickness, aquifer thickness, construction activity intensity, and land reclamation, are selected. Using the expert scoring method, we analyze the occurrence probability of land subsidence in different areas under two scenarios with the weighted Bayesian model. A hazard (intensity–probability) matrix is used to present the hazard zoning of land subsidence in Shanghai.

2. Data and Methods

2.1. Study Area

Shanghai is located at the estuary of the Yangtze River, covering a total area of 6340 km² (Figure 1). The city is situated in a flat, low-lying coastal zone with an average elevation of about 4 m. It is mainly covered by Quaternary loose strata, with complex sediment types and alternating sand and clay layers, which form the background conditions for land subsidence [46,47]. Between 1921 and 1965, the maximum cumulative subsidence in the central city reached up to 2.6 m (nearly 59 mm per year). In 1966, recognizing the severe consequences of land subsidence, the Shanghai municipal government began prohibiting groundwater extraction in urban areas (2). By 1985, land subsidence in the central urban areas was well controlled (only 1 mm per year). However, following rapid urbanization and socio-economic development post-1986, land subsidence began to aggravate again in both the urban and suburban areas of Shanghai [48]. Since 2000, multiple control measures have limited annual average land subsidence to below 6 mm in Shanghai (3).

2.2. Data

The datasets used in this study include cumulative land subsidence, geological, Shanghai Districts Master Plan and Land Use Master Plan (2017–2035), and Shanghai administrative division (1958 and 2021) data.

The cumulative land subsidence data, aquifer distribution, and the soft soil thickness data were sourced from the Shanghai Geological Data Information Sharing Platform accessible via the Chinese language website: https://data.sigs.cn/Home/Index (accessed on 23 December 2024). The cumulative land subsidence dataset covers two main periods: 2012–2016 and 2017–2021. Shanghai is covered by Quaternary loose sediment layers with complex stratigraphy, consisting of alternating sand and clay soil layers. The lower portion primarily comprises dark grey silty clay and silty chalky clay, with localized sandy chalk, chalk, and fine sand. The upper portion is dominated by grey and grey-yellow sandy chalky clay, clayey chalky clay, and powdery clay, which form the material basis of land subsidence. Based on the depositional era and the soil layer’s physical index, the subsurface is classified into nine engineering geological layers, and five distinct pressurized aquifers (I–V). The characteristics and thicknesses of these layers and aquifers are detailed in Table 1 and Table 2. In addition, urban construction activities significantly impact land subsidence in the urban area by lowering the shallow groundwater levels. The new, planned construction areas are key zones that may cause regional uneven subsidence in the future. According to the Shanghai Urban Master Plan (2017–2035) and the urban development boundary planning maps of the Shanghai Districts Master Plan and the Land Use Master Plan (2017–2035), the planned new construction areas in 16 districts of Shanghai were vectorized to analyze the potential intensity of construction activities. The data on land reclamation in recent decades was obtained from the Bulletin of Maritime Domain Use Management (https://mds.nmdis.org.cn/pages/home.html, Chinese language website, accessed on 23 December 2024). Additionally, information on Shanghai’s administrative division from 1958 to 2021 was sourced from https://www.shanghai-map.net/shtdt/main.html (Chinese language website, accessed on 23 December 2024). In 1958, administrative reorganization was the most significant since the city’s founding, establishing the foundation for Shanghai’s current administrative boundaries.

2.3. Data Preprocessing

2.3.1. Indicators and Independence Analysis

Selecting the appropriate influencing factors is crucial for accurately evaluating the possibility of land subsidence. Based on the drivers of land subsidence in Shanghai related to environmental and human activities [46,47], five indicators were selected: cumulative land subsidence, the distribution of aquifers, the thickness of soft soil layers, the intensity of construction activities, and land reclamation areas. Additionally, to ensure the rationality of analysis, influencing factors with high intercorrelation were excluded to maintain independence among the variables. Zhang et al. [49] suggested that if the correlation coefficients between factors are less than 0.3, they can be considered independent. Following this criterion, we used SPSS Statistics 29 to analyze the independence of the influencing factors, and the maximum correlation coefficient value was 0.273, which meets the independence requirement.

2.3.2. Indicator Rating

• [1]. Confined Aquifers

In this study, the influence of different aquifers on subsidence was considered. Shanghai’s Quaternary sedimentary layers contain five confined aquifers from top to bottom. The thickness of these aquifers was aggregated (Figure 2a) and categorized into four levels using the equal interval method. The thickness ranges from levels 1 to 4 are as follows: 0–45 m, 45–90 m, 90–135 m, and above 135 m. The common methods for index classification include natural break, quantile, equal interval, and manual classification [50]. The equal interval method is widely used in geographic information systems (GISs) and disaster risk assessment studies [32,51,52,53,54]. It generates classes with equal ranges, which is advantageous for mapping disaster severity levels based on numerical indices [50,55]. This method ensures the equitable distribution of records across categories, making them visually interpretable when mapped.

• [2]. Thickness of Soft Soil Layers

The thickness of the soft soil layers was also aggregated and classified into four levels using the equal interval method: level 1 (0–13 m), level 2 (13–26 m), level 3 (26–39 m), and level 4 (39–50 m) (Figure 2b). The degree of bedrock undulation in Shanghai is low in the north and east and high in the southwest. Deeper bedrocks are found in Jiading, Baoshan, Pudong, and Chongming Districts, while shallower ones are in Qingpu, Jinshan, Songjiang, and Fengxian Districts. In Chongming Island and the northern Baoshan, bedrock depths exceed 300 m, with soft soil layers up to 50 m thick.

• [3]. Intensity of Construction Activity

Urban construction activities, which lower shallow groundwater levels, are a critical factor causing land subsidence. The intensity of construction activity refers to the frequency and scale of construction activities within a specific area. The areas marked in red in Figure 2c represent new planning areas for construction or resettlement, indicating intense construction activities. The key future development areas include Jiading New Town, Qingpu New Town, Songjiang New Town, Fengxian New Town, and Nanhui New Town, which have significant, new, planned construction areas [46]. The construction activity intensity in Shanghai is classified into two levels; level 1 represents the areas with less-intense construction activities, and level 2 represents the areas with intense construction activities.

• [4]. Land Reclamation Areas

Land reclamation areas, primarily covered by blown-in soil, often experience severe land subsidence. The filled soil layer in the large-scale reclamation areas shows noticeable heterogeneity due to uneven material composition and varying thickness, leading to significantly differential subsidence. This study used the administrative division of Shanghai Municipality in 1958 as the baseline, identifying newly reclaimed areas based on land coverage changes from 1958 to the present (Figure 2d). The reclaimed areas present since 1958 are classified as level 1, with the other regions being level 2.

• [5]. Cumulative Land Subsidence

The spatial distributions of cumulative land subsidence from 2012–2016 and 2017–2021 are shown in Figure 3a and Figure 3b, respectively. The map of cumulative land subsidence in Shanghai is derived from the Shanghai Institute of Geological Survey and is constructed using measurements from tens of thousands of leveling points. These points are evenly distributed across Shanghai, with a higher density in the central urban area and fewer in the suburbs, ensuring accurate coverage of the entire city. The leveling points are remeasured every five years with high-level accuracy. Shanghai is divided into subsidence zones (cumulative land subsidence > 0) and non-subsidence zones (cumulative land subsidence < 0). These zones are further classified into four levels based on the cumulative land subsidence: level 1 from −50 to 0 mm (non-subsidence zone); level 2 from 0 to 50 mm; level 3 from 50 to 100 mm; and level 4 from 100 to 150 mm. From 2017 to 2021, the proportion of areas with cumulative subsidence exceeding 100 mm significantly decreased, and the proportion of non-subsidence areas increased by 3.28%. Random sampling statistics show that the peak of cumulative land subsidence in Shanghai is 25 mm. Based on skewness and kurtosis analyses, the cumulative land subsidence probability density function exhibits skewed distribution characteristics, with values primarily distributed within the 0–50 mm range (Figure 3e).

2.4. Methods

This study assesses the hazard of land subsidence in Shanghai using a hazard matrix model, which comprise the intensity and probability of land subsidence. Intensity is represented by the rate of land subsidence from 2017 to 2021, while probability is calculated using a weighted Bayesian model based on expert scoring. The specific methodology of this study is detailed below.

2.4.1. Defining the Scenarios

According to the mechanism of land subsidence, two scenarios are considered in this study. Scenario I considers the aquifer layers of 1–5, and soft soil layer thickness layers of 3, 4, and 5 in Shanghai. Given the fact that groundwater extraction has been prohibited in Shanghai, Scenario II focuses on the impact of construction activities, particularly uneven subsidence caused by the excavation of deep foundation pits. Consequently, in Scenario II, aquifer layers 1 and 2 were selected as the aquifer distribution indicator, while soft soil layers 3 and 4 were used as the soft soil layer thickness indicator.

2.4.2. Weighted Bayesian Network Model

A Bayesian network model consists of a set of random variables with complex causal relationships, which can be represented using a directed acyclic graph. In this graph, random variables are depicted as eigenvector nodes [38]. In a directed acyclic graph (Figure 4a), the influencing factors related to land subsidence are the parent nodes ($Y_j$), and the subsidence hazard is the child node ($T$). The arrows represent the probabilistic dependence between nodes [56]. If the directed acyclic graph satisfies the conditional independence assumption, the joint probability distribution $P\left(T\right)$ of the Bayesian network nodes can be expressed as the product of the conditional probabilities of each child node with respect to its parent nodes. This study constructs a Bayesian structure (Figure 4b) for each influencing factor of land subsidence and calculates the probability distribution of each indicator, and Figure 4c shows the probability of land subsidence. Figure 4b illustrates the probability of the spatial distribution of the indicators affecting land subsidence, and Figure 4c presents the probability of Figure 4b to obtain the conditional probability of parent nodes $Y_j$. The land subsidence probability is calculated as follows:

(1)$P\left(X_{i1}\left|S\right.\right)={\displaystyle \frac{P\left(X_{i1}\right)\times P\left(S\left|X_{i1}\right.\right)}{P\left(S\right)}}$

(2)$P\left(T\left|Y_1\right.,\dots ,Y_j,\dots ,Y_m\right)={\prod _{j=1}^{m}P\left(T\left|Y_j\right.\right)}^{w_j}$

where $P\left(S\right)$ is posterior probability; $P\left(X_{i1}\right)$ is the probability distribution of each indicator at different levels; $P\left(S\left|X_{i1}\right.\right)$ is the probability of land subsidence at different levels of individual indicators; $P\left(X_{i1}\left|S\right.\right)$ is the probability distribution at different levels of each indicator under the condition of subsidence; $P\left(T\left|Y_j\right.\right)$ is the probability of subsidence under indicators; and $w_j$ is the weight of each influencing factor.

The methodology framework for analyzing the probability of land subsidence is illustrated in Figure 5. First, 2000 sampling points were generated by random sampling across Shanghai. In this study, we employed a stratified sampling approach to randomly select the 2000 points, ensuring comprehensive coverage of the entire area. Shanghai was divided into 16 districts, and the number of points selected from each district was proportional to its area size. Within each district, the points were randomly selected to account for subsidence differences across the different regions. This approach ensures that the selected points are representative of the entire area. The proportions of sampling points falling into the subsidence zone and the non-subsidence zone were denoted as m and n (m + n = 100%). Five indicators were then extracted for these sampling points using the spatial analysis tools in ArcGIS: aquifer thickness, soft soil layer thickness, construction activity intensity, land reclamation, and cumulative land subsidence. Using the indicator attribute table of these 2000 points, the conditional probability of each indicator under both the subsidence and non-subsidence conditions was calculated. Third, the spatial distribution of the subsidence occurrence probability of subsidence was determined by combining the conditional probability distributions of each indicator using a weighted Bayesian model. Finally, normalization was performed to obtain the overall probability of subsidence occurrence. The methodology framework is shown in Figure 5.

The probabilities of land subsidence occurrence and non-subsidence occurrence under influencing factors were calculated as follows:

(3)$p\left(x=T_0|Y_i\right)=\left(x=T_0\right)\prod {p\left(Y_i|T_0\right)}^{w_i}$

(4)$p\left(x=T_1|Y_i\right)=\left(x=T_1\right)\prod {p\left(Y_i|T_1\right)}^{w_i}$

Finally, the occurrence probability of land subsidence was normalized:

(5)$p\left(T\right)={\displaystyle \frac{p\left(x=T_0|Y_i\right)}{p\left(x=T_0|Y_i\right)+p\left(x=T_1|Y_i\right)}}$

where $T_0$ indicates non-subsidence, $T_1$ indicates land subsidence, $i$ represents indicators affecting land subsidence ($i=1,2,3,4$), $P\left(T\right)$ is the probability of land subsidence occurrence after standardization, $P\left(T_0\left|Y_j\right.\right)$ is the probability of non-subsidence occurrence, $P\left(T_1\left|Y_j\right.\right)$ is the probability of land subsidence occurrence, and $w_i$ is the weight of the indicators.

2.4.3. Weight Computation

The expert scoring method was utilized to determine the importance of the indicators affecting land subsidence. This method, noted for its accuracy, comprehensiveness, and traceability, provides a relatively comprehensive and objective evaluation [57]. A pairwise comparison approach was employed to assess the relative importance of each indicator. The indicators were categorized into three levels based on their significance: less important (scoring 0 points), equally important (scoring 1 point each), and more important (scoring 1 point). To ensure robustness, 14 experts from the Shanghai Geological Survey Institute participated in evaluation. Each expert conducted pairwise comparison, assigning importance scores to derive the final weightings. The aggregated results of this expert scoring process are shown in Figure 6. Consequently, weights of 0.21, 0.24, 0.28, and 0.27 were assigned to the indicators of aquifer thickness, soft soil layer thickness, urban construction activity, and land reclamation, respectively.

2.4.4. Sensitivity Analysis

A Fit statistic was applied to analyze the discrepancy between the modeled probabilistic results and the actual subsidence data. This statistic compares the distribution of calculated probable subsidence with reference subsidence (i.e., the cumulative subsidence map from 2017 to 2021). A larger proportion of overlapping areas indicates better modeled results. The Fit statistic ranges from 0 to 1, with values closer to 1 denoting more accurate results. The Fit Statistic equation is as follows:

(6)$Fit={\displaystyle \frac{A_o}{A_r+A_s-A_o}}$

where $A_o$ represents to the overlapping area between the reference subsidence areas and the map of possible subsidence areas, $A_r$ refers to the reference subsidence areas, and $A_s$ denotes the possible future subsidence areas.

2.4.5. Land Subsidence Hazard Matrix

Based on cumulative land subsidence intensity (the rate of land subsidence from 2017–2021) and the corresponding probability of occurrence, a subsidence hazard matrix was developed (Figure 7) to map the spatial distribution of land subsidence hazards. The horizontal axis of the matrix represents the probability classification of occurrence, divided into five levels using the equal interval method. The vertical axis represents the intensity classification of land subsidence, also divided into four levels using the equal-interval method, forming a 5 × 4 matrix. To further refine ranking within the matrix, this study applied ordered sample cluster analysis (Figure 7) to reclassify the hazard levels. The resulting land subsidence hazard map categorizes hazards into four classes: very low (green), low (yellow), medium (orange), and high (red). According to the matrix diagram, the higher the number, the higher the hazard level.

3. Results

3.1. Probability ofIndicators Under Two Scenarios

A weighted Bayesian network model was used to calculate the conditional probability of each indicator under Scenarios I and II to assess the likelihood of land subsidence in Shanghai based on 2017–2021 cumulative land subsidence (Figure 8). Using 2017–2021 land subsidence as a measure of posterior probability, the probability of the subsidence zone is 0.725, and the probability of the non-subsidence zone is 0.275 (Figure 8). The probabilities of each indicator were calculated for both the scenarios.

For the aquifer distribution indicator, in Scenario I, level 3 has the highest probability (0.580), followed by level 2 (0.272), while level 1 and level 4 have lower probabilities. In Scenario II, the distribution of the aquifer is more uniform, with level 4 having the highest probability (0.390), followed by level 3 (0.281), while level 1 and level 2 have lower probabilities. For the soft soil layers, in Scenario I, level 2 has the highest probability (0.397), followed by level 3 (0.411), while level 1 and level 4 have lower probabilities. In Scenario II, the results are similar to Scenario I; the probability of level 2 is the highest (0.496), but the probability of level 1 (0.196) is relatively high as well, while level 3 and level 4 have lower probabilities.

3.2. Spatial Distribution of Land Subsidence Probability

The spatial distribution of land subsidence probability in Shanghai under the two scenarios is shown in Figure 9 using 2017–2021 cumulative land subsidence as a measure of posterior probability. The range of likelihood of land subsidence occurrence is 0.02 to 0.97 under Scenario I (Figure 9a). The probability of occurrence was categorized into five levels: high probability (p ≥ 0.8), medium–high probability (0.6 ≤ p < 0.8), medium probability (0.4 ≤ p < 0.6), medium–low probability (0.2 ≤ p < 0.4), and low probability (p < 0.2).

The areas with a very high subsidence probability are primarily distributed in the eastern suburbs of Shanghai and the surrounding areas of Chongming District due to large-scale land reclamation in recent decades. The medium probability areas are mainly distributed in the Central City, the central areas of Pudong and Chongming Districts, which are mainly affected by the combined effects of three indicators: the distribution of aquifers, the thickness of the soft soil layers, and the intensity of construction activity. The lower probability areas are mainly located in the northwestern region of Shanghai.

Under Scenario II, the probability range of land subsidence is between 0.04 and 0.98 (Figure 9b). The very high probability zones are primarily situated in the eastern coastal region of Pudong District, as well as the areas with substantial construction activities. The lower probability area is primarily located within the developed regions of Qingpu District. Additionally, within the high probability zones, there are some “isolated islands” with very high likelihood, primarily attributed to the influence of construction activities.

3.3. Hazard Zoning of Land Subsidence

Based on the intensity distribution of land subsidence (Figure 3b) and the probability distribution of subsidence (Figure 9), a hazard zoning map of land subsidence in Shanghai was generated using the land subsidence hazard matrix. Land subsidence hazard zoning in Shanghai was categorized into four levels: very low, low, medium, and high (Figure 10). The results show that the areas of high, medium, low, and very low subsidence hazards are 1619.9 km², 1244.7 km², 2298.9 km², and 1177.0 km², accounting for 25.5%, 19.6%, 36.3%, and 18.6% of the total land area in Shanghai, respectively. The high-hazard areas are mainly distributed in the peripheral areas of Chongming District, with patchy areas in the eastern part of Pudong District and the central and western parts of Minhang District. The medium-hazard area has the most widespread distribution, particularly in Huangpu, Hongkou, Pudong, Minhang, Fengxian, Songjiang and Jinshan Districts, as well as the central part of Chongming District. The low-hazard areas are mainly located on the west and south sides of the medium-hazard zones, while the very low-hazard areas are primarily found in Qingpu and Jiading Districts to the west and north of Shanghai (Figure 10).

Chongming District has the highest proportion of high-hazard areas, accounting for 41.8% of the entire district. Xuhui District has the highest proportion (75.2%) of medium-hazard areas. Hongkou District has the highest proportion (89.0%) of low-hazard areas, while Jiading District has the highest proportion (76.8%) of very-low-hazard areas, followed by Qingpu District (72.4%). Additionally, five districts, including Yangpu, Putuo, Jingan, Xuhui, and Hongkou, do not have high-hazard areas.

4. Discussion

The previous studies used a multi-criteria approach to assess the hazard of land subsidence in Shanghai, selecting indicators, such as subsidence susceptibility, the development level, the prediction rate, and elevation [3]. This method has the problem of conceptual confusion; for instance, elevation is not related to the geophysical process of land subsidence, and therefore should not be used as an indicator for assessing the land subsidence hazard. Additionally, this is a semi-quantitative analysis method and cannot provide the likelihood of subsidence occurrence.

Although the exploitation of groundwater has a close relationship with land subsidence, the amount of groundwater recharged has been greater than that exploited in Shanghai since 2003. Thus, the exploitation of groundwater is no longer a major factor in land subsidence [33]. In this work, explicit indicators were selected to analyze the hazard of land subsidence according to the factors affecting the subsidence geophysical processes. Based on the Bayesian theory, the hazard of land subsidence in Shanghai was quantitatively assessed, including subsidence probability and intensity, and hazard zoning is also presented.

4.1. Sensitivity Analysis

Using 2012–2016 cumulative land subsidence as a measure of posterior probability, the probability of a subsidence zone is 0.758, and the probability of a non-subsidence zone is 0.242. Under the subsidence condition of Scenario I (Figure 11), soft soil and aquifer layer level 2 and level 3 have the highest probability of subsidence, indicating that these layers significantly influence subsidence. In Scenario II, aquifer level 1 and soft soil layer level 3 have the highest subsidence probabilities. The probability of land subsidence is higher in areas with intense construction activity and new reclamation.

When 2012–2016 cumulative probability of land subsidence was used as a measure of posterior probability, the probability of the land subsidence occurrence ranged from 0.02 to 0.98 based on Scenario I (Figure 12a), which is relatively lower compared to that for 2017–2021 cumulative land subsidence. Under Scenario II, the probability of land subsidence ranges from 0.03 to 0.98 (Figure 12b).

The probabilistic results of land subsidence were tested in Shanghai using Fit statistics. The predicted subsidence probability based on 2012–2016 cumulative land subsidence was selected for sensitivity analysis with cumulative land subsidence from 2017 to 2021. The distribution of the compared results was reclassified into two classes based on whether or not subsidence occurred (Figure 13a). A probability greater than 0.5 indicates an area where land subsidence will occur [37]. The results for Scenarios I and II are shown in Figure 13b,c. The yellow area in Figure 13d,e indicates consistent results, the blue areas are underestimated, and the orange areas are overestimated. Scenario II shows better results with a Fit statistic of 70% compared to 67% for Scenario I. It is worth noting that the overestimated areas are those where future construction activities will take place, making these areas prone to land subsidence. Therefore, the fitting results should be better than 70%. Thus, using a weighted Bayesian model to study the occurrence probability of land subsidence is an effective method.

4.2. Uncertainties

The probabilistic results of land subsidence using the weighted Bayesian model were validated using the Fit statistic. However, land subsidence is affected by a variety of factors. In this study, four main indicators affecting land subsidence were considered, but there are other indicators that were not fully accounted for, such as groundwater exploitation and recharge. Additionally, the indicator of construction activity intensity has some inherent uncertainty. This is closely related to the planning and construction policies of Shanghai, which includes not only the construction of new planning areas, but also infrastructure network projects, such as the construction of the subways and highways, which have not been fully considered.

4.3. Recommendations

According to the land subsidence hazard zoning map obtained in this study, the density of building development is strictly controlled in areas with a high risk of ground subsidence. A scientific urban construction plan should be formulated to avoid over-concentrated construction. Especially, the construction of tall buildings should try to avoid the high-hazard zone of land subsidence. For the medium-risk areas, a detailed geological investigation should be carried out, and targeted foundation treatment measures should be taken in engineering construction to enhance the settlement resistance of buildings. Given the effectiveness and generalizability of the weighted Bayesian model in quantitatively assessing the hazard of land subsidence, the model is generalized and applied to other areas facing similar risks of geologic hazards. The parameters of the model are adjusted in the light of local conditions to provide scientific methods and tools for land subsidence risk assessment, risk management and urban planning in these areas.

5. Conclusions

This study provides a quantitative assessment of the land subsidence hazard using the weighted Bayesian model, offering insights into subsidence probability, intensity, and hazard zoning. The findings contribute to the understanding of land subsidence processes and their potential impacts, providing a methodological framework applicable to other regions facing a similar geohazard.

In this study, five key indicators were selected to determine the likelihood of land subsidence using a weighted Bayesian model: cumulative land subsidence, soft soil layer thickness, aquifer thickness, construction activity, and land reclamation. The findings are as follows:

The key scientific contribution of this study is the development of a probabilistic model that quantifies land subsidence based on both environmental and anthropogenic factors. Analysis revealed that from 2017 to 2021, the extent of significant land subsidence in Shanghai decreased, while that of the non-subsidence areas increased, highlighting the dynamic nature of subsidence patterns in response to changing human activities and environmental conditions. The probability density function of cumulative land subsidence follows a normal distribution, with the highest density observed in the 0–50 mm range.

The probability of land subsidence under Scenario I ranges from 0.02 to 0.97, with the highest probability areas strongly influenced by factors such as land reclamation activities. The medium probability zones are typically influenced by subsurface characteristics, including aquifer distribution, soil composition, and urbanization intensity. Scenario II yielded a similar probability range (from 0.04 to 0.98), with the high probability regions correlating with dense construction activities and coastal geotechnical conditions. This study offers valuable insights for risk management and urban planning.

The effectiveness of the weighted Bayesian model was validated using Fit statistic analysis, comparing the predicted subsidence probabilities with the observed data. The results demonstrated a high degree of accuracy, with Scenario II providing a superior predictive performance, confirming the robustness of the modeling approach.

This study also developed a hazard zoning map, identifying the areas with varying levels of subsidence hazard. The high-hazard zones, particularly in areas with intense construction activities and land reclamation, were identified as critical for land use planning and mitigation strategies. This zoning framework can serve as a useful tool for prioritizing subsidence monitoring and mitigation efforts.

In summary, this study advances the scientific understanding of land subsidence hazard modeling by integrating probabilistic assessments and spatial hazard zoning. The spatial hazard zoning provides a basis for land subsidence risk assessment in Shanghai. The approach presented here can be applied to other regions with similar geological and anthropogenic conditions, contributing to broader efforts in land subsidence hazard assessment and management worldwide.

Author Contributions

C.J.: writing and editing; formal analysis; conceptualization. J.W.: methodology; supervision; funding acquisition. Q.Z.: review and editing; methodology; conceptualization. Y.S.: review and editing. C.W.: writing—review and editing. H.Z.: review and editing. J.L.: review and editing. T.T.: review and editing. Z.L.: writing—review and editing. L.Z.: writing—review and editing. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

Data will be made available on request.

Conflicts of Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1. Map showing study area of Shanghai City with 16 districts.

Figure 2. Spatial distribution of influencing factors of land subsidence in Shanghai. (a) Aquifers thickness; (b) Soft soil layer thickness; (c) Intensity of construction activities; (d) Newly reclaimed areas since 1958.

Figure 3. Cumulative land subsidence maps in Shanghai. (a) Cumulative land subsidence in 2012–2016; (b) cumulative land subsidence in 2017–2021; (c) percentage of different cumulative land subsidence in 2012–2016; (d) percentage of different cumulative land subsidence in 2017–2021; (e) probability distribution of cumulative land subsidence in 2012–2016 and in 2017–2021.

Figure 4. A Bayesian structural probabilistic computational model. (a) A directed acyclic graph of the weighted Bayesian structural model; (b) the probability of the spatial distribution of the indicators affecting land subsidence; and (c) the probability of land subsidence (posterior probability).

Figure 5. The methodology framework of land subsidence probability analysis in this study. (a) Aquifers thickness; (b) Soft soil layer thickness; (c) Intensity of construction activities; (d) Newly reclaimed areas since 1958.

Figure 6. Map of results of expert scoring of importance of indicators. (a) Aquifer thickness; (b) soft soil layer thickness; (c) intensity of construction activities; (d) newly reclaimed areas since 1958.

Figure 7. Land subsidence hazard (intensity–probability) matrix modeling.

Figure 8. Probabilities of each indicator under land subsidence conditions (yellow) and non-subsidence conditions (green) for Scenario I and Scenario II using 2017–2021 cumulative land subsidence probability as measure of posterior probability.

Figure 9. Spatial distribution of land subsidence probability using 2017–2021 cumulative land subsidence as measure of posterior probability. (a) Scenario I; (b) Scenario II.

Figure 10. Hazard zoning map of land subsidence in Shanghai.

Figure 11. Probabilities of each indicator under land subsidence conditions (yellow) and non-subsidence conditions (green) for Scenario I and Scenario II using 2012–2016 cumulative land subsidence probability as measure of posterior probability.

Figure 12. Spatial distribution of land subsidence probability using 2012–2016 cumulative land subsidence as measure of posterior probability. (a) Scenario I; (b) Scenario II.

Figure 13. Comparison of land subsidence probability distribution in Shanghai using weighted Bayesian model and actual subsidence results. (a) Map of land subsidence and non-subsidence in 2017–2021. (b) Map of land subsidence categories under Scenario I. (c) Map of land subsidence categories under Scenario II. (d) Map of differences between (a,b). (e) Map of differences between (a,c).

Table 1

Distribution of soil layers in Shanghai.

Soil Layer	Soil Types	Characterization	Thicknesses (m)
①	Landfill	Low bearing capacity, uneven, suitable for farming but poor for engineering applications	1–20
②	Silty clay	Highly compressible, highwater content, common near river channels	1–20
③ + ④	Silty clayey soil (Soft soil)	High compressibility, low permeability, a sensitive layer for land subsidence	5–45
⑤	Clayey soil	High compressibility, low permeability, some blockage of groundwater flow	20–50
⑥	Yellow clayey soil	Highly permeable, shallow pressurized aquifer	2–60
⑦	Sandy chalky soil	Low permeability, mainly in deeper strata	5–10
⑧	Grey clayey soil interbedded with chalky soil	Good permeability, abundant groundwater resources	5–40
⑨	Sandy soil	Acts as a protective underlying aquifer	5–20

Table 2

Distribution of aquifers in Shanghai.

Pressurized Aquifer I	High Water Storage Capacity, a Primary Extractive Layer, Vulnerable to Over-Extraction	Thicknesses (m)
Pressurized aquifer II	Deeply buried and protected by a water barrier	10–50
Pressurized aquifer III	High permeability, abundant water storage	10–40
Pressurized aquifer IV	Deeply buried, with limited water resource	10–50
Pressurized aquifer V	Controlled by bedrock, deeply buried	20–50
Pressurized aquifer I	High water storage capacity, a primary extractive layer, vulnerable to over-extraction	20–50

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