Evaluation of the Heavy Metal Pollution Induced by Sand Mining in Poyang Lake Based on the Fuzzy PERI Model

Abstract

Sand mining significantly impacts heavy metal pollution in aquatic ecosystems. However, uncertainties in measured heavy metal concentrations in sediments caused by sand mining activities are unavoidable. To address this, a fuzzy potential ecological risk index (PERI) model was developed based on the triangular fuzzy number (TFN) theory. The model incorporates the ecological risk TFN of individual heavy metals, a comprehensive ecological risk TFN, and a transitional PERI model. This approach was applied to sand mining regions of Poyang Lake, with the following results: (i) In the Jiujiang region, the ecological risk TFNs of Cu, Pb, and Cd before sand mining were {11.84, 16.61, 19.45}, {8.58, 11.73, 14.46}, and {32.80, 34.80, 37.20}, respectively, all categorized as “low” grade. (ii) Before sand mining, the comprehensive PERI vectors for the Jiujiang and Shangrao regions were {0.000, 1.000, 0.000, 0.000} and {0.000, 0.344, 0.656, 0.000}, respectively, whereas after sand mining, they changed to {0.184, 0.816, 0.000, 0.000} and {0.000, 0.195, 0.805, 0.000}, respectively. (iii) After sand mining, the probabilities of the transitional TFN for Cu, Pb, and Cd exceeding 0 were 0.566, 0.549, and 0.952, respectively, with the comprehensive transitional TFN of heavy metals showing a probability of 0.626 of exceeding 0 in the Shangrao region. (iv) Compared to the conventional PERI model, the fuzzy PERI model more effectively evaluates ecological risks, including uncertainties and cumulative effects. It reflects variations in ecological risk induced by sand mining and offers insights for heavy metal pollution assessment in sand mining regions and other ecologically sensitive areas.

1. Introduction

As the construction industry continues to grow, the demand for sand is increasing, with 32–50 billion tons extracted globally each year [1]. Poyang Lake, a major provider of sandy gravel in China, extracts approximately 236 million m³ of sand annually [2]. The negative impact of sand mining on the aquatic environment has received significant attention. For example, Yan et al. found that sand mining alters the water-soil interface, releasing heavy metal pollutants and thereby disrupting the ecological integrity of aquatic ecosystems [3]. Wang et al. suggested that sand mining in the Jialing River should be closely monitored to prevent heavy metal contamination [4]. Ndimele et al. conducted a water health assessment of heavy metals in southwestern Nigeria, where sand mining activities are prevalent [5]. Therefore, the potential ecological risks of heavy metals in sand mining areas should not be overlooked.

The potential ecological risk index (PERI) model, developed by Swedish scientist Håkanson, has been widely used to assess ecological risks associated with heavy metal contamination [6]. For example, Gu applied the PERI model to assess beryllium toxicity in the Rong River Basin [7]. Tang et al. used the PERI model to evaluate the comprehensive ecological risks of lead-zinc tailings, revealing associations between soil micro-organisms and heavy metal pollution [8]. Korkanç et al. assessed the ecological risk of heavy metals in Sultan Marshland using the PERI model [9].

However, the traditional PERI model is not applicable to the assessment of heavy metal pollution in sand mining regions due to two main challenges: (i) A key assumption of the PERI model is that the heavy metal content in sediment is determined [10]. In contrast, sand mining can disturb the sediment, releasing heavy metals into the water [11]. Additionally, uneconomical sediments like clay and silt, which are discharged by sand dredgers, reabsorb heavy metals during the settlement process, further disrupting the balance of heavy metal distribution in the sediment [12]. Thus, the exposure contents of heavy metals are uncertain variables rather than determined values. (ii) Monitoring data in sand mining areas is limited. Sand mining sites are often located far from urban areas and monitoring stations, as the noise generated by sand mining activities can disturb local residents. Moreover, hydrological and environmental stations depend on stable underwater topography, which can be altered by sand mining [2]. Due to the remote locations of sand mining areas, regular environmental monitoring data are scarce, making it difficult to use conventional mathematical statistics or machine learning methods to assess changes in ecological risks of heavy metals before and after sand mining [10].

To accurately assess the potential ecological risks of heavy metal pollution in sand mining regions or other ecologically sensitive areas, this study improves the PERI model. The triangular fuzzy number (TFN) theory is introduced to address the two challenges faced by the PERI model: the uncertainty of measured pollutant content and the need to effectively evaluate the changes in ecological risk caused by sand mining.

TFN is an uncertainty analysis method based on fuzzy set theory [13]. It has two advantages: (i) TFN transforms uncertain variables into definite values using three parameters and a membership function. (ii) TFN is highly applicable in situations where data are insufficient or imprecise. As a result, TFN has been widely used in risk assessments. For example, Guan et al. developed a method for evaluating the flood risk of urban metro systems based on TFN theory [14]. Zheng et al. assessed geohazard risks along the Cheng-Kun railway by combining TFN with geographic information systems [15]. Chen et al. performed a fuzzy health risk assessment of soil heavy metals in China using TFN theory [16].

The objectives of this study are as follows: (i) To construct a fuzzy PERI model based on TFN theory, including ecological risk TFNs for individual heavy metals, a comprehensive ecological risk TFN, and a transitional PERI model. (ii) To apply the fuzzy PERI model to Poyang Lake, a typical sand mining region. The ecological risk TFNs for individual heavy metals and the comprehensive ecological risk TFN are used to evaluate ecological risks before and after sand mining. Additionally, the transitional PERI model is used to examine the variation in ecological risks and the influence trend of heavy metals on aquatic ecosystems before and after sand mining in Poyang Lake. The fuzzy PERI model is expected to provide insights for assessing heavy metal pollution in sand mining regions and other ecologically sensitive areas.

2. Methods and Materials

2.1. Study Area

Figure 1 illustrates Poyang Lake, the largest freshwater lake in China, located at 115°49′–116°46′ E longitude and 28°24′–29°46′ N latitude [17]. Poyang Lake covers an area of approximately 1.62 × 10⁵ km² and receives water from five major tributaries: the Ganjiang River, Fu River, Xin River, Rao River, and Xiu River. The region experiences a subtropical humid monsoon climate, with an average annual rainfall of 1654 mm [17]. Additionally, Poyang Lake is the largest natural flood storage area in the Yangtze River Basin and serves as a crucial habitat for various organisms, including the Yangtze River finless porpoise and migratory birds [18].

Long-term sediment deposition in Poyang Lake provides abundant mineral resources, fueling sand mining activities. Poyang Lake is the primary source of sand for China, with approximately 1.29 × 10⁹ m³ mined between 2000 and 2010 [2]. However, these sand mining operations significantly impact the local ecological environment and economic livelihoods.

The primary sources of heavy metal pollution in the Poyang Lake Basin stem from human activities, including metal mining, smelting, and the discharge of industrial wastewater [19,20]. Yan et al. [21] identified copper (Cu), lead (Pb), and cadmium (Cd) as the key heavy metals present in the sediment of Poyang Lake. According to Jian et al. [22], the background values for Cu, Pb, and Cd are 4.75, 12.50, and 0.75 mg/kg, respectively. These metals pose significant ecological risks. High levels of Cu can severely damage the respiratory system and liver of fish [23]. Excessive Pb exposure may harm cell tissues and disrupt metabolic functions in organisms [24]. Additionally, Cd is known for its considerable acute or chronic toxicity to aquatic life [25]. Therefore, Cu, Pb, and Cd are used as evaluation indicators.

As shown in Figure 1, a total of 10 sampling sites were established in the sand mining areas of Jiujiang and Shangrao in Poyang Lake. Sampling occurred on 13 September 2020 and 13 October 2020. On 13 September, three samples were collected at each site prior to sand mining activities. Sand mining occurred in the Jiujiang and Shangrao areas from 16 September to 20 September and 19 September to 23 September 2020, respectively. A preliminary investigation indicated that underwater topography stabilizes approximately two weeks post-sand mining. Thus, on 13 October, three samples were again collected at each site following the mining activities.

2.2. Chemical Analysis

At each sampling site, sediment from the surface 0–5 cm was collected using a Peterson grab sampler. The samples were placed in clean polyethylene bags and stored at 4 °C before being sent to the Key Laboratory of Poyang Lake Environment and Resource Utilization, Ministry of Education. The samples were initially screened through a 1 mm sieve and air-dried naturally. They were then ground in an agate mortar, homogenized, and sifted through a 100 μm mesh. An accurate weight of 0.5 g of each sample was placed in a microwave digestion tank. A small amount of pure water was added to moisten the sample, followed by 9 mL of HNO₃, 3 mL of HCl, and 2 mL of HF in sequence [26]. After 30 min, a microwave digestion system (CEM MARS6, PyNN, MA, USA) was used for the digestion process, condensing the samples to 1–2 mL for analysis.

Cd was measured using graphite furnace atomic absorption spectrophotometry (ICE3500, Thermo Fisher Corporation, Waltham, MA, USA), whereas Cu and Pb were determined via flame atomic absorption spectrophotometry (SK-2003, Persee Corporation, Beijing, China). The average values of three parallel samples were recorded as the heavy metal concentration data.

During the determination of heavy metal content, quality control measures were implemented [26]. This included a blank control group, a parallel control group, and a certified reference material (CRM) group. The CRM used in the current study was GBW07309, produced by the Institute of Geophysical and Geochemical Exploration, Chinese Academy of Geological Sciences. The heavy metal concentrations in the blank control group were significantly lower than those in the samples. The relative standard deviations of the parallel control group results were within 10%, and the recovery rates for the CRM ranged from 95% to 105%.

2.3. Conventional PERI Model

The PERI model, developed by esteemed environmental scientist Håkanson [6], is widely used to assess the ecological risks associated with heavy metals. The potential ecological risk degree for a specific heavy metal (E_i) and the comprehensive ecological risk for multiple metals (E) are considered [27].

When evaluating m heavy metal pollutants, the content, background value, and toxicity coefficient for the ith metal are represented as x_i, b_i, and c_i, respectively. The calculation formula for E_i is [27]:

$$E_i=c_i\cdot {\displaystyle \frac{x_i}{b_i}}$$

(1)

Notably, the environmental hazards of different heavy metal pollutants have cumulative effects. Therefore, E is defined as [27]:

$$E={\displaystyle \sum _{i=1}^m{E}_i}$$

(2)

Agyeman et al. [28] and Ma et al. [27] indicate the toxicity coefficient of Cu, Pb, and Cd are 5, 5, and 30, respectively. According to the survey by Ma et al. [27], the classification of E_i and RI in the sediment is shown in

Table 1. Classification of E_i and E.

Ei	Risk Grade	RI	Risk Grade
Ei < 40	Low	E < 50	Low
40 ≤ Ei < 80	Medium	50 ≤ E < 100	Medium
80 ≤ Ei < 160	Considerable	100 ≤ E < 200	High
160 ≤ Ei < 320	High	200 ≤ E	Very High
320 ≤ Ei	Very high

.

The conventional PERI model, defined by Equations (1) and (2), is straightforward and intuitive. However, long-term and extensive sand mining activities gradually alter the physical and chemical properties and hydrodynamic conditions of the river, leading to uneven pollutant distribution in sediments [29]. Consequently, the measured heavy metal content in sediments (x_i) is uncertain.

Thus, the traditional PERI model encounters several challenges: (i) The calculation relies on definitive heavy metal content values in sediments [10], making ecological risk evaluations difficult in cases with uncertain measurements. (ii) Sand mining areas are often remote from urban areas, limiting the availability of heavy metal monitoring data. This makes it challenging to evaluate the changes in sediment ecological risk following sand mining using conventional statistical methods, time series analysis, or machine learning approaches [10]. To address these challenges, the traditional PERI must be enhanced to account for the uncertainty in measured pollutant content and to effectively assess the changes in ecological risk resulting from sand mining.

2.4. TFN Theory

The TFN is an uncertainty analysis method based on fuzzy set theory [13]. For a fuzzy variable, the TFN is typically represented as T(x) = (x_L, x_Q, x_S), where x_L, x_Q, and x_S denote the lower limit, most likely value, and upper limit of x, respectively. The membership function u(x) can be calculated using the following method:

$$u(x)=\{\begin{array}{cc}0& x<x_L \mathrm{or} x>x_S\\ {\displaystyle \frac{x-x_L}{x_Q-x_L}}& x_L\le x\le x_Q\\ {\displaystyle \frac{x_S-x}{x_S-x_Q}}& x_Q<x\le x_S\end{array}$$

(3)

Accordingly, u(x) is illustrated in Figure 2.

Compared to conventional mathematical statistics, time series analysis, or machine learning techniques, the TFN has lower data requirements. Additionally, TFN employs the membership function to quantify the possibility that an object belongs to each category [30]. According to Dong et al. [30], if the range of a specific ecological risk grade is defined as x ∈ [a, b], the probability that T(x) falls within this grade is

$$P={\displaystyle \frac{{\displaystyle \underset{x=a}{\overset{b}{\int }}u(x)dx}}{{\displaystyle \underset{x=-\infty }{\overset{+\infty }{\int }}u(x)dx}}}$$

(4)

Moreover, assuming that T(x) = (x_L,x_Q,x_S) and T(y) = (y_L,y_Q,y_S) are two different TFNs and λ is a constant greater than 0. According to Li et al. [31] and Wang et al. [32], they satisfy the following algorithm:

(i)

Addition rule:

$$T\left(x\right)+T\left(y\right)=\left(x_L+y_L,x_Q+y_Q,x_S+y_S\right)$$

(5)

(ii)

Subtraction rule:

$$T(x)-T(y)=(x_L-y_S,x_Q-y_Q,x_S-y_L)$$

(6)

(iii)

Number multiplication rule:

$$T(x)=(\lambda \cdot x_L,\lambda \cdot x_Q,\lambda \cdot x_S)$$

(7)

2.5. Fuzzy PERI Model

A fuzzy PERI model is designed based on TFN theory. Compared with the conventional PERI method, this model incorporates the ecological risk TFN of individual heavy metals, the comprehensive ecological risk TFN, and the transitional PERI model. The ecological risk TFN of individual heavy metal is designed to assess the ecological risk of heavy metals with uncertainties. The comprehensive ecological risk TFN evaluates the cumulative effects of multiple heavy metals, while the transitional PERI model measures the ecological risk changes resulting from sand mining.

2.5.1. Ecological Risk TFN of Individual Heavy Metal

According to Section 2.2, the measured values of heavy metal content in sediment exhibit uncertainty due to the impact of sand mining operations on the water environment. In the TFN theory, the setting of the parameters x_L, x_Q, and x_S is critical. Wang [33] and Xu et al. [34] applied TFN in multiattribute group decision-making. Wang [33] defined the three parameters of TFN as the minimum, median, and maximum values. Meanwhile, Xu et al. [34] defined them as the minimum, mode, and maximum values. Zhu et al. [35] built on TFN to propose an evaluation method for brake pedal sensation, characterizing the parameters as the most conservative, most likely, and most optimistic estimates. In the study by Yan et al. [36], on the ecological risk changes of pollutants caused by the construction of the Baihetan Dam, the three parameters of TFN were defined as the minimum, average, and maximum values of observed concentration data. Consequently, in this study, x_L, x_Q, and x_S are defined as the minimum, average, and maximum values of heavy metal content monitoring data, effectively reflecting the actual conditions of heavy metal ecological risk assessment.

Suppose that the observation data of the ith heavy metal content at the jth site are denoted as x_ij. The minimum, average, and maximum values of the monitoring data of the ith pollutant are denoted as x_iL, x_iQ, and x_iS, respectively. Therefore, the heavy metal content of the ith pollutant can be expressed as TFN: T(x_i) = (x_iL, x_iQ, x_iS), which is generated by

$$T(x_i)=\left\{x_{iL},x_{iQ},x_{iS}\right\}=\left\{\underset{j=1,2\dots n}{\min }\{x_{ij}\},{\displaystyle \sum _{j=1}^n{x}_{ij}/n},\underset{j=1,2\dots n}{\max }\{x_{ij}\}\right\}$$

(8)

As discussed in Section 2.3, the toxicity coefficient and background value are considered as constants. Based on the number multiplication rule of Equation (7), the heavy metal ecological risk TFN can be expressed as T(E_i) = (E_iL, E_iQ, E_iS), and the calculation method is:

$$T(E_i)=\left\{E_{iL},E_{iQ},E_{iS}\right\}=\left\{{\displaystyle \frac{c_i\cdot x_{iL}}{b_i}},{\displaystyle \frac{c_i\cdot x_{iQ}}{b_i}},{\displaystyle \frac{c_i\cdot x_{iS}}{b_i}}\right\}$$

(9)

where b_i and c_i are the background value and toxicity coefficient of the ith heavy metal, x_iL, x_iQ, and x_iS are the minimum, average, and maximum values of the observation data of the ith heavy metal content, respectively.

Accordingly, T(E_i) is as shown in Figure 3.

As shown in Figure 3, the PERI of the ith heavy metal may be distributed in multiple grades after sand mining. In this study, the PERI vector $\left\{p_{i1}^L,p_{i2}^L,p_{i3}^L,p_{i4}^L,p_{i5}^L\right\}$ is further designed for five levels. $p_{i1}^L$, $p_{i2}^L$, $p_{i3}^L$, $p_{i4}^L$, and $p_{i5}^L$ quantify the probabilities that the PERI of the ith heavy metal is classified as “low”, “medium”, “considerable”, “high”, and “very high”, respectively. According to the probability calculation rule of TFN in Equation (4), $p_{i1}^L$, $p_{i2}^L$, $p_{i3}^L$, $p_{i4}^L$, and $p_{i5}^L$ are generated as follows:

$$p_{i1}^L=\{\begin{array}{cc}0& 40\le E_{iL}\\ {\displaystyle \frac{{\left(40-E_{iL}\right)}^2}{\left(E_{iQ}-E_{iL}\right)\cdot \left(E_{iS}-E_{iL}\right)}}& E_{iL}<40\le E_{iQ}\\ 1-{\displaystyle \frac{{\left(E_{iS}-40\right)}^2}{\left(E_{iS}-E_{iL}\right)\cdot \left(E_{iS}-E_{iQ}\right)}}& E_{iQ}\le 40<E_{iS}\\ 1& E_{iS}\le 40\end{array}$$

(10)

$$p_{i2}^L=\{\begin{array}{cc}0& 80\le E_{iL}\\ {\displaystyle \frac{{\left(80-E_{iL}\right)}^2}{\left(E_{iS}-E_{iL}\right)\cdot \left(E_{iQ}-E_{iL}\right)}}& 40<E_{iL}<80<E_{iQ}\\ 1-{\displaystyle \frac{{\left(E_{iS}-80\right)}^2}{\left(E_{iS}-E_{iL}\right)\cdot \left(E_{iS}-E_{iQ}\right)}}& 40<E_{iL}<E_{iQ}<80\le E_{iS}\\ 1& 40\le E_{iL}<E_{iS}\le 80\\ {\displaystyle \frac{40\cdot \left(120-2\cdot E_{iL}\right)}{\left(E_{iS}-E_{iL}\right)\cdot \left(E_{iQ}-E_{iL}\right)}}& E_{iL}\le 40<80\le E_{iQ}\\ 1-{\displaystyle \frac{{\left(40-E_{iL}\right)}^2\cdot \left(E_{iS}-E_{iQ}\right)+{\left(E_{iS}-80\right)}^2\cdot \left(E_{iQ}-E_{iL}\right)}{\left(E_{iS}-E_{iL}\right)\cdot \left(E_{iQ}-E_{iL}\right)\cdot \left(E_{iS}-E_{iQ}\right)}}& E_{iL}<40<E_{iQ}\le 80<E_{iS}\\ 1-{\displaystyle \frac{{\left(40-E_{iL}\right)}^2}{\left(E_{iS}-E_{iL}\right)\cdot \left(E_{iQ}-E_{iL}\right)}}& E_{iL}<40<E_{iQ}<E_{iS}<80\\ {\displaystyle \frac{40\cdot \left(2\cdot E_{iS}-120\right)}{\left(E_{iS}-E_{iL}\right)\cdot \left(E_{iS}-E_{iQ}\right)}}& E_{iQ}\le 40<80\le E_{iS}\\ {\displaystyle \frac{{\left(E_{iS}-40\right)}^2}{\left(E_{iS}-E_{iL}\right)\cdot \left(E_{iS}-E_{iQ}\right)}}& E_{iQ}\le 40<E_{iS}<80\\ 0& E_{iS}\le 40\end{array}$$

(11)

$$p_{i3}^L=\{\begin{array}{cc}0& 160\le E_{iL}\\ {\displaystyle \frac{{\left(160-E_{iL}\right)}^2}{\left(E_{iS}-E_{iL}\right)\cdot \left(E_{iQ}-E_{iL}\right)}}& 80<E_{iL}<160<E_{iQ}\\ 1-{\displaystyle \frac{{\left(E_{iS}-160\right)}^2}{\left(E_{iS}-E_{iL}\right)\cdot \left(E_{iS}-E_{iQ}\right)}}& 80<E_{iL}<E_{iQ}\le 160<E_{iS}\\ 1& 80\le E_{iL}<E_{iS}\le 160\\ {\displaystyle \frac{80\cdot \left(240-2\cdot E_{iL}\right)}{\left(E_{iS}-E_{iL}\right)\cdot \left(E_{iQ}-E_{iL}\right)}}& E_{iL}\le 80<160\le E_{iQ}\\ 1-{\displaystyle \frac{{\left(80-E_{iL}\right)}^2\cdot \left(E_{iS}-E_{iQ}\right)+{\left(E_{iS}-160\right)}^2\cdot \left(E_{iQ}-E_{iL}\right)}{\left(E_{iS}-E_{iL}\right)\cdot \left(E_{iQ}-E_{iL}\right)\cdot \left(E_{iS}-E_{iQ}\right)}}& E_{iL}<80<E_{iQ}\le 160<E_{iS}\\ 1-{\displaystyle \frac{{\left(80-E_{iL}\right)}^2}{\left(E_{iS}-E_{iL}\right)\cdot \left(E_{iQ}-E_{iL}\right)}}& E_{iL}<80<E_{iQ}<E_{iS}<160\\ {\displaystyle \frac{80\cdot \left(2\cdot E_{iS}-240\right)}{\left(E_{iS}-E_{iL}\right)\cdot \left(E_{iS}-E_{iQ}\right)}}& {\displaystyle \frac{c_i\cdot x_{iQ}}{b_i}}\le 80<160\le E_{iS}\\ {\displaystyle \frac{{\left(E_{iS}-80\right)}^2}{\left(E_{iS}-E_{iL}\right)\cdot \left(E_{iS}-E_{iQ}\right)}}& E_{iQ}\le 80<E_{iS}<160\\ 0& E_{iS}\le 80\end{array}$$

(12)

$$p_{i4}^L=\{\begin{array}{cc}0& 320\le E_{iL}\\ {\displaystyle \frac{{\left(320-E_{iL}\right)}^2}{\left(E_{iS}-E_{iL}\right)\cdot \left(E_{iQ}-E_{iL}\right)}}& 160<E_{iL}<320<E_{iQ}\\ 1-{\displaystyle \frac{{\left(E_{iS}-320\right)}^2}{\left(E_{iS}-E_{iL}\right)\cdot \left(E_{iS}-E_{iQ}\right)}}& 160<E_{iL}<E_{iQ}\le 320<E_{iS}\\ 1& 160\le E_{iL}<E_{iS}\le 320\\ {\displaystyle \frac{160\cdot \left(480-2\cdot E_{iL}\right)}{\left(E_{iS}-E_{iL}\right)\cdot \left(E_{iQ}-E_{iL}\right)}}& E_{iL}\le 160<320\le E_{iQ}\\ 1-{\displaystyle \frac{{\left(160-E_{iL}\right)}^2\cdot \left(E_{iS}-E_{iQ}\right)+{\left(E_{iS}-320\right)}^2\cdot \left(E_{iQ}-E_{iL}\right)}{\left(E_{iS}-E_{iL}\right)\cdot \left(E_{iQ}-E_{iL}\right)\cdot \left(E_{iS}-E_{iQ}\right)}}& E_{iL}<160<E_{iQ}\le 320<E_{iS}\\ 1-{\displaystyle \frac{{\left(160-E_{iL}\right)}^2}{\left(E_{iS}-E_{iL}\right)\cdot \left(E_{iQ}-E_{iL}\right)}}& E_{iL}<160<E_{iQ}<E_{iS}<320\\ {\displaystyle \frac{160\cdot \left(2\cdot E_{iS}-480\right)}{\left(E_{iS}-E_{iL}\right)\cdot \left(E_{iS}-E_{iQ}\right)}}& E_{iQ}\le 160<320\le E_{iS}\\ {\displaystyle \frac{{\left(E_{iS}-160\right)}^2}{\left(E_{iS}-E_{iL}\right)\cdot \left(E_{iS}-E_{iQ}\right)}}& E_{iQ}\le 160<E_{iS}<320\\ 0& E_{iS}\le 160\end{array}$$

(13)

$$p_{i5}^L=\{\begin{array}{cc}1& 320\le E_{iL}\\ {\displaystyle \frac{{\left(E_{iS}-320\right)}^2}{\left(E_{iS}-E_{iQ}\right)\cdot \left(E_{iS}-E_{iL}\right)}}& E_{iQ}<320<E_{iS}\\ 1-{\displaystyle \frac{{\left(320-E_{iL}\right)}^2}{\left(E_{iS}-E_{iL}\right)\cdot \left(E_{iQ}-E_{iL}\right)}}& E_{iL}<320\le E_{iQ}\\ 0& E_{iS}\le 320\end{array}$$

(14)

where E_iL, E_iQ, and E_iS are the minimum, average, and maximum values of the PERI of the ith heavy metal, respectively.

2.5.2. Comprehensive Ecological Risk TFN

According to Section 2.3, environmental hazards posed by various heavy metal pollutants have cumulative effects. Assuming there are m heavy metals in the monitoring area, the comprehensive PERI of m heavy metals is denoted as E, which is the sum of the PERI values for the different heavy metals. Using the addition rule from Equation (5), the comprehensive ecological risk TFN can be expressed as T(E) = (E_L,E_Q,E_S). The calculation method is as follows:

$$T(E)=\left\{E_L,E_Q,E_S\right\}=\left\{{\displaystyle \sum _{i=1}^m{E}_{iL}},{\displaystyle \sum _{i=1}^m{E}_{iQ}},{\displaystyle \sum _{i=1}^m{E}_{iS}}\right\}=\left\{{\displaystyle \sum _{i=1}^m\frac{c_i\cdot x_{iL}}{b_i}},{\displaystyle \sum _{i=1}^m\frac{c_i\cdot x_{iQ}}{b_i}},{\displaystyle \sum _{i=1}^m\frac{c_i\cdot x_{iS}}{b_i}}\right\}$$

(15)

Accordingly, T(E) is illustrated in Figure 4.

As described in Section 2.5.1, the comprehensive PERI vector $\left\{P_1^L,P_2^L,P_3^L,P_4^L\right\}$ is further designed for four grades. $p_1^L$, $p_2^L$, $p_3^L$, and $p_4^L$ quantify the probabilities that E is classified as “low”, “medium”, “high” and “very high”, respectively. According to the probability calculation rule of TFN in Equation (4), $p_1^L$, $p_2^L$, $p_3^L$, and $p_4^L$ are generated as follows:

$$P_1^L=\{\begin{array}{cc}0& 50\le E_L\\ {\displaystyle \frac{{\left(50-E_L\right)}^2}{\left(E_Q-E_L\right)\cdot \left(E_S-E_L\right)}}& E_L<50\le E_Q\\ 1-{\displaystyle \frac{{\left(E_S-50\right)}^2}{\left(E_S-E_L\right)\cdot \left(E_S-E_Q\right)}}& E_Q\le 50<E_S\\ 1& E_S\le 50\end{array}$$

(16)

$$P_2^L=\{\begin{array}{cc}0& 50\le E_L\\ {\displaystyle \frac{{\left(100-E_L\right)}^2}{\left(E_S-E_L\right)\cdot \left(E_Q-E_L\right)}}& 50<E_L<100<E_Q\\ 1-{\displaystyle \frac{{\left(E_S-100\right)}^2}{\left(E_S-E_L\right)\cdot \left(E_S-E_Q\right)}}& 50<E_L<E_Q\le 100<E_S\\ 1& 50\le E_L<E_S\le 100\\ {\displaystyle \frac{50\cdot \left(150-2\cdot E_L\right)}{\left(E_S-E_L\right)\cdot \left(E_Q-E_L\right)}}& E_L\le 50<100<E_Q\\ 1-{\displaystyle \frac{{\left(50-E_L\right)}^2\cdot \left(E_S-E_Q\right)+{\left(E_S-100\right)}^2\cdot \left(E_Q-E_L\right)}{\left(E_S-E_L\right)\cdot \left(E_Q-E_L\right)\cdot \left(E_S-E_Q\right)}}& E_L<50<E_Q\le 100<E_S\\ 1-{\displaystyle \frac{{\left(50-E_L\right)}^2}{\left(E_S-E_L\right)\cdot \left(E_Q-E_L\right)}}& E_L<50<E_Q<E_S<100\\ {\displaystyle \frac{50\cdot \left(2\cdot E_S-150\right)}{\left(E_S-E_L\right)\cdot \left(E_S-E_Q\right)}}& E_Q\le 50<100\le E_S\\ {\displaystyle \frac{{\left(E_S-50\right)}^2}{\left(E_S-E_L\right)\cdot \left(E_S-E_Q\right)}}& E_Q\le 50<E_S<100\\ 0& E_S\le 50\end{array}$$

(17)

$$P_3^L=\{\begin{array}{cc}0& 100\le E_L\\ {\displaystyle \frac{{\left(200-E_L\right)}^2}{\left(E_S-E_L\right)\cdot \left(E_Q-E_L\right)}}& 100<E_L<200<E_Q\\ 1-{\displaystyle \frac{{\left(E_S-200\right)}^2}{\left(E_S-E_L\right)\cdot \left(E_S-E_Q\right)}}& 100<E_L<E_Q\le 200<E_S\\ 1& 100\le E_L<E_S\le 200\\ {\displaystyle \frac{100\cdot \left(300-2\cdot E_L\right)}{\left(E_S-E_L\right)\cdot \left(E_Q-E_L\right)}}& E_L\le 100<200<E_Q\\ 1-{\displaystyle \frac{{\left(100-E_L\right)}^2\cdot \left(E_S-E_Q\right)+{\left(E_S-200\right)}^2\cdot \left(E_Q-E_L\right)}{\left(E_S-E_L\right)\cdot \left(E_Q-E_L\right)\cdot \left(E_S-E_Q\right)}}& E_L<100<E_Q\le 200<E_S\\ 1-{\displaystyle \frac{{\left(100-E_L\right)}^2}{\left(E_S-E_L\right)\cdot \left(E_Q-E_L\right)}}& E_L<100<E_Q<E_S<200\\ {\displaystyle \frac{100\cdot \left(2\cdot E_S-300\right)}{\left(E_S-E_L\right)\cdot \left(E_S-E_Q\right)}}& E_Q\le 100<200\le E_S\\ {\displaystyle \frac{{\left(E_S-100\right)}^2}{\left(E_S-E_L\right)\cdot \left(E_S-E_Q\right)}}& E_Q\le 100<E_S<200\\ 0& E_S\le 100\end{array}$$

(18)

$$P_4^L=\{\begin{array}{cc}1& 200\le E_L\\ {\displaystyle \frac{{\left(E_S-200\right)}^2}{\left(E_S-E_Q\right)\cdot \left(E_S-E_L\right)}}& E_Q<200<E_S\\ 1-{\displaystyle \frac{{\left(200-E_L\right)}^2}{\left(E_S-E_L\right)\cdot \left(E_Q-E_L\right)}}& E_L<200\le E_Q\\ 0& E_S\le 200\end{array}$$

(19)

where E_L, E_Q, and E_S are the minimum, average, and maximum values of the comprehensive PERI of m heavy metals, respectively.

2.5.3. Transitional PERI Model

Although the ecological risk TFN can assess uncertain ecological risks; it does not account for variations in ecological risk resulting from sand mining. To address this, a transitional PERI model is proposed.

The ecological risk TFNs of the ith heavy metal before and after sand mining are expressed as $T(E_i)=\left\{E_{iL},E_{iQ},E_{iS}\right\}=\left\{{\displaystyle \frac{c_i\cdot x_{iL}}{b_i}},{\displaystyle \frac{c_i\cdot x_{iQ}}{b_i}},{\displaystyle \frac{c_i\cdot x_{iS}}{b_i}}\right\}$ and $T(E_i^{\ast })=\left\{E_{iL}^{\ast },E_{iQ}^{\ast },E_{iS}^{\ast }\right\}=\left\{{\displaystyle \frac{c_i\cdot x_{iL}^{\ast }}{b_i}},{\displaystyle \frac{c_i\cdot x_{iQ}^{\ast }}{b_i}},{\displaystyle \frac{c_i\cdot x_{iS}^{\ast }}{b_i}}\right\}$, respectively. According to the probability subtraction rule of TFN in Equation (6), D_i is a difference introduced to reflect the transitional TFN, and the expression is $T(D_i)=\left\{D_{iL},D_{iQ},D_{iS}\right\}$. The calculation method is:

$$T(D_i)=\left\{D_{iL},D_{iQ},D_{iS}\right\}=T(E_i^{*})-T(E_i)=\left\{E_{iL}^{*}-E_{iS},E_{iQ}^{*}-E_{iQ},E_{iS}^{*}-E_{iL}\right\}=\left\{{\displaystyle \frac{c_i\cdot x_{iL}^{\ast }}{b_i}}-{\displaystyle \frac{c_i\cdot x_{iS}}{b_i}},{\displaystyle \frac{c_i\cdot x_{iQ}^{\ast }}{b_i}}-{\displaystyle \frac{c_i\cdot x_{iQ}}{b_i}},{\displaystyle \frac{c_i\cdot x_{iS}^{\ast }}{b_i}}-{\displaystyle \frac{c_i\cdot x_{iL}}{b_i}}\right\}$$

(20)

where b_i and c_i are the background value and toxicity coefficient of the ith heavy metal. x_iL, x_iQ, and x_iS are the minimum, average, and maximum values of the observation data of the ith heavy metal before sand mining, respectively. $x_{iL}^{\ast }$, $x_{iQ}^{\ast }$, and $x_{iS}^{\ast }$ are the minimum, average, and maximum values of the observation data of the ith heavy metal after sand mining, respectively.

Accordingly, T(D_i) is illustrated in Figure 5.

Figure 5 shows that T(D_i) represents the variation in ecological risk before and after sand mining. In this analysis, if D_i > 0, it indicates an increase in the ecological risk associated with the ith heavy metal after sand mining. Conversely, if D_i < 0, the ecological risk of the ith heavy metal decreases. Hence, the probabilities P(D_i > 0) and P(D_i < 0) quantify the variations in ecological risk due to sand mining.

Based on the probability calculation rule of TFN in Equation (4), P(D_i > 0) and P(D_i < 0) are generated as follows:

$$P(D_i>0)=\{\begin{array}{cc}1& 0<D_{iL}\\ 1-{\displaystyle \frac{{D_{iL}}^2}{\left\{D_{iS}-D_{iL}\right\}\cdot \left\{D_{iQ}-D_{iL}\right\}}}& D_{iL}\le 0<D_{iQ}\\ {\displaystyle \frac{{D_{iS}}^2}{\left\{D_{iS}-D_{iL}\right\}\cdot \left\{D_{iS}-D_{iQ}\right\}}}& D_{iQ}\le 0<D_{iS}\\ 0& D_{iS}\le 0\end{array}$$

(21)

$$P(D_i<0)=\{\begin{array}{cc}0& 0<D_{iL}\\ {\displaystyle \frac{{D_{iL}}^2}{\left\{D_{iS}-D_{iL}\right\}\cdot \left\{D_{iQ}-D_{iL}\right\}}}& D_{iL}\le 0<D_{iQ}\\ 1-{\displaystyle \frac{{D_{iS}}^2}{\left\{D_{iS}-D_{iL}\right\}\cdot \left\{D_{iS}-D_{iQ}\right\}}}& D_{iQ}\le 0<D_{iS}\\ 1& D_{iS}\le 0\end{array}$$

(22)

As described in Section 2.5.2, the comprehensive PERIs of heavy metals are expressed as $T(E)=\left\{E_L,E_Q,E_S\right\}=\left\{{\displaystyle \sum _{i=1}^m{E}_{iL}},{\displaystyle \sum _{i=1}^m{E}_{iQ}},{\displaystyle \sum _{i=1}^m{E}_{iS}}\right\}=\left\{{\displaystyle \sum _{i=1}^m\frac{c_i\cdot x_{iL}}{b_i}},{\displaystyle \sum _{i=1}^m\frac{c_i\cdot x_{iQ}}{b_i}},{\displaystyle \sum _{i=1}^m\frac{c_i\cdot x_{iS}}{b_i}}\right\}$ and $T(E^{\ast })=\left\{E_L^{\ast },E_Q^{\ast },E_S^{\ast }\right\}=\left\{{\displaystyle \sum _{i=1}^m{E}_{iL}^{\ast }},{\displaystyle \sum _{i=1}^m{E}_{iQ}^{\ast }},{\displaystyle \sum _{i=1}^m{E}_{iS}^{\ast }}\right\}=\left\{{\displaystyle \sum _{i=1}^m\frac{c_i\cdot x_{iL}^{\ast }}{b_i}},{\displaystyle \sum _{i=1}^m\frac{c_i\cdot x_{iQ}^{\ast }}{b_i}},{\displaystyle \sum _{i=1}^m\frac{c_i\cdot x_{iS}^{\ast }}{b_i}}\right\}$ before and after sand mining, respectively. Its transitional TFN is denoted as: T(D) = (D_L,D_Q,D_S), and the calculation method is:

$$T(D)=\left\{D_L,D_Q,D_S\right\}=T(E^{\ast })-T(E)=\left\{E_L^{*}-E_S,E_Q^{*}-E_Q,E_S^{*}-E_L\right\}=\left\{{\displaystyle \sum _{i=1}^m\frac{c_i\cdot x_{iL}^{\ast }}{b_i}}-{\displaystyle \sum _{i=1}^m\frac{c_i\cdot x_{iS}}{b_i}},{\displaystyle \sum _{i=1}^m\frac{c_i\cdot x_{iQ}^{\ast }}{b_i}}-{\displaystyle \sum _{i=1}^m\frac{c_i\cdot x_{iQ}}{b_i}},{\displaystyle \sum _{i=1}^m\frac{c_i\cdot x_{iS}^{\ast }}{b_i}}-{\displaystyle \sum _{i=1}^m\frac{c_i\cdot x_{iL}}{b_i}}\right\}$$

(23)

where b_i and c_i are the background value and toxicity coefficient of the ith heavy metal. x_iL, x_iQ, and x_iS are the minimum, average, and maximum values of the observation data of the ith heavy metal before sand mining, respectively. $x_{iL}^{\ast }$, $x_{iQ}^{\ast }$, and $x_{iS}^{\ast }$ are the minimum, average, and maximum values of the observation data of the ith heavy metal after sand mining, respectively.

Similarly, the probabilities P(D > 0) and P(D < 0) reflect the variation in comprehensive ecological risk hazards resulting from sand mining. Their calculation approach mirrors that of P(D_i > 0) and P(D_i < 0), requiring the substitution of D_iL, D_iQ, and D_iS in Equations (21) and (22) with D_L, D_Q, and D_S, respectively.

2.5.4. Calculation Process of Fuzzy PERI Model

In summary, the calculation process of fuzzy PERI model is shown in Figure 6.

As depicted in Figure 6, the fuzzy PERI model includes the ecological risk TFN for individual heavy metals, the comprehensive ecological risk TFN, and the transitional PERI model. The ecological risk TFN for individual heavy metals assesses the ecological risk of heavy metals, accounting for uncertainties. The comprehensive ecological risk TFN evaluates the cumulative ecological risk of heavy metals. Finally, the transitional PERI model assesses the variation in ecological risk induced by sand mining.

3. Result

3.1. Concentrations of Pollutants

The pollutant contents of each station in the Jiujiang and Shangrao regions before and after sand mining are shown in

Table 2. Concentrations of pollutants in Jiujiang and Shangrao Regions.

Pollutant Contents of Sampling Sites		Cu (mg/kg)		Pb (mg/kg)		Cd (mg/kg)
		Before Sand Mining	After Sand Mining	Before Sand Mining	After Sand Mining	Before Sand Mining	After Sand Mining
Jiujiang	1#	11.25	8.12	19.03	25.89	0.90	0.82
	2#	18.48	11.88	25.58	33.25	0.84	0.88
	3#	16.80	13.16	23.52	21.44	0.93	0.79
	4#	14.84	10.69	21.55	36.14	0.82	0.85
	5#	17.51	12.65	13.64	29.92	0.86	0.80
	average	15.78	11.30	20.66	29.33	0.87	0.83
	Standard deviation	2.56	1.79	4.13	5.22	0.04	0.03
Shangrao	6#	48.12	68.46	46.68	56.12	0.92	1.23
	7#	23.01	62.31	57.23	64.18	1.14	1.11
	8#	56.15	39.36	71.88	77.76	1.01	1.34
	9#	62.52	20.61	34.71	39.42	1.11	1.07
	10#	32.79	54.13	22.62	18.78	1.03	1.16
	average	44.52	48.97	46.62	51.25	1.04	1.18
	Standard deviation	14.65	17.21	17.14	20.43	0.08	0.10

.

According to Table 2, in the Jiujiang region, the average concentrations of Cu, Pb, and Cd decreased from 15.78, 29.33, and 0.87 mg/kg before sand mining to 11.30, 20.66, and 0.83 mg/kg after sand mining, respectively. Conversely, in the Shangrao region, the average concentrations of Cu, Pb, and Cd increased from 44.52, 46.62, and 1.04 mg/kg before sand mining to 48.97, 51.25, and 1.18 mg/kg after sand mining, respectively.

In comparison to the background values, the average observed concentrations of Cu, Pb, and Cd in the Jiujiang region before sand mining were 3.32, 1.65, and 1.16 times higher than their corresponding background values. In the Shangrao region, the average observed concentrations of Cu, Pb, and Cd after sand mining were 10.31, 4.10, and 1.58 times greater than their background values, respectively.

Notably, the measured values from the sampling sites show significant uncertainty. The individual sample groups demonstrate considerable variation from their average values. For instance, in the Jiujiang region, the standard deviations for Pb are 4.13 mg/kg before sand mining and 5.22 mg/kg after. Similarly, in the Shangrao region, the standard deviations for Pb are 17.14 mg/kg before and 20.43 mg/kg after sand mining. These observations indicate that the heavy metal concentrations in sediments during sand mining in both regions are uncertain, and average values alone do not adequately capture this uncertainty.

3.2. Ecological Risk Assessment Before Sand Mining

The ecological risk TFNs for Cu, Pb, and Cd before sand mining, estimated using the fuzzy PERI model, are depicted in Figure 7 and Figure 8.

In Figure 7, the ecological risk TFNs for Cu, Pb, and Cd in the Jiujiang region before sand mining are {11.84, 16.61, 19.45}, {8.58, 11.73, 14.46}, and {32.80, 34.80, 37.20}, respectively. All these values fall within the “low” grade. The comprehensive ecological risk TFN is {53.22, 63.14, 71.11}, categorizing it as “medium” grade.

In Figure 8, the ecological risk TFNs for Cu, Pb, and Cd in the Shangrao region before sand mining are {24.22, 46.86, 65.81}, {9.05, 18.65, 28.75}, and {36.80, 41.68, 45.60}, respectively. The PERI vectors for Cu and Cd are {0.264, 0.736, 0.000, 0.000, 0.000} and {0.238, 0.762, 0.000, 0.000, 0.000}, indicating that their ecological risks are primarily classified as “medium”, with few in the “low” grade. Additionally, the comprehensive ecological risk TFN is {70.07, 107.19, 140.16}, and the comprehensive PERI vector is {0, 0.344, 0.656, 0.000, 0.000}, suggesting it predominantly falls under the “high” grade, with a few classified as “medium”.

Overall, the ecological risk of heavy metals in the Shangrao region is notably higher than that in the Jiujiang region. Cd is the critical threat factor in Jiujiang, while Cd and Cu are the main concerns in Shangrao before sand mining.

3.3. Ecological Risk Assessment After Sand Mining

The ecological risk TFNs for Cu, Pb, and Cd after sand mining, as estimated by the fuzzy PERI model, are illustrated in Figure 9 and Figure 10.

Figure 9 illustrates the ecological risk TFNs for Cu, Pb, and Cd in the Jiujiang region after sand mining. The TFNs are {8.55, 11.89, 13.85} for Cu, {5.46, 8.27, 10.23} for Pb, and {31.60, 33.12, 35.20} for Cd. All of these values fall within the “low” risk category. The comprehensive ecological risk TFN is {45.60, 53.28, 59.28}, which primarily belongs to the “medium” risk category.

Figure 10 presents the ecological risk TFNs for the Shangrao region. The values for Cu, Pb, and Cd are {21.59, 51.55, 72.06}, {7.51, 20.50, 31.10}, and {42.80, 47.28, 53.60}, respectively. The PERI vector for Cu is {0.223, 0.777, 0.000, 0.000, 0.000}, indicating that most ecological risks are categorized as “medium”, with a few in the “low” category. For Pb, the ecological risk is classified as “low”, while the ecological risk grade of Cd is “medium”. Furthermore, the comprehensive ecological risk TFN is {72.01, 119.33, 156.77}, and the comprehensive PERI vector is {0.000, 0.195, 0.805, 0.000}, reflecting that it belongs mainly to the “high” grade and few to the “medium” category.

Overall, the ecological risk presented by heavy metals in the Jiujiang region is notably lower than that in the Shangrao region. The primary contributing factors to the ecological risks in Jiujiang and Shangrao are Cd, and Cu and Cd, respectively. Importantly, these phenomena after sand mining are similar to those observed before sand mining.

3.4. Variations in Ecological Risks of Heavy Metals Before and After Sand Mining

The variations in ecological risks for heavy metals before and after sand mining are depicted in Figure 11 and Figure 12 based on the transitional PERI model.

As shown in Figure 11, the ecological risk of heavy metals in the Jiujiang region shows a substantial downward trend after sand mining. The transitional TFNs for Cu and Pb have an approximately 0.95 probability of being less than 0, while Cd’s transitional TFN demonstrates a probability of 0.824 of being less than 0. Additionally, the comprehensive transitional TFN for heavy metals has a 0.927 probability of falling below 0.

Conversely, Figure 12 indicates an increasing trend in ecological risks for heavy metals in the Shangrao region. The transitional TFN for Cd has a 0.952 probability of being greater than 0, showing a notable increase in Cd’s threat after sand mining. The transitional TFNs for Cu and Pb exhibit approximately a 0.55 probability of being greater than 0, indicating a slight rise in their ecological risks after sand mining. Furthermore, the comprehensive transitional risk TFN for heavy metals has a 0.626 probability of exceeding 0, warranting attention from the relevant water conservancy authorities.

Overall, the ecological risk posed by heavy metals in the Jiujiang region shows a decreasing trend after sand mining operations. In contrast, the ecological risk in the Shangrao region is on the rise.

4. Discussion

4.1. Influence of Sand Mining on Ecological Risk of Heavy Metals

(i) Key threat factors for the ecological risk of heavy metals before and after sand mining

As identified in Section 3.2 and Section 3.3, Cd is the primary threat factor in the Jiujiang region, and in the Shangrao region, both Cd and Cu pose risks before and after sand mining. Table 1 indicates that the background value of Cd is 0.75 mg/kg, significantly lower than Cu (4.75 mg/kg) and Pb (12.5 mg/kg). However, Cd’s toxicity coefficient is 30, far exceeding that of Cu and Pb (both at 5). Thus, the potential ecological risk of Cd is greater than that of Cu and Pb under similar conditions. Additionally, high concentrations of Cu can severely harm the respiratory system and liver of fish [24]. Therefore, the ecological risks posed by both Cd and Cu should not be underestimated.

(ii) Comparisons between the Jiujiang and Shangrao regions

Section 3.2 and Section 3.3 reveal that the ecological risk of heavy metals in the Shangrao region is significantly higher than in the Jiujiang region, both before and after sand mining. This discrepancy arises because the Shangrao sand mining area is located near the estuary of the Rao River [37]. The upstream tributary of the Rao River, the Le’an River, flows through the Dexing copper mine, the largest open-pit copper mine in Asia, which primarily contains heavy metals like Cu, Pb, and Cd [38]. Furthermore, the banks of the Le’an River host various lead-zinc ores, metal smelters, and paper mills [38]. As a result, substantial amounts of metal-containing wastewater are discharged into the Shangrao area of Poyang Lake, leading to elevated levels of heavy metal pollutants in this region.

Section 3.4 indicates that following sand mining, the ecological risk of heavy metals in the Jiujiang region shows a significant decline, while the risk in the Shangrao region is on the rise. This discrepancy is due to the differing hydrodynamic conditions and pollution sources in the two areas. Jiujiang is located along the Ganjiang and Xiu Rivers, which have higher water flow velocities and greater dilution capacities [39]. These factors promote the dispersion of heavy metals, leading to lower concentrations. Additionally, the heavy metal pollution levels in the Ganjiang and Xiu Rivers are relatively low, resulting in minimal readsorption of heavy metals in the sediment [40]. In contrast, the Shangrao region, situated along the Rao River, experiences lower water flow velocities and weaker dilution capacities [39], contributing to increased heavy metal concentrations in the water. Furthermore, the clay and powder particles released by sand dredging do not disperse easily, leading to greater absorption of heavy metals when they settle on the lake bottom [12]. The Rao River Basin is also a major hub for nonferrous metal industries, which significantly contribute to heavy metal pollution [19].

4.2. Comparisons Between Two PERI Models

As detailed in Section 2.2 and Section 2.4, the evaluation results of the conventional PERI model and the fuzzy PERI model are presented in

Table 3. The evaluation result of the conventional PERI model.

Evaluation Items		Jiujiang Sand Mining Region		Shangrao Sand Mining Region
		Before Sand Mining	After Sand Mining	Before Sand Mining	After Sand Mining
Cu	PERI	[11.84,19.45]	[8.55,13.85]	[24.22,65.81]	[21.69,72.06]
	Grade	Low	Low	/	/
Pb	PERI	[8.58,14.46]	[5.46,10.23]	[9.05,28.75]	[7.51,31.10]
	Grade	Low	Low	Low	Low
Cd	PERI	[32.80,37.20]	[31.60,35.20]	[36.80,45.60]	[42.80,53.60]
	Grade	Low	Low	/	Medium
Comprehensive evaluation	PERI	[58.20,66.35]	[48.96,57.94]	[84.76,128.26]	[80.26,143.71]
	Grade	Medium	/	/	/
Changes in ecological risk		/		/

and

Table 4. The evaluation results of the fuzzy PERI model.

Evaluation Items		Jiujiang Sand Mining Region		Shangrao Sand Mining Region
		Before Sand Mining	After Sand Mining	Before Sand Mining	After Sand Mining
Cu	PERI	{11.84,16.61,19.45}	{8.55,11.89,13.85}	{24.22,46.86,65.81}	{21.69,51.55,72.06}
	Grade	Low	Low	Medium	Medium
	PERI vector	{1,0,0,0,0}	{1,0,0,0,0}	{0.264,0.736,0,0,0}	{0.232,0.777,0,0,0}
Pb	PERI	{8.58,11.73,14.46}	{5.46,8.27,10.23}	{9.05,18.65,28.75}	{7.51,20.50,31.10}
	Grade	Low	Low	Low	Low
	PERI vector	{1,0,0,0,0}	{1,0,0,0,0}	{1,0,0,0,0}	{1,0,0,0,0}
Cd	PERI	{32.80,34.80,37.20}	{31.60,33.12,35.20}	{36.80,41.68,45.60}	{42.80,47.28,53.60}
	Grade	Low	Low	Medium	Medium
	PERI vector	{1,0,0,0,0}	{1,0,0,0,0}	{0.238,0.762,0,0,0}	{0,1,0,0,0}
Comprehensive evaluation	PERI	{53.22,63.14,71.11}	{45.60,53.28,59.28}	{70.07,107.19,140.16}	{72.01,119.33,156.77}
	Grade	Medium	Medium	High	High
	PERI vector	{0,1,0,0}	{0.184,0.816,0,0}	{0,0.344,0.656,0}	{0,0.195,0.805,0}
Overall change in ecological risk	Increasing probability	0.073		0.626
	Decreasing probability	0.927		0.374

, highlighting the differences between the two models.

Table 3 and Table 4 reveal three key differences between the conventional PERI model and the fuzzy PERI model.

(i) The conventional PERI model produces only a rough domain of pollution indices based on limited data, making it challenging to capture the uncertain distribution of pollutant values. In contrast, the fuzzy PERI model quantifies the likelihood of a pollution condition belonging to each grade using TFN and their membership vectors. This allows for a more comprehensive representation of uncertainties in pollutant concentration distributions and enhances risk identification accuracy.

(ii) The traditional PERI model struggles to assess at intervals, complicating evaluations of ecological risk under cumulative effects. In comparison, the fuzzy RERI model incorporates vector calculations of TFN to address this issue, evaluating cumulative ecological risk using the comprehensive potential risk TFN.

(iii) The conventional PERI model fails to accurately reflect changes in ecological risks associated with sand mining. In contrast, the fuzzy PERI model leverages a transitional PERI model to capture the variations in ecological risk stemming from sand mining activities. The evaluation results indicate a decrease in ecological risk of heavy metals in the Jiujiang region following sand mining, whereas an increase is noted in the Shangrao sand mining area.

5. Conclusions

The fuzzy PERI model developed in this study incorporates an ecological risk TFN model for individual heavy metals, a comprehensive ecological risk TFN model, and a transitional PERI model. It has been applied to the sand mining areas of Poyang Lake, specifically the Jiujiang and Shangrao regions. The main findings are as follows:

(i)

In the Shangrao region, before sand mining, the ecological risk TFNs for Cu, Pb, and Cd are {24.22, 46.86, 65.81}, {9.05, 18.65, 28.75}, and {36.80, 41.68, 45.60}, respectively. The PERI vectors for Cu and Cd are {0.264, 0.736, 0.000, 0.000, 0.000} and {0.238, 0.762, 0.000, 0.000, 0.000}, respectively. These indicate that their ecological risks are primarily classified as “medium”, with few instances in the “low” category. This demonstrates that the ecological risk TFN model can evaluate heavy metal risks with limited observation data, capture the uncertainty in pollutant distribution, and quantify the probability of pollution falling into various risk categories.

(ii)

In the Jiujiang region, the comprehensive ecological risk TFN before sand mining is {53.22, 63.14, 71.11}, categorized as “medium”, while the ecological risk TFNs for Cu, Pb, and Cd fall into the “low” category. This suggests that the comprehensive ecological risk TFN model effectively accounts for cumulative heavy metal effects.

(iii)

After sand mining operations, Jiujiang shows a downward trend in heavy metal ecological risk, with a probability of comprehensive risk decrease at 0.927. Conversely, Shangrao experiences an upward trend, with a comprehensive risk increase probability of 0.626. This indicates that the transitional PERI model effectively captures variations in the ecological risks of heavy metals due to sand mining.

(iv)

In the Jiujiang sand mining area, Cd poses the most significant threat, while both Cd and Cu are critical in the Shangrao region. The primary sources of heavy metal pollution in these regions are industrial wastewater from Nanchang City and the Dexing Cu mine, respectively. To address ecological risks in Poyang Lake, government intervention is vital. Increased control over urban industrial wastewater discharge and stringent oversight of mining activities are necessary.

In conclusion, the fuzzy PERI model is effective for assessing heavy metal pollution in sand mining regions. It captures the uncertainty in pollutant distribution and accounts for the ecological risk associated with cumulative heavy metal effects. Additionally, the model reflects variations in ecological risks before and after sand mining and shows a strong ability to identify key factors accurately. This makes it a valuable tool for assessing heavy metal pollution in sand mining areas and other ecologically sensitive regions.