Keywords

1 Introduction

Over half of human population in the world lives within 60 km of coast, and the population proportion is increasing [1]. Consequently, large-scale development of land reclamation were conducted to meet the demand for land. Many countries, such as United States, South Korea, Netherlands and China reclaimed over 1000 km2 lands [2], more than 1860 km2 lands were reclaimed in China during 2000–2016, and a large portion of the lands held significant contamination risks [3]. Field surveys showed that contamination including heavy metal contamination within marine sediments and dredged materials existed in many regions [4], especially in river estuaries [5,6,7]. Many land reclamation programs using sediments of unknown quality for fills were conducted under poor environmental supervision especially in developing regions, but soil contamination usually was not considered in studies on those new lands.

The city of Shanghai, China obtained over 300 km2 land using land reclamation [8], and the area is still expanding for the need of city development. Contamination of Zn [9], Cd [10,11,12], As [11] within surface sediments in some Shanghai’s coastal zones were detected to be contaminated. The authors conducted series of field surveys on both geotechnical properties and soil environmental properties during 2016–2018, obtaining numbers of correlated data therein. Worrying surface subsidence risks and heavy metal contamination (HMC) were revealed within Shanghai’s typical reclaimed lands.

Bayesian network (BN) is practical in multi-variables analysis [13, 14], and has been widely used in many cases, e.g., earthquake disaster chain analysis [15], marine transportation risk assessment [16], and coastal hazard risk reduction assessment [17].

This work aims to build a comprehensive BN to evaluate surface subsidence risks and HMC in Shanghai’s typical reclaimed regions, and analyze correlations among the considered variables.

2 Materials and Methods

2.1 Shanghai’s Typical Reclaimed Lands

Detailed borehole surveys and lab tests on both geotechnical data and soil environmental data was done since 2016 in typical reclaimed fields of Hengsha Island and Laogang Town, Shanghai [3]. Depth of the boreholes ranged from 45 m to 75 m, the investigated layers are listed in Table 1.

Table 1. Strata in the study regions.
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Using the data detected in 2016–2018, the authors evaluated surface subsidence risks on basis of one dimensional Terzaghi’s soil consolidation theory [18]. The evaluated land subsidence caused by land reclamation was comprised of self-weight consolidation subsidence of reclaimed layers and compression consolidation subsidence of underlying sedimentary beddings. Land subsidence since July 1st 2018 (s18) was evaluated to characterize the total land subsidence risk. The land subsidence from July 1st 2018 to January 1st 2019 (v18) was evaluated to act as the land subsidence velocity in the analyzed points. And comprehensive land subsidence risk (Rc) simultaneously considering s18 and v18 was also evaluated. Heavy metal contamination within soils considering concentration of seven heavy metal elements, i.e., Zn, Cd, As, Ni, Cu, Pb and Cr was evaluated in thirty two boreholes among which eleven boreholes were drilled in Laogang Town and twenty one in Hengsha Island. Considering that the contaminated layers including the reclaimed layer ①3-2 to layer ⑤1-1, and that layer ②2–③1 were dredged as the major fill source for land reclamation in the study regions, only the top layers downward to layer ⑤1-1 were analyzed in the HMC analysis, and they were divided into three groups, i.e., the fill layers, shallow sediments (layer ②2–③1) and deep sediments (layer ④–⑤1-1).

2.2 BN Analysis

BNs are acyclic directed graphs with nodes that represent random variables and arcs that represent direct probabilistic dependences among them [13, 14, 16]. BN’s structure is a qualitative illustration of the interactions among the modeled variables. Based on the conditional independence and the chain rule [13], the joint probability distribution of a set of random variables U = {B1, …, Bn} can be defined in the BN as follows:

$$ P\left( U \right) = \prod\limits_{i = 1}^{n} P \left\{ {B_{i} \left| {Pa\left( {B_{i} } \right)} \right.} \right\} $$
(1)

where P(U) is the joint probability distribution of U, and Pa(Bi) is the parent set of variable Bi. Information flow in BN obeys the following rules: (1) information may flow through a serial (B1→B2→B3)/diverging (B1←B2→B3) connection unless the evidence for the intermediate variable B2 is given; (2) information may flow through a converging (B1→B2←B3) connection whenever the state of the intermediate variable B2 or one of its descendants is given [19]. BN determines the relevant variables to a given target variable by using these rules. According to Bayes theorem, posterior probability distribution of events can be yielded by updating their prior probability given new observations, i.e. evidence E [20]:

$$ P\left( {U\left| E \right.} \right) = {{P\left( {U,E} \right)} \mathord{\left/ {\vphantom {{P\left( {U,E} \right)} {P\left( E \right) = {{P\left( {U,E} \right)} \mathord{\left/ {\vphantom {{P\left( {U,E} \right)} {\sum\limits_{U} {P\left( {U,E} \right)} }}} \right. \kern-0pt} {\sum\limits_{U} {P\left( {U,E} \right)} }}}}} \right. \kern-0pt} {P\left( E \right) = {{P\left( {U,E} \right)} \mathord{\left/ {\vphantom {{P\left( {U,E} \right)} {\sum\limits_{U} {P\left( {U,E} \right)} }}} \right. \kern-0pt} {\sum\limits_{U} {P\left( {U,E} \right)} }}}} $$
(2)

In the BN analysis, subject-matter-expert judgments [16] from correlated sources, such as geotechnical field surveys, laboratory tests, data collection, and standards learning, were firstly executed to determine concrete BN variables and global BN structure and to build a BN for risk evaluation in the study regions. The BN was constituted of sixteen nodes among which four nodes (N01-N04) are basic characteristics of the data points, six nodes (N05-N10) showing geotechnical parameters of analyzed layers, three nodes (N011-N013) used for evaluating subsidence risk levels, and three (N14-N16) used to assess soil contamination (Table 2). Secondly, data preparation based on the analysis in the first step was conducted carefully. The continuous variables were transformed into discrete variables to make BN a discrete network that can be applicable to discrete information in practice (Table 2). Variable discretization was conducted on the basis of subject matter experts’ judgments. Thirdly, primary structure learning was performed with the prepared data and outlined global BN structure. The primarily learned BN structure was further adjusted to rectify the arcs among the BN nodes that go against common theories and logic. Finally, data learning was conducted using the established BN structure, thus producing the final BN model.

Table 2. Categorization of analyzed variables in the BN.
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3 Results

Influence strength between the Node N04 with its connected nodes generally shows stronger than other arcs, indicating the point location holds robust correlation with other variables, especially the soil type, land reclamation time, s18 and shallow sediment HMC. Influence between the three geotechnical parameters of fill layers, average initial soil void ratio (N05), average hydraulic conductivity (N06) and average compressibility coefficient (N07), only appears strong between Node N05 and Node N07. Contrastingly, influence among the three geotechnical parameters all shows similarly strong. Influence among the three HMC nodes is significantly strong, especially that between the fill HMC (N14) and the shallow sediment HMC (N15) (Fig. 1).

Fig. 1.
figure 1

Land subsidence risk and soil HMC contamination BN showing arc influence strength.

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Sensitivity analysis on both the land subsidence risk levels and soil contamination indicates the factors which can provide a high probability of correct evaluation on the target node (Figs. 2, 3, 4, 5 and 6). The s18 risk is remarkably sensitive to the four basic characteristics of the data points (N01-N04), the void ratio nodes and the compressibility coefficient nodes (Fig. 2a). The v18 risk is sensitive to all the basic characteristics of the data points and the geotechnical parameter nodes among which the point location, land reclamation time and the fill layer thickness hold the highest sensitivity (Fig. 2b). Sensitivity of the Rc risk reflects a combination of that of s18 risk and v18 risk (Fig. 3). The fill HMC shows sensitive to point location, land reclamation time and fill layer thickness (Fig. 4). The shallow sediment HMC acts sensitive to the fill HMC, but only slightly sensitive to point location (Fig. 5). The deep sediment HMC shows sensitive to the other two HMC nodes, land reclamation time and point location (Fig. 6). Sensitivity between the three subsidence risk nodes and the three HMC nodes appears slight.

Fig. 2.
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Sensitivity analysis respectively setting N11 (a), N12 (b) as the target variable (Bar chart color: the more red indicating the sensitivity more high, gray showing no sensitivity).

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Fig. 3.
figure 3

Sensitivity analysis setting N13 as the target variable (Bar chart color: the more red indicating the sensitivity more high, gray showing no sensitivity).

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Fig. 4.
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Sensitivity analysis setting N14 as the target variable (Bar chart color: the more red indicating the sensitivity more high, gray showing no sensitivity).

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Fig. 5.
figure 5

Sensitivity analysis setting N15 as the target variable (Bar chart color: the more red indicating the sensitivity more high, gray showing no sensitivity).

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Fig. 6.
figure 6

Sensitivity analysis setting N16 as the target variable (Bar chart color: the more red indicating the sensitivity more high, gray showing no sensitivity).

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4 Discussion and Conclusions

Point location holds strong influence on other three basic characteristics, geotechnical parameters and shallow sediment HMC, meanwhile it shows high sensitivity to the three subsidence risk nodes, fill HMC and deep sediment HMC, this essentially reflects significant differences in both land reclamation construction and sedimentary environments between the two study zones, i.e., YEIZ and YECPZ. The different influence strength of arcs among geotechnical parameters of the fill layers and the underlying strata, probably was caused by different texture between the fill soils and sedimentary soils. Rationally, the three land subsidence risk nodes appear sensitive to the six geotechnical parameter nodes since the land subsidence was evaluated using those parameters. But the three HMC nodes develop low sensitivity to the six geotechnical parameters, s18 risk and v18 risk, indicating that the soil HMC in the study regions hold no significant correlation with the soil geotechnical parameters. The HMC distribution was controlled more by the basic characteristics such as the point location, land reclamation time and fill layer thickness. Noticeably, the three HMC nodes show almost no sensitivity to fill soil types, meaning the HMC distribution held no correlation with the fill soil types in the study regions. The BN can be used as a basis for land subsidence controlling and field remediation planning in the study regions, further field survey data on soil geotechnical properties and HMC distribution would enhance reliability of the BN.